### Fama–French three-factor model

In asset pricing and portfolio management the Fama–French three-factor model is a model designed by Eugene Fama and Kenneth French to describe stock returns. Fama and French were professors at the University of Chicago Booth School of Business, where Fama still resides. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences.[1] The three factors are (1) market risk, (2) the outperformance of small versus big companies, and (3) the outperformance of high book/market versus small book/market companies. However, the size and book/market ratio themselves are not in the model. For this reason, there is academic debate about the meaning of the last two factors.[2]

## Development

The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to describe the returns of a portfolio or stock with the returns of the market as a whole. In contrast, the Fama–French model uses three variables. Fama and French started with the observation that two classes of stocks have tended to do better than the market as a whole: (i) small caps and (ii) stocks with a high book-to-market ratio (B/P, customarily called value stocks, contrasted with growth stocks).

They then added two factors to CAPM to reflect a portfolio’s exposure to these two classes:[3]

{\displaystyle r=R_{f}+\beta (R_{m}-R_{f})+b_{s}\cdot {\mathit {SMB}}+b_{v}\cdot {\mathit {HML}}+\alpha }

Here r is the portfolio’s expected rate of return, Rf is the risk-free return rate, and Rm is the return of the market portfolio. The “three factor” β is analogous to the classical β but not equal to it, since there are now two additional factors to do some of the work. SMB stands for “Small [market capitalization] Minus Big” and HML for “High [book-to-market ratio] Minus Low”; they measure the historic excess returns of small caps over big caps and of value stocks over growth stocks.

These factors are calculated with combinations of portfolios composed by ranked stocks (BtM ranking, Cap ranking) and available historical market data. Historical values may be accessed on Kenneth French’s web page. Moreover, once SMB and HML are defined, the corresponding coefficients bs and bv are determined by linear regressions and can take negative values as well as positive values.

## Discussion

The Fama–French three-factor model explains over 90% of the diversified portfolios returns, compared with the average 70% given by the CAPM (within sample). They find positive returns from small size as well as value factors, high book-to-market ratio and related ratios. Examining β and size, they find that higher returns, small size, and higher β are all correlated. They then test returns for β, controlling for size, and find no relationship. Assuming stocks are first partitioned by size the predictive power of β then disappears. They discuss whether β can be saved and the Sharpe-Lintner-Black model resuscitated by mistakes in their analysis, and find it unlikely.[4]

Griffin shows that the Fama and French factors are country specific (Canada, Japan, the U.K., and the U.S.) and concludes that the local factors provide a better explanation of time-series variation in stock returns than the global factors.[5] Therefore, updated risk factors are available for other stock markets in the world, including the United Kingdom, Germany and Switzerland. Eugene Fama and Kenneth French also analysed models with local and global risk factors for four developed market regions (North America, Europe, Japan and Asia Pacific) and conclude that local factors work better than global developed factors for regional portfolios.[6] The global and local risk factors may also be accessed on Kenneth French’s web page. Finally, recent studies confirm the developed market results also hold for emerging markets.[7][8]

A number of studies have reported that when the Fama–French model is applied to emerging markets the book-to-market factor retains its explanatory ability but the market value of equity factor performs poorly. In a recent paper, Foye, Mramor and Pahor (2013) propose an alternative three factor model that replaces the market value of equity component with a term that acts as a proxy for accounting manipulation. [9]

The α from the Fama–French three factor model can be thought of as the extent to which a portfolio out-returns a benchmark consisting of long and short positions in various assets, with the portfolio shares in these positions described by β, bs, and bv.

The α, β, bs, and bv from the Fama–French regression model are identical to those calculated using William F. Sharpe’s, “Management Style and Performance Measurement,” Journal of Portfolio Management,1992, technique of performance measurement when the Sharpe benchmark weights are invariant during the same period covered by the Fama–French regression and the items which comprise the Sharpe benchmark and the Fama-French independent variables are the same.

More precisely, an alternative way to calculate the Fama-French model is to find the β and b’s which minimize the standard deviation of the difference between the returns of the portfolio and a benchmark portfolio consisting of investment shares: β in the market portfolio, 1- β in the risk free asset, bs long in small stocks and short in big stocks, and βv long in high book-to-market value stocks and short in low book-to-market stocks, rebalanced monthly. The β and b’s that emerge from the minimization are identical to those from the Fama-French regression, and the excess return of the asset is the Fama-French α.Thus, the Fama-French β and b’s describe the benchmark portfolio which most closely tracks the returns of the asset, and their α is the excess return of the asset over that benchmark. This equivalence holds when the benchmark consists of many assets. See J. E. McCarthy and E. Tower, “Static Indexing Beats Tactical Asset Allocation.” The Journal of Indexing, Spring 2021 for the proof or demonstrate the proposition yourself using Microsoft Excel.

## Fama–French five-factor model

In 2015, Fama and French extended the model, adding a further two factors — profitability and investment. Defined analogously to the HML factor, the profitability factor (RMW) is the difference between the returns of firms with robust (high) and weak (low) operating profitability; and the investment factor (CMA) is the difference between the returns of firms that invest conservatively and firms that invest aggressively. In the US (1963-2013), adding these two factors makes the HML factors redundant since the time series of HML returns are completely explained by the other four factors (most notably CMA which has a -0.7 correlation with HML).[10]

Whilst the model still fails the Gibbons, Ross & Shanken (1989) test,[11] which tests whether the factors fully explain the expected returns of various portfolios, the test suggests that the five-factor model improves the explanatory power of the returns of stocks relative to the three-factor model. The failure to fully explain all portfolios tested is driven by the particularly poor performance (i.e. large negative five-factor alpha) of portfolios made up of small firms that invest a lot despite low profitability (i.e. portfolios whose returns covary positively with SMB and negatively with RMW and CMA). If the model fully explains stock returns, the estimated alpha should be statistically indistinguishable from zero.

Whilst a momentum factor wasn’t included in the model since few portfolios had statistically significant loading on it, Cliff Asness, former PhD student of Eugene Fama and co-founder of AQR Capital has made the case for its inclusion.[12] Foye (2018) tested the five-factor model in the UK and raises some serious concerns. Firstly, he questions the way in which Fama and French measure profitability. Furthermore, he shows that the five-factor model is unable to offer a convincing asset pricing model for the UK.[13]

• Returns-based style analysis, a model that uses style indices rather than market factors
• Carhart four-factor model (1997)[14] — extension of the Fama–French model, containing an additional momentum factor (MOM), which is long prior-month winners and short prior-month losers

## References

1. ^ https://www.nobelprize.org/prizes/economic-sciences/2013/fama/facts/
2. ^ Petkova, Ralitsa (2006). “Do the Fama–French Factors Proxy for Innovations in Predictive Variables?”. Journal of Finance61 (2): 581–612. doi:10.1111/j.1540-6261.2006.00849.x.
3. ^ Fama, E. F.; French, K. R. (1993). “Common risk factors in the returns on stocks and bonds”. Journal of Financial Economics33: 3–56. CiteSeerX 10.1.1.139.5892. doi:10.1016/0304-405X(93)90023-5.
4. ^ Fama, E. F.; French, K. R. (1992). “The Cross-Section of Expected Stock Returns”. The Journal of Finance47 (2): 427. doi:10.1111/j.1540-6261.1992.tb04398.x. JSTOR 2329112.
5. ^ Griffin, J. M. (2002). “Are the Fama and French Factors Global or Country Specific?” (PDF)Review of Financial Studies15 (3): 783–803. doi:10.1093/rfs/15.3.783. JSTOR 2696721.[permanent dead link]
6. ^ Fama, E. F.; French, K. R. (2012). “Size, value, and momentum in international stock returns”. Journal of Financial Economics105(3): 457. doi:10.1016/j.jfineco.2012.05.011.
7. ^ Cakici, N.; Fabozzi, F. J.; Tan, S. (2013). “Size, value, and momentum in emerging market stock returns”. Emerging Markets Review16 (3): 46–65. doi:10.1016/j.ememar.2013.03.001.
8. ^ Hanauer, M.X.; Linhart, M. (2015). “Size, Value, and Momentum in Emerging Market Stock Returns: Integrated or Segmented Pricing?”. Asia-Pacific Journal of Financial Studies44 (2): 175–214. doi:10.1111/ajfs.12086.
9. ^ Pahor, Marko; Mramor, Dusan; Foye, James (2016-03-04). “A Respecified Fama French Three Factor Model for the Eastern European Transition Nations”. SSRN 2742170.
10. ^ Fama, E. F.; French, K. R. (2015). “A Five-Factor Asset Pricing Model”. Journal of Financial Economics116: 1–22. CiteSeerX 10.1.1.645.3745. doi:10.1016/j.jfineco.2014.10.010.
11. ^ Gibbons M; Ross S; Shanken J (September 1989). “A test of the efficiency of a given portfolio”. Econometrica57 (5): 1121–1152. CiteSeerX 10.1.1.557.1995. doi:10.2307/1913625. JSTOR 1913625.
12. ^ “Our Model Goes to Six and Saves Value from Redundancy Along the Way”.
13. ^ Foye, James (2018-05-02). “Testing Alternative Versions of the Fama-French Five-Factor Model in the UK”. Risk Management20(2): 167–183. doi:10.1057/s41283-018-0034-3.
14. ^ Carhart, M. M. (1997). “On Persistence in Mutual Fund Performance”. The Journal of Finance52 (1): 57–82. doi:10.1111/j.1540-6261.1997.tb03808.x. JSTOR 2329556.

### Binomial options pricing model

In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a “discrete-time” (lattice based) model of the varying price over time of the underlying financial instrument, addressing cases where the closed-form Black–Scholes formula is wanting.

The binomial model was first proposed by William Sharpe in the 1978 edition of Investments (ISBN 013504605X),[1] and formalized by Cox, Ross and Rubinstein in 1979[2] and by Rendleman and Bartter in that same year.[3]

For binomial trees as applied to fixed income and interest rate derivatives see Lattice model (finance) § Interest rate derivatives.

## Use of the model

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software (including a spreadsheet).

Although computationally slower than the Black–Scholes formula, it is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets.[citation needed]

For options with several sources of uncertainty (e.g., real options) and for options with complicated features (e.g., Asian options), binomial methods are less practical due to several difficulties, and Monte Carlo option models are commonly used instead. When simulating a small number of time steps Monte Carlo simulation will be more computationally time-consuming than BOPM (cf. Monte Carlo methods in finance). However, the worst-case runtime of BOPM will be O(2n), where n is the number of time steps in the simulation. Monte Carlo simulations will generally have a polynomial time complexity, and will be faster for large numbers of simulation steps. Monte Carlo simulations are also less susceptible to sampling errors, since binomial techniques use discrete time units. This becomes more true the smaller the discrete units become.

## Method

 function americanPut(T, S, K, r, sigma, q, n) { ' T... expiration time ' S... stock price ' K... strike price ' q... dividend yield ' n... height of the binomial tree deltaT := T / n; up := exp(sigma * sqrt(deltaT)); p0 := (up*exp(-q * deltaT) - exp(-r * deltaT)) / (up^2 - 1); p1 := exp(-r * deltaT) - p0; ' initial values at time T for i := 0 to n { p[i] := K - S * up^(2*i - n); if p[i] < 0 then p[i] := 0; } ' move to earlier times for j := n-1 down to 0 { for i := 0 to j { ' binomial value p[i] := p0 * p[i+1] + p1 * p[i]; ' exercise value exercise := K - S * up^(2*i - j); if p[i] < exercise then p[i] := exercise; } } return americanPut := p[0]; } 

The binomial pricing model traces the evolution of the option’s key underlying variables in discrete-time. This is done by means of a binomial lattice (Tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.

Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time.

Option valuation using this method is, as described, a three-step process:

1. Price tree generation,
2. Calculation of option value at each final node,
3. Sequential calculation of the option value at each preceding node.

### Step 1: Create the binomial price tree

The tree of prices is produced by working forward from valuation date to expiration.

At each step, it is assumed that the underlying instrument will move up or down by a specific factor ({\displaystyle u} or {\displaystyle d}) per step of the tree (where, by definition, {\displaystyle u\geq 1} and {\displaystyle 0<d\leq 1}). So, if {\displaystyle S} is the current price, then in the next period the price will either be {\displaystyle S_{up}=S\cdot u} or {\displaystyle S_{down}=S\cdot d}.

The up and down factors are calculated using the underlying volatility, {\displaystyle \sigma }, and the time duration of a step, {\displaystyle t}, measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is {\displaystyle \sigma ^{2}t}, we have:

{\displaystyle u=e^{\sigma {\sqrt {t}}}}
{\displaystyle d=e^{-\sigma {\sqrt {t}}}={\frac {1}{u}}.}

Above is the original Cox, Ross, & Rubinstein (CRR) method; there are various other techniques for generating the lattice, such as “the equal probabilities” tree, see.[4][5]

The CRR method ensures that the tree is recombinant, i.e. if the underlying asset moves up and then down (u,d), the price will be the same as if it had moved down and then up (d,u)—here the two paths merge or recombine. This property reduces the number of tree nodes, and thus accelerates the computation of the option price.

This property also allows that the value of the underlying asset at each node can be calculated directly via formula, and does not require that the tree be built first. The node-value will be:

{\displaystyle S_{n}=S_{0}\times u^{N_{u}-N_{d}},}

Where {\displaystyle N_{u}} is the number of up ticks and {\displaystyle N_{d}} is the number of down ticks.

### Step 2: Find option value at each final node

At each final node of the tree—i.e. at expiration of the option—the option value is simply its intrinsic, or exercise, value:

Max [ (Sn − K), 0 ], for a call option
Max [ (K − Sn), 0 ], for a put option,

Where K is the strike price and {\displaystyle S_{n}} is the spot price of the underlying asset at the nth period.

### Step 3: Find option value at earlier nodes

Once the above step is complete, the option value is then found for each node, starting at the penultimate time step, and working back to the first node of the tree (the valuation date) where the calculated result is the value of the option.

In overview: the “binomial value” is found at each node, using the risk neutrality assumption; see Risk neutral valuation. If exercise is permitted at the node, then the model takes the greater of binomial and exercise value at the node.

The steps are as follows:

1. Under the risk neutrality assumption, today’s fair price of a derivative is equal to the expected value of its future payoff discounted by the risk free rate. Therefore, expected value is calculated using the option values from the later two nodes (Option up and Option down) weighted by their respective probabilities—”probability” p of an up move in the underlying, and “probability” (1−p) of a down move. The expected value is then discounted at r, the risk free rate corresponding to the life of the option.
The following formula to compute the expectation value is applied at each node:
{\displaystyle {\text{ Binomial Value }}=[p\times {\text{ Option up }}+(1-p)\times {\text{ Option down] }}\times \exp(-r\times \Delta t)}, or
{\displaystyle C_{t-\Delta t,i}=e^{-r\Delta t}(pC_{t,i}+(1-p)C_{t,i+1})\,}
where
{\displaystyle C_{t,i}\,} is the option’s value for the {\displaystyle i^{th}\,} node at time t,
{\displaystyle p={\frac {e^{(r-q)\Delta t}-d}{u-d}}} is chosen such that the related binomial distribution simulates the geometric Brownian motion of the underlying stock with parameters r and σ,
q is the dividend yield of the underlying corresponding to the life of the option. It follows that in a risk-neutral world futures price should have an expected growth rate of zero and therefore we can consider {\displaystyle q=r} for futures.
Note that for p to be in the interval {\displaystyle (0,1)} the following condition on {\displaystyle \Delta t} has to be satisfied {\displaystyle \Delta t<{\frac {\sigma ^{2}}{(r-q)^{2}}}}.
(Note that the alternative valuation approach, arbitrage-free pricing, yields identical results; see “delta-hedging”.)
2. This result is the “Binomial Value”. It represents the fair price of the derivative at a particular point in time (i.e. at each node), given the evolution in the price of the underlying to that point. It is the value of the option if it were to be held—as opposed to exercised at that point.
3. Depending on the style of the option, evaluate the possibility of early exercise at each node: if (1) the option can be exercised, and (2) the exercise value exceeds the Binomial Value, then (3) the value at the node is the exercise value.
• For a European option, there is no option of early exercise, and the binomial value applies at all nodes.
• For an American option, since the option may either be held or exercised prior to expiry, the value at each node is: Max (Binomial Value, Exercise Value).
• For a Bermudan option, the value at nodes where early exercise is allowed is: Max (Binomial Value, Exercise Value); at nodes where early exercise is not allowed, only the binomial value applies.

In calculating the value at the next time step calculated—i.e. one step closer to valuation—the model must use the value selected here, for “Option up”/”Option down” as appropriate, in the formula at the node. The aside algorithm demonstrates the approach computing the price of an American put option, although is easily generalized for calls and for European and Bermudan options:

## Relationship with Black–Scholes

Similar assumptions underpin both the binomial model and the Black–Scholes model, and the binomial model thus provides a discrete time approximation to the continuous process underlying the Black–Scholes model. The binomial model assumes that movements in the price follow a binomial distribution; for many trials, this binomial distribution approaches the lognormal distribution assumed by Black–Scholes. In this case then, for European options without dividends, the binomial model value converges on the Black–Scholes formula value as the number of time steps increases.[4][5]

In addition, when analyzed as a numerical procedure, the CRR binomial method can be viewed as a special case of the explicit finite difference method for the Black–Scholes PDE; see finite difference methods for option pricing.[citation needed]

• Trinomial tree, a similar model with three possible paths per node.
• Tree (data structure)
• Lattice model (finance), for more general discussion and application to other underlyings
• Black–Scholes: binomial lattices are able to handle a variety of conditions for which Black–Scholes cannot be applied.
• Monte Carlo option model, used in the valuation of options with complicated features that make them difficult to value through other methods.
• Real options analysis, where the BOPM is widely used.
• Quantum finance, quantum binomial pricing model.
• Mathematical finance, which has a list of related articles.
• Employee stock option § Valuation, where the BOPM is widely used.
• Implied binomial tree
• Edgeworth binomial tree

## References

1. ^ William F. Sharpe, Biographical, nobelprize.org
2. ^ Cox, J. C.; Ross, S. A.; Rubinstein, M. (1979). “Option pricing: A simplified approach”. Journal of Financial Economics7 (3): 229. CiteSeerX 10.1.1.379.7582. doi:10.1016/0304-405X(79)90015-1.
3. ^ Richard J. Rendleman, Jr. and Brit J. Bartter. 1979. “Two-State Option Pricing”. Journal of Finance 24: 1093-1110. doi:10.2307/2327237
4. Jump up to:a b Mark s. Joshi (2008). The Convergence of Binomial Trees for Pricing the American Put
5. Jump up to:a b Chance, Don M. March 2008 A Synthesis of Binomial Option Pricing Models for Lognormally Distributed Assets Archived 2016-03-04 at the Wayback Machine. Journal of Applied Finance, Vol. 18

### United States housing bubble

Fig. 1: Robert Shiller’s plot of U.S. home prices, population, building costs, and bond yields, from Irrational Exuberance, 2nd ed.[1] Shiller shows that inflation-adjusted U.S. home prices increased 0.4% per year from 1890 to 2004 and 0.7% per year from 1940 to 2004, whereas U.S. census data from 1940 to 2004 shows that the self-assessed value increased 2% per year.

The United States housing bubble was a real estate bubble affecting over half of the U.S. states. It was the impetus for the subprime mortgage crisis. Housing prices peaked in early 2006, started to decline in 2006 and 2007, and reached new lows in 2012.[2] On December 30, 2008, the Case–Shiller home price index reported its largest price drop in its history.[3] The credit crisis resulting from the bursting of the housing bubble is an important cause of the Great Recession in the United States.[4]

Increased foreclosure rates in 2006–2007 among U.S. homeowners led to a crisis in August 2008 for the subprime, Alt-A, collateralized debt obligation (CDO), mortgage, credit, hedge fund, and foreign bank markets.[5] In October 2007, the U.S. Secretary of the Treasury called the bursting housing bubble “the most significant risk to our economy”.[6]

Any collapse of the U.S. housing bubble has a direct impact not only on home valuations, but mortgage markets, home builders, real estate, home supply retail outlets, Wall Street hedge funds held by large institutional investors, and foreign banks, increasing the risk of a nationwide recession.[7][8][9][10] Concerns about the impact of the collapsing housing and credit markets on the larger U.S. economy caused President George W. Bush and the Chairman of the Federal Reserve Ben Bernanke to announce a limited bailout of the U.S. housing market for homeowners who were unable to pay their mortgage debts.[11]

## Housing market correction

Comparison of the percentage change in the Case-Shiller Home Price Index for the housing corrections in the periods beginning in 2005 (red) and the 1980s–1990s (blue), comparing monthly CSI values with the peak values immediately prior to the first month of decline all the way through the downturn and the full recovery of home prices.

 NAR chief economist David Lereah’s explanation, “What Happened”, from the 2006 NAR Leadership Conference[79] Boom ended in August 2005 Mortgage rates rose almost one point Affordability conditions deteriorated Speculative investors pulled out Homebuyer confidence plunged Resort buyers went to sidelines Trade-up buyers went to sidelines First-time buyers priced out of market

Basing their statements on historic U.S. housing valuation trends,[1][80] in 2005 and 2006 many economists and business writers predicted market corrections ranging from a few percentage points to 50% or more from peak values in some markets,[26][81][82][83][84][85] and although this cooling had not yet affected all areas of the U.S., some warned that it still could, and that the correction would be “nasty” and “severe”.[86][87] Chief economist Mark Zandi of the economic research firm Moody’s Economy.com predicted a “crash” of double-digit depreciation in some U.S. cities by 2007–2009.[5][88][89] In a paper he presented to a Federal Reserve Board economic symposium in August 2007, Yale University economist Robert Shiller warned, “The examples we have of past cycles indicate that major declines in real home prices—even 50 percent declines in some places—are entirely possible going forward from today or from the not-too-distant future.”[90]

To better understand how the mortgage crisis played out, a 2012 report from the University of Michigan analyzed data from the Panel Study of Income Dynamics (PSID), which surveyed roughly 9,000 representative households in 2009 and 2011. The data seem to indicate that, while conditions are still difficult, in some ways the crisis is easing: Over the period studied, the percentage of families behind on mortgage payments fell from 2.2 to 1.9; homeowners who thought it was “very likely or somewhat likely” that they would fall behind on payments fell from 6% to 4.6% of families. On the other hand, family’s financial liquidity has decreased: “As of 2009, 18.5% of families had no liquid assets, and by 2011 this had grown to 23.4% of families.”[91][92]

By mid-2016, the national housing price index was “about 1 percent shy of that 2006 bubble peak” in nominal terms[93] but 20% below in inflation adjusted terms.[94]

### Subprime mortgage industry collapse

Bank run on the U.K.’s Northern Rock Bank by customers queuing to withdraw savings in a panic related to the U.S. subprime crisis.

