Now that we are dealing with near-zero, and in certain instances, negative short-term interest rates, is it worth retaining the highly cherished Sharpe Ratio as a tool of investment performance? Measuring and ranking the intersection of risk and reward is a foundational principle of investment management, first introduced by Noble Laureate William F. Sharpe back in 1966. Although the Sharpe Ratio is not without its critics, it remains a primary selection tool for both asset allocators and stock pickers alike. After all, the intuition behind the concept - that an investment should offer a return above a risk-free alternative, commensurate with its riskiness - is both highly intuitive and appealing. But what happens when there is no risk-free security with which to compare risky alternatives?
A security that offers 100% certainty of outcome, at least in nominal terms, is the standard definition of a risk-free asset. The assumption has always been that the traded risk-free asset, such as a T-bill, is strictly positive - meaning that the future value of the investment should exceed its present value. Well, that is no longer the case. Bloomberg, LP estimates there are $2.35 trillion of negative-yielding assets in global developed bond markets, mostly from Japan and Europe. Of course, the U.S. is not far behind, particularly now that some banks have started to charge larger depositors fees to warehouse their savings.
The short answer is yes, the Shape Ratio still offers utility and should be preserved, despite the lack of a true risk-free asset. The key to ensuring that the Sharpe Ratio works as intended is to ensure that the all the inputs are internally consistent. For example, a Sharpe Ratio can only be calculated ex-post, using historical data, or ex-ante, using forecasted parameters. Let's look at the formula in more detail:
S_{a = [}R_{a -} R_{f ]/}σ
where S_{a} is the Sharpe Ratio, R_{a} is the return on a risky asset, R_{f} is the return on the benchmark or risk-free asset, R_{a} - R_{f} is called the "excess return" and σ is the standard deviation of the excess return. It would be unwise to combine expectations or predictions of future returns on a risky asset with the historical levels of risk-free asset and variance to calculate a Sharpe Ratio. The problem is compounded when the differences between expected returns and historical returns are wide, or when current variance is at odds with expected future variance. Otherwise, it does not matter that the risk-free rate is zero or even negative, as long as all the inputs are derived from the same observation period, either historical or forecasted.
The more problematic concern with the Sharpe Ratio is that it is plainly not reflective of today's investing reality for most professional and institutional money managers tasked with providing retirement solutions for their clients and their families. That is because investing in risk-free securities, rather than in risky assets, is simply no longer a viable income-producing or wealth preservation strategy - one that will maintain purchasing power. Risk-free assets, such as T-bills and short-dated Treasury notes and bonds, are now almost exclusively used as liquidity management tools rather than as investment vehicles. That has not always been the case. Since 1960, the 1-year T-bill rate has averaged about 5%, peaking at over 13% in the early Volcker years, providing reasonable substitutes for stocks, even when accounting for inflation. The concept of an "excess return" has effectively been rendered useless for all but very few extremely conservative money managers. Why bother with the Sharpe Ratio when one of its key inputs, the risk-free rate, is not a realistic part of the investable universe?
Fortunately, investors already have an easy to use and understand ordinal ranking tool based upon risk-adjusted returns, without having to be troubled by the level of risk-free rates. It is called the Skew Score, and it is used by many of the big sell-side banks to rank asset classes and securities. The idea simply calls for investors to skew their return expectations based upon the likelihood of actual results occurring in the middle of the distribution, called the base return, or in the left-sided tail called the worst return, or in the right-hand tail called the best return. Rather than calculating an "excess return" over a risk-free asset, the Skew Score ranks a security's attractiveness based upon the likelihood and magnitude of three potential outcomes - the base, worst and best cases. The average of the three outcomes is risk-adjusted by dividing the result by the standard deviation. The result, similar to the Sharpe Ratio, is a risk-adjusted return metric, without any reference to the risk-free rate. Here is an example:
Parameter |
Weight |
SPY |
AGG |
Best Return |
25% |
32.31% |
7.90% |
Base Return |
50% |
9.42% |
4.54% |
Worst Return |
25% |
-36.81% |
-1.97% |
Weighted Average Return |
100% |
3.58% |
3.76% |
Standard Deviation |
100% |
15.87% |
3.39% |
Skew Score |
- |
.225 |
1.11 |
I used annual total return and standard deviation data for the SPDR S&P 500 Trust ETF (NYSEARCA:SPY) and the iShares Barclays Aggregate Bond Fund ETF (NYSEARCA:AGG) for the ten-year period ending 2014. The base return is the arithmetic average of each year's total return data. The best and worst returns are the highest and lowest annual return for each ETF during the ten-year period. The weights are a handy way to incorporate your expectations and risk preferences into the calculation. For example, I assigned the heaviest weight to the base case and assigned equal weights to the left and right tails, since not feeling fatidic, I do not have a strong view about future market outcomes right now. So I rely on what has happened instead of speculating on what may happen. More conservative investors may want to weight the worst case higher. Aggressive investors can assign an above-average weight to the best case.
Using a ten-year look-back period for our analysis, it seems that the broadly diversified bond ETF AGG out ranks its stock equivalent SPY by a long way. In fact, based on our analysis here, AGG dominates SPY by a factor of almost 5x (1.11/.22). It's easy to find why this is the case. The data includes 2008, when the S&P 500 suffered a 37% decline, meaning that our left-tailed skew is quite steep for SPY. Now, many investors may want to assume that 2008 was an anomaly and is not likely to be repeated. That's fine. You can use any period you like, or even use forecasted values, as long as the in and out of sample data reflects your views. It will make little sense to ignore 2008 if you believe the market can once again experience a severe decline during your investment horizon. Similarly, you can assume that today's low interest rates are an irregularity and will soon be reversed, leading to outsized losses in the bond markets.
If you followed this suggested methodology, you would have picked or overweighted AGG over SPY as your preferred investment vehicle. You would have left about 4% of return on the table, the difference between the base return of SPY and AGG, but you would have avoided the gut-wrenching SPY drawdown of 2008. However, on a risk-adjusted basis, the Skew Score clearly indicates AGG leads SPY. I bet there are plenty of investors that would have willingly given up the extra 4% return differential in exchange for relief from all the stress and aggregation of the 2008 crisis.
Obviously, the Skew Score, in my example, is using the past ten years of historical data, and tells us nothing about the next ten years. But it is a start. We have all learned that it is perilous to disregard extreme outcomes, whether big down moves or big up moves, when formulating expected returns. The Skew Score forces investors and money managers to explicitly incorporate a range of possible results, however unlikely, into their forecasts.
Lastly, I think the Skew Score has an important behavioral advantage over the more popular Sharpe Ratio. Under the Sharpe Ratio, most "excess returns" look great right now, since the risk-free rate is basically zero and volatility is well behaved. That may encourage investors to change their risk preferences in haste, and chase riskier returns. Look at it this way. Investors that were encouraged to participate in the commodity boom may have thought twice before investing when realizing that during the past five years, commodities were the near-top performing asset once (2010) and the absolute worst four times (2011, 2012, 2013 and 2014). Now that's some downside skew!
Disclosure: The author is long SPY, AGG.
The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.