Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns. The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market

https://www0.gsb.columbia.edu/faculty/rhodrick/crosssection.pdf

Investor sentiment, defined broadly, is a belief about future cash flows and investment risks that is not justified by the facts at hand. The question is no longer whether investor sentiment affects stock prices, but how to measure investor sentiment and quantify its effects. One approach is "bottom up," using biases in individual investor psychology, such as overconfidence, representativeness, and conservatism, to explain how individual investors underreact or overreact to past returns or fundamentals. The investor sentiment approach that we develop in this paper is, by contrast, distinctly "top down" and macroeconomic: we take the origin of investor sentiment as exogenous and focus on its empirical effects. We show that it is quite possible to measure investor sentiment and that waves of sentiment have clearly discernible, important, and regular effects on individual firms and on the stock market as a whole. The top-down approach builds on the two broader and more irrefutable assumptions of behavioral finance -- sentiment and the limits to arbitrage -- to explain which stocks are likely to be most affected by sentiment. In particular, stocks that are difficult to arbitrage or to value are most affected by sentiment.

/pdf/investor-sentiment-in-the-stock-market-50cs28ylr8.pdf

Investor Sentiment in the Stock Market

Investor Psychology and Security Market Under- and Overreactions

https://w4.stern.nyu.edu/finance/docs/pdfs/Seminars/081w-whitelaw.pdf

Maxing Out: Stocks as Lotteries 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) data frequency used to estimate idiosyncratic volatility, (ii) weighting scheme used to compute average portfolio returns, (iii) breakpoints utilized to sort stocks into quintile portfolios, and (iv) using a screen for size, price and liquidity play a critical role in determining the existence and significance of a relation between idiosyncratic risk and the cross-section of expected returns. Portfolio-level 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 there is no robust, significant relation between idiosyncratic volatility and expected returns.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID922092_code235620.pdf?abstractid=922092&rulid=284452&mirid=1

Idiosyncratic Volatility and the Cross-Section of Expected Returns

Goyal and Santa-Clara (2003) find a significantly positive relation between the equalweighted average stock volatility and the value-weighted portfolio returns on the NYSE/AMEX/Nasdaq stocks for the period of 1963:08 to 1999:12. We show that this result is driven by small stocks traded on the Nasdaq, and is in part due to a liquidity premium. In addition, their result does not hold for the extended sample of 1963:08 to 2001:12 and for the NYSE/AMEX and NYSE stocks. More importantly, we find no evidence of a significant link between the value-weighted portfolio returns and the median and value-weighted average stock volatility. THE INTERTEMPORAL RELATION BETWEEN RISK AND RETURN has long been an important topic in asset pricing literature. Most asset pricing models postulate a positive relationship between a stock portfolio’s expected returns and risk, which is often modeled by the variance or standard deviation of the portfolio’s returns. However, there is no agreement about the existence of such a trade-off for stock market indices. 1 While return volatility is an intuitively appealing measure of risk, different approaches used by previous researchers suggest that no clear consensus has emerged regarding its relevance. 2 Whether or not investors require a larger risk premium on average for investing in a security during times when the security is more risky remains an open question.

Does Idiosyncratic Risk Really Matter

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.

Idiosyncratic Volatility 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).

/pdf/maxing-out-stocks-as-lotteries-and-the-cross-section-of-4i3m6ggjji.pdf

Nusret Cakici

Papers

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

Idiosyncratic Volatility and the Cross-Section of Expected Returns

Does Idiosyncratic Risk Really Matter

Idiosyncratic Volatility and the Cross Section of Expected Returns

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