Risk-free Debt Research Articles

Optimal fiscal and monetary policy with sticky wages and sticky prices

We determine the optimal degree of price inflation volatility when nominal wages are sticky and the government uses state-contingent inflation to finance government spending. We address this question in a well-understood Ramsey model of fiscal and monetary policy, in which the benevolent planner has access to labor income taxes, nominally risk-free debt, and money creation. Our main result is that sticky wages alone make price stability optimal in the face of shocks to the government budget, to a degree quantitatively similar as sticky prices alone. Key for our results is an equilibrium restriction between nominal price inflation and nominal wage inflation that holds trivially in a Ramsey model featuring only sticky prices. Our results thus show that when nominal wages are sticky, setting real wages as close as possible to their efficient path is a more important goal of optimal monetary policy than is financing innovations in the government budget via state-contingent inflation. A second important result is that the nominal interest rate can be used to indirectly tax the rents of monopolistic labor suppliers. Taken together, our results uncover features of Ramsey fiscal and monetary policy in the presence of a type of labor market imperfection that is widely-believed to be important.

Optimal Capital Income Taxation in an Asymmetric Small Open Economy

This paper examines the structure of the optimal capital income taxation policy for a stochastic small open economy with a financial asymmetry in which the households have access to complete financial markets, while the government is constrained to issue risk-free debt and to announce the capital income tax rate one period in advance. In this setting, the optimal capital income tax rate is nonzero in general. However, with standard restrictions on the production and utility functions, the optimal tax rate on capital income is zero in all periods except the initial one.

The Non-Conventional WACC With Risky Debt and Risky Tax Shield (WACC Dac Biet Doi Voi No Co Rui Ro va La Chan Thue Co Rui Ro) (Vietnamese version)

In the traditional formulation of the WACC, the debt and the tax shield are risk-free. However, even though the debt is risk-free, the tax shield can be risky. Furthermore, both the debt and the tax shield can be risky. In this paper, we present the non-conventional weighted everage cost of capital (WACC) for the single period binomial process with risky debt and risky tax shield, and derive the relevant formulas for the returns to the levered equity holder and the debt holder. Risk-free debt does not imply that the tax shield is risk-free. Unlike the traditional formulation, with the non-conventional WACC, the discount rate for the tax shield is not be restricted to two values, the risk-free rate rf and the return to unlevered equity rho. We make no prior assumption about the value of the discount rate for the tax shield psi. The value of psi depends on the riskiness of the tax shield. If the tax shield is risk-free, then the value of psi is equal to risk-free rate rf. If the tax shield is risky, the the value of psi is simply higher than the risk-free rate rf. In particular, if the payoff structure of the tax shield is the same as the payoff structure for the levered equity holder, the value of psi is equal to the return to the levered equity holder. In Section One, we present the non-conventional WACC for the single period with the capital cash flow (CCF) rather than the free cash flow (FCF) and examine the traditional position, where both the debt and the tax shield are risk-free. In Section Two, we assume that both the debt and the tax shield are risky.

Nondefault Components of Investment-Grade Bond Spreads

Traditionally, attempts at decomposing the spread between risk-free debt and corporate debt has focused exclusively on default risk. This focus continues despite the fact that the data indicate that the required spreads for higher-rated corporate bonds are normally far smaller than the spreads available in the market. This article challenges the traditional notion of an “excess spread” and, instead, attributes the additional spread to non-default-related factors, such as liquidity and spread volatility. The costs associated with both liquidity and spread volatility are examined, and a framework is provided for the investor to calculate adequate compensation for such costs.

