Analyses of Mortgage-Backed Securities Based on Unobservable Prepayment Cost Processes

We propose a prepayment model of mortgage based on a structural approach in order to analyze prepayment risk of mortgage-backed securities (MBS). We introduce a continuous process named prepayment cost process. Specifically, each mortgager's prepayment time is defined by the first time when her or his prepayment cost process falls below zero, but prepayment cost processes are supposed to be unobservable in the market. We also introduce a risk unique to each loan pool of mortgages, called a loan pool risk (LPR), and we regard LPR as a systematic risk other than interest rate. Using the model, we discuss the conditional distribution of prepayment times and a risk-neutral valuation of pass-through MBS. It is shown that each mortgager's conditional non-prepayment probability and the posterior distribution of LPR play quite important roles in our study.This research is partially supported by Grant-in-Aid for Young Scientists (B) No. 16710108 from the Ministry of Education, Culture, Sports, Science and Technology.     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

Mortgage convexity

Most home mortgages in the United States are fixed-rate loans with an embedded prepayment option. When long-term rates decline, the effective duration of mortgage-backed securities (MBS) falls due to heightened refinancing expectations. I show that these changes in MBS duration function as large-scale shocks to the quantity of interest rate risk that must be borne by professional bond investors. I develop a simple model in which the risk tolerance of bond investors is limited in the short run, so these fluctuations in MBS duration generate significant variation in bond risk premia. Specifically, bond risk premia are high when aggregate MBS duration is high. The model offers an explanation for why long-term rates could appear to be excessively sensitive to movements in short rates and explains how changes in MBS duration act as a positive-feedback mechanism that amplifies interest rate volatility. I find strong support for these predictions in the time series of US government bond returns.     

Investor Sentiment and the Closed‐end Fund Puzzle: Out‐of‐sample Evidence

In this paper we examine the proposition that small investor sentiment, measured by the change in the discount/premium on closed‐end funds, is an important factor in stock returns. We conduct an out‐of‐sample test of the investor sentiment hypothesis in a market environment that is more likely to be prone to investor sentiment than the USA. We fail to provide supporting evidence for the claim of Lee et al. (1991) that investor sentiment affects the risk of common stocks. Consistent with Elton et al. (1998) , who show that investor sentiment does not enter the return generating process, our tests do not detect investor sentiment in a capital market that is more susceptible to small investor sentiment. Our results provide additional support against the claim that investor sentiment represents an independent and systematic asset pricing risk.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

What Drives Default and Prepayment on Subprime Auto Loans?

This paper uses novel data on the performance of loan pools underlying asset-backed securities to estimate a competing risks model of default and prepayment on subprime automobile loans. We find that prepayment rates increase rapidly with loan age but are not affected by prevailing market interest rates. Default rates are much more sensitive to aggregate shocks than are prepayment rates. Increases in unemployment precede increases in default rates, suggesting that defaults on subprime automobile loans are driven largely by shocks to household liquidity. There are significant differences in the default and prepayment rates faced by different subprime lenders. Those lenders that charge the highest interest rates experience the highest default rates, but also experience somewhat lower prepayment rates. We conjecture that there is substantial heterogeneity among subprime borrowers, and that different lenders target different segments of the subprime market. Because of their higher default rates, loans that carry the highest interest rates do not appear to yield the highest expected returns.     

Presidential Address: Sophisticated Investors and Market Efficiency

Stock‐market trading is increasingly dominated by sophisticated professionals, as opposed to individual investors. Will this trend ultimately lead to greater market efficiency? I consider two complicating factors. The first is crowding—the fact that, for a wide range of “unanchored” strategies, an arbitrageur cannot know how many of his peers are simultaneously entering the same trade. The second is leverage—when an arbitrageur chooses a privately optimal leverage ratio, he may create a fire‐sale externality that raises the likelihood of a severe crash. In some cases, capital regulation may be helpful in dealing with the latter problem.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

Conditional Equity Premium and Aggregate Corporate Investment

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment's market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin's q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.     

