Sudipto Sarkar

On the investment-uncertainty relationship in a real options model

Abstract It appears to be widely accepted in the real options literature that an increase in uncertainty should have an inhibiting effect on investment. Our article demonstrates that the notion of a negative uncertainty–investment relationship is not always correct. We show that in certain situations, an increase in uncertainty can actually increase the probability of investing, and thereby have a positive impact on investment.

The effect of mean reversion on investment under uncertainty

Abstract Mean-Reverting processes are appropriate for most “real option” investment models, yet Geometric Brownian Motion (GBM) processes are generally used for tractability. Hassett and Metcalf (J. Econom. Dyn. Control 19 (1995) 1471–1488) argue that using a GBM process is justified because mean-reversion has two opposing effects—it brings the investment trigger closer, and also reduces the conditional volatility (thereby lowering the likelihood of reaching the trigger)—and the overall effect on investment should be negligible for most reasonable parameter values. This paper extends the Hassett and Metcalf model by incorporating a third factor, the effect of mean-reversion on systematic risk . The main result is that mean reversion, in general, does have a significant impact on investment. Moreover, this effect could be either positive or negative, depending on various factors such as project duration, cost of investing, interest rate, etc. Thus it is generally inappropriate to use the GBM process to approximate a mean-reverting process.

OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR

Motivated by empirical evidence and economic arguments, we assume that the cash reservoir of a financial corporation follows a mean reverting process. The firm must decide the optimal dividend strategy, which consists of the optimal times and the optimal amounts to pay as dividends. We model this as a stochastic impulse control problem, and succeed in finding an analytical solution. We also find a formula for the expected time between dividend payments. A crucial and surprising economic result of our paper is that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. This results in a reduction of the probability of default of the firm.

Probability of call and likelihood of the call feature in a corporate bond

Abstract This paper suggests a new way of predicting the likelihood of a corporate bond being callable. We compute the probability that a bond, if callable, would actually be called within a certain period. We also hypothesize a positive relationship between this probability and the likelihood of the bond being issued with a call feature. Comparative static results yield the following empirical implications: the likelihood of a call feature should be an increasing function of coupon rate, corporate tax rate and leverage ratio, and a decreasing function of interest rate and firm risk (volatility). Tests with recently issued corporate bonds provide fairly strong support for the model’s predictions.

Early and late calls of convertible bonds: Theory and evidence

Many convertible bonds are called too early or too late relative to the perfect markets decision rule of Ingersoll, 1977a and Ingersoll, 1977b. We re-examine the convertible call decision under corporate taxation and possible default prior to maturity. Our model predicts that early calls will be associated with high coupon and low call premium, dividend income, volatility, tax rate and interest rate; and late calls will be associated with high call premium, dividend income, tax rate and interest rate, and low coupon and volatility. These implications are supported by empirical tests carried out with five years of convertible call data.

Banks' option to lend, interest rate sensitivity, and credit availability

Interest rate risk is a major concern for banks because of the nominal nature of their assets and the asset-liability maturity mismatch. This paper proposes a new way to derive a banks interest rate sensitivity, by examining separately the effects of interest rate changes on existing loans(loans-in-place) and potential loans (loans-in-process). A potential loan is shown to be equivalent to an American option to lend, and is valued using option theory. An increase in interest rates generally has a negative effect on existing loans. However, if both deposit and lending rates rise by the same amount, the value of a potential loan generally increases. Hence a banks lending slack (or ratio of loans-in-process to loans-in-place) will determine its overall interest rate risk. Empirical evidence indicates that low-slack banks indeed have significantly more interest rate risk than high-slack banks. The model also makes predictions regarding the effect of deposit and lending rate parameters on bank credit availability. Empirical tests with quarterly data are generally supportive of these predictions. Copyright Kluwer Academic Publishers 2002

Effective duration of callable corporate bonds: Theory and evidence

Abstract This paper computes the effective duration of callable corporate bonds, using a contingent-claims model that incorporates both default risk and call risk. The model generates empirical implications regarding the cross-sectional variation and the firm-specific determinants of duration, and demonstrates that the effect of the call feature is to shorten duration (except for low-grade bonds). The effective duration is also estimated empirically for a large sample of long-term corporate bonds, using monthly bond price and interest rate data. Cross-sectional regression analysis is used to test the empirical implications of the model regarding the determinants of effective duration, and the empirical results are quite supportive of the model’s predictions.

Empirical Evidence on Corporate Risk-Shifting

We study empirically whether nonfinancial firms’ behavior is consistent with systematic risk‐shifting. We compare firms’ operating risk before and after a debt issue, under the assumption that if there is any risk‐shifting it is most likely to occur right after a debt issue. We document a significant increase in firms’ operating risk, even after adjusting for industry influences. The risk‐shifting is higher for firms with no subsequent debt issues, and for firms with lower credit ratings. Other determinants are earnings volatility, size of debt issue, and whether the bond is callable.

Duration and convexity of zero-coupon convertible bonds

Abstract Duration and convexity are important measures in fixed-income portfolio management. We have derived closed-form expressions for duration and convexity of zero-coupon convertibles, incorporating the impact of default risk, conversion option, and subordination. The overall effect is to shorten duration, while the effect on convexity is ambiguous. Both measures were found to be very different from those of straight bonds, in magnitude and in their response to parameter changes; e.g., a subordinated convertible duration can even be negative. Thus, it would be inappropriate to use traditional duration/convexity measures for evaluating or hedging interest rate risk in convertibles.

Optimal Expansion Financing and Prior Financial Structure

This paper identifies jointly the optimal investment trigger and the optimal financing package for a corporate expansion project, using a real-option trade-off model with agency problems. It also identifies the optimal initial capital structure of the firm (before the expansion). We show that it is generally optimal to use more debt than equity to finance the expansion. The other results are as follows: (i) existing debt has a negative effect, while the debt component of expansion financing has a positive effect, on investment; (ii) the debt component of the optimal expansion financing package is a decreasing function of the pre-expansion leverage ratio (consistent with mean reverting leverage ratios), and is also decreasing in the magnitude of the expansion opportunity; and (iii) the optimal pre-expansion leverage ratio is a decreasing function of both the firms profitability and the magnitude of the growth opportunity. These relationships are generally consistent with empirical evidence, and help reconcile the trade-off theory of capital structure with apparently contradictory empirical evidence.