Applying The Sharpe Ratio To Low Beta Investments

by: Bennington Investment Ideas

This is the third and final article in a three part series (see previous articles here and here) where I looked at investments that could provide diversification benefits for a market portfolio. While simply smoothing out the portfolio's price fluctuations might help investors sleep better at night, the real goal is find better returns as well. Is a given stock providing a good return for the risk that it poses?

One approach to evaluating the performance of a stock relative to its risk is to look at the Sharpe Ratio, which is defined as:

A ratio developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe ratio is calculated by subtracting the risk-free rate - such as that of the 10-year U.S. Treasury bond - from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.


In mathematical terms, the Sharpe Ratio, S, would be

S = (Rp - Rf)/sigma_p,

where Rp is the expected return of the portfolio or the security, Rf is the appropriate risk free rate, and sigma_p is the standard deviation of the portfolio or security. The standard deviation will be very close to the volatility of the price returns.

Calculating the Sharpe Ratio for Select Investments

I will look at the following list of securities from my previous articles:

Low Correlation Securities
Ticker Name Correlation 36 months
SPY S&P 500 Index Trust ETF 100%
PCY PowerShares Emerging Mkts Sovereign Debt 48%
XLU Utilities Select Sector SPDR 45%
MCD McDonalds Corp. 37%
PCG PG&E Corp. 31%
GLD SPDR Gold Shares ETF 16%
LQD iShares iBoxx $ Invest Grade Corp Bond 8%
TIP iShares Barclays TIPS Bond -15%
SHY iShares Barclays 1-3 Year Treasury Bond -32%
IEF iShares Barclays 7-10 Year Treasury -66%
VXX iPath S&P 500 VIX ST Futures ETN -81%

Source: Yahoo!Finance for split and dividend adjusted prices, Author calculations. Three year correlations are based upon monthly returns of the securities listed.

This is the same list, except for the addition of IEF which will be used as the risk free benchmark investment. One should note that it has done pretty well over the past three years. Applying the formula for calculating the Sharpe Ratio for each of these securities gives the following result:

Sharpe Ratio for Select Investments
Ticker 3 year return "Risk free" return Excess Return 3 Year Monthly Volatility Sharpe Ratio
PCY 43.8% 26.8% 17.0% 2.3% 7.6
MCD 45.8% 26.8% 19.0% 3.4% 5.5
GLD 45.1% 26.8% 18.3% 5.3% 3.5
LQD 29.3% 26.8% 2.5% 1.5% 1.6
SPY 33.5% 26.8% 6.7% 4.4% 1.5
XLU 29.5% 26.8% 2.7% 2.9% 0.9
IEF 26.8% 26.8% 0.0% 1.7% 0.0
TIP 25.9% 26.8% -0.9% 1.2% -0.8
PCG 9.4% 26.8% -17.4% 3.9% -4.4
VXX -94.2% 26.8% -121.0% 20.3% -6.0
SHY 3.1% 26.8% -23.7% 0.2% -104.9

Source: Yahoo!Finance for split and dividend adjusted prices, Author calculations. Three year correlations are based upon monthly returns of the securities listed. Volatility is used for Standard Deviation given the relatively high number of data points.

This table shows that these low beta investments have a wide range of Sharpe Ratios. PCY, an emerging market bond ETF, had the best ratio with a significant excess return and a very low volatility. In contrast, the short term Treasury bond ETF SHY had a pretty poor performance. Despite a very low volatility, it had a substantial negative investment return.

However, this is historical data and so the question is how should one apply these insights to picking forward looking investments? Or is this more a descriptive tool to understand what happened in the past?

Looking forward the goal is to find investments that will produce superior Sharpe Ratios. The following table shows some comparisons among Sharpe Ratio and Portfolio Volatility impact.

Metrics of Select Investments
Ticker 3 year return Sharpe Ratio Portfolio Volatility Impact
PCY 43.8% 7.6 -1.5%
MCD 45.8% 5.5 -1.1%
GLD 45.1% 3.5 -0.7%
LQD 29.3% 1.6 -2.0%
SPY 33.5% 1.5 0.0%
XLU 29.5% 0.9 -1.3%
TIP 25.9% -0.8 -2.2%
PCG 9.4% -4.4 -1.0%
VXX -94.2% -6.0 4.1%
SHY 3.1% -104.9 -2.2%

Source: Yahoo!Finance for split and dividend adjusted prices, Author calculations. Three year correlations are based upon monthly returns of the securities listed. Portfolio Volatility Impact is the impact of adding the listed security to a pure SPY portfolio (hence the SPY impact here is 0).

Once can see that PCY from this list appears to be a very attractive option. It has a relatively high Sharpe Ratio and a very good impact on the portfolio volatility. I would also highlight GLD which also shows good scores in both dimensions. While MCD also looks attractive, I am more concerned about individual stocks which will carry additional risks. A key question here would be whether one can identify inherent characteristics of companies that would lend themselves to producing favorable Sharpe Ratios. The other question is whether MCD has had strong historical Sharpe Ratios.

The recommendation from this analysis is that emerging markets sovereign debt could be an interesting area for exploration to help optimize one's personal portfolio.

Disclosure: I am long SPY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Disclaimer: This article is for informational and educational purposes only and shall not be construed to constitute investment advice. Nothing contained herein shall constitute a solicitation, recommendation or endorsement to buy or sell any security.

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