Stare Down the Barrel and Center the Crosshairs: Targeting the Ex Ante Equity Premium

Abstract: The premium of interest in theoretical models is the extra return investors anticipate when purchasing risky stock instead of risk-free debt. Unfortunately, we do not observe this ex ante premium in the data; we only observe the returns that investors actually receive ex post, after they purchase the stock and hold it over some period of time during which random economic shocks affect prices. Over the past century U.S. stocks have returned roughly 6 percent more than risk-free debt, which is higher than warranted by standard economic theory; hence the equity premium puzzle. In this paper we devise a method to simulate the distribution from which ex post premia are drawn, conditional on various assumptions about investors' ex ante premium. Comparing statistics that arise from our simulations with key financial characteristics of the U.S. economy, including dividend yields, Sharpe ratios, and interest rates, suggests a much narrower range of plausible premia than has been supported to date. Our results imply that the true ex ante premium likely lies very close to 4 percent. JEL classification: G12, C13, C15, C22 Key words: risk premium, premium puzzle, Monte Carlo simulation ********** Over the past century the average annual return to investing in the US stock market has been roughly 6% higher than the return to investing in risk-free US T-bills. Mehra and Prescott [1985] argue that consumption within the US has not been sufficiently volatile to warrant such a large premium on risky stocks relative to riskless bonds; hence the well known equity premium puzzle. (1) The premium at issue in economic theory is the premium investors anticipate ex ante, at the moment they first make the decision to purchase stocks instead of risk-free debt. Conversely, the premium we observe in market data is the return investors actually received ex post, after they have held the stock for some time and nature has buffeted the economy with its random shocks. To examine the premium puzzle, we devise a method to simulate the distribution from which ex post premia are drawn, conditional on various values for investors' ex ante premium. We calibrate our approach to SP conversely, we develop a method for determining the probability of observing a 6% premium ex post even if the ex ante premium is as low as, say, 2%. …

A General Theory of Stock Market Valuation and Return

We show that the long-term total market and average investor's compounded stock returns are determined by GDP growth and are much less than believed because of the infeasible assumption that dividends can be fully reinvested. The long-term stock return closely approximates the return on risk-free debt, thus yielding a zero premium on a compounded per-capita basis. We demonstrate that the market earnings yield ratio (inverse P/E) is akin to a minimum nominal expected return and a direct function of inflation and a real required yield equal to long-term real GDP per capita growth, with marginal regard to risk. Our derived valuation formula is tested against the S&P 500 index and produces a 21% mean percentage tracking error, compared to 32% for the 'Fed Model' over the period 1954 - 2002.

Dette publique

Cet article etudie le risque de defaut associe a la dette publique comme la consequence de l'interaction entre l'Etat et les preteurs prives. Dans ce modele, l'Etat ne dispose que d'un controle imparfait des finances publiques. Une suite de chocs budgetaires peut alors porter la dette au-dela du seuil de soutenabilite, seuil communement defini par la valeur actualisee au taux sans risque des excedents futurs. Ce risque d'insoutenabilite genere en retour un important risque d'illiquidite associe au refus des investisseurs de renouveler leurs engagements. Au terme de cette etude, le niveau maximal d'endettement acceptable par les investisseurs se revele potentiellement tres inferieur au seuil de soutenabilite.

DEFAULTABLE DEBT PRICING IN MULTI-FACTOR MODELS

This paper employs the structural approach to study defaultable debt pricing under multi-factor models. We extend existing results under the structural approach in two directions. By incorporating multiple factors, we can capture the impact of other economic variables on the debt prices apart from the interest rate factor. In our approach, we provide credit spread pricing using both the real interest rate and inflation rate as state variables. We also extend the analyses to a more general default boundary. In our paper we assume that default happens when the firm value hits a given fraction of the corresponding risk-free debt for the first time. This is also the recovery rate of the defaulted debt. Analytical solutions for both the case of constant recovery rate and the extended case of recovery rate being a deterministic function of time in the multi-factor models are provided in our study. We also provide comparison of the performance of our model with other relevant credit spread models.

