Example: Using Vectors to Replicate a Mutual Fund with an ETF and a Hedge Fund
| Aug 20th, 2006 | Filed under: CAPM / Alpha Theory, Performance, Analytics & Metrics | By: Alpha Male |
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By: Alpha Male
Another posting on this site introduces the idea of using vectors for analyzing active and passive management. Specifically, that posting suggested that a mutual fund can be viewed as a “host” for a market ETF and an “embedded market neutral hedge fund” (or any other active fund with a different market correlation than the host). Below, I’ve tried to work through a simple example of how vectors can be used to isolate these components.
Let’s go back to a basic example. Let’s assume the market volatility is 20%, but let’s not concern ourselves with adding a fund to an index as we did adding B to A above. Let’s just look at one fund. Let’s call it the Active Opportunities Fund. The Active Opportunities Fund has a market correlation of 0.5 and a volatility of 15% per annum. Thus, it can be represented by the following chart:
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