Connect with us

Research Review | 11 January 2024 | Fat Tail Distributions

Optimal Portfolio Choice with Fat Tails and Parameter Uncertainty
Raymond Kan (U. of Toronto) and Nathan Lassance (LFIN/LIDAM)
December 2023
Existing portfolio combination rules that optimize the out-of-sample performance under estimation risk are calibrated assuming multivariate normally distributed returns. In this paper, we show that this assumption is not innocuous because fat tails in returns increase the out-of-sample mean and variance of sample portfolios relative to normality. Consequently, portfolio combination rules should allocate less weights to the sample mean-variance portfolio and the sample global minimum-variance portfolio, and more weight to the risk-free asset, than the normality assumption prescribes. Empirically, accounting for the impact of fat tails in the construction of optimal portfolio combination rules significantly improves their out-of-sample performance.

Heuristics For Fat-Tailed Stock Market Returns
Ivo Welch (University of California)
December 2023
Daily and monthly value-weighted stock returns are best described in the family of Student-t distributions as having 3 degrees of freedom. My note offers a good heuristic to academics and practitioners alike to adjust one’s inference when using only normally distributed moment estimates: For large negative Z-statistics, one can work with a transformed (i.e., adjusted) ordinary Z-score of (–1.5 – 1.9 × log10(–Z)). For example, one should expect a realization of 15 times the standard deviations below the mean (a one-day return of –16% or lower) to occur as frequently as if it one had observed a T-statistic of about –3.7 under a Normal distribution.

Asymmetric Asset Allocation by a Black-Litterman Model
Fan Zhang (Liverpool John Moores University)
July 2023
The paper extends the Black-Litterman model from elliptical distributions to the extended skew-normal and extended skew-student-t distributions. In addition to fat-tails, a non-Gaussian distributional feature already captured by the elliptical family, the extended model analytically incorporates skewness into the two key elements of a Black-Litterman model, i.e., the derivation of the prior from a market view and the specification and integration of an investor’s personal view. Out-of-sample tests of 500,000 portfolios over a period of 30 years demonstrate the effectiveness and robustness of skewness incorporation in improving portfolio stability and profitability. The Black-Litterman has been proved to an effective way to utilise skewness in portfolio management.

Risk-On Risk-Off: A Multifaceted Approach to Measuring Global Investor Risk Aversion
Anusha Chari (University of North Carolina at Chapel Hill), et al.
November 2023
This paper defines risk-on risk-off (RORO), an elusive terminology in pervasive use, as the variation in global investor risk aversion. Our high-frequency RORO index captures time-varying investor risk appetite across multiple dimensions: advanced economy credit risk, equity market volatility, funding conditions, and currency dynamics. The index exhibits risk-off skewness and pronounced fat tails, suggesting its amplifying potential for extreme, destabilizing events. Compared with the conventional VIX measure, the RORO index reflects the multifaceted nature of risk, underscoring the diverse provenance of investor risk sentiment. Practical applications of the RORO index highlight its significance for international portfolio reallocation and return predictability.

On Climate Fat Tails and Politics
Charles F. Mason (U. of Wyoming) and Neil A. Wilmot (U. of Minnesota)
December 2023
Transitioning the economy from one that relies on fossil fuels to one that emphasizes renewable energy sources will have important implications for the pattern of natural resource use. Such a transition depends on government policies. As elected politicians have an incentive to weigh the spatially heterogeneous costs and benefits on their constituents from taking political action, one might hope that particularly unusual climate events might provide an impetus to increased action. We undertake an analysis using a variety of data sources. We first investigate the stochastic process governing temperature anomalies allowing for “fat tails”, which can arise either from a “jump” diffusion process or a time-varying volatility process. Using the parameter estimates from this first stage, combined with demographic and socio-economic variables, we analyze features promoting support for policies addressing climate change. Several of the parameter estimates that capture fat tails in temperature anomalies play a statistically important relation.

Risk Parity Portfolio Optimization under Heavy-Tailed Returns and Time-Varying Volatility
Marc S. Paolella (University of Zurich), et al.
December 2023
Risk parity portfolio optimization, using expected shortfall as the risk measure, is investigated when asset returns are fat-tailed and heteroscedastic. The conditional return distribution is modeled by an elliptical multivariate generalized hyperbolic distribution, allowing for fast parameter estimation, via an expectation-maximization algorithm and a semi-closed form of the risk contributions. The efficient computation of non-Gaussian risk parity weights sidesteps the need for numerical simulations or Cornish-Fisher-type approximations. Accounting for fat-tailed returns, the risk parity allocation is less sensitive to volatility shocks, thereby generating lower portfolio turnover, in particular during market turmoils such as the global financial crisis. Although risk parity portfolios are surprisingly robust to the misuse of the Gaussian distribution, a more realistic model for conditional returns and time-varying volatilies can improve risk-adjusted returns, reduces turnover during periods of market stress and enables the use of a holistic risk model for portfolio and risk management.


Learn To Use R For Portfolio Analysis
Quantitative Investment Portfolio Analytics In R:
An Introduction To R For Modeling Portfolio Risk and Return

By James Picerno


renewable