Investors and academics have long sought for a way to compare the performance of portfolios on a risk-adjusted basis. If you can adjust for risk, you can directly compare the performance of portfolios that have little or nothing in common, like a corporate bond portfolio and a stock portfolio, for instance.
The Treynor ratio does just that. It calculates an investment's performance per unit of risk.
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How the Treynor ratio works
The Treynor ratio uses a portfolio's "beta" as its risk. Beta measures the volatility of an investment relative to the stock market, generally the S&P 500 index, which is given a beta of one. More volatile stocks will have a beta greater than one, whereas less volatile stocks have a beta lower than one.
High beta stocks rise and fall faster than low beta stocks in up or down markets. Thus, a direct comparison between high- and low-beta portfolios, especially during a short time period, doesn't result in a fair comparison. The high-beta portfolio should, according to the Capital Asset Pricing Model, have a higher or lower return than low-beta stocks, depending on the performance of the market average.
The Treynor ratio attempts to put all investments on equal footing. The formula for the Treynor Ratio is as follows:
(Ri - Rf)/B, where:
- Ri is the return of the investment.
- Rf is the risk-free rate, generally accepted as the yield on short-term U.S. Treasury bills in the United States.
- B is the beta of the portfolio.
An example of the Treynor ratio in practice
Below, I've created a few example portfolios with made up returns and beta measures. By calculating the Treynor ratio for each investment, we can determine which portfolio performed best on a risk-adjusted basis.
|
Investment |
Return |
Beta |
|---|---|---|
|
S&P 500 Index |
10% |
1.00 |
|
Fancy Fund |
12% |
0.9 |
|
Risks for Reward Fund |
22% |
2.5 |
We'll assume that the current yield on the one-month U.S. Treasury bill is currently 1%. This is our risk-free rate.
We can now calculate the Treynor ratio for each investment using the formula above:
- S&P 500 Index: (.10-.01)/1 = 0.09
- Fancy Fund: (.12-.01)/0.9 = 0.122
- Risks for Reward Fund: (.22-.01)/2.5 = 0.084
The results show how much performance investors enjoyed for each unit of risk (return in excess of the risk-free rate divided by risk as measured by beta). A "good" investment will have a higher Treynor ratio than the S&P 500 index, as it should provide higher-returns on a risk-adjusted basis than the stock market average.
Notice that the Fancy Fund was the second-best fund in terms of raw performance, generating a 12% return, but it is by far the leader in terms of generating the best risk-adjusted return. It generated 12.2 percentage points of return for each unit of stock market risk.
The Risks for Reward Fund put up the highest unadjusted return, but the lowest performance relative to its risk, which we determine from its low Treynor ratio relative to the other investments. If you looked solely at the raw returns, you'd think that the Risks for Reward Fund was the best investment, given that it had the highest return. But that's not the case when risk is accounted for.
Some final words
The Treynor ratio has an inherent weakness in that it is backward-looking by design. It's quite possible, perhaps even expected, for an investment to perform differently in the future than it has in the past. A stock with a beta of three won't necessarily have three times the volatility of the market forever, for example. Likewise, you shouldn't automatically expect a portfolio to generate 8% returns over the next 10 years simply because it returned 8% over the previous 10 years.
In addition, some may take issue with the use of beta as a measure of risk. Many accomplished investors would say that beta is not risk -- Warren Buffett and Charlie Munger have argued for decades that the volatility of an investment is not true risk. They would argue that risk is the chance of a permanent, not temporary, loss of capital.
Ratios, which include beta (the Treynor ratio being one of many), may be best suited for comparing short-term performance. A number of studies of long-term stock market performance -- and a study of Buffett's record at Berkshire Hathaway -- have shown that low beta stocks have actually performed better than high beta stocks, whether on a risk-adjusted basis or in terms of raw, unadjusted performance. That is to say that the direct and linear relationship between higher beta and higher long-run returns may not be as strong as it is believed to be.
Academics and investors will invariably argue the best methods for measuring risk for years to come. In truth, there may be no perfect measure of risk. But despite this, the Treynor ratio can at least give you a way to compare the performance of a portfolio per unit of beta, which may make for more useful comparisons than an unadjusted comparison of performance.