Market Risk of Mortgage-Backed Securities with Consistent Measures

Due to the complex prepayment behavior, mortgage contracts and their derivatives are generally priced using Monte Carlo simulations. The typical approach used by the industry, which involves simulating interest rates under the risk-neutral measure and applying a physically measured prepayment function, is subject to the problem of internal inconsistency. This is the first paper that directly investigates the potential impact of this issue. Following the general equilibrium setting by Cox, Ingersoll and Ross, we incorporate the market risk price parameter to derive the physical interest rate process from an observed yield curve. This allows us to model mortgage values under the consistent physical measures of interest rates and prepayment functions. By analyzing a default-free Ginnie Mae MBS, we find that the mixed measures lead to slower prepayment rate estimates and overpriced mortgage securities by approximately 5%. Further, there can be substantial biases in the duration and convexity measures depending on market condition and the particular security of interest. The internal inconsistency also leads to biased predictions of both expected and stressed returns for different investment horizons. Depending on the particular security, the bias in expected and stressed returns can be either positive or negative. These biases in risk estimates can introduce misallocation of risk-based capital and/or failure in hedging the market risk of a mortgage-related portfolio.

Limited Arbitrage in Equity Markets

We examine 82 situations where the market value of a company is less than its subsidiary. These situations imply arbitrage opportunities, providing an ideal setting to study the risks and market frictions that prevent arbitrageurs from immediately forcing prices to fundamental values. For 30 percent of the sample, the link between the parent and its subsidiary is severed before the relative value discrepancy is corrected. Furthermore, returns to a specialized arbitrageur would be 50 percent larger if the path to convergence was smooth rather than as observed. Uncertainty about the distribution of returns and characteristics of the risks limits arbitrage.     

Arbitrage With Holding Costs: A Utility-Based Approach

Unit time costs, or holding costs, are incurred in many arbitrage contexts. Examples include losing the use of short sale proceeds and lending funds at below market rates in reverse repurchase agreements. This paper analyzes the investment problem of a risk averse arbitrageur who faces holding costs. The model allows prices to deviate from “fundamental” values without allowing for riskless arbitrage opportunities. After characterizing an arbitrageur's optimal strategy, the model is examined in the context of the Treasury market. The analysis reveals that holding costs are an important friction in this market and that they can significantly affect arbitrageur behavior.     

Valuation of Mortgage-Backed Securities Based upon a Structural Approach

This paper studies the valuation of mortgage-backed securities (MBS) based upon a structural approach of several risks involving the prepayment and/or default behavior of mortgagors. For the Kariya and Kobayashi (1999) model using a time-consuming Monte-Carlosimulation, we provide an alternative semi-analytic valuation methodology closely related to solving the (Volterra type) integral equation with respectto the first hitting time density for a curved/flat boundary; consequently that enables us to calculate the MBS price faster and more precisely. Next, to capture the path-dependent prepayment behavior of the interest ratemovements we give some prepayment models based upon a two-dimensional Markov process of the interest rate and its long-run average rate. Third, we study the simultaneous assessment issue of prepayment and defaultrisks, encountered in practice.Finally we discuss the calculation of the joint probability density ofmultiple first hitting times.     

Aggregate insider trading and market returns: The role of transparency

Using a sample of countries that require timely disclosures of insider trades, I investigate the effect of country‐level institutions that promote transparency on the extent to which aggregate insider trades predict market returns. I find that financial information transparency mitigates the predictive content of aggregate insider trades when markets are more likely to deviate from fundamentals (i.e., during market fads), and when there is greater co‐movement in stock prices. In contrast, there is some evidence that governance and investor protection mitigate the association between aggregate insider trades and future earnings surprises. Hence, holding constant the timely disclosures of insider trades, other capital market institutions play complementary roles in mitigating the informational frictions that give rise to the predictive content of aggregate insider trades.     

