How to Sharpe-n Your ETF Selection Process

Reward vs risk, that is a universal, pervasive, constant and critical trade-off and comparison that we must make as investors. There is plenty of descriptive qualitative assessment of reward-risk factors and indeed that is useful but how can we get a quantitative assessment and put a number on it?

Enter William Sharpe, Nobel prize-winner for his work advancing investment theory, with the formula he created in 1966 called by others, not himself, the Sharpe ratio. Sharpe himself gave it a more explanatory name, the "reward-to-variability" ratio. The "rewards" part refers to returns, or performance, composed of price changes and dividends. The "variability" part refers to the familiar ups and downs of price, the volatility, which is the finance industry standard used to characterize the riskiness of securities like stocks and bonds and by extension to ETFs.

Things are not quite so simple and uniform in application!
Unfortunately, the excellent basic idea was found to be too worthwhile to leave alone in its original form. The academics, along with Sharpe himself, got busy expanding and perfecting it, as related in the Wikipedia Sharpe Ratio article, which contains a link to Sharpe's own expansion and generalization of the concept.

Depending on the formulation used, the Sharpe ratio may be calculated quite differently according to choice of benchmark, and may sometimes show a reward-risk variant called the Information Ratio (for those interested, a couple of good explanations of the difference are Clarifying the Information Ratio and Sharpe Ratio on Seeking Alpha and Adding Value in Fund Evaluations on Advisor Perspectives). Thus, we should not be too surprised that the actual values, often for the same time period, differ from source to source as we see below in our sample of some ETFs. None of the sources give enough detail on how the figures are calculated to know exactly what is going on so we have to take them as they are and use them as we can.

Delving into the details and the math can get very subtle. Let's simplify for us mere mortals. The bottom line - when comparing ETFs, higher Sharpe ratios are better. In other words, when returns in the numerator are divided by the risk/volatility in the denominator, the greater the ratio, the better. Higher returns with same risk gives a higher Sharpe Ratio, as does the same return with lower volatility. That makes intuitive sense.

Sources for Sharpe Ratios
Here are some websites that publish Sharpe Ratios for ETFs. The usual place for the Ratio is under the Risk tab.

• Yahoo Finance - covers both US and Canadian ETFs but only has data for latest 3-year and 5-year periods (if the ETF has existed that long) i.e. no 1-year figures
• Zecco - only US ETFs; time period not specified but looks like 3-years
• IndexUniverse - only US ETFs; only for 3-years
• BMO Investorline - US and Canadian ETFs for 1-year and 3-years; access under the ETF Compare tool; must be a BMOIL client to access;
• TD Waterhouse - US and Canadian ETFs for 1-year, 3-years, 5-years, 10-years; access under the ETFs Fund Comparison tool; must be a TDW client to access;
• Other online brokers possibly have this capability too - check under ETFs 

Example table
We looked up a sample of commodity and Canadian equity ETFs to come up with the following comparison table.

Ins and Outs of using the Sharpe Ratios

• Look for patterns of higher results across sources and time periods e.g. in green highlighting iShares S&P/TSX Canadian Dividend Aristocrats Index Fund Common Class (TSX: CDZ) does best by quite a lot in both 1- and 3-year periods. However, as a dividend fund is it truly in the same category as the others in the list which are either cap-weighted (symbols XIU and ZCN), fundamentally-weighted (CRQ) or low volatility (ZLB)? We tend to think so but others may not. Note also how the barely year-old ZLB has an even better Sharpe Ratio than CDZ over the 1-year period. Will that continue? The 1-year blue highlighted Ratio in the table suggests that might be the case though it is early days. For an interpretation on how these types of ETFs might perform, see Tomatoes and the Low Vol Effect at Research Affiliates. It's interesting that much of the difference in Sharpe Ratio amongst these funds arises because of lower volatility (standard deviation) in CDZ versus XIU and CRQ and even lower volatility in ZLB (see our previous post on Low Volatility ETFs for a discussion of their promise). 
• Sometimes the data may be wrong - we cannot be sure but the vast difference of Ratios for BLND and BCM in Zecco from others in the category looks too dissimilar to be true (yellow background cells). Neither ETF is three years old yet but the rest of the data looks like 3-year figures. Maybe Zecco has mixed time periods?
• Sharpe Ratio is not the be-all and end-all - Other factors enter the picture in comparing and picking the best ETFs, as we have always done with our postings e.g. the latest on Commodity ETFs. Asset allocation and correlation, fit within portfolio goals, along with other risk factors (inflation and currency, default, management cost and taxes, required rate of return) all should play a role in ETF selection.
• The future may not be like the past - Using data that goes back only three years or even five is not a long history that proves superiority conclusively. 

Bottom line: The Sharpe Ratio is another useful tool in the investor's arsenal. 

Disclaimer: this post is my opinion only and should not be construed as investment advice. Readers should be aware that the above comparisons are not an investment recommendation. They rest on other sources, whose accuracy is not guaranteed and the article may not interpret such results correctly. Do your homework before making any decisions and consider consulting a professional advisor.