Capital Decimation Partners and Capital Multiplication Partners

 

What makes a good hedge fund? Can you replicate hedge fund returns? These questions are not easy to answer when you think about replication strategies. You can create through bundling ideas a good hedge fund with a high Sharpe ratio, but there are hidden risks that may not seem obvious on the surface. We can think about the classic examples provided by Andy Lo with his humorous firms, Capital Decimation Partners (CDP) and Capital Multiplication Partners (CMP) as a case study on the drivers of hedge fund returns and replication. 

The returns of his fictitious hedge fund CDP are a combination of holding the stock index with selling out of the money puts for protection. You do well because you pick up premium every month until the time there is a large market downturn and then the pain begins. The hedge fund manager hopes that the size and frequency of a market decline just does not occur. Hope is not a strategy. The high Sharpe ratio comes because the tail event is not accounted for in the return to risk ratio. Increase carry in exchange for tail risk and you improve the Sharpe but create a different risk profile.

So, let's look at (CMP). In this case, the returns are generated through a switching model between the SPX and one-month Treasury bills assuming that you have perfect foresight on what will do better.  This timing model is like buying the SPX and with a put option struck at the price of the index plus the one-month bill return. Unfortunately, you cannot get those returns given the cost of the option and the issue not having perfect timing. We can only receive something less than the perfect forecast.  Nevertheless, we can use the thinking behind forming a hedge fund in theory to develop replication strategies through linear approximation. These will not be perfect, but it can be an alternative to buying hedge funds. 

Replication of a hedge fund can be tried through using several factors to find a linear fit, regression, between the hedge funds returns and a model. The alpha from the manager is the constant and residual or returns not associated with the linear regression. The results suggest that it is possible to clone the average return for hedge funds within a style category. Unfortunately, getting average returns is not what many investors want. Additionally, there is an error term with replication so you will not get something that will be close in the short run.

Looking at hedge funds as either an option program or a linear combination of factors is a good start to describe the risks when investing with these alternatives.