Uncovering the risk-return relation in the stock market

There is an ongoing debate about the apparent weak or negative relation between risk (conditional variance) and expected returns in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM that separately identifies the two components of expected returns–the risk component and the component due to the desire to hedge changes in investment opportunities. The estimated coefficient of relative risk aversion is positive, statistically significant, and reasonable in magnitude. However, expected returns are driven primarily by the hedge component. The omission of this component is partly responsible for the existing contradictory results.Stock market ; Econometric models ; Asset pricing

Uncovering the Risk-Return Relation in the Stock Market

There is an ongoing debate in the literature about the apparent weak or negative relation between risk (conditional variance) and return (expected returns) in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM to investigate this relation. Our primary innovation is to model and identify empirically the two components of expected returns--the risk component and the component due to the desire to hedge changes in investment opportunities. We also explicitly model the effect of shocks to expected returns on ex post returns and use implied volatility from traded options to increase estimation efficiency. As a result, the coefficient of relative risk aversion is estimated more precisely, and we find it to be positive and reasonable in magnitude. Although volatility risk is priced, as theory dictates, it contributes only a small amount to the time-variation in expected returns. Expected returns are driven primarily by the desire to hedge changes in investment opportunities. It is the omission of this hedge component that is responsible for the contradictory and counter-intuitive results in the existing literature.

The Information in Long-Maturity Forward Rates: Implications for Exchange Rates and the Forward Premium Anomaly

The forward premium anomaly is one of the most robust puzzles in financial economics. We recast the underlying parity relation in terms of cross-country differences between forward interest rates rather than spot interest rates with dramatic results. These forward interest rate differentials have statistically and economically significant forecast power for annual exchange rate movements, both in- and out-of-sample, and the signs and magnitudes of the corresponding coefficients are consistent with economic theory. Forward interest rates also forecast future spot interest rates and future inflation. Thus, we attribute much of the forward premium anomaly to the anomalous behavior of short-term interest rates, not to a breakdown of the link between fundamentals and exchange rates.

The Myth of Long-Horizon Predictability

The prevailing view in finance is that the evidence for long-horizon stock return predictability is significantly stronger than that for short horizons. We show that for persistent regressors, a characteristic of most of the predictive variables used in the literature, the estimators are almost perfectly correlated across horizons under the null hypothesis of no predictability. For example, for the persistence levels of dividend yields, the analytical correlation is 99% between the 1- and 2-year horizon estimators and 94% between the 1- and 5-year horizons, due to the combined effects of overlapping returns and the persistence of the predictive variable. Common sampling error across equations leads to ordinary least squares coefficient estimates and R2s that are roughly proportional to the horizon under the null hypothesis. This is the precise pattern found in the data. The asymptotic theory is corroborated, and the analysis extended by extensive simulation evidence. We perform joint tests across horizons for a variety of explanatory variables, and provide an alternative view of the existing evidence.

Recent Creation and Worldwide Flood: The Perfect Agreement Between Biblical Chronology, Recorded History, and Other Extra-biblical Geochronometers

By careful study, the Bible gives us an almost exact chronology from the Cross back to the Genesis Flood and to Creation, which is then shown to be in complete agreement with other historical and archaeological data as well as with all reliable geochronometers known today

Supplement to Pathology and the Conserved Ovary: A Statistical Survey From the Thesis Ovarian Activity Following Hysterectomy

The object of this survey was to obtain statistical information concerning the incidence of pathological change, and in particular of malignant change, in ovaries conserved at hysterectomy. The subject is an important one as the possibility of the conserved ovary subsequently becoming diseased has been used to justify routine oophorectomy when the uterus has to be removed for a benign condition. Precise information on this question is difficult to obtain, and no important investigation of this problem would appear to have been undertaken recently in this country. Reycraft (1955) in a survey of the records of the Cleveland University Hospitals from 1944 to 1955 found 9 cases of carcinoma in ovaries which had been conserved at hysterectomy, an incidence of .2. Counsellor Hunt and Eaigler (1955) surveyed 1,500 cases of proved carcinoma of the ovary, and found that 67 of these occurred in women who had previously had the uterus removed for a benign condition. Rendall and Gerhardt (1954), basing their calculations on the statistics of the Health Departments of the States of Connecticut and Hew York (excluding Hew York City), estimate that the likelihood of a woman who has reached the age of forty developing carcinoma of the ovaries is .9/. In a survey of 1,215 cases of hysterectomy with conservation of one or both ovaries performed during the years 1927-1955 in the Glasgow Royal Samaritan Hospital for Women, it was found that four of the patients were subsequently readmitted to that hospital on account of ovarian pathology. Ho case of readmission for malignant ovarian disease was discovered. In a parallel series of 872 cases of oophorectomy, ovariotomy, and laparotomy for inoperable conditions which may have been ovarian, it was found that four of the patients had previously had the uterus removed. One of these was a case of adenocarcinoma of the ovary but doubt was expressed by the pathologist concerning the origin of the tumour. While the limitations of these surveys are appreciated and stated, it is felt that they indicate that the risk of malignant disease developing in ovaries conserved at hysterectomy has probably been exaggerated by some gynaecologists who argue that when hysterectomy is performed for a benign condition, the ovaries ought also to be removed lest they should subsequently undergo neoplastic change