Reconciling the Two Definitions of the Present Value of the Tax Shield (PVTS)

There are two ways to define the present value of the tax shield (PVTS). First, the (present) value of the tax shield VTS is simply the tax shield, discounted by y, which is the appropriate discount rate for the tax shield. Second, the (present) value of the tax shield VTS is the difference in the present values of the tax payments for the unlevered firm and the levered firm, where the risk profiles of the two tax payments are different. Happily, in this note, we show that both definitions of the present value of the tax shield are equivalent. To reconcile the two definitions of VTS, it is important to specify the risk profile of the free cash flow (FCF) and estimate the appropriate discount rates for the different cash flow profiles. We use a simple binomial model to specify the risk profile of the FCF and present simple numerical examples to illustrate the equivalence between the two definitions of the present value of the tax shield. The growth rate of the FCF and the leverage cost are zero. We assume that the reader is familiar with risk-neutral valuation. In Section One, we present a numerical example with risk-free debt. In Section Two, we present a numerical example with risky debt.

Optimal Taxation without State-Contingent Debt

In Lucas and Stokey's (1983) economy, tax rates inherit the serial correlation structure of government expenditures, belying Barro's (1979) result that taxes should be a random walk for any stochastic process of government expenditures. To recover a version of Barro's 'random walk' tax-smoothing outcome, we modify Lucas and Stokey's (1983) economy to permit only risk-free debt. Having only risk-free debt confronts the Ramsey planner with additional constraints on equilibrium allocations beyond one imposed by Lucas and Stokey's assumption of complete markets. The Ramsey outcome blends features of Barro's model with Lucas and Stokey's. In our model, the contemporaneous effects of exogenous government expenditures on the government deficit and taxes resemble those in Lucas and Stokey's model, but incomplete markets put a near unit root component into government debt and taxes, an outcome like Barro's. However, we show that without ad hoc limits on the government's asset holdings, outcomes can diverge in important ways from Barro's. Our results use and extend recent advances in the consumption smoothing literature.

Equivalence Between the FCF Method, the CCF Method and the APV Approach

In a recent paper, Ruback (2000) assumes that the discount rate for the tax shield in the Adjusted Present Value (APV) approach is the cost of debt and shows that the Capital Cash Flow (CCF) method and the Adjusted Present Value (APV) approach give different answers for the levered value. In this paper, using a simple numerical example with the Miles and Ezzell formulation for the tax shield, we show that the Free Cash Flow (FCF) method, the Capital Cash Flow (CCF) method and the APV approach give the same answers. The FCF method captures the benefit of the tax shield by lowering the cost of capital, the CCF method adds the tax shield directly to the FCF and the APV approach calculates the value of the tax shield separately. We organize the paper as follows. In Section One, we briefly review the assumptions underlying the three methods. In Section Two, we use a simple five-period binomial process to represent a finite stream of free cash flow and calculate the unlevered value with the risk-neutral method. In Section Three, we introduce risk-free debt financing with risk-free tax shields, and calculate the levered value with the three ways, the Free Cash Flow (FCF) method, the Capital Cash Flow (CCF) method and the APV approach. In addition, we verify that the APV approach is consistent with the answer from the risk-neutral method.

The Non-Conventional WACC with Risky Debt and Risky Tax Shield

In the traditional formulation of the WACC, the debt and the tax shield are risk-free. However, even though the debt is risk-free, the tax shield can be risky. Furthermore, both the debt and the tax shield can be risky. In this paper, we present the non-conventional weighted average cost of capital (WACC) for the single period binomial process with risky debt and risky tax shield, and derive the relevant formulas for the returns to the levered equity holder and the debt holder. Risk-free debt does not imply that the tax shield is risk-free. Unlike the traditional formulation, with the non-conventional WACC, the discount rate for the tax shield is not be restricted to two values, the risk-free rate rf and the return to unlevered equity rho. We make no prior assumption about the value of the discount rate for the tax shield psi. The value of psi depends on the riskiness of the tax shield. If the tax shield is risk-free, then the value of psi is equal to the risk-free rate rf. If the tax shield is risky, then the value of psi is simply higher than the risk-free rate rf. In particular, if the payoff structure of the tax shield is the same as the payoff structure for the levered equity holder, the value of psi is equal to the return to the levered equity holder. In Section One, we present the non-conventional WACC for the single period with the capital cash flow (CCF) rather than the free cash flow (FCF) and examine the traditional position, where both the debt and the tax shield are risk-free. In Section Two, we assume that both the debt and the tax shield are risky.

