We all know risk and return go hand in hand. If you want higher returns, you must invest in riskier assets. This is a fundamental concept underlying capital markets, but it is valuable to look at how this idea is actually manifested in real assets—real funds, for example, including the impacts of fees. There are plenty of theoretical treatments that look at assets broken down into style classes such as bonds, large-cap domestic stocks, small-cap domestic stocks, emerging market stocks, etc. The classic relationship between standard deviation in return and average return is evident for these broad indices over long periods of time—see for example these notes by Campbell Harvey at Duke.

While these studies show us that very broad ‘style’ classes of assets over very long periods of time (typically several decades or longer) tend to yield a nice relationship between risk and return, it is of considerable interest to know how well these relationships hold up over shorter periods of time. Do you need to wait a decade before you can expect to see risk and return balance out? Longer? For shorter periods of time (several years), we know that the risk-return balance for individual assets is not stable at all. Some asset classes tend to out-perform relative to risk and some under-perform and these effects tend not to stabilize for shorter periods. In recent years, international funds, value funds, and energy funds have generated very high returns compared to their risk levels (i.e. volatility) while technology, growth, and healthcare have under-performed relative to their respective risk levels. For shorter periods of time, the key is to look at aggregate performance statistics as a function of risk to see if the market is consistently balancing risk and return. Are risk and return reasonably balanced over shorter time horizons? Another interesting question is whether you need to consider the ‘style’ of a fund to assess its risk and potential future return or can you just look at market statistics such as average return, Beta, and standard deviation in return?

**In this article, I take a look at the risk-return balance for the entire group of iShares Exchange Traded Funds [ETFs] that have been in existence for three years or more**. Rather than grouping these ETFs by ‘style’, I have simply sorted them into quartiles based on standard deviation in return or Beta. There are seventy four iShares ETFs with at least three years of market data, and these cover a wide range of styles (below).

*iShares ETFs with three or more years of market data*

Across this family of funds, many different ‘style classes’ are represented. **How can we best compare the balance of risk and return among these?** Many investors will look at Beta as a measure of risk, but the more fundamental measure of risk is standard deviation in returns. There is typically a very high correlation between Beta and standard deviation, but they are not the same thing—as analysis will show.

Taking three years of data, the simplest way (for non-statisticians) to examine the relationship of risk and return is to sort these funds into groups, based upon risk. I have created four classes in which the funds have been ranked by standard deviation in returns [SD]. Class A is the highest risk group, based on the most recent three years of data. Class B is the second riskiest group, etc. Simply by creating these rankings—with 18 funds in the two extreme groups (Class A and Class D) and 19 funds in the two middle groups (Class B and Class C)—you can see that the average annual return in each group has a strong relationship to the standard deviation [SD] in return:

*Funds sorted by standard deviation in return. Group A is the quarter of funds with highest volatility, Group D is the quarter of funds with lowest volatility, etc.*The ETFs in Group A have historical standard deviations in annual return ranging from 16.6% to 30.3% per year. This is the high volatility group of funds. The average annual return over the past three years for these ETFs is 26% per year. The ETFs in Group D have historical standard deviations [SDs] ranging from 7.2% to 9.6% per year. The average annual return of the ETFs in this group has been 11% over the past three years. Clearly there is a strong relationship between standard deviation in return and average return for these ETFs. The quarter of funds with the highest volatility (as measured by SD) have generated average annual returns more than twice as high (actually 2.36x) as the quarter of funds with the lowest volatility over the past three years.

What does this chart show us? Over a time horizon as short as three years, you cannot expect that you will see a consistent relationship in risk and return (like the one for the 1926-1990 period in the Campbell Harvey’s article linked above) across all of these ETFs. Some asset classes are in fashion, while others are out of fashion. What the chart shows is that if you group asset classes together, you do get a nice consistent balance of risk and return. This result explains why Monte Carlo portfolio planning tools such as Quantext Portfolio Planner can work. The average return-to-risk that you get for any individual asset over multi-year periods may not converge to a nice balance, but when you combine a range of assets they will tend to converge to a ‘rational’ risk-return balance even for relatively short periods.

Switching tracks slightly, I have performed the same ranking analysis in terms of Beta rather than standard deviation in return. When we rank funds in terms of Beta, the relationship between average return and Beta is far weaker (below). It is important to note that there are many possible Betas that we can calculate. For consistency, all Betas calculated for this analysis are taken relative to the S&P500. The quarter of funds with the highest Betas (Group A*) generate an average annual return of 20%, whereas the quarter of funds with the lowest Betas (Group D*) generate an average annual return of 14%. The ratio of average returns between these two quartiles is 1.42—as compared to 2.36 when we rank funds by standard deviation in return. This relatively weak segregation of funds by Beta is not because there is a small range of Betas represented. The average Beta for a fund in Group D* is 85% while the average Beta for a fund in Group A* is 192%.

*Funds sorted by Beta: Group A* is the quarter of fund with highest Beta, Group D* is the quarter of fund with lowest Beta, etc.*So what does all of this mean in practical terms? Over the past three years, there is a high correspondence on average between the average rate of return and the standard deviation in return for a wide range of iShares ETFs—even though this is not the case for individual ETFs. The list of ETFs includes broad market index funds, growth and value funds, sector-specific funds, country-specific funds and market-cap-specific funds. Across this range, there is a very robust balance between average return and standard deviation in return. Some asset classes have out-performed over this period and some have under-performed. Technology stocks have tended to under-perform in terms of average return relative to risk (IGM, IGV, and IGW for example). International and emerging market funds have tended to out-perform (EEM, ILF, EWZ), as have energy funds such as IXC. The aggregate balance between risk and return across asset classes has been maintained, however.

From a theoretical standpoint, these results suggest that it is better to look at volatility in return (Standard Deviation in returns) rather than Beta as a measure of risk—certainly insofar as you want to identify higher risk / higher return investment opportunities. While the results that I have shown here are a small sample of the market in time, this idea is supported by research (*pdf*) that has indicated that an increasing fraction of the volatility in individual assets is specific to these assets rather than being driven by the market as a whole.

In other words, the component of risk measured by Beta appears to be diminishing in time. If this effect is real and persists, it would help to explain why standard deviation in return appears to be a better measure of risk than Beta—the component of risk represented by Beta is getting smaller with time as compared to non-Beta risk.

It is quite striking that there is such a consistent balance between risk and return once we aggregate ETFs by volatility—even though the risk/return balance of individuals ETFs are tremendously variable. An intriguing proposition from these results is that it may make sense to combine ETFs that have recently been out-performing relative to their risk levels with those that have been under-performing relative to their risk levels. In this way, one might a portfolio that converges to a consistent risk-return balance for your overall portfolio—even for relatively short periods of time.