Sharpe ratio and Treynor index

Manage
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I just read William Sharpe’s original 1966 paper in which he came up with what we now know as the Sharpe ratio (http://finance.martinsewell.com/fund-performance/Sharpe1966.pdf). I found several very interesting things about it that have not been, as far as I know, discussed here before.

First, Sharpe only used annual returns, not monthly. This, to me, makes a huge difference in terms of the validity of his work. Using the arithmetic mean of monthly returns to measure performance is, as anyone who studies finance on even a basic level, terribly flawed–you need to use the geometric mean. By using the average of annual excess returns, Sharpe largely avoided this pitfall.

Second, the ratio was definitely not meant to include fixed-income instruments. Sharpe was writing solely about mutual-fund performance. This, again, avoids the terrible flaw of how the Sharpe ratio is used today to rank fixed-income ETFs like MINT higher than practically any equity-based ETF.

Third, the ratio of the funds Sharpe looked at were all between 0 and 1.

Fourth, and perhaps most importantly, Sharpe looked at how past ratios of mutual funds measured over a 9-year period corresponded with the performance of the same funds over the subsequent 9-year period and found a correlation coefficient of 0.306, which isn’t bad. He then tried the same study with the Treynor index and found a correlation coefficient of 0.974, which is, to my mind, very hard to beat.

The Treynor index is the same as the Sharpe ratio except that the denominator is volatility rather than variability. Exactly how Sharpe and Treynor calculated volatility is unclear from this paper–did he use what we now think of as beta? If so, was it an annual measure, like the standard deviation of annual returns he used for his own ratio?

At any rate, I was having a very hard time wrapping my mind around the flaws in the Sharpe ratio as it’s currently used, and as I outlined in a previous post (see my first post in this thread: https://www.portfolio123.com/mvnforum/viewthread_thread,10036). It seems that the ratio as originally proposed was not subject to these flaws–at least not to the same degree–and that Sharpe himself thought the Treynor index was clearly superior to his own ratio when it came to predicting future returns.

(Two asides:

  1. Wikipedia says that rankings based on the Treynor index would be the same as those based on Jensen’s alpha. That doesn’t seem to me to be the case. Let’s say the market return was 10% and the risk-free rate is 0%. Then a fund with a 60% return and a beta of 3 is going to have an alpha of 30 and a Treynor index of 17, while a fund with a 35% return and a beta of 1 is going to have an alpha of 25 and a Treynor index of 25.

  2. In the previous thread, Hunter suggested a ranking system for ETFs that divides by beta, which is pretty similar to the Treynor index.)

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Actually, the Treynor index that Sharpe created was based not upon division by beta, but a different measure of volatility. In a 2008 interview, Treynor said, “There are some people who say that the Treynor Index has a denominator which is beta. . . . beta is an inappropriate divisor. . . . A few months ago I went back and read the old Harvard Business Review article, which I hadn’t read in years. Basically, it says to regress the return on the fund in question against the return on the appropriate market index to find out what the slope of that regression line is.” This is the measure that Sharpe was using when he came up with the Treynor index. So the Treynor index would be defined as the average annual rate of return minus the risk-free rate of return all divided by the slope of the regression of the return against the return of the appropriate market index. I’m not very familiar with regression analysis and don’t quite understand covariance yet, so I can’t tell how different this measure is from beta, but the fact that Treynor himself thought it was quite different makes me wonder. I haven’t been able to access Treynor’s original paper from 1965, so I don’t know if he used annual or monthly returns, but I would guess that Sharpe was using annual returns when he invented the index.

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Looking at Benjamin Graham’s concept of risk, he always talks about paying too much for a stock and not having a wide enough margin of safety. He does not talk about variability or volatility as far as I know. I think Graham’s measure would be more P/B than Standard Deviation related. I am reading one of his books now and that stood out to me.
I am not sure what to do with something like P/E or P/B as a measure of ‘risk’ though.
The trick always seems to figuring out the intrinsic value of the stock versus what it is valued at today by the market and then buying below the market. At least that is the theory. I know there are several ways to value a stock but most are educated guesses and some math (ie, a DCF).
One persons take on it:
https://blogs.cfainstitute.org/investor/2015/04/07/margin-of-safety-the-lost-art/

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What interests me is predictability. It seems logical to me that a strategy with low volatility will be more predictable than one with high volatility. Sharpe’s work confirms this. Here’s my thinking. Let’s say you have five different strategies to choose among, all of which make equal financial sense to you. Do you go with the one with the highest CAGR? Do you go with the one with the lowest volatility? Or do you find a way to combine the two into a number that has some correlation with future returns? Sharpe’s work–which is now over 50 years old–suggests that if you divide the average annual return by the volatility you can come up with a measure with some predictive ability. But you have to do it in the right way.

This is all quite unrelated to what I think of as risk, which is the probability of losing your money. Sharpe used the word “risk” in a very different way than Graham did, or than I do. In my opinion, the best way to minimize risk is to make as much money as you can as quickly as you can so you have a cushion to fall back on. :wink: But for Sharpe and Treynor, risk was the possibility of not meeting expectations. So there’s the predictability thing.

As for the margin of safety, when I look at the incredible drawdowns of value-based strategies over the last few years, I have to wonder where it’s gone.