Working Paper Abstracts – 1991
This paper studies predictable variation through time in the returns of common stocks and bonds, using linear models with constant “beta” coefficients. Both individual stocks and portfolios, formed on the basis of firm size and industry, are examined. The methods of Gibbons and Ferson (1985) are nested in a sequence of more general latent variables models. This generalization allows the examination of the separate elements of their joint hypothesis. The results indicate that more than a single premium is needed to model expected returns. The number of latent variables in the time-varying expected returns is similar for daily and monthly returns, and is small. Two or three latent variables are indicated in all cases. There is strong evidence that conditional expected risk premiums are nonzero in months other than January.
We develop and test a model of intraday price formation based on an explicit description of a representative market maker whose beliefs evolve according to Bayes’ rule. We derive an estimating equation where the weight the market maker places on the order flow as an information signal can be recovered from the parameter estimates. This weight is a natural measure of information asymmetry since it is the ratio of the quality of private information to the quality of public information. The model is interesting for other reasons as well. First, the model encompasses several other models of intraday price formation. Second, the error term arises endogenously and possesses a natural economic interpretation. Third, the model permits us to partially distinguish the price effects of information asymmetry and inventory control by market makers. Fourth, the model provides a method to assess the implicit costs of trading. We show that there are substantial non-linearities in pricing that may reflect the way in which large blocks are traded in the upstairs market. We estimate the model with a new data set obtained from a NYSE specialist. The data set comprises almost 75,000 records for most of the year 1987 and is o independent interest given the paucity of inventory data. The results provide strong support of information asymmetries, as perceived by the market.
The paper provides a historical perspective on the issue of whether budget deficits are typically eliminated by increased taxes or by reduced spending. By examining U.S. budget data from 1792-1988, I conclude that about 50-65% of all deficits due to tax cuts and about 65-70% of all deficits due to higher government spending have been eliminated by subsequent spending cuts, while the remainder was eliminated by subsequent tax increases. In contrast to previous studies, the empirical analysis uses error-correction models in a way that the intertemporal budget constraint is imposed in the estimation stage.
This paper traces the evolution of the concept of “mortgage yield”, starting with the yield to prepayment which held sway until the mid-seventies, to the cash flow yield which dominated until the late eighties, to the option adjusted yield which is intellectually dominant today. It is argued that while each of these concepts represented an improvement over the one that preceded it, the cash flow yield should have given way to the holding period yield, and then to an option adjusted holding period yield of which the (currently fashionable) option adjusted yield is merely a special case. The holding period yield is the ideal tool for scenario analysis because of its sensitivity to the particular circumstances of the user, and the option adjusted variant provides better information about whether a security is correctly priced because it does not prejudge the market’s consensus holding period.
Despite increasing criticism by economists and forecasters of the ability of the stock market to predict economic recessions, it is shown that 38 of the 41 measured recessions since 1802 have been preceded by an eight percent decline in the stock returns index. There have been twelve “false alarms” using this criterion, where stock declines have not been followed by recessions, and seven of these have occurred since World War II. Despite these faulty signals, there is a significant gain to stock investors from being able to predict turning points in the business cycle over all time periods. During the post-War period, a four month lead time in forecasting cycle turning points results in the 4.7% annual (risk-adjusted) excess return on a stock portfolio. Since World War II, stock returns have reacted three to four months earlier than during pre-War business cycles, indicating either an improvement in forecasting, or the mis-dating of earlier turning points.
This paper shows that the effects of bid-ask spreads and price discreteness on observed stock returns are related to stock price level, properties of the bid-ask spread and the nature of the rounding process. Using a mole similar to Harris (1990), we derive robust Taylor series approximations relating the moments of observed stock returns to the underlying true return moments. Previous results from the literature are shown to be simple special cases of our results. We suggest explanations for seemingly anomalous empirical results such as the average non-January size effect, changes in post-split stock return volatility and the serial correlation of stock returns.
The paper is concerned with time-consistency problems caused by monetary policy in an open economy. The temptation to generate surprise inflation is shown to depend positively on the amounts of nominal debt issued by the government or issued by individuals. Private debt matters, because inflationary money growth causes redistribution between domestic residents and foreigners. A government that cares about the welfare of its residents will be tempted to inflate whenever it or its residents have issued nominal debt to foreigners. A net creditor position, however, may eliminate the time-consistency problem.
For the United States, these international considerations should become increasingly relevant as the country accumulates external deficits. My estimates indicate that the incentive to inflate more than doubled between 1982 and 1988. More than two-thirds of this increase was due to higher external debt, which was largely financed in nominal terms.