Limited Arbitrage and Short Sales Restrictions: Evidence from the Options Markets

In this paper, we investigate empirically the well-known put-call parity no-arbitrage relation in the presence of short sale restrictions. We use a new and comprehensive sample of options on individual stocks in combination with a measure of the cost and difficulty of short selling, specifically the spread between the rate a short-seller earns on the proceeds from the sale relative to the standard rate (the rebate rate spread). We find that violations of put-call parity are asymmetric in the direction of short sales constraints, their magnitudes are strongly related to the rebate rate spread, and they are maintained even in the presence of transactions costs both in the options and equity lending market. These violations appear to be related to both the maturity of the option and the level of valuations in the stock market, consistent with a behavioral finance theory that relies on over-optimistic investors in the stock market and segmentation between the stock and options markets. Moreover, the extent of violations of put-call parity and the rebate rate spread for individual stocks are significant predictors of future stock returns. For example, cumulative abnormal returns, net of borrowing costs, over a 2«-year sample period can exceed 65%.

Risk and Return: Some New Evidence

We develop a structural asset pricing model to investigate the relationship between stock market risk and return. The structural model is estimated using the conditional market variance implied by S&P 100 index option prices. Relative risk aversion is precisely identified and is found to be positive, with point estimates ranging from 3.06 to 4.01. However, the implied volatility data only spans the period November 1983 to May 1995. As a robustness check, the structural model is also examined with postwar monthly data, in which the conditional market variance is estimated. We again find a positive and significant risk-return relation and get similar point estimates for relative risk aversion. Additionally, we document some facts about stock market return. First, stock price movements are primarily driven by changes in investment opportunities, not by changes in market volatility. Second, there is some evidence of a leverage effect. Third, relative risk aversion is quite stable over time

Do Asset Prices Reflect Fundamentals? Freshly Squeezed Evidence from the OJ Market

The behavioral finance literature cites the frozen concentrated orange juice (FCOJ) futures market as a prominent example of the failure of prices to reflect fundamentals. This paper reexamines the relation between FCOJ futures returns and fundamentals, focusing primarily on temperature. We show that when theory clearly identifies the fundamental, i.e., at temperatures close to or below freezing, there is a close link between FCOJ prices and that fundamental. Using a simple, theoretically-motivated, nonlinear, state dependent model of the relation between FCOJ returns and temperature, we can explain approximately 50% of the return variation. This is important because while only 4.5% of the days in winter coincide with freezing temperatures, two-thirds of the entire winter return variability occurs on these days. Moreover, when theory suggests no such relation, i.e., at most temperature levels, we show empirically that none exists. The fact that there is no relation the majority of the time is good news for the theory and for market efficiency, not bad news. In terms of residual FCOJ return volatility, we also show that other fundamental information about supply, such as USDA production forecasts and news about Brazil production, generate significant return variation that is consistent with theoretical predictions. The fact that, even in the comparatively simple setting of the FCOJ market, it is easy to erroneously conclude that fundamentals have little explanatory power for returns serves as an important warning to researchers who attempt to interpret the evidence in markets where both fundamentals and their relation to prices are more complex.

Uncovering the Risk-Return Relation in the Stock Market

There is an ongoing debate in the literature about the apparent weak or negative relation between risk (conditional variance) and return (expected returns) in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM to investigate this relation. Our primary innovation is to model and identify empirically the two components of expected returns –the risk component and the component due to the desire to hedge changes in investment opportunities. We also explicitly model the effect of shocks to expected returns on ex post returns and use implied volatility from added options to increase estimation efficiency. As a result, the coefficient of relative risk aversion is estimated more precisely, and we find it to be positive and reasonable in magnitude. Although volatility risk is priced, as theory dictates, it contributes only a small amount to the time-variation in expected returns. Expected returns are driven primarily by the desire to hedge changes in investment opportunities. It is the omission of this hedge component that is responsible for the contradictory and counter-intuitive results in the existing literature