## Sunday, August 2, 2009

### The Problem with Risk-Adjusted Returns

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy.

You may have heard of risk-adjusted returns in connection with mutual funds. The basic idea is that a risky investment may not be better than a predictable investment even if the risky investment has a higher expected return. There is some validity to this, although it is too often used to justify the poor returns of mutual funds compared to the overall stock market.

Normally, any discussion of risk-adjusted returns includes some intimidating math. I’ll explain the problems with risk-adjusted returns without needing the math, and I’ll give pointers to where the math can be found for those who are interested.

According to the theory, before comparing investments, you should do a risk-adjusted return calculation that will reduce the returns according to how risky they are. The riskier they are, the more the returns are lowered before any comparison. By “risk” here, we mean volatility, which is a measure of how much the returns vary over time. An investment that grows steadily has low risk, and another investment whose value jumps up and down unpredictably has high risk.

Sharpe Ratio

For those interested in the details of the calculations, Wikipedia has a good explanation of one theory based on the Sharpe ratio. According to this theory, the following two investments are equally desirable:

Investment A: 100% stocks
Investment B: 50% stocks + 50% government debt

The stocks could consist of a broad market index fund, and the government debt could be U.S. Treasuries or Canadian T-Bills. Investment A has a higher expected return, but is twice as volatile, and so both investments end up with the same Sharpe Ratio.

In one year, Investment A will probably have a higher return than B. But it is also possible that A will have a significantly lower return, and it would be reasonable for some investors to prefer Investment B if it is only going to be held for one year. However, over a long period of time (say 25 years), Investment A is preferable because it is overwhelmingly likely to outperform B.

This cuts to the heart of the problem with the way risk-adjusted returns are usually calculated: it doesn’t take into account how long the investment will be held. Over time an investment’s ups and downs tend to balance out somewhat. The average yearly return on an investment gets more predictable (and less risky) the longer it is held. This means that the longer you are invested, the more risk you can tolerate while seeking higher returns.

Some investments are too risky even over a 25-year period. A portfolio full of penny stocks would likely be too risky even over the course of a full lifetime. Another thing to remember is that it never makes sense to take on more risk unless you get a higher expected return. Stocks are a better bet for the long term than government debt because the expected returns are enough higher to justify the added risk.

Morningstar’s Method

Morningstar provides detailed information about both U.S. and Canadian mutual funds. They use a different theory for adjusting mutual fund returns when they assign their star ratings (1 star to 5 stars). However, this theory suffers from the same problem as the Sharpe Ratio; it doesn’t take into account how long the investor will hold the investment.

Suppose that we have a choice of two investments: an adventurous investment that we expect to have a long-term compounded return of 12% with high volatility, and a safe investment that we expect to have a long-term compounded return of 9% with low volatility. For a one-year period, the adventurous investment might deserve to have its return adjusted down to 7% because of the risk, and the safe investment might deserve to be adjusted to 8%. This makes the safe investment preferable.

Now let’s consider a 25-year period to give the volatility a chance to balance out somewhat. Now the adventurous investment deserves to have its yearly return adjusted down to 11%, and the safe investment deserves to be adjusted down to 8.8% per year. In this case, the adventurous investment is better.

Morningstar will discount the adventurous investment by the same amount regardless of how many years it is held. The same is true for the safe investment. So, if you use Morningstar’s method, one of the two investments will be judged better for both the 1-year and 25-year cases, and one of these answers will be wrong.

All of this helps to explain the rule of thumb that money not needed for longer than 3 or 5 years can go into stocks, and money needed sooner than this should go into some less volatile investment.

#### 2 comments:

1. Hi Michael,
The ex-post reality that equities have outperformed bonds in the past in the USA, Canada and a few other countries over very long periods like 25 years may not happen in the future. Countries and stock markets do go into decline just like individual companies. The other uncertainty I see is that while one may intend to have a very long holding period, it may not turn out that way - the oft-noted behavioural errors that cause premature selling and the life events that call for cashing out sooner may curtail the holding period.

The Sharpe ratio doesn't address the first problem since it assumes the past volatility will be repeated in future but it does the second I think.

2. Canadian Investor: It's true that countries can go into long declines leading to poor stock market returns. It's also true that countries can go into periods of high inflation which are devastating for real bond returns. Unless one can predict the future, the important question is what are the best guesses of expected returns and volatilities. I can't do much to help people who get scared and cash out their investments in their entirety, but life events rarely require a full cash-out. Most life events can be handled with a reserve of liquid assets (usually cash). Even bonds may be too volatile depending on a person's situation. The Sharpe ratio doesn't address this problem. The Sharpe ratio is indifferent to whether a portfolio is 100% stocks or 100% short-term government debt.