Value-at-risk capital requirement regulation, risk taking and asset allocation: a mean–variance analysis

This paper examines the performance of a naïve equally weighted buy-and-hold portfolio and optimization-based commodity futures portfolios for various lookback and holding periods using data from January 1986 to December 2018. The application of Monte Carlo simulation-based mean-variance and conditional value-at-risk optimization techniques are used to construct the robust commodity futures portfolios. This paper documents the benefits of applying a sophisticated, robust optimization technique to construct commodity futures portfolios. We find that a 12-month lookback period contains the most useful information in constructing optimization-based portfolios, and a 1-month holding period yields the highest returns among all the holding periods examined in the paper. We also find that an optimized conditional value-at-risk portfolio using a 12-month lookback period outperforms an optimized mean-variance portfolio using the same lookback period. Our findings highlight the advantages of using robust optimization for portfolio formation in the presence of return uncertainty in the commodity futures markets. The results also highlight the practical importance of choosing the appropriate lookback and holding period when using robust optimization in the commodity portfolio formation process.

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DRAWDOWN MEASURE IN PORTFOLIO OPTIMIZATION

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024905002767 ◽

2005 ◽

Vol 08 (01) ◽

pp. 13-58 ◽

Cited By ~ 146

Author(s):

ALEXEI CHEKHLOV ◽

STANISLAV URYASEV ◽

MICHAEL ZABARANKIN

Keyword(s):

At Risk ◽

Portfolio Management ◽

Asset Allocation ◽

Value At Risk ◽

Risk Measures ◽

Sample Path ◽

Real Life ◽

Optimization Techniques ◽

Conditional Value At Risk ◽

Excess Loss

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - α) * 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

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