Risk-neutral Valuation: A Gentle Introduction (2)

This teaching note is a continuation of the previous teaching note on risk-neutral valuation. In Section One, we estimate the value of levered equity in a levered company in an M & M world with risk-free debt and without taxes. The structure of the presentation will facilitate the subsequent analysis with taxes. We find the value of the levered firm in two ways. First, we use the replicating portfolio method. Second, we use the risk-neutral approach, which is equivalent to the replicating portfolio method. In Section Two, we analyze risky debt in a world without taxes. In Section Three, we introduce taxes. However, we continue to assume risk-free debt. The risk of the tax shield is indeterminate. In Section Four, we analyze risky debt in the presence of taxes and derive the relevant expressions for the returns to the equity and debt holders.

Unconventional Wisdom on PSI, the Appropriate Discount Rate for the Tax Shield

The conventional wisdom about psi, the appropriate discount rate for the tax shield, is as follows. If the tax shield is risk-free, that is, the revenue is sufficient to ensure that the interest deduction will be used with full certainty in the relevant period, then the appropriate discount rate for the tax shield is d, which is the cost of the risk-free debt. On the other hand, if the revenue is stochastic, there may be a finite probability that the revenue will be insufficient to allow for the use of the tax shield. In such a case, whether the debt is risk-free or not, the tax shield is no longer risk-free. In the single period case, some authors suggest that if the tax shield is risky, then the risk of the tax shield is the same as the risk of the free cash flow (FCF) and consequently, the appropriate discount rate is rho, which is the return to unlevered equity. In this teaching note, using a single period binomial example, we show that the conventional wisdom on the appropriate discount rate for the tax shield is incorrect when the tax shield is risky. The appropriate discount rate for the tax shield depends on the risk of the tax shield and the value of psi may be higher than e, the return to levered equity. If the tax shield is correlated with the cash flow to equity, that is, the payoff structure for the tax shield is similar to the payoff structure for the cash flow to equity, then the value of psi is equal to e, which is higher than rho.

Estimating the term structures of corporate debt

This paper investigates the corporate bond market by estimating monthly interest rate term structures for investment grade credit classes using both S&P's and Moody's ratings. Term structures are modeled by a piecewise constant forward rate curve and estimated on noncallable coupon paying bonds issued by industrial firms. The iterative estimation algorithm minimizes the sum of squared errors between market prices and model prices while identifying and removing outliers from the sample. Although the forward rate model is successful at pricing corporate debt, additional factors are found to be significant at explaining the residual price error that remains after the forward rate model is fit to market prices. Six necessary no-arbitrage conditions are derived for the term structures of risky and risk-free debt. Occasionally, some of these no-arbitrage conditions are violated and a few violations are asymptotically statistically significant. Finally, trading strategies that capture mispricing in the corporate debt market and violations of no-arbitrage bounds are discussed.

The risk-free rate in heterogeneous-agent incomplete-insurance economies

Why has the average real risk-free interest rate been less than one percent? The question is motivated by the failure of a class of calibrated representative-agent economies to explain the average return to equity and risk-free debt. I construct an economy where agents experience uninsurable idiosyncratic endowment shocks and smooth consumption by holding a risk-free asset. I calibrate the economy and characterize equilibria computationally. With a borrowing constraint of one year's income, the resulting risk-free rate is more than one percent below the rate in the comparable representative-agent economy.