In March 2007, the United States’ subprime mortgage industry collapsed due to higher-than-expected home foreclosure rates (no verifying source), with more than 25 subprime lenders declaring bankruptcy, announcing significant losses, or putting themselves up for sale.[95] The stock of the country’s largest subprime lender, New Century Financial, plunged 84% amid Justice Department investigations, before ultimately filing for Chapter 11 bankruptcy on April 2, 2007, with liabilities exceeding $100 million.[96] The manager of the world’s largest bond fund, PIMCO, warned in June 2007 that the subprime mortgage crisis was not an isolated event and would eventually take a toll on the economy and ultimately have an impact in the form of impaired home prices.[97] Bill Gross, a “most reputable financial guru”,[10] sarcastically and ominously criticized the credit ratings of the mortgage-based CDOs now facing collapse: AAA? You were wooed, Mr. Moody’s and Mr. Poor’s, by the makeup, those six-inch hooker heels, and a “tramp stamp.” Many of these good-looking girls are not high-class assets worth 100 cents on the dollar … [T]he point is that there are hundreds of billions of dollars of this toxic waste … This problem [ultimately] resides in America’s heartland, with millions and millions of overpriced homes.[10] Business Week has featured predictions by financial analysts that the subprime mortgage market meltdown would result in earnings reductions for large Wall Street investment banks trading in mortgage-backed securities, especially Bear Stearns, Lehman Brothers, Goldman Sachs, Merrill Lynch, and Morgan Stanley.[95] The solvency of two troubled hedge funds managed by Bear Stearns was imperiled in June 2007 after Merrill Lynch sold off assets seized from the funds and three other banks closed out their positions with them. The Bear Stearns funds once had over$20 billion of assets, but lost billions of dollars on securities backed by subprime mortgages.[98]

H&R Block reported that it had made a quarterly loss of $677 million on discontinued operations, which included the subprime lender Option One, as well as writedowns, loss provisions for mortgage loans and the lower prices achievable for mortgages in the secondary market. The unit’s net asset value had fallen 21% to$1.1 billion as of April 30, 2007.[99] The head of the mortgage industry consulting firm Wakefield Co. warned, “This is going to be a meltdown of unparalleled proportions. Billions will be lost.” Bear Stearns pledged up to U.S. $3.2 billion in loans on June 22, 2007, to bail out one of its hedge funds that was collapsing because of bad bets on subprime mortgages.[100] Peter Schiff, president of Euro Pacific Capital, argued that if the bonds in the Bear Stearns funds were auctioned on the open market, much weaker values would be plainly revealed. Schiff added, “This would force other hedge funds to similarly mark down the value of their holdings. Is it any wonder that Wall street is pulling out the stops to avoid such a catastrophe? … Their true weakness will finally reveal the abyss into which the housing market is about to plummet.”[101] The New York Times report connects the hedge fund crisis with lax lending standards: “The crisis this week from the near collapse of two hedge funds managed by Bear Stearns stems directly from the slumping housing market and the fallout from loose lending practices that showered money on people with weak, or subprime, credit, leaving many of them struggling to stay in their homes.”[100] On August 9, 2007, BNP Paribas announced that it could not fairly value the underlying assets in three funds because of its exposure to U.S. subprime mortgage lending markets.[102] Faced with potentially massive (though unquantifiable) exposure, the European Central Bank (ECB) immediately stepped in to ease market worries by opening lines of €96.8 billion (U.S.$130 billion) of low-interest credit.[103] One day after the financial panic about a credit crunch had swept through Europe, the U.S. Federal Reserve Bank conducted an “open market operation” to inject U.S. $38 billion in temporary reserves into the system to help overcome the ill effects of a spreading credit crunch, on top of a similar move the previous day.[citation needed] In order to further ease the credit crunch in the U.S. credit market, at 8:15 a.m. on August 17, 2007, the chairman of the Federal Reserve Bank Ben Bernanke decided to lower the discount window rate, which is the lending rate between banks and the Federal Reserve Bank, by 50 basis points to 5.75% from 6.25%. The Federal Reserve Bank stated that the recent turmoil in the U.S. financial markets had raised the risk of an economic downturn. In the wake of the mortgage industry meltdown, Senator Chris Dodd, chairman of the Banking Committee, held hearings in March 2007 in which he asked executives from the top five subprime mortgage companies to testify and explain their lending practices. Dodd said that “predatory lending practices” were endangering home ownership for millions of people.[17] In addition, Democratic senators such as Senator Charles Schumer of New York were already proposing a federal government bailout of subprime borrowers like the bailout made in the savings and loan crisis, in order to save homeowners from losing their residences. Opponents of such a proposal[who?] asserted that a government bailout of subprime borrowers was not in the best interests of the U.S. economy because it would simply set a bad precedent, create a moral hazard, and worsen the speculation problem in the housing market. Lou Ranieri of Salomon Brothers, creator of the mortgage-backed securities market in the 1970s, warned of the future impact of mortgage defaults: “This is the leading edge of the storm … If you think this is bad, imagine what it’s going to be like in the middle of the crisis.” In his opinion, more than$100 billion of home loans were likely to default when the problems seen in the subprime industry also emerge in the prime mortgage markets.[104]

Former Federal Reserve Chairman Alan Greenspan had praised the rise of the subprime mortgage industry and the tools which it uses to assess credit-worthiness in an April 2005 speech.[105] Because of these remarks, as well as his encouragement of the use of adjustable-rate mortgages, Greenspan has been criticized for his role in the rise of the housing bubble and the subsequent problems in the mortgage industry that triggered the economic crisis of 2008.[106][107] On October 15, 2008, Anthony Faiola, Ellen Nakashima and Jill Drew wrote a lengthy article in the Washington Post titled, “What Went Wrong”.[108] In their investigation, the authors claim that Greenspan vehemently opposed any regulation of financial instruments known as derivatives. They further claim that Greenspan actively sought to undermine the office of the Commodity Futures Trading Commission, specifically under the leadership of Brooksley E. Born, when the Commission sought to initiate the regulation of derivatives. Ultimately, it was the collapse of a specific kind of derivative, the mortgage-backed security, that triggered the economic crisis of 2008. Concerning the subprime mortgage mess, Greenspan later admitted that “I really didn’t get it until very late in 2005 and 2006.”[34]

On September 13, 2007, the British bank Northern Rock applied to the Bank of England for emergency funds because of liquidity problems related to the subprime crisis.[109] This precipitated a bank run at Northern Rock branches across the UK by concerned customers who took out “an estimated £2bn withdrawn in just three days”.[110]

• 2010 United States foreclosure crisis
• Financial crisis of 2007–08
• Great Recession
• Mortgage Electronic Registration Systems
• Synthetic CDO
• Real estate trend

