Unlike previous studies on alternative investment vehicles, Liang examines Commodity Trading Advisors (CTAs), hedge funds and funds of hedge funds as three distinctive investment classes. The distinction is due to the dramatic differences between the classes. The trading strategies, regulations and correlation structures of CTAs and hedge funds are different. The fee structures of funds of funds and hedge funds are different.

The author chooses a portfolio approach to investigate the performance and risk characteristics of the three groups. The database used, provided by Zurich Capital Markets, covers the period from 1994 to 2001.

Markets are considered to be up markets if the monthly S&P 500 returns are positive and down markets if the monthly S&P 500 returns are negative. Hedge funds show an average attrition rate of 13.23% in up markets (16.97% in down markets), funds of funds show an attrition rate of 9.5% (10.55%), and CTAs show an attrition rate of 23.5% (20.3%). Funds of funds have lower attrition rates than hedge funds because they are better diversified. Except for CTAs, the better the market conditions, the lower the attrition rates. The CTAs are different because of their use of derivatives and leverage, which increases the risk.

The survivorship bias is 2.32% per year for hedge funds, 1.18% per year for funds of funds, and 5.89% per year for CTAs. The results are consistent: the lower the attrition rate, the lower the survivorship bias. In order to avoid survivorship bias, dead funds are included in the sample.

Performance measures are computed from 1994 to 2000, based on a regular Sharpe ratio and on the autocorrelation-adjusted Sharpe ratio. The two indicators lead to the same conclusions on a stand-alone basis.

Hedge funds outperform funds of funds during this period. It can be argued that this is due to the two-tier fee structure of funds of funds, which reduces the post-fee performance. Hedge funds and funds of funds outperform CTAs too. Possible explanations are the high attrition rates, high fees, less diversified positions and high leverage of CTAs.

For performance attribution, Liang built a multi-asset class factor model with 14 class and risk factors representing the US equity market, other developed equity markets, emerging markets, government bonds, broad bond markets, currencies, commodities, cash, size, value/book-to-market and four option-based factors (call ATM, put ATM, call OTM and put OTM).

On a stand-alone basis, hedge fund returns are significantly explained by developed equity markets, emerging markets, government bonds, broad bond markets and size. By referring to the adjusted R² of the full model (91.64%), we see that the explanatory power of the model is high.

Funds of fund returns are significantly explained by the same factors, because of the coverage of similar investment styles. The adjusted R² of the full model is 79.4%. Conversely the explanatory power of the full model is very low in the case of CTAs (14.3%): this implies that CTAs use different strategies from hedge funds and funds of funds.

After that, Liang focuses the analysis on a portfolio framework under different market environments. He distinguishes the correlation structure in up markets from that of down markets, mainly because of the option-like payoff of fee structures and the market liquidity.

In terms of non-linearity in fund returns, beta asymmetry in the up and down markets is observed. Here the non-linearity is measured with respect to the S&P 500 Index. In the case of hedge funds and funds of funds, the non-directional strategies exhibit non-significant up market betas, whereas three directional strategies exhibit significant up market betas (global established, long only and short selling). All strategies show significant and positive down market betas (except for short selling). The conclusion is that hedge funds and funds of funds are positively related to the S&P 500 Index in the down market.

In the case of CTAs, only stock trading CTAs have a significant market beta (which is positive). Only currency CTAs have a non-significant down market beta. Agriculture, diversified and financial CTAs have negative down market betas. Stock trading CTAs have a positive down market beta. The conclusion is that CTAs are negatively related to the S&P 500 Index in down markets.

In terms of correlation, the same distinction is made between up and down markets. In up markets, all the coefficients are significant across hedge fund styles, except for short selling, which is negatively correlated with the other styles. This can be explained by the style level, which decreases the impact of the return variations of an individual fund. Funds of funds are positively correlated with all hedge fund styles, except short selling. CTAs are weakly correlated with hedge funds and fund of fund styles. This may allow managers to improve the risk-return profile of their portfolios by adding CTAs to hedge funds and funds of funds. In down markets, the results are the same across hedge fund styles, with a higher degree of magnitude. Agriculture, currency, diversified and financial trading CTAs are negatively and significantly correlated with hedge fund and fund of fund styles. Stock trading CTAs are positively correlated with hedge fund styles.

In terms of autocorrelation, the Ljung and Box (1978) Q-statistic is used over the period 1998-1999 for the bull markets and 2000-2001 for the bear markets. For most of the styles, higher Chi-square values are recorded in the bear markets than in the bull markets. However the Chi-square values are not significant. A possible reason is that the computations are at the style level, not at the individual fund level, and this reduces the autocorrelation.

The correlation is then studied at the individual fund level, both in up and down markets. For hedge funds, intra-style correlations are generally low. They are significantly higher in the down markets, except for the global international style. This is not an attractive characteristic for investors, because they need more diversification in down markets. If the correlations depend on market conditions, then hedge funds are not entirely market-neutral and not well hedged. For CTAs, results are similar.

Finally Liang examines the benefit of adding CTAs to hedge funds and to funds of funds in an investment portfolio, by computing autocorrelation-adjusted Sharpe ratios for different combinations. In up market conditions, the optimal portfolio combination for hedge funds and CTAs is 30% hedge funds and 70% CTAs (with a Sharpe ratio of 2.08). The optimal portfolio combination for funds of funds and CTAs is 40% hedge funds and 60% CTAs (with a Sharpe ratio of 1.74). In down market conditions, the optimal portfolio combination for hedge funds and CTAs is 40% hedge funds and 60% CTAs (with a Sharpe ratio of 0.83). The optimal portfolio combination for funds of funds and CTAs is 50% hedge funds and 50% CTAs (with a Sharpe ratio of 0.79). It appears that adding CTAs to hedge funds or funds of funds can improve the Sharpe ratios for most portfolio combinations.