Fannie Mae and Freddie Mac assume a significant amount of interest and prepayment risk and all of the credit risk for about half of the $8 trillion U.S. residential mortgage market. Their hybrid government-private status, and the perception that they are too big to fail, make them a potentially large, but largely unaccounted for, risk to the federal government. Measuring the size and risk of this liability is technically difficult, but important for the debate over the appropriate regulation of these institutions. Here we take an options pricing approach to evaluating these costs and risks. We evaluate the sensitivity of our estimates to various modeling assumptions, and also to the regulatory regime, including forbearance policies and capital requirements. The analysis highlights the benefits, but also the challenges, of taking on options-based approach to evaluating the value of federal credit guarantees.

It is common for firms to issue or purchase options on the firm's own stock. Examples include convertible bonds, warrants, call options as employee compensation, or the sale of put options as part of share repurchase programs. This paper shows that option positions with implicit borrowing---such as put sales and call purchases---are tax-disadvantaged relative to the equivalent synthetic option with explicit borrowing. Conversely, option positions with implicit lending---such as compensation calls---are tax-advantaged. We also show that firms are better off from a tax perspective issuing bifurcated convertible bonds---bonds plus warrants---rather than an otherwise equivalent standard convertible. The put option sales which have been popular with some firms are like issuing debt with non-deductible interest and thus have a tax cost. For example, we estimate that in 1999 the tax cost to Microsoft of written puts was about $80m per year.

German dividends typically carry a tax credit which makes the dividend worth 42.86% more to a taxable German shareholder than to a tax-exempt or foreign shareholder. As a result of the credit, the ex-dividend-day share price drop exceeds the amount of the dividend. I document that the ex-day drop reflects approximately one-half of the tax credit, and show that futures and option prices embed approximately one-half of the tax credit. The existence of the tax credit creates possibilities for cross-border tax arbitrage and also has implications for market integration, market efficiency, tax policy, and tax-efficient foreign investment. In particular, it is tax-efficient for foreign investors to hold DAX index futures rather than investing directly in the DAX cash index.

This paper demonstrates that when the price of the underlying asset is governed by geometric Brownian motion the price of a call option with underlying asset price S, strike price K, interest rate ã, and dividend yield ä is equal to the price of an otherwise identical put option with asset price K, strike price S, interest rate ä, and dividend yield ã. The result is true for both European and American options, and implies that the prices of at-the-money American call and put options on futures are equal.

When shareholders have different plans to sell their shares, they will, in general, have different preferences concerning the firm's decision to pay out cash using dividends or share repurchase. We illustrate these different preferences and explore a model of payout policy that highlights the adverse selection costs of repurchases when managers have superior information about the value of the firm. We show that, in the absence of fixed costs to repurchasing shares, there is a separating equilibrium in which managers use taxable dividends to signal the quality of the firm, with better firms paying lower dividends, using repurchases for the remainder of the payout. With fixed costs to repurchasing, small payouts are made via dividend and large payouts are divided between repurchases and dividends, as in the no-fixed cost case. In both cases, the percentage of shares repurchased increases with the size of the payout and larger repurchases are better news.

Banks know more about the quality of their assets than do outside investors. This informational asymmetry can distort investment decisions if the bank must raise funds from uninformed outsiders. We model the effect of asymmetric information about loan quality on the asset and liability decisions of banks and the market valuation of bank liabilities. The existence of a precautionary demand for riskless securities against future liquidity needs depends on both the regulatory environment and the informational structure. If banks are ex ante identical, they prefer issuing risky debt to fund a withdrawal to holding riskless securities ex ante. If banks have partial knowledge of loan quality, however, high-quality banks may hold riskless securities to signal their quality, enabling them to issue risky debt at a lower interest rate. We present new empirical evidence that banks with higher asset quality do in fact hold more cash and securities.

This paper develops a formal model of the effect of time-varying asymmetric information on the timing and pricing of equity issues when managers are better informed than outside investors. We assume that as time passes, the adverse selection problem becomes more severe as more managers receive a private signal. Under this assumption, the model predicts temporal variation in the quantity of issues, with a bunching of issues after information releases. It also predicts that the price drop at issue announcement increases with the time since the last information release. These predictions are consistent with several recent empirical studies relating equity issues to earnings and dividend announcements.

With time-varying adverse selection in the market for new equity issues, firms will prefer to issue equity when the market is most informed about the quality of the firm. This implies that equity issues tend to follow credible information releases. In addition, if the asymmetry in information increases over time between information releases, the price drop at the announcement of an equity issue should increase in the time since the last information release. Using earnings releases as a proxy for informative events, we find evidence supporting these propositions.

This paper presents an information-theoretic, infinite horizon model of the equity issue decision. The model predicts that (a) equity issues on average are preceded by an abnormal positive return on the stock, although for some firms the issue is preceded by a loss; (b) equity issues on average are preceded by an abnormal rise in the market; and (c) the stock price drops at the announcement of an issue. The model provides a measure of the welfare cost of asymmetric information; the welfare loss may be small even if the price drop at issue announcement is large.