## Notes

1. Jump up to:a b c d Shiller, Robert (2005). Irrational Exuberance (2d ed.). Princeton University Press. ISBN 978-0-691-12335-6.
2. ^ “S&P CoreLogic Case-Shiller Home Price Indices – S&P Dow Jones Indices”. standardandpoors.com. Archived from the original on May 22, 2013. Retrieved October 5, 2017.
3. ^ Mantell, Ruth. “Home prices off record 18% in past year, Case-Schiller says”. marketwatch.com. Retrieved April 29, 2009.
4. ^ Holt, Jeff. “A Summary of the Primary Causes of the Housing Bubble and the Resulting Credit Crisis: A Non-Technical Paper”(PDF)2009, 8, 1, 120-129. The Journal of Business Inquiry. Archived from the original (PDF) on October 17, 2014. Retrieved February 15, 2013.
5. Jump up to:a b c “In Washington, big business and big money are writing the rules on trade …”. Bill Moyers Journal. June 29, 2007. PBS.
6. ^ “Housing woes take bigger toll on economy than expected: Paulson”. AFP. October 17, 2007. Archived from the original on September 18, 2010.
7. Jump up to:a b c Laperriere, Andrew (April 10, 2006). “Housing Bubble Trouble: Have we been living beyond our means?”. The Weekly Standard.
8. Jump up to:a b Bajaj, Vikas (July 25, 2007). “Lender Sees Mortgage Woes for ‘Good’ Risks”. The New York Times. Retrieved May 26, 2010.
9. Jump up to:a b Roubini, Nouriel (August 23, 2006). “Recession will be nasty and deep, economist says”. MarketWatchThis is the biggest housing slump in the last four or five decades: every housing indicator is in free fall, including now housing prices.
10. Jump up to:a b c “When mainstream analysts compare CDOs to ‘subslime’, ‘toxic waste’ and ‘six-inch hooker heels’ …” RGE Monitor. June 27, 2007. Archived from the original on June 29, 2007.
11. ^ Solomon, Deborah (August 31, 2007). “Bush Moves to Aid Homeowners”. The Wall Street Journal.
12. ^ Reuters. (2008). FACTBOX – U.S. government bailout tally tops 504 billion pounds.
13. Jump up to:a b c Wisconsin School of Business & The Lincoln Institute of Land Policy (2015). “Land Prices for 46 Metro Areas”. Updated Quarterly.
14. ^ Tax Break May Have Helped Cause Housing Bubble, The New York Times, December 18, 2008
15. ^ Evans-Pritchard, Ambrose (March 23, 2006). “No mercy now, no bail-out later”. The Daily Telegraph. London. Retrieved May 26,2010[T]he American housing boom is now the mother of all bubbles—in sheer volume, if not in degrees of speculative madness.
16. ^ Levenson, Eugenia (March 15, 2006). “Lowering the Boom? Speculators Gone Mild”. FortuneAmerica was awash in a stark, raving frenzy that looked every bit as crazy as dot-com stocks.
17. Jump up to:a b c d Poirier, John (March 19, 2007). “Top five US subprime lenders asked to testify-Dodd”. Reuters. Retrieved March 17,2008.
18. ^ “Intended federal funds rate, Change and level, 1990 to present”.
19. ^ Shiller, Robert (June 20, 2005). “The Bubble’s New Home”. Barron’sThe home-price bubble feels like the stock-market mania in the fall of 1999, just before the stock bubble burst in early 2000, with all the hype, herd investing and absolute confidence in the inevitability of continuing price appreciation. My blood ran slightly cold at a cocktail party the other night when a recent Yale Medical School graduate told me that she was buying a condo to live in Boston during her year-long internship, so that she could flip it for a profit next year. Tulipmania reigns. Plot of inflation-adjusted home price appreciation in several U.S. cities, 1990–2005:
 Plot of inflation-adjusted home price appreciation in several U.S. cities, 1990–2005.
20. ^ “Is A Housing Bubble About To Burst?”. BusinessWeek. July 19, 2004. Archived from the original on March 4, 2008. Retrieved March 17, 2008.
21. ^ Shiller, Robert (June 20, 2005). “The Bubble’s New Home”. Barron’sOnce stocks fell, real estate became the primary outlet for the speculative frenzy that the stock market had unleashed. Where else could plungers apply their newly acquired trading talents? The materialistic display of the big house also has become a salve to bruised egos of disappointed stock investors. These days, the only thing that comes close to real estate as a national obsession is poker.
22. ^ “DETECCIÓN DE BURBUJAS INMOBILIARIAS: EL CASO ESPAÑOL”. eumed.net. Retrieved October 5, 2017.
23. ^ G.R. Putland (June 1, 2009). “From the subprime to the terrigenous: Recession begins at home”. Land Values Research Group.
24. ^ “The end of Poland’s house price boom”. Global Property Guide. August 25, 2008.
25. Jump up to:a b A prediction of a correction in the housing market, possibly after the “fall” of 2005, is implied by The Economist magazine’s cover story for the article “After the fall”, which illustrates a brick falling, with the label “House Prices”. “After the fall”. The Economist. June 16, 2005.
26. Jump up to:a b “The No-Money-Down Disaster”. Barron’s. August 21, 2006.
27. Jump up to:a b Tully, Shawn (May 5, 2006). “Welcome to the Dead Zone”. Fortune. Retrieved March 17, 2008. This article classified several U.S. real-estate regions as “Dead Zones”, “Danger Zones”, and “Safe Havens”.
Fortune magazine Housing Bubble “Dead Zones”
“Dead Zones” “Danger Zones” “Safe Havens”
Boston Chicago Cleveland
Las Vegas Los Angeles Columbus
Miami New York Dallas
Washington D.C. / Northern Virginia San Francisco / Oakland Houston
Phoenix Seattle Kansas City
Sacramento Omaha
San Diego Pittsburgh
28. ^ “Adjustable-rate loans come home to roost: Some squeezed as interest rises, home values sag”. Seek Estate. June 2, 2014. Archived from the original on June 2, 2014.
29. ^ “Over 14,000 Phoenix For-Sale Homes Vacant”. The Housing Bubble Blog. March 10, 2006.
 Inventory of houses for sale in Phoenix, AZ from July 2005 through March 2006. As of March 10, 2006, well over 14,000 (nearly half) of these for-sale homes were vacant. (Source: Arizona Regional Multiple Listing Service.)
30. Jump up to:a b Lereah, David (August 24, 2005). “Existing home sales drop 4.1% in July, median prices drop in most regions”. USA Today.
31. Jump up to:a b Nancy Trejos (April 24, 2007). “Existing-Home Sales Fall Steeply”. The Washington Post. Retrieved March 17, 2008.
32. ^ “Alan Greenspan Interview with Jim Lehrer”. The NewsHour with Jim Lehrer. September 18, 2007.
33. Jump up to:a b c d “Greenspan alert on US house prices”. Financial Times. September 17, 2007.
34. Jump up to:a b Felsenthal, Mark (September 14, 2007). “Greenspan says didn’t see subprime storm brewing”. Reuters.
35. Jump up to:a b “Subprime shockwaves”. Bloomberg. July 19, 2007.
36. ^ “Median and Average Sales Prices of New Homes Sold in United States” (PDF). Census.gov. Retrieved May 30, 2014.
37. ^ Hudson, Michael (May 2006). “The New Road to Serfdom”. Harper’s312 (1872). pp. 39–46.
38. ^ Leamer, Ed (August 23, 2006). “Is economy headed to a soft landing?”. USA TodayThis soft-landing scenario is a fantasy … Anything housing-related is going to feel like a recession, almost like a depression.
39. ^ Hamilton, Jim (August 25, 2006). “New home sales continue to fall”. Econbrowser. Archived from the original on September 1, 2006. No question about it, the housing downturn is here now, and it’s big.
40. ^ Shiller, Robert (August 20, 2006). “Bloomberg Interview of Robert Shiller”. Bloomberg.
41. ^ Roubini, Nouriel (August 26, 2006). “Eight Market Spins About Housing by Perma-Bull Spin-Doctors … And the Reality of the Coming Ugliest Housing Bust Ever …” RGE Monitor. Archived from the original on September 3, 2006. A lot of spin is being furiously spinned [sic] around–often from folks close to real estate interests–to minimize the importance of this housing bust, it is worth to point out a number of flawed arguments and misperception that are being peddled around. You will hear many of these arguments over and over again in the financial pages of the media, in sell-side research reports and in innumerous [sic] TV programs. So, be prepared to understand this misinformation, myths and spins.
42. ^ Baker, Dean (August 2002). “The Run-Up in Home Prices: Is it Real or Is it Another Bubble?”. Center for Economic and Policy Research. Retrieved June 12, 2011.
43. ^ Baker, Dean (August 9, 2004). “Bush’s House of Card”. The Nation.
44. ^ Jeffrey Robert, Why are my investments diving…and what can I do about it? Archived April 21, 2011, at the Wayback Machine.
45. ^ The Unofficial List of Pundits/Experts Who Were Wrong on the Housing Bubble, July 16, 2008, by “Economics of Contempt”, lists 25 sources rejecting the “bubble” label.
46. ^ Bubble Denial, Paul Krugman, cites Was there a Housing Bubble?, by Alex Tabarrok, February 13, 2008 as rejecting the label “bubble”.
47. ^ Duhigg, Charles (August 5, 2008). “At Freddie Mac, Chief Discarded Warning Signs” – via NYTimes.com.
48. ^ Ip, Greg (June 9, 2007). “Did Greenspan Add to Subprime Woes?”. Retrieved October 5, 2017 – via wsj.com.
49. ^ “Archived copy”. Archived from the original on May 21, 2012. Retrieved May 22, 2012.
50. ^ “In come the waves: The worldwide rise in house prices is the biggest bubble in history. Prepare for the economic pain when it pops”. The Economist. June 16, 2005. The worldwide rise in house prices is the biggest bubble in history. Prepare for the economic pain when it pops.
51. ^ “President Highlights Importance of Small Business in Economic Growth” (Press release). The White House. January 19, 2006. [President Bush was asked about the housing boom’s impact on the ability of the questioner’s children to purchase a home. The President answered:] ‘ … If houses get too expensive, people will stop buying them, which will cause people to adjust their spending habits … Let the market function properly. I guarantee that your kind of question has been asked throughout the history of homebuilding – you know, prices for my homes are getting bid up so high that I’m afraid I’m not going to have any consumers – or my kid – and yet, things cycle. That’s just the way it works. Economies should cycle.’
52. ^ Baker, Dean (August 2, 2006). “The Slow Motion Train Wreck”. The American Prospect. Archived from the original on September 28, 2007.
53. ^ “Housing Bubble—or Bunk? Are home prices soaring unsustainably and due for plunge? A group of experts takes a look—and come to very different conclusions”. Business Week. June 22, 2005. Archived from the original on July 19, 2008.
54. ^ “The State of the Nation’s Housing 2006” (PDF). Harvard University, Joint Center for Housing Studies. 2006. Archived from the original (PDF) on October 13, 2006.
55. ^ Retsinas, Nicolas (September 26, 2006). “The housing wail”. Scripps Howard News Service. Archived from the original on October 5, 2006. Retrieved October 2, 2006The headline hints of catastrophe: a dot-com repeat, a bubble bursting, an economic apocalypse. Cassandra, though, can stop wailing: the expected price corrections mark a slowing in the rate of increase—not a precipitous decline. This will not spark a chain reaction that will devastate homeowners, builders and communities. Contradicting another gloomy seer, Chicken Little, the sky is not falling.
56. ^ “Harvard Hypes Housing, but Why?”. Motley Fool. September 29, 2006. Archived from the original on January 23, 2013.
57. ^ Lereah, David (August 2005). “Anti-Bubble Reports”. National Association of Realtors. Archived from the original on November 26, 2005.
58. ^ Tully, Shawn (August 25, 2005). “Getting real about the real estate bubble”. Fortune.
59. ^ “Housing market may be on ice, but the blame market is red hot”. Chicago Tribune. September 10, 2006. Archived from the original on January 13, 2009.
60. ^ Howley, Kathleen (June 14, 2007). “U.S. Mortgages Enter Foreclosure at Record Pace”. Bloomberg News.
61. ^ “Greenspan: ‘Local bubbles’ build in housing sector”. USA Today. May 20, 2005.
62. ^ “S&P/Case-Shiller Home Price Indices-historical spreadsheets”.
63. Jump up to:a b Christie, Les (August 14, 2007). “California cities fill top 10 foreclosure list”. CNNMoney.com. Retrieved May 26, 2010.
64. ^ “Home prices tumble as consumer confidence sinks”. Reuters. November 27, 2007. Retrieved March 17, 2008.
65. ^ Knox, Noelle (November 21, 2006). “Cleveland: Foreclosures weigh on market”. USA Today.
66. ^ Lynch, Sharon (October 2, 2008). “Metro U.S. Home Prices Fall on Higher Foreclosures”. Bloomberg. Retrieved October 10,2008.
67. ^ “Number of Stories in New One-Family Houses Sold” (PDF).
68. ^ “D.R. Horton, Inc. (DHI) Stock Historical Prices & Data – Yahoo Finance”. finance.yahoo.com.
69. ^ “Pulte Corp. 2006 Annual Report”. Archived from the originalon August 19, 2007.
70. ^ “Pulte Corp. 1996 Form 10-K – Annual report”.
71. ^ “Sources and Uses of Equity Extracted from Homes” (PDF).
72. ^ “America’s Unsustainable Boom”. Mises Institute. November 5, 2004.
73. ^ “LOUDOUN COUNTY POPULATION: 2017 ESTIMATE SERIES”. Loudoun County, Virginia. October 2017. Retrieved August 28, 2018.[dead link]
74. ^ “Bureau of Economic Analysis GDP estimate, Q2 2007” (PDF)(Press release). July 27, 2007. Archived from the original (PDF)on May 2, 2017. Retrieved March 24, 2008.
75. ^ “Chicago Fed index indicates recession has probably begun”. Forbes. Thomson Financial. March 24, 2008. Archived from the original on May 14, 2008. Retrieved March 24, 2008.
76. ^ Grynbaum, Michael M. (July 12, 2008). “Woes at Loan Agencies and Oil-Price Spike Roil Markets”. Retrieved October 5, 2017 – via nytimes.com.
77. ^ “Fannie, Freddie Delisting Signals Firms Have No Value”. Wall Street Journal. June 16, 2010. Archived from the original on June 21, 2010.
78. ^ Lereah, David (August 17, 2006). “Real Estate Reality Check (Powerpoint talk)”. National Association of Realtors Leadership Summit. Archived from the original (Powerpoint) on September 1, 2006. Retrieved August 28, 2006.
 Condominium Price Appreciation (percentages) in the south and west United States, 2002–2006. (Source: NAR.)
79. ^ Baker, Dean (July 27, 2004). “The bubble question”. CNNMoney.comThere has never been a run up in home prices like this.
80. ^ Searjeant, Graham (August 27, 2005). “US heading for house price crash, Greenspan tells buyers”. The Times. London. Retrieved May 26, 2010Alan Greenspan, the United States’s central banker, warned American homebuyers that they risk a crash if they continue to drive property prices higher … On traditional tests, about a third of U.S. local homes markets are now markedly overpriced.
81. ^ Zweig, Jason (May 8, 2006). “Buffett: Real estate slowdown ahead”. CNNMoney.comOnce a price history develops, and people hear that their neighbor made a lot of money on something, that impulse takes over, and we’re seeing that in commodities and housing … Orgies tend to be wildest toward the end. It’s like being Cinderella at the ball. You know that at midnight everything’s going to turn back to pumpkins and mice. But you look around and say, ‘one more dance,’ and so does everyone else. The party does get to be more fun—and besides, there are no clocks on the wall. And then suddenly the clock strikes 12, and everything turns back to pumpkins and mice.
82. ^ “Surviving a Real-Estate Slowdown”. The Wall Street Journal. July 5, 2006. A significant decline in prices is coming. A huge buildup of inventories is taking place, and then we’re going to see a major [retrenchment] in hot markets in California, Arizona, Florida and up the East Coast. These markets could fall 50% from their peaks.
83. ^ “Surviving Real Estate Slowdown”. Seek.estate. June 1, 2014.[permanent dead link]
84. ^ “Bubble Blog”. Newsweek. August 8, 2006. Archived from the original on August 22, 2006.
85. ^ Krugman, Paul (January 2, 2006). “No bubble trouble?”. The New York Times[T]he overall market value of housing has lost touch with economic reality. And there’s a nasty correction ahead.
86. ^ “Housing bubble correction could be severe”. US News & World Report. June 13, 2006. Archived from the original on July 4, 2007.
87. ^ “Study sees ’07 ‘crash’ in some housing”. Chicago Tribune. October 5, 2006. Archived from the original on January 14, 2009.
88. ^ Clabaugh, Jeff (October 2, 2006). “Moody’s predicts big drop in Washington housing prices”. Washington Business Journal.
89. ^ “Two top US economists present scary scenarios for US economy; House prices in some areas may fall as much as 50% – Housing contraction threatens a broader recession”. Finfacts Ireland. September 3, 2007. The examples we have of past cycles indicate that major declines in real home prices—even 50 per cent declines in some places—are entirely possible going forward from today or from the not-too-distant future.
90. ^ “Mortgage Distress and Financial Liquidity: How U.S. Families are Handling Savings, Mortgages and Other Debts”.JournalistsResource.org, retrieved June 18, 2012
91. ^ Stafford, Frank; Chen, Bing; Schoeni, Robert (2012). “Mortgage Distress and Financial Liquidity: How U.S. Families are Handling Savings, Mortgages and Other Debts” (PDF)Institute for Social Research. Archived from the original (PDF) on May 11, 2013.
92. ^ Diana Olick (August 29, 2016). “We’re in a new housing bubble: Why it’s less scary this time”. CNBC.
93. ^ “American house prices: realty check”. The Economist. August 24, 2016.
94. Jump up to:a b “The Mortgage Mess Spreads”. BusinessWeek. March 7, 2007.
95. ^ “New Century Financial files for Chapter 11 bankruptcy”. MarketWatch. April 2, 2007.
97. ^ “Merrill sells off assets from Bear hedge funds”. Reuters. June 21, 2007.
98. ^ “H&R Block struck by subprime loss”. Financial Times. June 21, 2007.

