Correlation, the S&P500, and Hedge Fund Portfolios
Don’t Choose Investments Based On Correlation Alone
Why isn’t Global Tactical Asset Allocation (GTAA) / Global Macro the obvious hedge fund strategy for a typical institutional investor? Compared to a diversified hedge fund program, it presents a lower stock/bond correlation. And doesn’t everyone say, the whole point of a portfolio is to assemble uncorrelated return streams?
Correlation, however, is only one leg of the stool.
Hedge Fund Investing - It’s not just Correlation
Correlation is just one of three critical inputs to classic, unconstrained, optimal portfolio selection. Investors must also balance correlation against expected return and risk (i.e., volatility) on a portfolio-specific basis. Even if GTAA/Global Macro and a diversified hedge fund program had identical expected returns and risks (i.e., “all else equal”), there is no universal theorem that states a lower correlation is better. It really just depends. Let me explain.
Appraisal Ratio – the key to choosing new investments
The Appraisal Ratio (“AR”) framework illustrates the problem with focusing on correlation. The AR is an easy to calculate, risk-adjusted, summary performance statistic that properly accounts for a new investment’s expected return, risk, and correlation – the three critical portfolio selection inputs. Although beyond the scope of this piece, it has been shown that the individual investment with the highest AR improves the investor’s total portfolio risk-adjusted return the most – the ultimate goal of an investor.
The Appraisal Ratio is a close cousin to the Sharpe Ratio and is just a simple application of standard linear regression techniques, which can be calculated in seconds within Microsoft Excel. The key difference is, the Appraisal Ratio beta adjusts the “return per unit of risk.”
For more detailed information on the above equations, I encourage you to read my Appraisal Ratio white paper.
Understanding the role of correlation through the Appraisal Ratio
So how does the AR framework help me understand the role of correlation in optimal portfolio selection? Referring to the equations above, for a given new investment’s expected return and risk (i.e., volatility), a higher correlation has two impacts:
“The Bad”: a higher correlation increases the beta (β), which lowers the expected alpha (α), all else equal. This decreases the Appraisal Ratio.
“The Good”: a higher correlation decreases the residual volatility (σ(ε)), making the alpha more consistent, all else equal. This increases the AR.
The net impact of the higher correlation on the AR is case dependent.
In order to convince you that a higher correlation can be better, all else equal, let’s go through a quick example. Assume the following:
The investor currently holds the S&P 500. The S&P 500 has a volatility of 15% and expected excess (in excess of T-Bills) return of 4%.
The investor is considering between two new investments with identical risk and expected returns, but differing correlations.
Investment #1 has a return equal to the S&P 500 + 5%. This investment is perfectly correlated with the investor’s current portfolio, has an expected excess return of 9% (= 4% + 5%), and a volatility of 15%. The alpha is 5% and the residual volatility is 0%, making the AR infinite.
Investment #2 has a return equal to T-Bill + Idiosyncratic White Noise + 9%, where the Idiosyncratic White Noise has an expected return of zero and volatility of 15%. This investment is uncorrelated with the investor’s current portfolio, has an expected excess return of 9%, and a volatility of 15%. The alpha is 9% and the residual volatility is 15%, making the AR equal to 0.6 (= 9%/15%).
Investment #1 is perfectly correlated with the existing portfolio, but it’s the better choice. Why? An investor that holds and can trade the S&P 500 desires Investment #1 due to the riskless arbitrage it presents. For every dollar allocated to Investment #1 from the current portfolio (buying Investment #1, selling S&P 500), the investor picks up a guaranteed 5%...no risk. The S&P 500 risk embedded in Investment #1 can be perfectly hedged out…creating the riskless arbitrage. While Investment #2 is an attractive investment, it’s not as good since it’s impossible for the investor to hedge out the uncorrelated, Idiosyncratic White Noise. Any allocation to Investment #2 from the current portfolio takes on the 15% volatility associated with the Idiosyncratic White Noise.
Bottom line
Correlation is an important input to the portfolio selection process, but it’s just one leg of the stool. The Appraisal Ratio considers the investment’s expected return and risk, alongside correlation, so one can understand the impact of new allocations to an investor’s portfolio. No one wants to sit on a one-legged stool.
Guest Contributor to Symmetric.io. Symmetric.io provides research, analytics and reporting on institutional hedge fund portfolios, trade-crowding, and returns. Click here for more information.
Peter Hecht is Managing Director and Senior Investment Strategist at Evanston Capital Management. Previously, he served in various portfolio manager and strategy roles for Allstate’s general account and pension plan assets in addition to chairing the Investment Strategy Committee. Prior to Allstate, Dr. Hecht was an Assistant Professor of Finance at Harvard Business School. His research and publications cover a variety of areas within finance, including behavioral and rational theories of asset pricing, liquidity, capital market efficiency, complex security valuation, credit risk, and asset allocation. A selection of his most recent research can be found here.
As always, the information contained herein does not constitute an offer to sell or a solicitation of an offer to purchase any securities and is not intended to provide investment advice. Before investing in any investment product you should consult with your financial, tax and/or legal advisors.