Nusret Cakici

Idiosyncratic Volatility and the Cross-Section of Expected Returns

This paper examines the cross-sectional relation between idiosyncratic volatility and expected stock returns. The results indicate that i) the data frequency used to estimate idiosyncratic volatility, ii) the weighting scheme used to compute average portfolio returns, iii) the breakpoints utilized to sort stocks into quintile portfolios, and iv) using a screen for size, price, and liquidity play critical roles in determining the existence and significance of a relation between idiosyncratic risk and the cross section of expected returns. Portfoliolevel analyses based on two different measures of idiosyncratic volatility (estimated using daily and monthly data), three weighting schemes (value-weighted, equal-weighted, inverse volatility-weighted), three breakpoints (CRSP, NYSE, equal market share), and two different samples (NYSE/AMEX/NASDAQ and NYSE) indicate that no robustly significant relation exists between idiosyncratic volatility and expected returns.

Size, Value, and Momentum in Emerging Market Stock Returns

In this paper, we examine value and momentum effects in 18 emerging stock markets. Using stock level data from January 1990 to December 2011, we find strong evidence for the value effect in all emerging markets and the momentum effect for all but Eastern Europe. We investigate size patterns in value and momentum. After forming portfolios sorted on size and book-to-market ratio, as well as size and lagged momentum, we use three well-known factor models to explain the returns for these portfolios based on factors constructed using local, U.S., and aggregate global developed stock markets data. Local factors perform much better, suggesting emerging market segmentation.

Value at Risk and Expected Stock Returns

Stock size, liquidity, and value at risk (VAR) can explain the cross-sectional variation in expected returns, but market beta and total volatility have almost no power to capture the cross-section of expected returns at the stock level. Furthermore, the strong positive relationship between average returns and VAR is robust for different investment horizons and loss-probability levels. In addition to the cross-sectional regressions at the stock level, this study used a time-series approach to test the empirical performance of VAR at the portfolio level. The results, based on 25 size/book-to-market portfolios, indicate that VAR has additional explanatory power after the characteristics of market return, size, book-to-market ratio, and liquidity are controlled for. Although previous empirical studies have used a variety of stock characteristics and other factors, such as total risk and diversifiable risk, to explain the cross-section of expected returns, researchers have not investigated value at risk (VAR) as an alternative risk factor that can explain stock returns. In conducting this study, our goal was to test whether the maximum likely loss measured by VAR can explain cross-sectional and time-series differences in expected returns. Using monthly and annual regressions, we provide evidence that size, liquidity, and VAR could capture the cross-sectional variation in expected returns of NYSE, Amex, and Nasdaq stocks for the period January 1963 to December 2001. Furthermore, we show that market beta and total volatility have almost no power to explain average stock returns at the individual-stock level. We also compared the relative performance of size, beta, and VAR in explaining the cross-sectional variation in portfolio returns. The results show that all the risk factors considered in the article can capture the cross-sectional differences in portfolio returns but that VAR has the best performance in terms of R2 values. The strong positive relationship between stock (or portfolio) returns and VAR turns out to be robust over various investment horizons and loss-probability levels. In addition to using cross-sectional regressions in an asset-pricing framework, we also used time-series regressions to evaluate the empirical performance of VAR at the portfolio level. To mimic the risk factor in returns related to VAR, we devised an alternative factor, HVARL, the difference between the simple average of the high-VAR portfolio returns and the low-VAR portfolio returns. Using 25 portfolios, we investigated the relative performance of total volatility, VAR, and liquidity in terms of their ability to capture time-series variation in stock returns. When we regressed monthly returns for a stock portfolio on the returns for portfolios based on market return, company size, the book-to-market ratio, liquidity, and VAR, we found that VAR can capture substantial time-series variation in stock returns and provide additional explanatory power even after the characteristics of market return, size, book-to-market ratio, and liquidity are controlled for. The results also imply that the relationship between VAR and expected stock returns is not the result of a reversal in long-term returns, of liquidity, or of volatility. Modern portfolio theory determines the optimum asset mix by maximizing the expected risk premium per unit of risk in a mean–variance framework or the expected value of some utility function approximated by the expected return and variance of the portfolio. In both cases, market risk of the portfolio is defined in terms of the variance (or standard deviation) of expected portfolio returns. Modeling portfolio risk as defined by traditional volatility measures implies that investors are concerned only about the average variation (and covariation) of individual stock returns and does not allow investors to treat the negative and positive tails of the return distribution separately. The standard risk measures determine the volatility of unexpected outcomes under normal market conditions, which corresponds to the normal functioning of financial markets during ordinary periods. Neither the variance nor the standard deviation, however, can yield an accurate characterization of actual portfolio risk during highly volatile periods. Therefore, the set of mean–variance-efficient portfolios may lead to an inefficient strategy for maximizing expected portfolio return while minimizing risk. Our findings suggest a new approach to optimal portfolio selection in a VAR framework. A mean–VAR approach can be introduced to allocate financial assets by maximizing the expected value of some utility function approximated by the expected return and VAR of the portfolio, as well as the investors aversion to VAR.

