Knowledge that Transforms

This paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options. In the context of the Black-Scholes economy, margin restrictions are shown to exclude continuous-trading arbitrage opportunities and, with two additional hypotheses, still to allow the Black-Scholes call model to apply. The Black-Scholes economy consists of a continuously traded stock with a price process that follows a geometric Brownian motion and a continuously traded bond with a price process that is deterministic.

In models where both investors and securities are subject to differential taxation, there may be no set of prices that rule out infinite gains to trade, or "tax arbitrage."This paper characterizes the joint restrictions on financial-asset returns and investors' tax schedules that preclude tax arbitrage in the absence of short-sale constraints.The authors show that, if there exists any configuration of marginal tax rates on investors' tax schedules that rule out infinite gains to trade, then "no-tax-arbitrage" prices will exist.They also show that the existence of "no-tax-arbitrage" prices ensures the existence of equilibrium prices. THE EFFECTS OF DIFFERENTIAL taxation on the equilibrium prices of financial assets have attracted much attention from financial economists in recent years.Otherwise identical securities that contribute to taxable income to different degrees will, in general, be valued differently by taxable investors.As a result, tax considerations have been useful in helping explain the effect of dividend yield on stock returns,' the effect of coupon levels and term to maturity on bond prices,2 the timing of investors' portfolio transactions,3 and the observed capital structures of firms.4While a rich set of observed behaviors can be better understood by reference to differential taxation, there are well-known difflculties in dealing with taxes in a general-equilibrium setting.To clear markets, relative prices must reflect the marginal rates of substitution of all agents simultaneously.When tax rates differ across investors, however, this condition can be impossible to achieve.To illustrate, consider a world of perfect certainty with two assets: a tax-exempt municipal bond and a taxable government bond.To equate marginal rates of substitution, the rate of return on the government bond, rg, must equal that on the municipal, rm, "grossed up" by one minus the investor's marginal tax rate, ti; that is, rg = rm/( 1 -ti).If there are investors in more than one tax bracket, this condition will obviously be impossible to satisfy for all of them simultaneously.

The development of organized markets for speculative-grade corporate debt has provided financial researchers with an opportunity to examine the pricing of default risk. By incorporating previous work on the default experience of low-rated corporate debt, this paper presents an introduction to risk-neutral models of risky-bond pricing and uses these to examine the relationship between the default premium embodied in bond yields and actual default rates. The contribution of macroeconomic information to the default premium is also examined. The author finds that holders of low-grade bonds have, on average, been compensated for losses due to default.

We report evidence of seasonality in the Fama and MacBeth estimate of the CAPM‐based risk premium in four stock exchanges: the NYSE and the London, Paris, and Brussels exchanges. Specifically, we found that, in Belgium and France, risk premia are positive in January and negative the rest of the year. There is no January seasonal in the U.K. risk premium. Instead, we observed in this country a positive April seasonal and a negative average risk premium over the rest of the year. In the U.S., the pattern of risk‐premium seasonality coincides with the pattern of stock‐return seasonality. Both are positive and significant only in January. We also found that the January risk premium in the U.S. is significantly larger than those observed in the European markets. Interestingly, the reported patterns of risk‐premium seasonality in European equity markets do not fully coincide with the observed patterns of stock‐return seasonality in these markets. For example, in the U.K., average stock returns are significant and positive in January and April, whereas the market risk premium is significantly positive only in April. A possible interpretation of this phenomenon is presented in the paper.

The development of organized markets for speculative‐grade corporate debt has provided financial researchers with an opportunity to examine the pricing of default risk. By incorporating previous work on the default experience of low‐rated corporate debt, this paper presents an introduction to risk‐neutral models of risky‐bond pricing and uses these to examine the relationship between the default premium embodied in bond yields and actual default rates. The contribution of macroeconomic information to the default premium is also examined. The author finds that holders of low‐grade bonds have, on average, been compensated for losses due to default.

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