The refinancing threshold pricing model: An economic approach to valuing MBS

Investigation of MBS prepayment data indicates that mortgagors have different interest rate levels, or thresholds, at which they exercise their option to prepay their mortgage. In order to properly value an MBS with heterogeneous mortgagors, Merrill Lynch has developed the Refinancing Threshold Pricing Model (RTP). The RTP model focuses on the refinancing decision of the mortgagor when pricing the mortgage pool. The model divides each pool into groups of mortgagors who share similar refinancing costs. Using market data, the RTP model endogenously determines both the implied costs that mortgagors face, as well as the proportion of the MBS pool in each refinancing cost group. In addition to determining pool value, the RTP model also calculates MBS duration, dP/dY and convexity. Comparison between RTP model values and actual market data reveals a strong correlation. The RTP has a wide range of applications, including valuing 15-year and 30-year conventional MBS; pricing interest-only (IO)/principal-only (PO) derivative MBS; determining new versus seasoned MBS price spreads; and valuing specific MBS pools.The information set forth was obtained from sources we believe reliable, but we do not guarantee its accuracy. Neither the information, nor any opinion expressed constitutes a solicitation by us for the purchase or sale of any securities or commodities. Merrill Lynch, Pierce, Fenner & Smith, Inc. or its affiliates may have either a long or short position in, and may buy and sell for its own account or the accounts of others, these securities.     

Volatility Risk Premium,Risk Aversion,and the Cross‐Section of Stock Returns

We test if innovations in investor risk aversion are a priced factor in the stock market. Using 25 portfolios sorted on book‐to‐market and size as test assets, our new factor together with the market factor explains 64% of the variation in average returns compared to 60% for the Fama‐French model. The new factor is generally significant with an estimated risk premium close to its time series mean also when industry portfolios and portfolios sorted on previous returns are augmented to the test assets.     

What's in a “China” Name? A Test of Investor Attention Hypothesis

We study whether a firm's name affects investor attention and firm valuation. Some Chinese firms listed on US stock exchanges have the word “China” included in their company names (“China‐name stocks”), while others do not (“non‐China‐name stocks”). During the 2007 China stock market boom, we find that China‐name stocks significantly outperform non‐China‐name stocks. This is not due to differences in firm characteristics, risk, or liquidity. The “China‐name effect” is largely consistent with the investor attention hypothesis that price pressure caused by increased investor attention on China‐name stocks during the boom period drives up China‐name stocks more than non‐China‐name stocks.     

Semi-analytical MBS Pricing

This paper presents a multi-factor valuation model for fixed-rate callable mortgage backed securities (MBS). The model yields semi-analytic solutions for the value of MBS in the sense that the MBS value is found by solving a system of ordinary differential equations. Instead of modelling the conditional prepayment rate (CPR), as is customary, the pool size is the primary modelling object. It is shown that the value of a single MBS payment due at time t _n can be found by computing two expectations of the pool size at time t _n–1 and t _n respectively. This is a general result independent of any interest rate model. However, if the pool size is specified in a way that makes the expectations solvable using transform methods, semi-analytic pricing formulas are achieved. The affine and quadratic pricing frameworks are combined to get flexible and sophisticated prepayment functions. We show that the model has no problem of generating negative convexity as the spot rate falls, and still be close to a similar non-callable bond when the spot rate rises.     

Consumption, Dividends, and the Cross Section of Equity Returns

We show that aggregate consumption risks embodied in cash flows can account for the puzzling differences in risk premia across book‐to‐market, momentum, and size‐sorted portfolios. The dynamics of aggregate consumption and cash flow growth rates, modeled as a vector autoregression, are used to measure the consumption beta of discounted cash flows. Differences in these cash flow betas account for more than 60% of the cross‐sectional variation in risk premia. The market price for risk in cash flows is highly significant. We argue that cash flow risk is important for interpreting differences in risk compensation across assets.     

How Does Investor Sentiment Affect Stock Market Crises? Evidence from Panel Data

We test the impact of investor sentiment on a panel of international stock markets. Specifically, we examine the influence of investor sentiment on the probability of stock market crises. We find that investor sentiment increases the probability of occurrence of stock market crises within a one‐year horizon. The impact of investor sentiment on stock markets is more pronounced in countries that are culturally more prone to herd‐like behavior, overreaction and low institutional involvement.