Sharpe Ratio Not the Best Metric for Maximizing Portfolio Efficiency

Sharpe Ratio Not the Best Metric for Maximizing Portfolio EfficiencyPeter Hecht, Ph.D., Senior Investment Strategist for Evanston Capital Management, says he cringes when people from the investment community criticize hedge funds for lagging the S&P 500 amid a broad and historic bull market. Many of these same people were also unduly impressed by hedge funds’ relatively superior performance during the 2008 bear market, in Dr. Hecht’s view, since the nature of hedge funds dictates that they are more likely to underperform in bull markets and outperform in bear markets – they are hedged funds, after all.

MV-MPT & EMH

“Mean-variance model portfolio theory” (MV-MPT) is a mouthful, but vitally important to understanding optimal asset allocation, according to Hecht’s new paper How to Evaluate Hedge Funds or Any New Investment. Theoretician Harry Markowitz revolutionized how investment managers allocate assets with MV-MPT in the 1950s, and economist Eugene Fama – Dr. Hecht’s dissertation adviser – built on MV-MPT for his “efficient market hypothesis” (EMH), which helped win him a Nobel prize in 2013.

But despite these widely accepted theoretical advancements, most people don’t properly understand the importance of “beta-adjusting returns and risk-adjusting alphas,” according to Hecht. He suggests they begin utilizing appraisal ratio (AR), a risk-adjusted performance statistic that accounts for a new investment’s expected return, risk, and diversification attributes “in a manner consistent with MV-MPT.”

Appraisal Ratio

Hecht also says investment allocators put too much focus on an individual investment’s Sharpe ratio, expected returns, and correlation properties – what’s really important, according to MV-MPT, is how adding a new investment impacts the entire portfolio. AR, by contrast, is defined as the expected alpha to alpha-volatility ratio, and it can only be calculated in the context of an existing portfolio of investments.

Unlike Sharpe ratio, which doesn’t correctly control for an individual investment’s beta, AR is a risk-adjusted measure of alpha. AR evaluates potential investments based on what they bring to the portfolio and discounts any redundancy and overlap – investments with the highest ARs will improve the total portfolio’s Sharpe ratio the most.

Efficient Frontier

The graphic below shows the theoretical relationship between expected return and volatility. The green line represents the most efficient “tangent” possible, called the “efficient frontier.” The objective of asset allocation is to move the portfolio “north” along its efficient frontier.

According to Hecht, the most efficient portfolios have expected returns that are exactly proportional to beta – even greater expected returns would be “inefficient,” and such a portfolio could be optimized by allocating more to the alpha-generating assets, thereby absorbing them into the portfolio’s adjusted beta. Using AR to evaluate potential new investments ensures that the new investment’s risk and return properties actually contribute to improving the portfolio’s “efficient frontier,” rather than duplicating existing portfolio features and adding little but transaction costs.

Evanston Capital Appraisal Ratio

Conclusion

Dr. Hecht concludes Evanston Capital’s excellent new whitepaper with a list of common “performance evaluation mistakes and misperceptions;” among them:

  • Don’t forget to deduct the risk-free rate when estimating alphas: Hecht says he commonly comes across analyses, even from vended software packages, that forget to work with “excess returns” – defined as returns above the “risk-free” (U.S. government debt) rate of return. This isn’t particularly significant now since short-term interest rates are basically at zero, but as rates move higher, this error could prove costly.
  • Don’t be “seduced” by high alphas: Just as portfolio returns need to be adjusted for beta; alphas need risk-adjusting, too.
  • Don’t necessarily avoid investments with high correlations to the existing portfolio: Hecht says a low-correlation portfolio with zero alpha “is worthless,” and that high correlation can result in low “residual volatility,” and thus a higher AR.

For more information, download a pdf copy of the whitepaper.

  • nickgogerty

    Efficient frontiers are a mathematical pantload. The assumptions underlying them are laughable.

    • Nick, love the “mathematical pantload” expression. I’ll have to work that in somewhere. No doubt there are a lot of inputs and assumptions that go into efficient frontiers, all of which can be wrong, but flying with some sort of instrument is generally better than not. I notice that your book, The Nature of Value, takes a different approach. Do you have a primer on your approach that we could share with readers?

      • nickgogerty

        the best way of explaining it is the title. It is best to understand the source of value and sensitivities. Moat’s, Innovation, etc. are all factors. Statistical analysis are often applied poorly and the co-variance matrix is one of the worst as it makes gross assumptions of stability of relationships while providing no insight or understanding for the allocator about the factors driving returns. On the site http://www.thenatureofvalue.com there are 2 free chapters from the book as well as 180 diagrams and charts from the book. I guest lecture at Columbia University’s b-school MBA program on Innovation and macro economics. For those interested in systemic risk I am speaking on the 3rd in NYC at NYSSA. http://www.nyssa.org/programs/mastercalendar/ctl/viewdetail/mid/512/itemid/2134/d/20141203.aspx Happy to speak and engage with all who attend. I will be on panels with govt. treasury officials discussing systemic risk and vice-chair of Blackrock $4.5 trillion AUM.

        …and actually flying with an instrument that is broken or gives bad readings is far more dangerous than no instruments at all. I say that as a former glider and para-glider pilot. Bad instruments and data lead to more reckless behaviors due to a false sense of knowledge or awareness. Witness the outcome of AAA rated CDO’s. etc.

        • Thanks Nick. I appreciate the additional information. The NYSSA event looks like one worth attending. I will be sure to put it on our events calendar. And I look forward to reading the 2 chapters of the book to get started.

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