Key Concepts

1. The Capital Decimation Partners (CDP) and Capital Multiplication Partners (CMP) are hypothetical trading strategies. The CDP involves selling out-of-the-money puts, and the CMP is a perfect market-timing strategy between the S&P 500 and Treasury bills (dynamic asset-allocation strategy). The perfect market-timing strategy is equivalent to owning the S&P 500 and buying a put option on the S&P 500 with a strike price that is equal to the risk-free rate (i.e., Treasury bill rate).

2. Convertible Arbitrage funds have the highest relative performance using the Sharpe measure; however, funds with this style also have high positive serial correlation, which is an indicator of illiquidity. A series of returns with illiquidity exposure will have lower measures of volatility and Sharpe ratios with an upward bias. The Fixed Income Arbitrage style and the Event Driven style also have high Sharpe ratios and higher values of positive serial correlation. The Dedicated Short Bias and the Managed Futures funds have the lowest Sharpe ratios and much lower serial correlations than the Convertible Arbitrage funds.

3. The three sources of return variance are: (1) the risk factors, (2) the weighted-pairwise covariances between each risk factor, and (3) the residual variance. That is, there exist multiple sources of risk, and each source of risk should generate a risk premium including a risk-based alpha.

4. Two methods are used to explain the relative performance of the categories of hedge fund strategies using factor analysis:

• First method is the size of the intercept from the model (manager-specific alpha).

♦ Emerging Markets style category has the largest average alpha.

♦ Managed Futures style category has the smallest, yet positive, alpha.

• Second method is the contribution of the manager-specific alpha to the mean return of the fund.

♦ Dedicated Short Bias style category has the largest manager contribution to returns.

♦ Convertible Arbitrage style category has the smallest manager contribution to returns.

5. The fixed-weight method for linear clones uses the whole sample and has constant portfolio weights through time. The rolling-window method for creating linear clones reduces the look-ahead bias inherent in the fixed-weighted version. The look-ahead bias exists in the fixed-weighted method because the entire data set of returns is used to construct the clones. The linear clones constructed with a 24-month rolling window use a five factor model and renormalize the factors across time and by fund. More active investors engaging in dynamic asset-allocation will prefer the rolling-window method, and more passive investors will prefer the fixed-weight approach. The results indicate that the Managed Futures and Global Macro linear clones outperform the actual fund for both the fixed-weight and the rolling-window constructions. The Event Driven and the Emerging Markets style clones are not able to perform as well as the actual hedge funds.

6. The liquidity and leverage of the linear clones can impact performance.

• An advantage of the linear clones is the liquidity of the assets used to replicate the hedge fund style. All of the linear clones have low values for autocorrelations, confirming that the clones are more liquid. However, many of the more liquid linear clones underperform the funds that they replicate based on average returns.

• The impact of leverage is evaluated by using a renormalization factor. An analysis of the values for the renormalization factors indicates that leverage can be replicated using futures contracts. Therefore, the implied leverage in the linear clones is achievable. The hedge fund style with the highest renormalization factor (i.e., leverage) is Managed Futures, and the hedge style category with the lowest renormalization factor is Fund of Funds.

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