This paper models bank asset choice when shareholders know more about loan quality than do outsiders. Because of this informational asymmetry, the price of loans in the secondary market is the price for poor quality loans. Banks desire to hold marketable securities in order to avoid liquidating good quality loans at the "lemons" price, but also have a countervailing desire to hold risky loans in order to maximize the value of deposit insurance. In this context, portfolio composition and bank safety is examined as a function of the market distribution of loan quality, and the distribution of deposits. The model suggests that off-balance sheet commitments have little effect on bankruptcy risk, and induce banks to hold more securities. We also show that an increase in the bank equity requirement will unambiguously increase bank safety in the long run. In the short run, banks are unambiguously riskier on-balance-sheet, although the effect on bank safety is ambiguous.

Equilibrium in the market for real assets requires that the price of those assets be bid up to reflect the tax shields they can offer to levered firms.Thus there must be an equality between the market values of real assets and the values of optimally levered firms. The standard measure of the advantage to leverage compares the values of levered and unlevered assets, and can be misleading and difficult to interpret. We show that a meaningful measure of the advantage to debt is the extra rate of return, net of a market premium for bankruptcy risk, earned by a levered firm relative to an otherwise-identical unlevered firm. We construct an option valuation model to calculate such a measure and present extensive simulation results. We use this model to compute optimal debt maturities, show how this approach can be used for capital budgeting, and discuss its implications for the comparison of bankruptcy costs versus tax shields.

This paper uses an option valuation model of the firm to answer the question, "What magnitude tax advantage to debt is consistent with the range of observed corporate debt ratios?" We incorporate into the model differential personal tax rates on capital gains and ordinary income. We conclude that variations in the magnitude of bankruptcy costs across firms can not by itself account for the simultaneous existence of levered and unlevered firms. When it is possible for the value of the underlying assets to jump discretely to zero, differences across firms in the probability of this jump can account for the simultaneous existence of levered and unlevered firms. Moreover, if the tax advantage to debt is small, the annual rate of return advantage offered by optimal leverage may be so small as to make the firm indifferent about debt policy over a wide range of debt-to-firm value ratios.

Analyzes the increase in the variance of return on long-term bonds in the U.S. between 1977 and 1981. Usage of the Capital Asset Pricing Model to help explain the behavior of interest rates; Calculation of the real risk premium on bonds.

Describes the design of commodity options contracts in Europe and United States. Introduction on the concept of futures options; Discussion on the pricing and properties of standard commodity options; Kinds of standard contracts.

This paper shows how government financing decisions can influence the corporate decision to use debt or equity finance. In particular, it is shown that an increase in the stock of taxable government debt reduces the equilibrium quantity of corporate debt, and that an increase in the stock of tax-free government debt reduces the equilibrium quantity of corporate equity. The effects of inflation rate and tax rate changes are also considered.

Upon exercise, non-qualified compensation options give rise to ordinary income for the option holder. Subsequent stock appreciation is taxed as capital gains. It is often asserted (for example in Scholes, Wolfson, Erickson, Maydew, and Shevlin) that because of this tax treatment, there are times when a holder of the option should exercise a non-qualified option before expiration. The argument---that it is worth incurring tax at high rates in order that subseqeunt gains can be taxed at a lower rate---is fallacious. The analysis in this paper also demonstrates that an employee who is granted stock should never perform a section 83(b) election.

Estimates for the size of the implicit Federal guarantees for debt issued by Fannie Mae and Freddie Mac have ranged from $200 million (Stiglitz et al, 2002) to $122 to $182 billion (Passmore, 2005). This paper extends and updates the estimates in Lucas and McDonald (2006), by simultaneously estimating the current stock price and the possible future loss, and permitting jumps in asset value. We annuitized expected losses of 15-20 basis points, with a present value in the vicinity of $20 billion.

Most firms do not make explicit use of real option techniques in evaluating investments. Nevertheless, real option considerations can be a significant component of value, and firms which approximately take them into account should outperform firms which do not. This paper asks whether the use of seemingly arbitrary investment criteria, such as hurdle rates and profitability indexes, can proxy for the use of more sophisticated real options calculation. We find that for a variety of parameters, particular hurdle rate and profitability index rules can provide close-to-optimal investment decisions. This suggests that firms using seemingly arbitrary "rules of thumb" may be trying to approximate optimal decisions.

The link between the real and financial decisions of firms has been studied for many years, yet it remains poorly understood. Neoclassical investment theories such as Tobin's q posit a direct, simple link between the market's valuation of the firm and investment decisions: firms invest when the market value of an investment exceeds the cost of the investment. For a variety of reasons—agency conflicts between management and security holders, conflicts among security holders, and asymmetric information between management and security holders—the relation between real and financial decisions may be quite complex.

In this paper we study seasoned equity issues as one piece of the corporate financing and investment puzzle. We expect equity issues to be particularly revealing about the role of asymmetric information in financing decisions.  First, to the extent that there is asymmetric information between management and outside security holders, the asymmetry should be of greatest concern to potential buyers of common stock since stock is the residual claim on the firm.  Second, it is well documented that stocks exhibit large abnormal returns during the period surrounding an equity issue. This suggests that equity issues do in fact reveal valuable information to the market. It is therefore natural to consider whether the price behavior of an equity-issuing firm sheds light on the importance of asymmetric information in the investment process.

This is a version of Derivatives Markets designed for a one-semester course.

This case provides a detailed practical example of some interesting option pricing issues arising from a tender offer for RJR Nabisco by KKR. Put-call parity was apparently violated during this period, but this was related to the specifics of the takeover offer. This case focuses on two issues: understanding the nature of the parity violation and why it could not have been arbitrated in the classical sense, and how a particular options trading strategy could have been used to speculate on the success of the KKR tender offer.