Bayesian posterior distributions allow one to investigate the approximate efficiency of a portfolio without specifying the maximum degree of inefficiency a priori. The difference in expected returns between the value-weighted equity portfolio and an efficient portfolio of equal variance has a disperse posterior distribution, and our experiments confirm that such uncertainty is inherent in the sample sizes typically encountered in empirical studies. The maximum correlation between the value-weighted portfolio and an efficient portfolio has a posterior that is concentrated, often around low values, but this result appears to reflect nonlinearity in the function rather than information in the sample.
Spurred by the work of Mehra and Prescott (M-P), economists have been attempting to explain the surprisingly low levels of real interest rates in light of the behavior of aggregate consumption. This paper constructs a continuous “risk-free” interest rate series for the United States and the United Kingdom from the beginning of the nineteenth century, extending the period analyzed by M-P, 1889-1978, both backward and forward. It is found that the real rate of return on both long and short-term bonds was over 400 basis points lower during the M-P period than outside that period and that this result holds for the U.K. as well as the U.S. In contrast, equities show almost identical real returns over the whole sample so that the equity premium is only about one-third as large outside the M-P period as within the period. These new data help reconcile the behavior of consumption and the real rate and reveal that the data from 1889-1979 were subject to factors or events, not well-understood, which depressed real interest rates.
The availability of long term data confirms the superiority of the returns of equity over fixed income instruments. This premium, particularly in the twentieth century, has been far greater than traditional finance models would have predicted on the basis of the available economic and financial data. New data from the nineteenth century suggest that the real rate of interest was far higher and the equity premium correspondingly lower. Several explanations for this premium are explored. It is concluded that the higher real rates of interest that the economy has experienced over the past decade may not be atypical of a longer- term financial perspective, although stocks still appear the asset of choice for long-term accumulation.
This work examines the relation between option prices and the true, as opposed to risk-neutral, distribution of the underlying asset. If the underlying asset follows a diffusion with an instantaneous expected return at least as large as the instantaneous risk-free rate, observed option prices can be used to place bounds on the moments of the true distribution. An illustration of the paper’s results is provided by the analysis of the information concerning the mean and standard deviation of market returns contained in the prices of S&P 100 Index Options.
This paper provides an asymptotically most powerful test for a particular class of statistics which test the hypothesis of no serial correlation. This class includes many of the statistics employed in the recent finance and macroeconomics literature. Furthermore, with respect to a popular mean reversion alternative model, we show that the asymptotically most powerful test is quite robust to distributional specifications.
Despite increasing criticism by economists and forecasters of the ability of the stock market to predict economic recessions, it is shown that 38 of the 41 measured recessions since 1802 have been preceded by an eight percent decline in the stock returns index. There have been twelve “false alarms” using this criterion, where stock declines have not been followed by recessions, and seven of these have occurred since World War II. Despite these faulty signals, there is a significant gain to stock investors from being able to predict turning points in the business cycle over all time periods. During the post-War period, a four month lead time in forecasting cycle turning points results in the 4.8% annual (risk-adjusted) excess return on a stock portfolio. Since World War II, stock returns have reacted three to four months earlier than during pre-War business cycles, indicating either an improvement in forecasting, or the mis-dating of earlier turning points.
Traditional theories of asset pricing assume there is complete market participation so all investors participate in all markets. In this case changes in preferences typically have only a small effect on asset prices and are not an important determinant of asset price volatility. However, there is considerable empirical evidence that most investors participate in a limited number of markets. We show that limited market participation can amplify the effect of changes in preferences so that an arbitrarily small degree of aggregate uncertainty in preferences can cause a large degree of price volatility. We also show that in addition to this equilibrium with limited participation and volatile asset prices, there may exist a Pareto-preferred equilibrium with complete participation and less volatility.
This paper updates previous analyses of the risks and returns of low-grade bonds to include 1990, a year during which the low-grade bond market experienced dramatic changes. The annual return of 8.7 percent for low-grade bonds over the 1977-1990 period is lower than the returns on long-term Treasury bonds, long-term corporate bonds, the S&P 500 or small stocks over the same span. Much of this poor relative performance can be traced to the 1989-1990 period when low-grade bonds realized an average annual loss of 5.4 percent. During this same period, small stock prices also fell dramatically. The high degree of correlation between the returns of low-grade bonds and small stock during the entire period of analysis, but especially in the latter half of 1990, suggests that a factor common to both small stocks and low-grade bonds can explain a significant portion of the losses of low-grade bonds over this latter period.
Several recent papers on dynamically optimal taxation have derived an indeterminacy result regarding state-contingent capital taxation in stochastic models with state-contingent government liabilities. The indeterminacy arises because the government has N degrees of freedom to set tax rates on capital income in N states of nature, only subject to a single constraint that assures an optimal level of capital investment. The paper shows that this indeterminacy result is a consequence of the assumption that the economy has only a single production technology. If there are many technologies, there will be additional constraints, because differences in capital income tax rates in different states of nature will create incentives to invest in those technologies that have high payoffs in states with relatively low tax rates. If there are a large number of technologies, both the structure of capital tax rates and the structure of government debt are tied down in many dimensions.
