The founder of CEO of MSR Indices, a Parsippany, N.J.-based index-investors consultancy, has authored a white paper on target volatility, also known as intertemporal risk parity.

The gist of the paper is that: (1) equity hedge funds do secure alpha for their investors, obvious if one measures their performance against traditional equity indices on a risk adjusted basis; and (2) that they do this through employing intertemporal risk parity, rather than through intuitive stock picks or insider tips.

**BHFI and GEDWTR**

As a preliminary matter, the paper begins with a discussion of whether hedge funds create diversification. The writer, Michael S. Rulle, observes that the Barclay Hedge Fund Index (BHFI) is in fact highly correlated with long-only equities, as reflected for example in the MSR Global Equity Dollar Weighted Total Return Index (GEDWTR).

The underlyings of the GEDWTR are about 43% US, 43% Europe, and 14% Japan. Dividends are reinvested and there is daily rebalancing.

The monthly correlation between GEDWTR and BHFI is .84; annual correlation is .94.

One cannot invest in the BHFI. But from an analytical perspective, those numbers suggest it is “virtually an equity replacement.” On the other hand, the hedge funds in the equity replacement do better than equities, in risk-adjusted terms.

MSR adjusts the Sharpe ratio to take account of what it sees as a mistake in the usual computation of that ratio. It is usually calculated on the assumption that hedge fund performance month-to-month is a “random walk,” that is, that there is no “serial correlation.”

As a refresher for non-wonks: serial correlation is a relationship between any variable and the lagged version of itself. The traditional example is a coin flip. There is no relationship between the fact that this coin came up “heads” the last time I flipped it and the possibility that it will come up “heads” the next time I do. None whatsoever.

But as a matter of empirical fact, hedge fund returns aren’t like that. The fact that a hedge fund did well last month is at least a loose predictor of the likelihood that it will do well this month. As Rulle writes, BHFI and its components have a serial correlation that is typically about .30.

MSR calculates the risk-adjusted returns in a manner that accounts for serial correlation, resulting in what it calls the “True Sharpe” ratio. Impressively, the True Sharpe ratio of BHFI is much better than the performance of long-only equities.

**So, where does the alpha come from? **

MSR says that this alpha is “the result of a definable risk resulting from Target Volatility strategies,” that is, from strategies that aim at maintaining a constant standard deviation of returns.

The paper offers a simple example that involves a rolling six month look-back period. As the underlying volatility of the equity market rises in certain periods, the manager employing this approach will reduce the absolute dollar size of the equity portfolio. As the volatility falls in other periods, the managers will increase that dollar size to maintain the constancy of its standard deviation.

Many studies have documented the success of Target Volatility, that is, of the sort of temporal risk parity just described, over traditional long-only indices. One example was a paper produced by AQR just last year.

**Peeling Away the Onion**

One of the constants of finance scholarship in recent years has been what some call the “onion effect.” Alpha is defined against indices, but as soon as someone formulates a view about the source of alpha, someone else takes this layer off the onion, by creating an index for that alleged source. The what remains of “alpha” must be in the onion below that, must be in performance defined as superior to *that* index.

The MSR paper says that once we see Target Volatility as the source of hedge fund alpha, we ought to peel that layer of the onion away by defining an index for target volatility.

The paper concludes, “Target Volatility Strategies can be viewed as a replacement for Equity Hedge Fund Strategies. Target Volatility Strategies not only outperform Long Only Equities but also outperform Equity Hedge Funds when fees are fixed below Hedge Fund fees.”

In the not-too-distant future, then, hedge funds may be expected to justify their fees by their performance against a new more restrictive definition of alpha, their ability to beat an index of target volatility.