Sharpe Ratios on 2007 ETF Returns

Even the casual investor couldn't have missed this year's financial news focus on "Increased Volatility" and "Split Markets." Exchange Traded Funds (ETFs) provide us with an easy tool to take a deeper look into these headlines across both Sectors & Styles alike.

In this regard, the table below catalogues total returns and historic volatility across 14 Select Spider-Sectors and six PowerShares-Style category ETFs, as ranked by their respective Sharpe ratios:

As a brief reminder, William Sharpe's ratio is one of the simplest measures of the historic risk/reward characteristics of a security's return series, as follows: (Total Return - Risk Free Rate)/ Standard Deviation of Returns. Yes, there are fancier, better measures than this out there these days, but the table above tells our two stories quite nicely on its own; thank you very much!

Looking across the select ETF categories, the two headline saws become most apparent. First, volatility increased dramatically in almost every ETF category, in some cases nearly doubling between the first and second halves of the trading year.

Second and equally dramatic was the much ballyhooed split-nature of returns. Not surprisingly, Energy (XLE) and Metals (XME) led the pack here, with Financials (XLF) and Homebuilders (XHB) bringing up the proverbial caboose. Similarly, Large- & Mid-Cap Growth ETFs (PWB/PWJ) ranked the leader board throughout the year, with the Small- & Mid-Cap Value ETFs (PWY/PWP) generally taking it on the chin. In case the increased volatility wasn't a strong enough "tell" for you, split returns like these are not characteristic of a healthy bull market!

The scatter plot chart below takes our analysis up a notch, showing a slight inverse linear (albeit dispersive) relationship between positive total returns and relatively lower historic volatility:

Note: Volatility is shown reversed, highest to lowest.

The Metals & Miners (XME) complex located in the upper-left hand quadrant above was a bit of an outlier last year, posting both strong returns and relatively higher volatility.

As you develop your investment allocation plans for 2008, perhaps you will consider the persistence of these risk-reward characteristics through time, as well as the linear relationship between the two elements of Mr. Sharpe's equation.

Comments

[JFD]

Excellent analysis. What would the international ETF's look like?

[JFD]

Excellent analysis. Id be curious about how the international ETF's would look under the same analysis.

[Fred S]

The slope is meaningless for this small data set because the single XLM outlier exerts so much leverage. Drop that one point and the line has the opposite slope.

For this data the regression line is misleading noise that should either be omitted, or calculated with a more robust means that isn't subject to outlier distortions.

[Fred S]

The slope is meaningless for this small data set because the single XLM outlier exerts so much leverage. Drop that one point and the line has the opposite slope.

For this data the regression line is misleading noise that should either be omitted, or calculated with a more robust means that isn't subject to outlier distortions.

[[e-mail]]

Hi Fred, you comment on the slope of the data set is correct! However, I have performed the same analysis on a larger data set and found the same thing. So the shown regression result is indeed rubbish per se, but the point of the finding will hold to further scrutiny. Happy New Year, Gang!

[NO DooDahs]

When you say "annualized daily data" – what exactly do you mean? How many data points of return are evaluated for each ETF, and how many are used in the calculation of standard deviation?

I am GUESSING that you have 250-ish data points, each one being a return for the year period ending on each trading day of 2007, with the 3% RF being used for each point. Is that correct?

Persistence of the relationships is indeed the key.

Is your larger dataset also composed of industry (or other) ETFs? I would be curious about the relationship between return and volatility for the universe of exchange-traded stocks, but that would just be academic and not functional curiousity.

[NO DooDahs]

Interesting. I've never looked at Sharpe or Sortinos on sub-annual timeframes by taking annual return data for year-ending on each point. Is this an industry norm of some sort, or are you innovating here?

When I've looked at ratios on shorter timeframes, I've taken the returns and standard deviations on that timeframe (daily, weekly, monthly, whatever) and calculated the ratios on that data. Of course, when doing it that way, it doesn't translate to an annualized ratio and one has to be consistent in making sure that statistics are only compared to the proper timeframes.

Speaking of translating, what is the correlation between daily year-ending return data Sharpes and non-overlapping year-period Sharpes? It would be interesting to see if what you've done translates to the larger scale.

Perhaps when you're bored over the holidays, you could some of the longer-running sector ETFs with 7-year Sharpes done both ways:

* 7 data points of non-overlapping years

* 7 x 252 data points of year-ending daily returns

... and see if they're consistent with each other. Purely academic, because as discussed previously, I'm not a huge fan of the Sharpes, Sortinos, Alphas, Betas.

[Fred S]

The line is supposed to slope that way (greater risk - greater return), so I'm not surprised larger amounts of data would support it. These small data sets allow one to get whatever result is desired, which is very nice if you want to "prove" something. :-) Thanks for the clarification on larger data sets, and Happy New Year.