An Educational Piece on the Appraisal Ratio…
Peter Hecht, Ph.D., a fellow Chicago Finance PhD and vice president of Evanston Capital Management, recently published an interesting white paper:
Peter highlights a practical, simple, performance statistic to evaluate any investment–the appraisal ratio.
First, Dr. Hecht reviews Markwitz’s “Mean-variance” Modern portfolio theory (MV-MPT), which is an algorithm that maximizes expected returns for a given level of risk.
Investors want new investments, which can help maximize “Sharpe Ratio”of the total portfolio. Sharpe Ratio is defined as the total portfolio’s expected excess return divided by the total portfolio volatility. In another words, investors want to add new investments that move the efficient frontier to the left (less volatility) and up (more expected return). The chart below highlights what we’re talking about
The paper also introduces the concept of an “alpha” in the context of portfolio theory/efficient frontiers. Citing from the white paper:
If an asset’s expected return is too high relative to its beta, i.e. there is alpha, the portfolio’s Sharpe Ratio could be improved by allocating more to that asset. Thus, statements about alpha are equivalent to statements about whether the investor’s portfolio is on the efficient frontier. A zero (nonzero) alpha implies that the investor’s portfolio is (not) on the efficient frontier. This is why the concept of alpha plays a central role in performance evaluation and portfolio construction.
The Important, Yet Underutilized, Appraisal Ratio
Dr. Hecht emphasizes the Appraisal Ratio (AR). The ratio is calculated by running a simple linear regression of the new investment’s excess return (in excess of T-bills) on the existing total portfolio’s excess returns:
The Appraisal Ratio (AR) is defined as follows, where α represents the new investment’s expected “alpha” and σ(ε) denotes the new investment’s residual volatility from the regression above:
New investments with a higher AR will help increase the Sharpe ratio of the total portfolio.
Dr. Hecht includes an example: A 60/40 global investor considering 3 potential “new” investments: Swiss Re Cat Bond Index, Credit Suisse Leveraged Loan Index (Bank Loans), and MSCI Emerging Market Equity Index (EM equities).
EM equities have the highest annualized return, but the lowest AR, while catastrophe bonds have a somewhat lower return, but the highest AR. Why? Although the EM equities have higher return, they don’t enhance the efficiency of the original 60/40 portfolio. Cat bonds are the clear winner and will enhance the 60/40 portfolio’s risk/return profile; however, the loan portfolio, while having a similar Sharpe Ratio to EM equity, has an appraisal ratio that is almost double EM equity. In theory, this bank loan strategy might be more beneficial to the entire portfolio than the EM equity, despite the fact the bank loan strategy has a slightly lower Sharpe Ratio.
A conclusion remark from Dr. Hecht:
Focusing on individual strategy returns does not correct for risk. Focusing on individual Sharpe Ratios does not correct for beta. Focusing on alpha controls for beta, but doesn’t account for the alpha’s volatility (risk). Only the Appraisal Ratio, defined as the expected alpha-to-alpha volatility ratio, correctly accounts for an individual investment’s return attributes.
6 Suggestions from Dr. Hecht to help you avoid common mistakes on performance evaluation:
- Do not forget to deduct the risk-free rate when estimating alphas.
- Unless the investment has zero beta and/or the investor plans to allocate 100% to one investment, do not focus on the individual investment’s Sharpe Ratio.
- Do not be seduced by high average alphas.
- Do not necessarily avoid investments with a high correlation to the existing portfolio.
- Do not focus too much on individual expected returns.
- Lastly, do not forget to beta-adjust returns when evaluating an individual investment’s performance.
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Definitions of common statistics used in our analysis are available here (towards the bottom)