The Intertemporal Relation between Expected Return and Risk on Currency

The literature has so far focused on the risk-return tradeoff in equity markets and ignored alternative risky assets. This paper is the first to examine the presence and significance of an intertemporal relation between expected return and risk in the foreign exchange market. The paper provides new evidence on the intertemporal capital asset pricing model by using high-frequency intraday data on currency and by presenting significant time-variation in the risk aversion parameter. Five-minute returns on the spot exchange rates of the U.S. dollar vis-à-vis six major currencies (the Euro, Japanese Yen, British Pound Sterling, Swiss Franc, Australian Dollar, and Canadian Dollar) are used to test the existence and significance of a daily risk-return tradeoff in the FX market based on the GARCH, realized, and range volatility estimators. The results indicate a positive, but statistically weak relation between risk and return on currency.Foreign exchange market, ICAPM, High-frequency data, Time-varying risk aversion, Daily realized volatility

A Cross-Sectional Investigation of the Conditional ICAPM

This paper provides a cross-sectional investigation of the conditional and unconditional intertemporal capital asset pricing model (ICAPM). The results indicate that estimating the conditional ICAPM with a pooled panel of time series and cross-sectional data in a multivariate GARCH-in-mean framework is crucial in identifying the positive risk-return tradeoff. Different from the traditional literature, the paper decomposes the aggregate stock market portfolio into ten book-to-market portfolios and then estimates a cross-sectionally consistent slope coefficient on the conditional variance-covariance matrix. The riskaversion coefficient, restricted to be the same across all portfolios, is estimated to be positive and highly significant. This is the first study testing the cross-sectional consistency of the intertemporal relation by estimating the multivariate GARCH-in-mean model with different slopes. The statistical results indicate the equality of slope coefficients across all portfolios, supporting the empirical validity and sufficiency of the conditional ICAPM. The paper also provides evidence that the time-varying conditional covariances can explain the value premium because the average risk-adjusted return difference between the value and growth portfolios is economically and statistically insignificant within the conditional ICAPM framework

Disturbing Extremal Behavior of Spot Rate Dynamics

This paper presents a study of extreme interest rate movements in the U.S. Federal Funds market over almost a half century of daily observations from the mid 1950s through the end of 2000. We analyze the fluctuations of the maximal and minimal changes in short term interest rates and test the significance of time-varying paths followed by the mean and volatility of extremes. We formally determine the relevance of introducing trend and serial correlation in the mean, and of incorporating the level and GARCH effects in the volatility of extreme changes in the federal funds rate. The empirical findings indicate the existence of volatility clustering in the standard deviation of extremes, and a significantly positive relationship between the level and the volatility of extremes. The results point to the presence of an autoregressive process in the means of both local maxima and local minima values. The paper proposes a conditional extreme value approach to calculating value at risk by specifying the location and scale parameters of the generalized Pareto distribution as a function of past information. Based on the estimated VaR thresholds, the statistical theory of extremes is found to provide more accurate estimates of the rate of occurrence and the size of extreme observations.extreme value theory, volatility, interest rates, value at risk

Cyclicality in Catastrophic and Operational Risk Measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973-2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the Generalized Pareto Distribution and the Skewed Generalized Error Distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events

Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns

Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month(MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX generally subsumes or reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008)

Investigating ICAPM with Dynamic Conditional Correlations

This paper examines the intertemporal relation between expected return and risk for 30 stocks in the Dow Jones Industrial Average. The mean-reverting dynamic conditional correlation model of Engle (2002) is used to estimate a stock’s conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s expected return. The risk-aversion coefficient, restricted to be the same across stocks in panel regression, is estimated to be between two and four and highly significant. This result is robust across different market portfolios, different sample periods, alternative specifications of the conditional mean and covariance processes, and including a wide variety of state variables that proxy for the intertemporal hedging demand component of the ICAPM. Risk premium induced by the conditional covariation of individual stocks with the market portfolio remains economically and statistically significant after controlling for risk premiums induced by conditional covariation with macroeconomic variables (federal funds rate, default spread, and term spread), financial factors (size, book-to-market, and momentum), and volatility measures (implied, GARCH, and range volatility)

Implied volatility spreads and expected market returns

This article investigates the intertemporal relation between volatility spreads and expected returns on the aggregate stock market. We provide evidence for a significantly negative link between volatility spreads and expected returns at the daily and weekly frequencies. We argue that this link is driven by the information flow from option markets to stock markets. The documented relation is significantly stronger for the periods during which (i) S&P 500 constituent firms announce their earnings; (ii) cash flow and discount rate news are large in magnitude; and (iii) consumer sentiment index takes extreme values. The intertemporal relation remains strongly negative after controlling for conditional volatility, variance risk premium, and macroeconomic variables. Moreover, a trading strategy based on the intertemporal relation with volatility spreads has higher portfolio returns compared to a passive strategy of investing in the S&P 500 index, after transaction costs are taken into account

Hybrid Tail Risk and Expected Stock Returns: When Does the Tail Wag the Dog?

This paper introduces a new, hybrid measure of covariance risk in the lower tail of the stock return distribution, motivated by the under-diversified portfolio holdings of individual investors, and investigates its performance in predicting the cross-sectional variation in stock returns over the sample period July 1963-December 2009. Our key innovation is that the covariance is measured across the states of the world in which the individual stock return is in its left tail, not across the corresponding tail states for the market return as in standard systematic risk measures. The results indicate a positive and significant relation between what we label hybrid tail covariance risk (H-TCR) and expected stock returns, in contrast to the insignificant or negative results for purely stock-specific or standard systematic tail risk measures. A trading strategy that goes long stocks in the highest H-TCR decile and shorts stocks in the lowest H-TCR decile produces average raw and risk-adjusted returns of 6% to 8% per annum, consistent with results from a cross-sectional regression analysis that controls for a battery of known predictors

Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns

Motivated by existing evidence of a preference among investors for assets with lottery-like payoffs and that many investors are poorly diversified, we investigate the significance of extreme positive returns in the cross-sectional pricing of stocks. Portfolio-level analyses and firm-level cross-sectional regressions indicate a negative and significant relation between the maximum daily return over the past one month (MAX) and expected stock returns. Average raw and risk-adjusted return differences between stocks in the lowest and highest MAX deciles exceed 1% per month. These results are robust to controls for size, book-to-market, momentum, short-term reversals, liquidity, and skewness. Of particular interest, including MAX reverses the puzzling negative relation between returns and idiosyncratic volatility recently documented in Ang et al. (2006, 2008).

Cyclicality in Catastrophic and Operational Risk Measurements

Using equity returns for financial institutions we estimate both catastrophic and operational risk measures over the period 1973-2003. We find evidence of cyclical components in both the catastrophic and operational risk measures obtained from the Generalized Pareto Distribution and the Skewed Generalized Error Distribution. Our new, comprehensive approach to measuring operational risk shows that approximately 18% of financial institutions’ returns represent compensation for operational risk. However, depository institutions are exposed to operational risk levels that average 39% of the overall equity risk premium. Moreover, operational risk events are more likely to be the cause of large unexpected catastrophic losses, although when they occur, the losses are smaller than those resulting from a combination of market risk, credit risk or other risk events