## Duration matching

A more practical alternative immunisation method is duration matching. Here, the duration of the assets is matched with the duration of the liabilities. To make the match actually profitable under changing interest rates, the assets and liabilities are arranged so that the total convexity of the assets exceed the convexity of the liabilities. In other words, one can match the first derivatives (with respect to interest rate) of the price functions of the assets and liabilities and make sure that the second derivative of the asset price function is set to be greater than or equal to the second derivative of the liability price function.

## Calculating immunisation

Immunisation starts with the assumption that the yield curve is flat. It then assumes that interest rate changes are parallel shifts up or down in that yield curve. Let the net cash flow at time {\displaystyle t} be denoted by {\displaystyle R_{t}}, i.e.:

{\displaystyle R_{t}=A_{t}-L_{t}{\text{ for }}t=1,2,3,\ldots ,n}

where {\displaystyle A_{t}} and {\displaystyle L_{t}} represent cash inflows and outflows or liabilities respectively.

Assuming that the present value of cash inflows from the assets is equal to the present value of the cash outflows from the liabilities, then:

{\displaystyle P(i)=0}  [1]

## Immunisation in practice

Immunisation can be done in a portfolio of a single asset type, such as government bonds, by creating long and short positions along the yield curve. It is usually possible to immunize a portfolio against the most prevalent risk factors. A principal component analysis of changes along the U.S. Government Treasury yield curve reveals that more than 90% of the yield curve shifts are parallel shifts, followed by a smaller percentage of slope shifts and a very small percentage of curvature shifts. Using that knowledge, an immunized portfolio can be created by creating long positions with durations at the long and short end of the curve, and a matching short position with a duration in the middle of the curve. These positions protect against parallel shifts and slope changes, in exchange for exposure to curvature changes.[citation needed]

## Difficulties

Immunisation, if possible and complete, can protect against term mismatch but not against other kinds of financial risk such as default by the borrower (i.e., the issuer of a bond). It might also be difficult to find assets with suitable cashflow structures that are necessary to ensure a particular level of overall volatility of assets to have a proper match with that of liabilities.

Once there is a change in interest rate, the entire portfolio has to be restructured to immunise it again. Such a process of continuous restructuring of portfolios makes immunisation a costly and tedious task.

Users of this technique include banks, insurance companies, pension funds and bond brokers; individual investors infrequently have the resources to properly immunise their portfolios.

The disadvantage associated with duration matching is that it assumes the durations of assets and liabilities remain unchanged, which is rarely the case.

## History

Immunisation was discovered independently by several researchers in the early 1940s and 1950s. This work was largely ignored before being re-introduced in the early 1970s, whereafter it gained popularity. See Dedicated Portfolio Theory#History for details.

• Arbitrage
• Asset–liability mismatch
• Bond convexity
• Bond duration
• Bond (finance)
• Covered interest arbitrage
• Debt sculpting
• Duration gap
• Hedging
• Interest rate parity
• Interest rate swap

## References

1. ^ The Theory of Interest, Stephen G. Kellison, McGraw Hill International,2009

### Credit channel

The credit channel mechanism of monetary policy describes the theory that a central bank’s policy changes affect the amount of credit that banks issue to firms and consumers for purchases, which in turn affects the real economy.

## Credit channel versus conventional monetary policy transmission mechanisms

Monetary policy transmission mechanisms describe how policy decisions are translated into effects on the real economy. Conventional monetary policy transmission mechanisms, such as the interest rate channel, focus on direct effects of monetary policy actions. The interest rate channel, for example, suggests that monetary policy makers use their leverage over nominal, short-term interest rates, such as the federal funds rate, to influence the cost of capital, and subsequently, purchases of durable goods and firm investment.[1] Because prices are assumed to be sticky in the short-run, short-term interest rate changes affect the real interest rate. Changes in the real interest rate influence firm investment and household spending decisions on durable goods. These changes in investment and durable good purchases affect the level of aggregate demand and final production.

By contrast, the credit channel of monetary policy transmission is an indirect amplification mechanism that works in tandem with the interest rate channel. The credit channel affects the economy by altering the amount of credit firms and/or households have access to in equilibrium. Factors that reduce the availability of credit reduce agents’ spending and investment, which leads to a reduction in output. In short, the main difference between the interest rate channel and the credit channel mechanism is how spending and investment decisions change due to monetary policy changes.

## How the credit channel works [2]

The credit channel view posits that monetary policy adjustments that affect the short-term interest rate are amplified by endogenous changes in the external finance premium.[3] The external finance premium is a wedge reflecting the difference in the cost of capital internally available to firms (i.e. retaining earnings) versus firms’ cost of raising capital externally via equity and debt markets. External financing is more expensive than internal financing and the external finance premium will exist so long as external financing is not fully collateralized. Fully collateralized financing implies that even under the worst-case scenario the expected payoff of the project is at least sufficient to guarantee full loan repayment.[4] In other words, full collateralization means that the firm who borrows for the project has enough internal funds relative to the size of the project that the lenders assume no risk. Contractionary monetary policy is thought to increase the size of the external finance premium, and subsequently, through the credit channel, reduce credit availability in the economy.

The external finance premium exists because of frictions—such as imperfect information or costly contract enforcement—in financial markets. The frictions prohibit efficient allocation of resources and result in dead-weight cost. For example, lenders may incur costs, also known as agency costs, to overcome the adverse selection problem that arises when evaluating the credit worthiness of borrowers. Adverse selection in this context refers to the notion that borrowers who need access to credit may be those who are least likely to be able to repay their debts. Additionally, lenders may incur a monitoring cost regarding the productive uses to which the borrowers have put the borrowed funds. In other words, if the ability to repay a loan used to finance a project is dependent on the project’s success—either ‘good’ or ‘bad’ for simplicity—borrowers may have the incentive to claim the project was ‘bad’. If the true value of the project is only known to the borrower, the lender must incur a monitoring or auditing cost in order to reveal the true project returns and receive full re-payment.

The size of the external finance premium that results from these market frictions may be affected by monetary policy actions. The credit channel—or, equivalently, changes in the external finance premium—can occur through two conduits: the balance sheet channel and the bank lending channel. The balance sheet channel refers to the notion that changes in interest rates affect borrowers’ balance sheets and income statements. The bank lending channel refers to the idea that changes in monetary policy may affect the supply of loans disbursed by depository institutions.

### Balance sheet channel

The balance sheet channel theorizes that the size of the external finance premium should be inversely related to the borrower’s net worth.[5][6][4] For example, the greater the net worth of the borrower, the more likely she may be to use self-financing as a means to fund investment. Higher net worth agents may have more collateral to put up against the funds they need to borrow, and thus are closer to being fully collateralized than low net worth agents. As a result, lenders assume less risk when lending to high-net-worth agents, and agency costs are lower. The cost of raising external funds should therefore be lower for high-net-worth agents.

Since the quality of borrowers’ financial positions affect the terms of their credit, changes in financial positions should result in changes to their investment and spending decisions. This idea is closely related to the financial accelerator. A basic model of the financial accelerator suggests that a firm’s spending on a variable input cannot exceed the sum of gross cash flows and net discounted value of assets.[7] This relationship is expressed as a “collateral-in-advance” constraint.[8] An increase in interest rates will tighten this constraint when it is binding; the firm’s ability to purchase inputs will be reduced. This can occur in two ways: directly, via increasing interest payments on outstanding debt or floating-rate debt, and decreasing the value of the firm’s collateral through decreased asset-prices typically associated with increased interest rates (reducing the net discounted value of the firm’s assets); and indirectly, by reducing the demand for a firm’s products, which reduces the firm’s revenue while its short-run fixed cost do not adjust (lowering the firm’s gross cash flow). The reduction in revenue relative to costs erodes the firm’s net worth and credit-worthiness over time.

The balance sheet channel can also manifest itself via consumer spending on durables and housing. These types of goods tend to be illiquid in nature. If consumers need to sell off these assets to cover debts they may have to sell at a steep discount and incur losses. Consumers who hold more liquid financial assets such as cash, stocks, or bonds can more easily cope with a negative shock to their income. Consumer balance sheets with large portions of financial assets may estimate their probability of becoming financially distressed as low and are more willing to spend on durable goods and housing. Monetary policy changes that decrease the valuation of financial assets on consumers’ balance sheets can result in lower spending on consumer durables and housing.

### Bank lending channel

The bank lending channel theorizes that changes in monetary policy will shift the supply of intermediated credit, especially credit extended through commercial banks. The bank lending channel is essentially the balance sheet channel as applied to the operations of lending institutions. Monetary policy actions may affect the supply of loanable funds available to banks (i.e. a bank’s liabilities), and consequently the total amount of loans they can make (i.e. a bank’s assets).[9] Banks serve to overcome informational problems in credit markets by acting as a screening agent for determining credit-worthiness.[10] Thus many agents are dependent on banks to access credit markets. If the supply of loanable funds banks possess is affected by monetary policy changes, then so too should be the borrowers who are dependent on banks’ funds for business operations. Firms reliant on bank credit may either be shut off from credit temporarily or incur additional search costs to find a different avenue through which to obtain credit. This will increase the external finance premium, consequently reducing real economic activity.

The bank lending channel presumes that monetary policy changes will drain bank deposits so long as banks cannot easily replace the short-fall in deposits by issuing other uninsured liabilities. The abolition of reserve requirements on certificates of deposit in the mid-1980s made it much easier for banks facing falling retail deposits to issue new liabilities not backed by reserve requirements.[10] This is not to say that the bank lending channel is no longer relevant. On the contrary, the fact that banks can raise funds through liabilities that pay market interest rates exposes banks to an external finance premium as well. Forms of uninsured lending carry some credit risk relative to insured deposits. The cost of raising uninsured funds will reflect that risk, and will be more expensive for banks to purchase.[11]

## Empirical evidence

The theory of a credit channel has been postulated as an explanation for a number of puzzling features of certain macroeconomic responses to monetary policy shocks, which the interest rate channel cannot fully explain. For example, Bernanke and Gertler (1995) [2] describe 3 puzzles in the data:

1. The magnitude of changes in the real economy is large compared to the small changes in open-market interest rates due to monetary policy adjustments.
2. Key components of spending do not respond to interest changes immediately. In fact, they respond only after the interest rate effect has passed.
3. Monetary policy adjustments that affect short-term interest rates have large effects on variables that should respond to long-term interest rates (e.g. residential investment).

