5.4 Modified value-at-risk
The last section concludes that combining different types of futures enhances the resultant portfolio’s risk-return profile relative to a portfolio of SIF and interest rate futures. This section examines the combined effect of all four distributional moments by using a Modified value-at risk measure.
Table 7 provides the basic statistics and Modified VaR values for a $100 investment for the equally-weighted portfolio, the benchmark portfolio of SIF and interest rate futures, the CRB index, the GSCI, and the S&P 500 contract in panel A, and for different equally weighted group portfolios in panel B. In panel A the equally weighted naive portfolio generally has a better return, smaller risk, less negative (or more positive) skewness and a smaller potential loss (via the VaR results) than the benchmark portfolios. What’s more, the naïve portfolio is least volatile among the four alternatives, with a low standard deviation and the smallest range of returns over the six-year period. The naïve portfolio possesses the same sign for the mean return as the GSCI and CRB in all six years, showing the common effect of commodities and energy on all three indexes. While the naïve portfolio return is generally superior to the S&P 500 return in stock bear markets (2001 and 2002), it did worse than the S&P 500 in bull markets (1998 and 1999). The Modified VaRs at two standard deviations show that the equally weighted portfolio of futures suffers from less potential extreme losses than any of the other indexes, especially the S&P 500. In panel B, the interest rate futures portfolio and currency futures portfolio have smaller return, risk and potential loss, while the SIF portfolio and
commodity futures portfolio returns are relatively more volatile. Energy futures portfolio has the highest risk and highest Modified VaR among all the groups.
Table 8 provides the Modified VaRs for each futures instrument and the equally weighted portfolio for each year and the entire sample period of this study. Interest rate futures have the least potential loss, with currency futures having the next lowest potential loss. The equally weighted portfolio has a low potential loss relative to most of the individual contracts. We conclude that a naively constructed portfolio of all highly liquid futures contracts is a good investment, with interest rate and currency futures playing a positive role towards reducing risk in this diversified portfolio.
The results in table 7 and 8 provide a different perspective on diversification, namely the influence of skewness and kurtosis on potential large loss events. These results show that, even after consideration of skewness and kurtosis, the diversification benefit of combining different types of futures is ample relative to a benchmark portfolio of SIF and interest rate futures.