My research is about Journey to the West, no I meant Journey to the Risk. Monkey King, Goku à la mode, would conform to stochastic dominance (SD) and exhibit loss aversion as Chen et al. (2006) document risk behaviors of capuchin monkeys.
After several happy years in the uni-bar-çity, Goku learned the fundamental mean-variance (MV) theory. However, Goku gradually realized that the MV theory hardly applies to him because it is neither consistent with SD nor with loss aversion. He was perplexed, asking me: “Am I wrong or the MV theory is wrong?”
“For me, the MV model is wrong but it is useful. Mean and variance capture a significant portion of risk information but also leave out some important risk features. For a better description of risk, we can either extend the MV framework or resort to SD to revise and improve decisions.“
Path 1: Adopting SD decision rules
(1). A key pillar of the MV-CAPM framework is that market portfolio is MV efficient. Is the market also SD efficient?🤔
Olga, Olivier, and I study this question in
“Is the Index Efficient? A Worldwide Tour with Stochastic Dominance,“
Journal of Financial Markets, 2022 (59, Part B), 100660.
We find that most stock market indices across the globe are not SD efficient, and past SD relation of industry sub-index predicts future dominance. Strategies incorporating SD implications improves utilities for risk averse investors.
(2). Another key concept of the MV-CAPM framework is beta. The literature remarks the low-beta anomaly as well as the success of betting against beta (BAB). Then, what is the SD implication for BAB?🤔
Olga and I examine this question in
“Enhancing Betting Against Beta with Stochastic Dominance,“
Journal of Empirical Finance, 2024 (76), 101465.
We find that beta ranking can go against SD ranking, and BAB can short SD dominating stocks. Using a SD pre-filtering that remove dominating stocks from the short leg and dominated stocks from the long leg significantly enhances a wide range of performance and risk measures.
(3). SD is very useful but SD comparisons can be very difficult to implement. Can we have a simple indicator to facilitate SD-consistent comparisons?🤔
Olivier and I propose such an index in
“Semivariance Below the Maximum: Assessing the Performance of Economic and Financial Prospects,“
Journal of Economic Behavior & Organization, 2023 (209): 185-199.
We find that the comparison of semivariance below the maximum (SBM) conveniently summarizes SD comparison. SBM also helps to explain prominent economic puzzles such as the restaurant puzzle and Rabin’s paradox.
Path 2: Extending the MV framework
(1). Including skewness and kurtosis for portfolio selection is the primary avenue to extend the MV framework. However, there is no analytical solution to mean-variance-skewness-kurtosis (MVSK) portfolio selection. Then, how can we implement MVSK optimization in practice to get efficient portfolios?🤔
Olivier and I propose a simple solution for the implementation in
“Efficient Efficient Portfolios and Extreme Risks: A Pareto–Dirichlet Approach,“
Annals of Operations Research, July 2023.
We notice that simulation methods are conventionally used for returns, while a discretization of simplex effectively transform portfolio selection problem into simple comparisons of portfolio return profile. We use Dirichlet portfolios to build an MVSK efficient frontier.
(2). BAB has a key feature of market neutrality, which is different from other risk factors. Does BAB really provide loss protection by being market neutral?🤔
I specify BAB crashes in
“Market Neutrality and Beta Crashes,“ working paper.
I find that BAB effectuates negative market timing and negative volatility timing amid volatile markets, promoting BAB crashes. The concern of imperfect market neutrality is shared by a broad range of market neutral low-beta strategies. Such a particular vulnerability to bull markets is not explained by liquidity and leverage constraints. Managing the crash risk of low-beta strategies produces significant performance improvements and mitigates beta crashes.
(3). Volatility management heavily relies on risk return tradeoff in the MV framework, while recent studies find poor out-of-sample performance for volatility-managed portfolios. Does the MV framework in fact properly relate risk to return such that investors cannot systematically benefit from timing volatility?🤔
I propose a simple improved strategy based on Moreira and Muir (2017)’s formation of volatility management
“Improving Volatility-Managed Portfolios in Real Time,“
Critical Finance Review, forthcoming.
The improved strategy features effective risk scaling, conditional expected return, and intercept from conditional risk return tradeoff. Using this strategy for a comprehensive set of 197 risk factors and anomaly portfolios, I document significant real-time performance improvements including 148 Sharpe ratio increases and 165 positive abnormal returns.