Since the credit channel operates as an amplification mechanism alongside the interest rate effect, small monetary policy changes can have large effects if the credit channel theory holds. Asset price boom and bust patterns in the 1980s may have led to the subsequent real fluctuations observed in many advanced economies.[12] It has also been found that small firms, who are credit constrained relative to larger firms, respond to cash flow squeezes by cutting production and employment. Large firms, by contrast, respond to cash flow squeezes by increasing their short-term borrowing.[13] Moreover, this empirical result still holds when controlling for industry characteristics and financial criteria.[14] Recent research at the Federal Reserve suggests that the bank lending channel manifests itself through the mortgage lending market as well. Monetary policy tightening may force banks to shift from retail deposits insured by the Federal Deposit Insurance Corporation to uninsured managed liabilities if they wish to continue financing mortgages. These sources of funding are more expensive than deposits, raising the bank’s average funding costs. Banks who lend heavily in sub-prime communities will face higher external finance premiums because the risk from holding assets composed largely of subprime borrowers is relatively high. As a result, banks have to raise funds through instruments that offer higher interest payments. The empirical evidence suggests that banks that lend heavily in subprime communities and rely mostly on retail deposits reduce mortgage issuance relative to other banks in the face of a monetary contraction. No evidence was found of reductions in mortgage lending initiating from other banks who do not lend heavily in subprime communities or who do not rely heavily on retail deposits in response to monetary policy tightening.[15]

• Accelerator effect
• Financial accelerator
• Monetary policy

## References

1. ^ Mishkin, Frederic. 1996. “The Channels of Monetary Transmission: Lessons for Monetary Policy.” NBER Working Paper Series w5464. 1996.
2. Jump up to:a b Bernanke, Ben and Mark Gertler. 1995. “Inside the Black Box: The Credit Channel of Monetary Policy Transmission.” Journal of Economic Perspectives. 1995, 9. 27–48.
3. ^ De Graeve, Ferre. 2007. “The External Finance Premium and the Macroeconomy: US post-WWII Evidence.” Universiteit Gent Working Paper.
4. Jump up to:a b Bernanke, Ben and Mark Gertler. 1989. “Agency Costs, Net Worth, and Business Fluctuations.” American Economic Review, 1989. 79, pp. 14–31.
5. ^ Townsend, Robert. 1979. “Optimal Contracts and Competitive Markets with Costly State Verification.” Journal of Economic Theory. 1979. 21, pp. 265–293.
6. ^ Bernanke, Ben, Mark Gertler, and Simon Gilchrist. 1996. “The Financial Accelerator and the Flight to Quality.” The Review of Economics and Statistics, 1996. 1, pp. 1–15.
7. ^ Kiyotaki, Nobuhiro and John Moore. 1997. “Credit Cycles.” Journal of Political Economy. 1997. 105, pp. 211–248.
8. ^ Hart, Oliver and John Moore. 1994. “A Theory of Debt Based on the Inalienability of Human Capital.” Quarterly Journal of Economics. 109, 4. pp. 841–879.
9. ^ Bernanke, Ben and Allen Blinder. 1988. “Credit, Money, and Aggregate Demand.” American Economic Review 1988, 78. pp. 435–439.
10. Jump up to:a b Mishkin, Frederic. 1996. “The Channels of Monetary Transmission: Lessons for Monetary Policy.” NBER Working Paper Series No. 5464.
11. ^ Bernanke, Ben. 2007. “The Financial Accelerator and the Credit Channel.” speech given at The Credit Channel and Monetary Policy in the Twenty-First Century Conference, Federal Reserve Bank of Atlanta.
12. ^ Borio, Claudio, N. Kennedy, and S.D Prowse. 1994. “Exploring Aggregate Asset Price Fluctuations Across Countries.” BIS Economic Papers. 1994, 40.
13. ^ Gertler, Mark and Simon Gilchrist. 1994. “Monetary Policy, Business Cycles, and the Behavior of Small Manufacturing Firms.” Quarterly Journal of Economics. 1994, vol. 190. pp. 309–340.
14. ^ Bernanke, Ben, Mark Gertler, and Simon Gilchrist. 1996. “The Financial Accelerator and the Flight to Quality.” The Review of Economics and Statistics. 1996, vol. 78, No. 1. pp. 1–15.
15. ^ Black, Lamont, Diana Hancock, and Wayne Passmore. 2010. “The Bank Lending Channel of Monetary Policy and Its Effect on Mortgage Lending.” Finance and Economics Discussion Series. Divisions of Research & Statistics and Monetary Affairs. Federal Reserve Board, Washington, D.C.

### Securitization

Securitization is the financial practice of pooling various types of contractual debt such as residential mortgages, commercial mortgages, auto loans or credit card debt obligations (or other non-debt assets which generate receivables) and selling their related cash flows to third party investors as securities, which may be described as bonds, pass-through securities, or collateralized debt obligations (CDOs). Investors are repaid from the principal and interest cash flows collected from the underlying debt and redistributed through the capital structure of the new financing. Securities backed by mortgage receivables are called mortgage-backed securities (MBS), while those backed by other types of receivables are asset-backed securities (ABS).

The granularity of pools of securitized assets can mitigate the credit risk of individual borrowers. Unlike general corporate debt, the credit quality of securitized debt is non-stationary due to changes in volatility that are time- and structure-dependent. If the transaction is properly structured and the pool performs as expected, the credit risk of all tranches of structured debt improves; if improperly structured, the affected tranches may experience dramatic credit deterioration and loss.[1]

Securitization has evolved from its beginnings in the late 18th century to an estimated outstanding of $10.24 trillion in the United States and$2.25 trillion in Europe as of the 2nd quarter of 2008. In 2007, ABS issuance amounted to $3.455 trillion in the US and$652 billion in Europe.[2] WBS (Whole Business Securitization) arrangements first appeared in the United Kingdom in the 1990s, and became common in various Commonwealth legal systems where senior creditors of an insolvent business effectively gain the right to control the company.[3]

## Structure

### Pooling and transfer

The originator initially owns the assets engaged in the deal. This is typically a company looking to either raise capital, restructure debt or otherwise adjust its finances (but also includes businesses established specifically to generate marketable debt (consumer or otherwise) for the purpose of subsequent securitization). Under traditional corporate finance concepts, such a company would have three options to raise new capital: a loan, bond issue, or issuance of stock. However, stock offerings dilute the ownership and control of the company, while loan or bond financing is often prohibitively expensive due to the credit rating of the company and the associated rise in interest rates.