Options Theory And Strategic Investment Decisions

Abstract This paper discusses use of options pricing theory far evaluating long-term capital investments. Specifically, what is the optimum expenditure level required to create an investment option? Can the Black & Scholes option pricing model be used to determine the approximate option value? This concept may have value to the petroleum industry in western Canada. Many oil companies have made strategic investments that could probably not have been justified by using standard economic analysis. The authors are unaware of any commonly used methodology to evaluate strategic investments. This paper includes a discussion of the variables in the Black & Scholes model to value having the option to develop hypothetical oil sands projects. The analysis will include consideration of the mode/'s limitations and the difficulties of applying it in a corporate setting. Introduction Options are specialized financial vehicles whose values are contingent upon those of other securities. The purchaser of a European call (or put) option obtains the right to buy (or sell) a specific asset, at a set price, on a predetermined date. American options can be exercised on or before the specified dare. In the case of a call option, the purchaser is betting that the price of a security will increase above a specified amount (exercise price) by a given expiry dare. The seller of the option uses the proceeds as additional revenue and is betting that the price will not rise significantly. Options are commonly used in financial and commodity markets to hedge, reduce risk and speculate. Investors typically want to lock in prices, exchange rates, interest rates or guard against portfolio losses. Options have been traded for many years, but with the creation of the Chicago Board Options Exchange in 1973 these transactions became relatively easy and inexpensive. Options trading has seen a tremendous increase in volume and complexity, since that time. Black & Scholes Option Pricing Model A development which added to the success of options trading was the publication of a theoretical options pricing model by Fisher Black and Myron Scholes(l). The model was empirically validated shortly after publication. Given the assumptions of unrestricted, frictionless markets, and continuous trading/stock prices, Black & Scholes were able to demonstrate that synthetic option can be created from portfolios containing the underlying stock and risk free debt. The primary attraction of the Black & Scholes model is that the required input data are relatively easy to obtain. Neither expected rates of return nor assumptions about individual investor risk preferences are required. Those inputs that are required are cit her directly observable or can be estimated from historical data. Black & Scholes used the following equation to describe the value of a European call option: Equation 1 (available in full paper) The value of any option can be described by a variation of this fundamental equation. Black & Scholes solved equation (1) using the following boundary and terminal conditions. Equation 1a-1c (available in full paper)

Banking Structure and the National Capital Market, 1869–1914: A Reply

In Gene Smiley's comment on our study of nineteenth-century American financial markets several issues are discussed. ' We group them into three areas. First, he argues that Davis's net rates of return on earning assets are not satisfactory estimates of the return on investment in loans. Second, he argues that our theoretical model of bank behavior is too simplistic to justify our empirical specifications and our conclusion that the New York Stock Exchange had an important impact on financial integration. Third, he argues that the relationship between the yield on securities of the New York Stock Exchange and the regional quantity of loans, which we estimated as a loan-demand relationship, could be explained in terms of the loan-supply behavior of regional banks. However, it is our contention that none of Professor Smiley's suggestions is warranted and that the results of our analysis remain valid. It should be emphasized that Professor Smiley had access to the longer, original version of our article which contained a more extensive treatment of the theoretical model, numerous references to the relevant literature, and an extensive amount of empirical results that were reviewed but not reported in the condensed published version.2 Smiley argues that Davis's net rates of return on earning assets are not satisfactory estimates of interest rates and that gross returns (although not available prior to 1888) are more useful.3 Although more refined data are always desirable, there are ample justifications for using net returns in our analysis of the integration of nineteenthcentury capital markets. In a well-integrated market expected rates of return (adjusted for risk) are equated by movements in the flow of capital. But this is distinct from the notion that stated rates of interest are equated for two reasons. First, investors recognize that a promised (stated) rate is not necessarily the rate actually realized given business and financial risk.4 Thus, the expected yield will be less than the promised yield on all but risk-free debt. In other words, if all ex ante rates were realized ex post, then all securities would be risk free. Clearly, riskier loans require higher promised returns to compensate bankers for the higher probability of default. Second, operating costs (monitoring costs and collection costs, for example) must be absorbed by bankers in their lending operations. If operating costs were not important factors, bankers would have shifted their entire portfolios into consumer loans and