Samih Antoine Azar

Measuring relative risk aversion

This note intends to estimate the Coefficient of Relative Risk Aversion (CRRA). The underlying model is expected utility and certainty equivalence. The utility function selected is of the power form and is shown to be independent of initial wealth. This property makes the results applicable to any individual, whatever her initial wealth, or even to a market measure. The equity premium that the CRRA must explain is calculated to be 9.5%. The CRRA is calibrated by assuming six different economies from an economy with two states of nature to an economy with seven states of nature, that all describe the same distribution of returns. The calibrated CRRAs are between 4.2 and 5.4. Running 100 replications of samples of 6000 observations of the risky outcome shows that the CRRA that satisfies the constraint on the equity premium is 4.5, a figure which is reasonable and plausible.

Measuring the US social discount rate

The purpose of this letter is to estimate the US social discount rate, the appropriate discount rate for public capital budgets. There are two methods. One assumes that public investment displaces private consumption, and the discount rate is labelled the social rate of time preference (SRTP). The other assumes that public investment crowds out private investment, and the underlying social discount rate is market-based. The approach in this letter follows the second method. It relies on wealth maximization with the presence of two assets: one risky and one riskless. The risky security is taken to be a portfolio of common stocks, while the riskless asset is taken to be the T-bill rate. The Euler or first-order condition is independent of initial wealth. Because of that the estimate of the discount rate applies to all unanimously, and can be considered a social rate by essence. The range of the estimated social discount rate is between 5.01% and 6.17%, and the 95% confidence interval for the inferred population mean discount rate is between 5.62% and 5.71%. These results are extremely precise and reasonable, and are at the upper limit of the estimates in the literature that use a completely different approach.

Another look at the rationality of the stock market

A model due to Lucas is estimated between the real stock market returns and real dividends on the market index. The sample spans the period from 1872 to 1987 on an annual basis. The results are close to theoretical expectations: the coefficient of relative risk aversion, which minimizes the sum of square residual, is estimated to be around 0.89, and the discount rate around 8%. This means that a relatively simple valuation model is capable of describing the stock market, lending support to the rationality of this market.

A duration-based equity premium

Theoretically the expected return on any financial asset need not equal the average of the actual return. In this paper, the expected equity premium is estimated based on two fundamentals: the Gordon dividend model with constant growth, and duration analysis. The result is that the ex ante, or expected, equity premium is around 3.24%, with a standard error between 0.30% and 0.87%. Taking 0.87% as the standard error, the 95% confidence interval is between 1.53% and 4.95%. These figures show clearly that the actual equity premium is much higher than the expected one. The reason for that is due to unpredictable changes in interest rates, and other growth rates.

The US Dow and the US dollar

This article considers the relation between the US Dow Jones Industrial Average (Dow) and the US dollar. Monthly data sets that cover the float period of foreign exchange rates are used. Least square regressions with calendar breakpoints are estimated. The evidence is strong that for the ten currencies that have breakpoints the recent samples uncover a significant relation between the US Dow and the US dollar, while the older samples negate such a relation. The conclusion is that this relation is subject to shifts and, when these shifts are accounted for, the relation is found to be statistically very significant.

Predictability of stock returns: is it rational?

This study identifies three anomalies in the British capital markets. It is statistically proven that the logs of six stock prices, in the British stock market, are cointegrated with the logs of a market index, a bond price, and an exchange rate. This means that the lagged residual of each cointegration regression appears in the regression of the first-differences of the above variables in what has been called the error-correction regression. This anomaly means that past information is helpful in predicting current stock returns and this may be due either to the presence of a fad, or to forward-looking rationality. Two other anomalies are 1) the correlation of cointegration residuals across stocks, which may be explained by a common factor absent from the regressions and 2) the fact that it is the first-difference of the interest rate, instead of the level, that explains stock returns, which is consistent with the evidence that the level of the interest rate is non-stationary.

Simulating the market coefficient of relative risk aversion

Abstract In this paper, expected utility, defined by a Taylor series expansion around expected wealth, is maximized. The coefficient of relative risk aversion (CRRA) that is commensurate with a 100% investment in the risky asset is simulated. The following parameters are varied: the riskless return, the market standard deviation, the market stock premium, and the skewness and the kurtosis of the risky return. Both the high extremes and the low extremes are considered. With these figures, the upper bound of the market CRRA is 3.021 and the lower bound is 0.466. Log utility, which corresponds to a CRRA of 1, is not excluded.

Oil prices, US inflation, US money supply and the US dollar

A central proposition in many macroeconomic models is price stickiness, while it is agreed that commodity prices are determined in auction markets, and are necessarily fully flexible. The overall price level is a weighted average of commodity prices and consumer prices. An exogenous increase in the money supply, keeping everything else constant, increases the overall price level proportionately. Because of stickiness of consumer prices, commodity prices overshoot the increase in the money supply. The purpose of this paper is to re‐examine the relations between the price of one specific commodity which is oil with US inflation, US money supply and the US dollar. One empirical fact is that during the sample period, global and US demand shocks have raised oil prices immediately while their effect on consumer prices was delayed. This overshooting of oil prices is expected to occur in the short run and to wane in the long run as consumer prices fully adjust. The overshooting of oil prices is the mirror image of the overshooting of the US dollar. This is true for two main reasons. One, both oil and the US dollar react in the same manner to money supply changes. Two, oil prices are quoted in US dollars and a depreciation of the US dollar is instantly compensated by a rise in the US price of oil. Additionally, the paper analyses and discusses the evidence on an apparent long run overshooting of oil prices and explains why it is just a statistical artefact that stems from the salient features of oil.

Commodity prices and the US money supply in the long run

Theoretically commodity prices are expected to overshoot the money supply in the short run but to vary with unit proportionality in the long run. This follows from the observation that consumer prices are sticky and that commodity prices, set in auction markets are fully flexible. There is empirical evidence in the literature that commodity indexes are indeed anchored in the long run to the money supply with unit proportionality. However there is a dearth of research on the long-run behaviour of individual commodities with respect to the money supply. This paper fills this gap in the literature. When 48 individual commodity series and six commodity indexes series are studied over the monthly period 1980/2011, there is fairly strong evidence for unit proportionality to money supply. Individual regressions and panel regressions are both supportive of unit proportionality. The preconception that commodity prices move haphazardly is hence rejected.

New Evidence on the Excess Smoothness of Consumption

The purpose of this paper is to revisit the evidence on the excess smoothness of consumption within the perma- nent income model, by using recently available monthly data. Two formulations of the univariate process of personal dis- posable income are adopted: in the levels and in the log-levels. More than one sample is studied. Three different impacts are defined and measured. In theory, the three of them should be equal. The conclusion that is strongly supported is that these three impacts are significantly different from each other, implying that excess smoothness is still a feature of the data. However a weak version of the permanent income hypothesis is endorsed which is that consumption changes by the annuity value of revised expectations of future income. In other terms, permanent income innovations have a significant, although relatively small, effect on consumption.