Book-to-Market and the Cross-Section ofExpected Returns in International Stock Markets

Individual stocks’ expected return estimates are a key input for equity selection models. A 2008 study by Eugene Fama and Kenneth French found evidence that past changes in book equity and price contain independent information about expected cash flows that can be used to improve estimates of expected returns. This study focuses on international stock markets and re-examines whether the origins of the book-to-market ratio (BM), in terms of past changes in book equity and price, enhance the estimates of expected returns provided by BM alone. Examining all stocks, as well as subcategories of microcap, small, large, and all-butmicrocap stocks trading in the United Kingdom, Germany, France, Italy, Canada, and Japan, the authors find that recent changes in book equity and price are more relevant than more distant changes in enhancing estimates of expected future cash flows and expected future returns. Their tests also show that changes in book equity say much more about expected stock returns than price changes do.

Cross-Sectional Stock Return Predictability in China

Cross-sectional stock return predictability has always been an intriguing issue for the researchers as it relates to a number of resilient puzzles in finance. This paper provides a comprehensive analysis on the stock return predictability in China form January 1994 to March 2011 by employing both portfolio method and cross-sectional regressions. We find strong predictive power of size, price, book-to-market ratio, cash-flow-to-price ratio, and earnings-to-price ratio. The total as well as idiosyncratic volatility are also consistent stock return predictors in China. The results exist for stocks listed in Shanghai Stock Exchange as well as Shenzhen Stock Exchange. Unlike evidence for the other markets (e.g. U.S), the momentum fails to qualify as a useful predictor in the portfolio method. It is only when used with other predictors that it exhibits predictive power for the Chinese stocks. Overall, the variables related to cheapness of stocks such as book-to-market ratio and cash-flow-to-price ratio demonstrate reliable forecast power, but earnings-to-price ratio is less reliable.

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

We introduce a new, hybrid measure of stock return tail covariance risk, motivated by the under-diversified portfolio holdings of individual investors, and investigate its cross-sectional predictive power. Our key innovation is that this covariance is measured across the left tail states of the individual stock return distribution, not across those of the market return as in standard systematic risk measures. We document a positive and significant relation between hybrid tail covariance risk (H-TCR) and expected stock returns, with an annualized premium of 9%, in contrast to the insignificant or negative results for purely stock-specific or systematic tail risk measures.

Value at Risk for Interest Rate-Dependent Securities

Value at risk (VaR) may be calculated for interest rate-dependent securities using an extension of a non-parametric estimator. The method here uses a two-dimensional kernel with adjustable bandwidth to model the risk as it changes with the level of interest rates. Since the variance, skewness, kurtosis, and higher moments of the distribution of interest rate changes are allowed to vary non-parametrically with the level of rates, the model produces dynamically changing boundaries of risk for VaR that are based only on the data and are independent of a modelers choices. These VaR bounds are shown to be significantly better measures by a variety of criteria. The hit rates using the model presented here are generally more accurate than a GARCH specification in backtesting.

Closed-End Equity Funds: Betting on Discounts and Premiums

Can discounts and premiums on closed-end equity funds be used to earn positive excess returns over a benchmark index? Research in the U.S. market has found that investors could have earned higher returns than a benchmark of U.S. stocks by purchasing shares of closed-end funds with discounts. This research examines an extensive sample of U.S. and U.K. listed closed-end funds September 4, 1998, through 1991, including transaction costs, an important element in evaluating portfolio performance that is absent from previous work. While long portfolios with deep discounts outperform a benchmark index, provided transaction costs are low, the surprise is that short portfolios with deep premiums outperform the benchmark and long portfolios, provided transaction costs are moderate to high.