The consistently revenue-generating part of the company may have a much higher credit rating than the company as a whole. For instance, a leasing company may have provided $10m nominal value of leases, and it will receive a cash flow over the next five years from these. It cannot demand early repayment on the leases and so cannot get its money back early if required. If it could sell the rights to the cash flows from the leases to someone else, it could transform that income stream into a lump sum today (in effect, receiving today the present value of a future cash flow). Where the originator is a bank or other organization that must meet capital adequacy requirements, the structure is usually more complex because a separate company is set up to buy the assets. A suitably large portfolio of assets is “pooled” and transferred to a “special purpose vehicle” or “SPV” (the issuer), a tax-exempt company or trust formed for the specific purpose of funding the assets. Once the assets are transferred to the issuer, there is normally no recourse to the originator. The issuer is “bankruptcy remote”, meaning that if the originator goes into bankruptcy, the assets of the issuer will not be distributed to the creditors of the originator. In order to achieve this, the governing documents of the issuer restrict its activities to only those necessary to complete the issuance of securities. Many issuers are typically “orphaned”. In the case of certain assets, such as credit card debt, where the portfolio is made up of a constantly changing pool of receivables, a trust in favor of the SPV may be declared in place of traditional transfer by assignment (see the outline of the master trust structure below). Accounting standards govern when such a transfer is a true sale, a financing, a partial sale, or a part-sale and part-financing.[4] In a true sale, the originator is allowed to remove the transferred assets from its balance sheet: in a financing, the assets are considered to remain the property of the originator.[5] Under US accounting standards, the originator achieves a sale by being at arm’s length from the issuer, in which case the issuer is classified as a “qualifying special purpose entity” or “qSPE“. Because of these structural issues, the originator typically needs the help of an investment bank (the arranger) in setting up the structure of the transaction. ### Issuance To be able to buy the assets from the originator, the issuer SPV issues tradable securities to fund the purchase. Investors purchase the securities, either through a private offering (targeting institutional investors) or on the open market. The performance of the securities is then directly linked to the performance of the assets. Credit rating agencies rate the securities which are issued to provide an external perspective on the liabilities being created and help the investor make a more informed decision. In transactions with static assets, a depositor will assemble the underlying collateral, help structure the securities and work with the financial markets to sell the securities to investors. The depositor has taken on added significance under Regulation AB. The depositor typically owns 100% of the beneficial interest in the issuing entity and is usually the parent or a wholly owned subsidiary of the parent which initiates the transaction. In transactions with managed (traded) assets, asset managers assemble the underlying collateral, help structure the securities and work with the financial markets in order to sell the securities to investors. Some deals may include a third-party guarantor which provides guarantees or partial guarantees for the assets, the principal and the interest payments, for a fee. The securities can be issued with either a fixed interest rate or a floating rate under currency pegging system. Fixed rate ABS set the “coupon” (rate) at the time of issuance, in a fashion similar to corporate bonds and T-Bills. Floating rate securities may be backed by both amortizing and non-amortizing assets in the floating market. In contrast to fixed rate securities, the rates on “floaters” will periodically adjust up or down according to a designated index such as a U.S. Treasury rate, or, more typically, the London Interbank Offered Rate (LIBOR). The floating rate usually reflects the movement in the index plus an additional fixed margin to cover the added risk.[6] ### Credit enhancement and tranching Unlike conventional corporate bonds which are unsecured, securities created in a securitization are “credit enhanced”, meaning their credit quality is increased above that of the originator’s unsecured debt or underlying asset pool. This increases the likelihood that the investors will receive the cash flows to which they are entitled, and thus enables the securities to have a higher credit rating than the originator. Some securitizations use external credit enhancement provided by third parties, such as surety bonds and parental guarantees (although this may introduce a conflict of interest). The issued securities are often split into tranches, or categorized into varying degrees of subordination. Each tranche has a different level of credit protection or risk exposure: there is generally a senior (“A”) class of securities and one or more junior subordinated (“B”, “C”, etc.) classes that function as protective layers for the “A” class. The senior classes have first claim on the cash that the SPV receives, and the more junior classes only start receiving repayment after the more senior classes have been repaid. Because of the cascading effect between classes, this arrangement is often referred to as a cash flow waterfall.[7] If the underlying asset pool becomes insufficient to make payments on the securities (e.g. when loans default within a portfolio of loan claims), the loss is absorbed first by the subordinated tranches, and the upper-level tranches remain unaffected until the losses exceed the entire amount of the subordinated tranches. The senior securities might be AAA or AA rated, signifying a lower risk, while the lower-credit quality subordinated classes receive a lower credit rating, signifying a higher risk.[6] The most junior class (often called the equity class) is the most exposed to payment risk. In some cases, this is a special type of instrument which is retained by the originator as a potential profit flow. In some cases the equity class receives no coupon (either fixed or floating), but only the residual cash flow (if any) after all the other classes have been paid. There may also be a special class which absorbs early repayments in the underlying assets. This is often the case where the underlying assets are mortgages which, in essence, are repaid whenever the properties are sold. Since any early repayments are passed on to this class, it means the other investors have a more predictable cash flow. If the underlying assets are mortgages or loans, there are usually two separate “waterfalls” because the principal and interest receipts can be easily allocated and matched. But if the assets are income-based transactions such as rental deals one cannot categorise the revenue so easily between income and principal repayment. In this case all the revenue is used to pay the cash flows due on the bonds as those cash flows become due. Credit enhancements affect credit risk by providing more or less protection for promised cash flows for a security. Additional protection can help a security achieve a higher rating, lower protection can help create new securities with differently desired risks, and these differential protections can make the securities more attractive. In addition to subordination, credit may be enhanced through:[5] • reserve or spread account, in which funds remaining after expenses such as principal and interest payments, charge-offs and other fees have been paid-off are accumulated, and can be used when SPE expenses are greater than its income. • Third-party insurance, or guarantees of principal and interest payments on the securities. • Over-collateralisation, usually by using finance income to pay off principal on some securities before principal on the corresponding share of collateral is collected. • Cash funding or a cash collateral account, generally consisting of short-term, highly rated investments purchased either from the seller’s own funds, or from funds borrowed from third parties that can be used to make up shortfalls in promised cash flows. • A third-party letter of credit or corporate guarantee. • A back-up servicer for the loans. • Discounted receivables for the pool. ### Servicing servicer collects payments and monitors the assets that are the crux of the structured financial deal. The servicer can often be the originator, because the servicer needs very similar expertise to the originator and would want to ensure that loan repayments are paid to the Special Purpose Vehicle. The servicer can significantly affect the cash flows to the investors because it controls the collection policy, which influences the proceeds collected, the charge-offs and the recoveries on the loans. Any income remaining after payments and expenses is usually accumulated to some extent in a reserve or spread account, and any further excess is returned to the seller. Bond rating agencies publish ratings of asset-backed securities based on the performance of the collateral pool, the credit enhancements and the probability of default.[5] When the issuer is structured as a trust, the trustee is a vital part of the deal as the gate-keeper of the assets that are being held in the issuer. Even though the trustee is part of the SPV, which is typically wholly owned by the Originator, the trustee has a fiduciary duty to protect the assets and those who own the assets, typically the investors. ### Repayment structures Unlike corporate bonds, most securitizations are amortized, meaning that the principal amount borrowed is paid back gradually over the specified term of the loan, rather than in one lump sum at the maturity of the loan. Fully amortizing securitizations are generally collateralised by fully amortizing assets, such as home equity loans, auto loans, and student loans. Prepayment uncertainty is an important concern with fully amortizing ABS. The possible rate of prepayment varies widely with the type of underlying asset pool, so many prepayment models have been developed to try to define common prepayment activity. The PSA prepayment model is a well-known example.[6][8] A controlled amortization structure can give investors a more predictable repayment schedule, even though the underlying assets may be nonamortising. After a predetermined “revolving period”, during which only interest payments are made, these securitizations attempt to return principal to investors in a series of defined periodic payments, usually within a year. An early amortization event is the risk of the debt being retired early.[6] On the other hand, bullet or slug structures return the principal to investors in a single payment. The most common bullet structure is called the soft bullet, meaning that the final bullet payment is not guaranteed to be paid on the scheduled maturity date; however, the majority of these securitizations are paid on time. The second type of bullet structure is the hard bullet, which guarantees that the principal will be paid on the scheduled maturity date. Hard bullet structures are less common for two reasons: investors are comfortable with soft bullet structures, and they are reluctant to accept the lower yields of hard bullet securities in exchange for a guarantee.[6] Securitizations are often structured as a sequential pay bond, paid off in a sequential manner based on maturity. This means that the first tranche, which may have a one-year average life, will receive all principal payments until it is retired; then the second tranche begins to receive principal, and so forth.[6] Pro rata bond structures pay each tranche a proportionate share of principal throughout the life of the security.[6] ### Structural risks and misincentives Some originators (e.g. of mortgages) have prioritised loan volume over credit quality, disregarding the long-term risk of the assets they have created in their enthusiasm to profit from the fees associated with origination and securitization. Other originators, aware of the reputational harm and added expense if risky loans are subject to repurchase requests or improperly originated loans lead to litigation, have paid more attention to credit quality.[citation needed] ## Special types of securitization ### Master trust A master trust is a type of SPV particularly suited to handle revolving credit card balances, and has the flexibility to handle different securities at different times. In a typical master trust transaction, an originator of credit card receivables transfers a pool of those receivables to the trust and then the trust issues securities backed by these receivables. Often there will be many tranched securities issued by the trust all based on one set of receivables. After this transaction, typically the originator would continue to service the receivables, in this case the credit cards. There are various risks involved with master trusts specifically. One risk is that timing of cash flows promised to investors might be different from timing of payments on the receivables. For example, credit card-backed securities can have maturities of up to 10 years, but credit card-backed receivables usually pay off much more quickly. To solve this issue these securities typically have a revolving period, an accumulation period, and an amortization period. All three of these periods are based on historical experience of the receivables. During the revolving period, principal payments received on the credit card balances are used to purchase additional receivables. During the accumulation period, these payments are accumulated in a separate account. During the amortization period, new payments are passed through to the investors. A second risk is that the total investor interests and the seller’s interest are limited to receivables generated by the credit cards, but the seller (originator) owns the accounts. This can cause issues with how the seller controls the terms and conditions of the accounts. Typically to solve this, there is language written into the securitization to protect the investors and potential receivables. A third risk is that payments on the receivables can shrink the pool balance and under-collateralize total investor interest. To prevent this, often there is a required minimum seller’s interest, and if there was a decrease then an early amortization event would occur.[5] ### Issuance trust In 2000, Citibank introduced a new structure for credit card-backed securities, called an issuance trust, which does not have limitations that master trusts sometimes do, that requires each issued series of securities to have both a senior and subordinate tranche. There are other benefits to an issuance trust: they provide more flexibility in issuing senior/subordinate securities, can increase demand because pension funds are eligible to invest in investment-grade securities issued by them, and they can significantly reduce the cost of issuing securities. Because of these issues, issuance trusts are now the dominant structure used by major issuers of credit card-backed securities.[5] ### Grantor trust Grantor trusts are typically used in automobile-backed securities and REMICs (Real Estate Mortgage Investment Conduits). Grantor trusts are very similar to pass-through trusts used in the earlier days of securitization. An originator pools together loans and sells them to a grantor trust, which issues classes of securities backed by these loans. Principal and interest received on the loans, after expenses are taken into account, are passed through to the holders of the securities on a pro-rata basis.[9] ### Owner trust In an owner trust, there is more flexibility in allocating principal and interest received to different classes of issued securities. In an owner trust, both interest and principal due to subordinate securities can be used to pay senior securities. Due to this, owner trusts can tailor maturity, risk and return profiles of issued securities to investor needs. Usually, any income remaining after expenses is kept in a reserve account up to a specified level and then after that, all income is returned to the seller. Owner trusts allow credit risk to be mitigated by over-collateralization by using excess reserves and excess finance income to prepay securities before principal, which leaves more collateral for the other classes. ## Motives for securitization ### Advantages to issuer Reduces funding costs: Through securitization, a company rated BB but with AAA worthy cash flow would be able to borrow at possibly AAA rates. This is the number one reason to securitize a cash flow and can have tremendous impacts on borrowing costs. The difference between BB debt and AAA debt can be multiple hundreds of basis points. For example, Moody’s downgraded Ford Motor Credit’s rating in January 2002, but senior automobile backed securities, issued by Ford Motor Credit in January 2002 and April 2002, continue to be rated AAA because of the strength of the underlying collateral and other credit enhancements.[5] Reduces asset-liability mismatch: “Depending on the structure chosen, securitization can offer perfect matched funding by eliminating funding exposure in terms of both duration and pricing basis.”[10] Essentially, in most banks and finance companies, the liability book or the funding is from borrowings. This often comes at a high cost. Securitization allows such banks and finance companies to create a self-funded asset book. Lower capital requirements: Some firms, due to legal, regulatory, or other reasons, have a limit or range that their leverage is allowed to be. By securitizing some of their assets, which qualifies as a sale for accounting purposes, these firms will be able to remove assets from their balance sheets while maintaining the “earning power” of the assets.[9] Locking in profits: For a given block of business, the total profits have not yet emerged and thus remain uncertain. Once the block has been securitized, the level of profits has now been locked in for that company, thus the risk of profit not emerging, or the benefit of super-profits, has now been passed on. Transfer risks (credit, liquidity, prepayment, reinvestment, asset concentration): Securitization makes it possible to transfer risks from an entity that does not want to bear it, to one that does. Two good examples of this are catastrophe bonds and Entertainment Securitizations. Similarly, by securitizing a block of business (thereby locking in a degree of profits), the company has effectively freed up its balance to go out and write more profitable business. Off balance sheet: Derivatives of many types have in the past been referred to as “off-balance-sheet”. This term implies that the use of derivatives has no balance sheet impact. While there are differences among the various accounting standards internationally, there is a general trend towards the requirement to record derivatives at fair value on the balance sheet. There is also a generally accepted principle that, where derivatives are being used as a hedge against underlying assets or liabilities, accounting adjustments are required to ensure that the gain/loss on the hedged instrument is recognized in the income statement on a similar basis as the underlying assets and liabilities. Certain credit derivatives products, particularly Credit Default Swaps, now have more or less universally accepted market standard documentation. In the case of Credit Default Swaps, this documentation has been formulated by the International Swaps and Derivatives Association (ISDA) who have for a long time provided documentation on how to treat such derivatives on balance sheets. Earnings: Securitization makes it possible to record an earnings bounce without any real addition to the firm. When a securitization takes place, there often is a “true sale” that takes place between the Originator (the parent company) and the SPE. This sale has to be for the market value of the underlying assets for the “true sale” to stick and thus this sale is reflected on the parent company’s balance sheet, which will boost earnings for that quarter by the amount of the sale. While not illegal in any respect, this does distort the true earnings of the parent company. Admissibility: Future cashflows may not get full credit in a company’s accounts (life insurance companies, for example, may not always get full credit for future surpluses in their regulatory balance sheet), and a securitization effectively turns an admissible future surplus flow into an admissible immediate cash asset. Liquidity: Future cashflows may simply be balance sheet items which currently are not available for spending, whereas once the book has been securitized, the cash would be available for immediate spending or investment. This also creates a reinvestment book which may well be at better rates. ### Disadvantages to issuer May reduce portfolio quality: If the AAA risks, for example, are being securitized out, this would leave a materially worse quality of residual risk. Costs: Securitizations are expensive due to management and system costs, legal fees, underwriting fees, rating fees and ongoing administration. An allowance for unforeseen costs is usually essential in securitizations, especially if it is an atypical securitization. Size limitations: Securitizations often require large scale structuring, and thus may not be cost-efficient for small and medium transactions. Risks: Since securitization is a structured transaction, it may include par structures as well as credit enhancements that are subject to risks of impairment, such as prepayment, as well as credit loss, especially for structures where there are some retained strips. ### Advantages to investors Opportunity to potentially earn a higher rate of return (on a risk-adjusted basis) Opportunity to invest in a specific pool of high quality assets: Due to the stringent requirements for corporations (for example) to attain high ratings, there is a dearth of highly rated entities that exist. Securitizations, however, allow for the creation of large quantities of AAA, AA or A rated bonds, and risk averse institutional investors, or investors that are required to invest in only highly rated assets, have access to a larger pool of investment options. Portfolio diversification: Depending on the securitization, hedge funds as well as other institutional investors tend to like investing in bonds created through securitizations because they may be uncorrelated to their other bonds and securities. Isolation of credit risk from the parent entity: Since the assets that are securitized are isolated (at least in theory) from the assets of the originating entity, under securitization it may be possible for the securitization to receive a higher credit rating than the “parent”, because the underlying risks are different. For example, a small bank may be considered more risky than the mortgage loans it makes to its customers; were the mortgage loans to remain with the bank, the borrowers may effectively be paying higher interest (or, just as likely, the bank would be paying higher interest to its creditors, and hence less profitable). ### Risks to investors Liquidity risk Credit/default: Default risk is generally accepted as a borrower’s inability to meet interest payment obligations on time.[11] For ABS, default may occur when maintenance obligations on the underlying collateral are not sufficiently met as detailed in its prospectus. A key indicator of a particular security’s default risk is its credit rating. Different tranches within the ABS are rated differently, with senior classes of most issues receiving the highest rating, and subordinated classes receiving correspondingly lower credit ratings.[6] Almost all mortgages, including reverse mortgages, and student loans, are now insured by the government, meaning that taxpayers are on the hook for any of these loans that go bad even if the asset is massively over-inflated. In other words, there are no limits or curbs on over-spending, or the liabilities to taxpayers. However, the credit crisis of 2007–2008 has exposed a potential flaw in the securitization process – loan originators retain no residual risk for the loans they make, but collect substantial fees on loan issuance and securitization, which doesn’t encourage improvement of underwriting standards. Event risk Prepayment/reinvestment/early amortization: The majority of revolving ABS are subject to some degree of early amortization risk. The risk stems from specific early amortization events or payout events that cause the security to be paid off prematurely. Typically, payout events include insufficient payments from the underlying borrowers, insufficient excess spread, a rise in the default rate on the underlying loans above a specified level, a decrease in credit enhancements below a specific level, and bankruptcy on the part of the sponsor or servicer.[6] Currency interest rate fluctuations: Like all fixed income securities, the prices of fixed rate ABS move in response to changes in interest rates. Fluctuations in interest rates affect floating rate ABS prices less than fixed rate securities, as the index against which the ABS rate adjusts will reflect interest rate changes in the economy. Furthermore, interest rate changes may affect the prepayment rates on underlying loans that back some types of ABS, which can affect yields. Home equity loans tend to be the most sensitive to changes in interest rates, while auto loans, student loans, and credit cards are generally less sensitive to interest rates.[6] Contractual agreements Moral hazard: Investors usually rely on the deal manager to price the securitizations’ underlying assets. If the manager earns fees based on performance, there may be a temptation to mark up the prices of the portfolio assets. Conflicts of interest can also arise with senior note holders when the manager has a claim on the deal’s excess spread.[12] Servicer risk: The transfer or collection of payments may be delayed or reduced if the servicer becomes insolvent. This risk is mitigated by having a backup servicer involved in the transaction.[6] ## History ### Early developments Modern practice of securitization has its roots in the 17th-century Dutch Republic.[13][14] Examples of securitization can be found at least as far back as the 18th century.[15] Among the early examples of mortgage-backed securities in the United States were the farm railroad mortgage bonds of the mid-19th century which contributed to the panic of 1857.[16] In February 1970, the U.S. Department of Housing and Urban Development created the first modern residential mortgage-backed security. The Government National Mortgage Association (GNMA or Ginnie Mae) sold securities backed by a portfolio of mortgage loans.[17] To facilitate the securitization of non-mortgage assets, businesses substituted private credit enhancements. First, they over-collateralised pools of assets; shortly thereafter, they improved third-party and structural enhancements. In 1985, securitization techniques that had been developed in the mortgage market were applied for the first time to a class of non-mortgage assets — automobile loans. A pool of assets second only to mortgages in volume, auto loans were a good match for structured finance; their maturities, considerably shorter than those of mortgages, made the timing of cash flows more predictable, and their long statistical histories of performance gave investors confidence.[18] This early auto loan deal was a$60 million securitization originated by Marine Midland Bank and securitised in 1985 by the Certificate for Automobile Receivables Trust (CARS, 1985-1).[19]