The paper studies the sustainability of government budget deficits in a stochastic economy. The general equilibrium setting permits a rigorous derivation of the relevant transversality conditions and intertemporal budget constraints. The transversality condition on government debt requires a zero limit of discounted future government debt, where the discount rate depends on the probability distribution of future debt over states of nature. The government’s intertemporal budget constraint requires that the discounted present value of primary surpluses matches initial debt, where the discount rate on future government spending and taxes depends again on the probability distribution of these variables over states of nature.
Contrary to assertions made in the literature, the discount rates on future government debt, spending, and taxes are generally not related to the rates of return on government debt. Most importantly, future government debt in the transversality condition cannot be discounted at the safe interest rate, not even if government debt is safe. Debt discounted at the safe interest rate may well diverge to infinity under sustainable policies. This result raises questions about some recent empirical papers testing the sustainability of U.S. fiscal policy.
In addition, the paper shows that the average level of primary deficits provides little evidence on sustainability. Policies with permanent expected primary deficits can be sustainable, in particular when the safe interest rate is below the average growth rate of the economy.
This paper analyzes the risks and returns of different types of real estate-related firms trade on the New York and American stock exchanges (NYSE and AMEX). We investigate the relation of real estate stock portfolio returns with returns on a standard appraisal-based index, and find that lagged values of traded real estate portfolio returns can predict returns on the appraisal-based index. The stock market appears to incorporate information about real estate markets that is later imbedded in property appraisals. Additional analysis suggests that the differences in the return and risk characteristics across different types of traded real estate firms can be explained in part by appealing to real estate market fundamentals relating to the degree of dependence of the real estate firm upon the rental cash flows from existing buildings. These findings highlight the heterogeneity of real estate-related firms and indicate that future work needs to consider other firms in addition to REITs.
In recent years, a number of empirical studies have examined the long-run sustainability of U.S. debt policy. Some studies conclude that U.S. fiscal policy has been sustainable, others disagree. This paper argues that the issue should be reexamined, because the traditional sustainability test explicitly or implicitly assume that the rate of return on government debt is “on average” above the rate of economic growth, a condition that does not hold for historical U.S. data. The paper derives and implements a new test for sustainability hat does not rely on a particular relation between interest rates and growth rates. I conclude that U.S. fiscal policy has historically satisfied a sufficient condition for sustainability.
This manuscript reviews the evolving literature on the pricing of assets and the structure of financial markets. It begins with the formulation of early stock valuation models and proceeds to a description of the efficient-market hypothesis. The survey then examines recent empirical data which led to a reevaluation of the assumptions underlying an efficient market and ends with a description of the recent literature on market-making and how these models relate to the studies of efficient markets.
In recent years, there has been a large literature on how stock exchange specialists set prices when there are investors who know more about the stock than they do. An important assumption in this literature is that there are “liquidity traders” who are equally likely to buy or sell for exogenous reasons. It is plausible that some buyers have cash needs and are forced to sell their stock. However, buyers will usually be able to choose the time at which they trade. It will be optimal for them to minimize the probability of trading with informed investors by choosing an appropriate time to trade and clustering at that time. This asymmetry means that when liquidity buyers are not clustering, purchases are more likely to be by an informed trader than sales so the price movement resulting from a purchase is larger than for a sale. As a result, profitable manipulation by uninformed investors may occur. A model where the specialist takes account of the possibility of manipulation in equilibrium is presented.
Disturbances to aggregate expenditure on consumer durables are much more persistent than predicted by an optimizing representative consumer model. Recent work in macroeconomics has explored this “slowness to adjust” in the context of consumers facing transactions costs when purchasing durable goods. This approach produces infrequent household purchases and requires explicit attention to aggregation of households.
This paper considers household behavior directly, using panel data on automobile purchases and finds that about half of the households purchase automobiles subject only to transactions costs. Explicit aggregation shows that the cross-section distribution of households according to their durables stocks is quite similar to that theoretically predicted. Simulated aggregate expenditures using observed household slowness to adjust show persistence of aggregate shocks and response to income growth consistent with the aggregate data.
The standard put-call parity result does not include equalities based on buy-and-hold strategies for options on the minimum or maximum of two risky assets and for quantity-adjusting options. This article generalizes put-call parity to these contracts. International put-call parity relations and the pricing of a new forward contract, an absolute-value spread forward, is derived from the put-call parity generalization to options on the minimum or maximum of two risky assets. Finally, an inequality comparing the price of quantity-adjusting options to portfolios of standard options is presented, showing that the QAO contract, in the absence of arbitrage opportunities, is cheaper than the portfolio of standard currency and equity contracts which might be used to hedge the domestic value of a foreign portfolio.