Closed-end Funds and Turnover Restrictions

Past studies have found that investors can earn higher returns than a benchmark by purchasing shares of closed-end funds with discounts or selling shares with premiums. These studies either ignored the impact of transaction costs or used equally weighted portfolio strategies without controls on turnover or transaction costs. We examined whether constraining the holdings of individual funds and turnover has any bearing on the excess returns earned by closed-end equity funds over a benchmark return. We found that when transaction costs were low, portfolios with frequent rebalancing and loose turnover constraints outperformed the benchmark and other portfolios in the period we studied. We found, in contrast, that when transaction costs were moderate to high, portfolios with less-frequent rebalancing and tight turnover constraints outperformed the benchmark and other portfolios. The implication for the portfolio manager is that excess returns may be achieved in a variety of trading-cost environments with the proper mix of policy variables. A popular view is that closed-end funds should be purchased for their discounts. If a closed-end fund trades at a discount, an investor can purchase shares at a price below net asset value or, at least, purchase shares cheaply. Selling these shares less cheaply at a later date can lead to excess returns. This view is supported by empirical findings. A number of studies have shown that managed portfolios of closed-end funds can outperform a benchmark when discounts and premiums form the basis for fund selection. One recent study found that outperformance could be achieved even in an environment of high transaction costs by selling short the funds with the deepest discounts. These studies did not control turnover and holdings of funds, however, which is an important practical issue that we attempt to address in this article. We examined whether constraining the amount of turnover and holdings of funds, thereby controlling trading costs, has any bearing on the excess returns earned by a managed portfolio of closed-end funds. We used an expected-return-optimization model that selects portfolios of closed-end funds in an environment defined by transaction costs. The expected return of each fund depends on its current discount. Our methodology allowed us to control trading costs by tightening or loosening the turnover constraints together with limiting the holdings of each fund. We back tested the model for the period January 11, 1991, to September 1, 2000, for various holding periods ranging from 1 to 13 weeks and various transaction-cost environments ranging from 0 to 4 percent rates. The data consisted of U.S.- and U.K.-traded closed-end equity funds. The sample contained 128 funds at the start in 1991 and ended with 206 funds in 2000. The benchmark was a capitalization-weighted portfolio of all funds in the sample. We found that portfolios with frequent rebalancing and loose constraints on turnover outperformed the benchmark and other portfolios when transaction costs were low. Lengthening the time between rebalancing and constraining the amount of turnover evidently prevent the model from capitalizing on the opportunities available in discounts. We also found, surprisingly, that when transaction costs were moderate to high, portfolios with less-frequent rebalancing and more-stringent restrictions on turnover outperformed the benchmark and other portfolios. In this case, constraints serve to protect the model from “wrong” decisions (i.e., being too aggressive on funds with high expected returns that subsequently produce low actual returns). The penalties for these decisions are more severe when transaction costs are high. The practical implication of the second finding for portfolio managers is that in an environment of high transaction costs, excess returns on discounted funds can still be achieved but only with the proper mix of policy variables. Specifically, the best-performing strategies in an environment of moderate-to-high (3–4 percent rate) transaction costs consist of tight constraints on turnover (about once a year) and infrequent rebalancing (about a month and a half between re-optimizations). Thus, not only is restricting turnover important when transaction costs are high, so also is limiting the frequency at which the model can reach “incorrect” decisions. This finding is in sharp contrast to the best mix of policy variables used in a low-transaction-cost environment.

A New Approach to Measuring Riskiness in the Equity Market: Implications for the Risk Premium

We introduce a new approach to measuring riskiness in the equity market. We propose option implied and physical measures of riskiness and investigate their performance in predicting future market returns. The predictive regressions indicate a positive and significant relation between time-varying riskiness and expected market returns. The significantly positive link between aggregate riskiness and market risk premium remains intact after controlling for the S&P 500 index option implied volatility (VIX), aggregate idiosyncratic volatility, and a large set of macroeconomic variables. We also provide alternative explanations for the positive relation by showing that aggregate riskiness is higher during economic downturns characterized by high aggregate risk aversion and high expected returns.