The first significant bank credit card sale came to market in 1986 with a private placement of $50 million of outstanding bank card loans. This transaction demonstrated to investors that, if the yields were high enough, loan pools could support asset sales with higher expected losses and administrative costs than was true within the mortgage market. Sales of this type — with no contractual obligation by the seller to provide recourse — allowed banks to receive sales treatment for accounting and regulatory purposes (easing balance sheet and capital constraints), while at the same time allowing them to retain origination and servicing fees. After the success of this initial transaction, investors grew to accept credit card receivables as collateral, and banks developed structures to normalize the cash flows.[18] Starting in the 1990s with some earlier private transactions, securitization technology was applied to a number of sectors of the reinsurance and insurance markets including life and catastrophe. This activity grew to nearly$15bn of issuance in 2006 following the disruptions in the underlying markets caused by Hurricane Katrina and Regulation XXX. Key areas of activity in the broad area of Alternative Risk Transfer include catastrophe bonds, Life Insurance Securitization and Reinsurance Sidecars.

The first public Securitization of Community Reinvestment Act (CRA) loans started in 1997. CRA loans are loans targeted to low and moderate income borrowers and neighborhoods.[20]

As estimated by the Bond Market Association, in the United States, the total amount outstanding[clarification needed] at the end of 2004 was $1.8 trillion. This amount was about 8 percent of total outstanding bond market debt ($23.6 trillion), about 33 percent of mortgage-related debt ($5.5 trillion), and about 39 percent of corporate debt ($4.7 trillion) in the United States. In nominal terms, over the previous ten years (1995–2004) ABS[clarification needed] amount outstanding had grown about 19 percent annually, with mortgage-related debt and corporate debt each growing at about 9 percent. Gross public issuance of asset-backed securities was strong, setting new records in many years. In 2004, issuance was at an all-time record of about $0.9 trillion.[5] At the end of 2004, the larger sectors of this market were credit card-backed securities (21 percent), home-equity backed securities (25 percent), automobile-backed securities (13 percent), and collateralized debt obligations (15 percent). Among the other market segments were student loan-backed securities (6 percent), equipment leases (4 percent), manufactured housing (2 percent), small business loans (such as loans to convenience stores and gas stations), and aircraft leases.[5] Modern securitization took off in the late 1990s or early 2000s, thanks to the innovative structures implemented across the asset classes, such as UK Mortgage Master Trusts (concept imported from the US Credit Cards), Insurance-backed transaction (such as those implemented by the insurance securitization guru Emmanuel Issanchou) or even more esoteric asset classes (for example securitization of lottery receivables). As the result of the credit crunch precipitated by the subprime mortgage crisis the US market for bonds backed by securitised loans was very weak in 2008 except for bonds guaranteed by a federally backed agency. As a result, interest rates rose for loans that were previously securitised such as home mortgages, student loans, auto loans and commercial mortgages.[21] ### Recent lawsuits Recently there have been several lawsuits attributable to the rating of securitizations by the three leading rating agencies. In July, 2009, the USA’s largest public pension fund has filed suit in California state court in connection with$1 billion in losses that it says were caused by “wildly inaccurate” credit ratings from the three leading ratings agencies.[22]

• Collateralized debt obligation, securitization vehicle for corporate debt securities
• Collateralized fund obligation, securitization vehicle for private equity and hedge fund assets
• Collateralized mortgage obligation, securitization vehicle for mortgage-backed securities
• Collateralized loan obligation, securitization vehicle for corporate loans
• Strip financing

## References

1. ^ Raynes; Sylvain; Rutledge, Ann (2003). The Analysis of Structured Securities. Oxford University Press. p. 103. ISBN 978-0-19-515273-9.
2. ^ “ESF Securitization Data Report Q2:business
3. ^ Hill, Claire A. (2002). “Whole Business Securitization in Emerging Markets”. Duke Journal of Comparative and International Law12(2). SSRN 333008.
4. ^ FASB Statement No. 140 “Accounting for transfers and servicing of financial assets and extinguishments of liabilities—a replacement of FASB Statement No. 125”. Financial Accounting Standards Board. September 2000.
5. Jump up to:a b c d e f g h Sabarwal, T. (29 December 2005). “Common Structures of Asset Backed Securities and Their Risks”. SSRN 3367860.
6. Jump up to:a b c d e f g h i j k “Fixed Income Sectors: Asset-Backed Securities – A primer on asset-backed securities” (PDF). Dwight Asset Management Company. 2005. Archived from the original (PDF)on 18 March 2009.
7. ^ Kim, M.; Hessami, A.; Sombolestani, E. (24 March 2010). CVEN 640 – Cash Flow Waterfall.
8. ^ The Committee on the Global Financial System (January 2005). The role of ratings in structured finance: issues and implications(PDF) (Report). Bank for International Settlements.
9. Jump up to:a b Reis-Roy, Calvin (1998). “Rating Securitisation Structures”. Journal of International Banking Law13 (9): 298–304.
10. ^ “The Handbook of Asset-Backed Securities”, Jess Lederman, 1990.
11. ^ Reis-Roy, Calvin (2003). An Analysis of the Law and Practice of Securitisation.
12. ^ Tavakoli, Janet (September–October 2005). “CDOs: Caveat Emptor”. GARP Risk Review. Global Association of Risk Professionals (26).
13. ^ Goetzmann, William N.; Rouwenhorst, K. Geert (2008). “The History of Financial Innovation”. Carbon Finance, Environmental Market Solutions to Climate Change. Yale School of Forestry and Environmental Studies. pp. 18–43. The 17th and 18th centuries in the Netherlands were a remarkable time for finance. Many of the financial products or instruments that we see today emerged during a relatively short period. In particular, merchants and bankers developed what we would today call securitization. Mutual funds and various other forms of structured finance that still exist today emerged in the 17th and 18th centuries in Holland.
14. ^ Markham, Jerry W. (2011). A Financial History of the United States from Enron-Era Scandals to the Great Recession (2004–2009) (1st ed.). Routledge. p. 355. ISBN 978-0765624314. An early example of securitization was found in Amsterdam in the seventeenth century.
15. ^ Frehen, Rik; Rouwenhorst, K. Geert; Goetzmann, William N. (2012). Dutch Securities for American Land Speculation in the Late-Eighteenth Century (PDF).
16. ^ Riddiough, Timothy J.; Thompson, Howard E. (2012). “Déjà Vu All Over Again: Agency, Uncertainty, Leverage and the Panic of 1857”. SSRN 2042316.
17. ^ Asset-Backed securities in Germany: the sale and Securitization of loans by German credit institutions (Report). Deutsche Bundesbank. July 1997.
18. Jump up to:a b Asset Securitization Comptroller’s Handbook. Comptroller of the Currency Administrator of National Banks. 1997.
19. ^ Hearing before the U.S. House subcommittee on Policy Research and Insurance in “Asset Securitization and Secondary Markets”. 31 July 1991. p. 13. ISBN 0160370140.
20. ^ “Wachovia Press Releases”. Archived from the original on 11 February 2009.
21. ^ Bajaj, Vikas (12 August 2008). “Mechanism for Credit Is Still Stuck”. New York Times.
22. ^ Leslie Wayne (15 July 2009). “Caper Sues over Ratings of Securities”. New York Times.

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