Financial Engineering

We develop a model of lending and borrowing in markets where the lender has no access to physical collateral and where the borrower is heavily capital constrained. Our model of micro loans, which incorporates a) the absence of access to physical collateral, b) peer monitoring, c) threat of punishment upon default, and d) costly monitoring by lenders is used to determine the equilibrium borrowing rates. Monitoring by lenders is shown to be critical for an equilibrium to exist in our model if the maturity of the loan is too long.

The role of private equity in global capital markets appears to be expanding at an extraordinary rate. Morgan Stanley estimates that there are now some 2,700 private equity funds that either have raised, or are in the process of raising, a total of $500 billion. With this abundance of available equity capital, the willingness of private equity firms to participate in "club" deals, and the leverage that can be put on top of the equity, private equity buyers now appear able and willing to pay higher prices for assets than ever before.

This paper compares methods for computing the distribution of loss from defaults in a credit portfolio. The methods are applied in the Gaussian copula framework for credit risk and take advantage of the conditional independence of defaults in this framework. As a benchmark we use vanilla Monte Carlo simulation to estimate the tail probabilities of the total losses of the credit portfolio. The first method to be compared is a recursive algorithm to obtain the exact distribution of the total loss of the portfolio, conditional on observed values for the systematic risk factors.

We present an equilibrium production economy in which default occurs in equilibrium. The borrower chooses optimal default and consumption policies, taking into account that default is costly and the lender gains access to the technology upon default. We derive asset prices and default premia in this economy. The borrower's relative risk aversion in wealth increases with decreases in wealth due to the increased possibility of default at low wealth levels. This produces a time-varying pricing kernel and a countercyclical equity premium.

We develop a general equilibrium model of a production economy which has a risky production technology as well as a growth option to expand the scale of the productive sector of the economy. We show that when confronted with growth options, the representative consumer may sharply alter consumption rates to improve the likelihood of investment. This reduction in consumption is accompanied by an erosion of the option value of waiting to invest, leading to investment near the zero NPV threshold.

This paper develops approximations for the distribution of losses from default in a normal copula framework for credit risk. We put particular emphasis on approximating small probabilities of large losses, as these are the main requirement for calculation of value at risk and related risk measures. Our starting point is an approximation to the rate of decay of the tail of the loss distribution for multifactor, heterogeneous portfolios. We use this decay rate in three approximations: a homogeneous single-factor approximation, a saddlepoint heuristic, and a Laplace approximation.

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This paper outlines a financial statement analysis for use in equity valuation. Standard profitability analysis is incorporated, and extended, and is complemented with an analysis of growth. The perspective is one of forecasting payoffs to equities. So financial statement analysis is presented first as a matter of pro forma analysis of the future, with forecasted ratios viewed as building blocks of forecasts of payoffs. The analysis of current financial statements is then seen as a matter of identifying current ratios as predictors of the future ratios that drive equity payoffs.