**By:** *Alpha Male*

Shorting out the equity market can isolate what I call the embedded hedge fund from within a long-only mutual fund. As many, including William Sharpe, have argued, you don’t need to know the actual holdings in a mutual fund to determine the amount of beta within it. One can simply regress returns against a chosen benchmark. This “top-down” process for determining market exposure has been proven by academics to have approximately the same predictive power as analyzing the actual holdings in a mutual fund to determine a hedge ratio (“Bottom-up”). However, a top-down process based on past performance alone cannot uncover an embedded hedge fund’s actual holdings. It can only determine an embedded hedge fund’s implied performance and capital requirements.

To compare the bottom-up and top-down approaches to isolating an embedded hedge fund, I shorted the TSX60 against the TD Canadian Equity Value Fund as of June 30, 2005…

Specifically, I used the weightings in the iUnits S&P/TSX 60 ETF. I deducted these weightings from the weightings of the same positions in the TD Canadian Value Fund. For S&P/TSX positions with NO representation in the TD Canadian Value Fund, we end up with a pure short position equal to the index weighting. For TD Canadian Value Fund positions not contained in the S&P/TSX, we end up with a pure long position equal to the weighting in the TD Canadian Value Fund (note the 19 positions at the end of the list that fall into this category). If we had used the S&P/TSX Composite Index containing over 200 positions, we would have far fewer of these situations â€“ and of course, all the other weightings would be different too.

Click Here to View the TD Canadian Value Fund’s Embedded Long/Short Hedge Fund.

We find that the embedded hedge fund has a net exposure that is slightly negative (-1.61). This is due to the fact that the weightings of both the ETF and the TD Canadian Equity Fund do not add up to 100%. If they did add up to 100% (ie. fully invested), then the embedded hedge fund would (and should) be perfectly market neutral. Net long positions are 40.77% and net short positions are -42.38%, leading to a gross exposure of approximately 83% (i.e. 83% of the original mutual fund).

On the surface, 40% net long and 40% net short suggests the fund might not actually be index-hugging. After all, a 40% deviation from the benchmark (in aggregate) suggests the fund differs markedly from the TSX 60.

As an aside, the maximum gross exposure theoretically possible would be 200% (no mutual fund positions contained in the index â€“ leading to -100% and 100% of the mutual fund in non-index positions). So 80% gross exposure sounds pretty significant. Is the manager really straying from the index in an attempt think for them selves and thus add value? If so, we would expect to see a relatively low market correlation when we do a top-down analysis. But strangely, the market correlation of the TD Canadian Value Fund is actually very high (89.3%)! How can this be?

The answer lies in the specific stocks the manager has selected for the TD Canadian Value Fund. While picking the same stocks as the index is a sure way to hug the index, there is another way. Picking representative stocks in each sector can also provide a very close approximation to the index (and is arguably a more efficient way to buy the index). This closet indexing (often called sampling) may make the fund manager look more thoughtful and deliberate, but once you know which 15 or so large-cap stocks approximate the entire index, you have essentially bought the entire index.

The bottom line is that, regardless of the *position-level* deviation from the index, an active mutual fund (in effect) contains an embedded ETF. No matter how hard a manager has tried to avoid literally buying the index, the proof is in the pudding. Perhaps the “unique” names in her portfolio were each highly correlated with the overall market or perhaps they were simply representative of the sectors in the index (and comprised the same proportions of the fund as they did in the index). In either case, the manager has not added a significant amount of value.

Students of institutional investment techniques such as portabel alpha will see that the “embedded hedge fund” identified here is simply an “alpha overlay”. It begs the question: Why not just buy the index and the overlay separately? And in fact, many sophisticated institutional investors are doing just that. In doing so, they reduce costs and increase flexibility.

*– Alpha Male*

## One Comment