Factor models

One of the motivations behind this blog is the work conducted by William Fung and David A. Hsieh in their paper Asset-based Hedge-fund Styles and Portfolio Diversification. In the paper the authors demonstrate that asset-based style factors link returns of hedge-fund strategies to observed market prices. From their earlier work it was shown that the returns from trend-following strategies can be replicated by a dynamically managed option-based strategy known as a lookback option. The lookback option model can be used to potential compute managers’ alpha if it exists as well as making the underlying mechanism of this class of strategies transparent to investors. The return of this option-based replication strategy has been shown to have a good degree of explanatory power for funds that utilize a trend-following style. This fact shows that the return distribution of trend-following funds is a systematic consequence of a broad class of trend-following strategies.

The key question in factor model analysis in the hedge fund context is: “Can we discern the return characteristics of hedge-fund strategies by looking at how hedge-fund returns are statistically clustered together?” The results from the work on lookback options show that there are systematic reasons why hedge fund strategies offer the returns distribution characteristics they do.

Now just jumping ahead a few pages, we look at a simple multi-factor model. Just for reference the classic Sharpe formula:-

Is simply expanded:-

Now, taking some well documented “classic” asset based style factor we can build a model. The values of the Betas are derived from a simple ordinary least squares regression against a fund of hedge fund index, in this case the HFRI Fund of Funds Composite Index. A separate discussion can be had on survivorship bias and why a fund of fund index mitigates this to some extent.

Market risk, taking the excess returns over says the S&P 100 or S&P 500 Index
Small and large cap spread, using the spread between the Russell 2000 and the S&P 500 Indices
Yield Spread, Change in 10-year US Treasury yields
Credit Spread, Change in the spread between 10-year Treasury Bonds and Moody’s BBa bonds
Trend following, taking the excess returns of the Barclays CTA index*

*In the paper Hedge Fund Benchmarks: A Risk-Based Approach. Financial Analysts Journal Volume 60 Number 5 ©2004, CFA Institute. The authors use three separate factors to model trend following behavior. A basket of look back options on bonds, commodities and finally FX.

No here comes the incredible fact, this simple model captures around 70% of the risk in a diversified portfolio of hedge funds. Yes just five factors, 70% of the risk! If we use the 3 trend following factors instead of the CTA proxy the risk captured increases to 80%!

All of the factors are significant at a 99% confidence level.

Large cap: 0.15 – 0.19
Small – Large cap: 0.05 – 0.09
Credit spread: -3.0 – -4.0
Yield spread: -0.9 – -1.1
Trend following: 0.16 – 0.20

Now, interesting the alpha of this model is around 0.15% per month or approx 1.8% per annum, but is not statistically significant. The T-stat is around 1.7. Depending on the time frame selected, this value does fluctuate into being significant at times. However, the point of this is not to argue if hedge funds produce alpha or not, but to demonstrate the fact that a lot of hedge fund returns are from exposure to “simple” risk premiums.

The model was run in sample; normally this causes statisticians a degree of discomfort. However, this is not a problem here as I simply wish to show that these factors are utilized. The predictive power of such models is clearly of concern when trying to use these types of model in a financial product, such as a hedge fund replication product.

Whist this very simple model captures c70% of the risk there is still 30% out there, and potentially 2% of unexplained returns. It is important to note that we have not taken into account the hedge fund fees.