Quantity-adjusting option and forward contracts deliver a payoff on a variable quantity of underlying. This paper explains the use, pricing and hedging of such contracts and extends them to sequential investment options. These are options which guarantee optimal asset selection at switching points among a fixed set of traded assets.
Applications include domestic equity derivatives held by a foreign investor and hedged into that investor’s home currency. Similar hedges on foreign equities for domestic investors can be constructed using symmetry considerations if the investors are running their own hedge. If, however, the hedge is run by the same investment bank, the problems are not symmetric. Such hedges are not attainable using a buy-and-hold strategy with standard options and currency contracts.
Finally, in the presence of a forward contract on an inflation index, the real value implied by the forward contract of equity derivatives may be hedged.
Economists have produced no identifiable event which could justify, on fundamental grounds, the stock market crash of October, 1987. This research confirms that changes in consensus corporate profit forecasts and interest rates were completely unable to explain the decline in stock prices that took place at that time. It is shown that the equity risk premium would have to have increased by about four percentage points between October and November 1987 to explain the stock decline on the basis of these fundamental variables. Several possible explanations for the rise in the risk premium are explored.
Another hypothesis is advanced that suggests that shifts in investor sentiment, perhaps induced by noise traders, was a factor in the stock decline. Analysis of historical data shows that investor sentiment, as well as profit forecasts and interest rates, are significantly associated with stock returns. On the basis of historical data analyzed for periods excluding the months around the crash, one can state that changing investor sentiment and profit forecasts can account for between 30 and 45% of the October, 1987 stock market decline. In contrast, changes in profit forecasts and interest rates alone would have, in fact, predicted a rise in stock prices. Hence it appears that a significant component of stock returns are driven by yet unexplained changes in investor sentiment unrelated to market fundamentals.
We estimate the conditional distribution of trade-to-trade price changes using ordered probit, a statistical model for discrete random variables. Such an approach takes into account the fact that transaction price changes occur in discrete increments, typically eighths of a dollar, and occur at irregularly spaced time intervals. Unlike existing continuous-time/discrete-state models of discrete transaction prices, ordered probit can capture the effects of other economic variables on price exchanges, such as volume, past price changes, and the time between trades. Using 1988 transactions data for over 100 randomly chosen U.S. stocks, we estimate the ordered probit model via maximum likelihood and use the parameter estimates to measure several transaction-related quantities, such as the price impact of trades of a given size, the tendency towards price reversals from one transaction to the next, and the empirical significance of price discreteness.
This paper updates through June 1991 the authors’ prior research on low-grade bonds. The paper finds further support for the hypothesis that low-grade bonds behave sometimes like high-grade bonds and sometimes like small stocks. Much of the drop in the prices of low-grade bonds in the last half of 1990 and the subsequent increase in the first half of 1991 parallel the price movements of small stocks. Also consistent with our earlier work, the volatility of low-grade bonds is less than that of high-grade corporates or long-term governments. The shorter “duration” of low-grade bonds accounts for this counter-intuitive result.
The paper discusses the economic relevance and the empirical measurement of government debt and budget deficits. I find that recent arguments about the irrelevance of labeling government payments and in favor of generational accounting (e.g., Kotlikoff, 1989) are critically dependent on the availability of lump-sum taxation. If all taxes are distortionary on the margin, government debt and the labeling of government payments are relevant not just for excess burden and solvency issues, but also for intergenerational redistribution.
The empirical part of the paper derives U.S. government balance sheets for 1947-89 and a set of simple income statements. For 1989, I find that net government liabilities are more than $1000 billion above the official value for publicly-held federal debt. Most of the difference is due to unfunded government employee pension obligations, which have been ignored in previous studies (e.g., Eisner, 1986). I argue that employee pensions are unambiguously a government liability, while social security claims have a different status. Nonetheless, social security is important for government finance: Over time, the government has given the social security system a more and more secure franchise to levy payroll taxes, which constrains government finance in a similar way as a very large liability.
Quantity-adjusting option and forward contracts deliver a payoff on a variable quantity of underlying. This article explains the use, pricing, and hedging of such contracts. The pricing of product options is also derived.
Product options include quantity-adjusting options as a special case and pay off as a function of the prices of four risky assets. The pricing formula for these options is reduced to an expression in a two-dimensional density from a four-dimensional one. Closed form solutions in terms of the bivariate normal are obtained. Similar formulae in terms of the univariate normal are obtained for quantity-adjusting options. The normal distribution is absent from the expression for quantity-adjusting forwards.
Product options also include sequential switching, or “guru” options. These are options which guarantee optimal asset selection at present dates among a fixed set of traded assets.