A common question we get from investors upon learning of the historical performance of the Barron’s 400 Index is “how risky is it?” Our typical answer is “what do you mean by risky?” To many, risk is defined as the uncertainty of achieving an expected return; to others it is not achieving a minimal return; and to others it is simply defined as losing money. While all of these are valid, they all vary widely based on each investor’s goals and expectations. Thus, the measurement of “risk” for any given instrument, in this case B400, should be clearly defined by the statistical measures used.
Standard deviation is often used by many as a measure of risk when, in fact, it’s a measure of dispersion. This simply refers to how returns (daily, monthly, annual) are dispersed around the mean, or average. B400, for example, has an annual standard deviation of 22.4% over the last 10 years, through November 30, 2013. This means that the annual returns used in calculating the mean over these 10 observations tend to be 22.4% off the mean, on average. Many would deem this as risky; we, instead, would prefer to say that based on its standard deviation, B400 is more volatile than comparable indexes. The Dow Jones Total Stock Market Index (B400’s benchmark), for example, has a 10-year annual standard deviation of 18.5%, yet over that stretch of time it has produced annual returns that are, on average, 4.6 percentage points lower, per year, than B400. Assessing an index simply based on standard deviation might unjustly penalize it, particularly if its volatility is skewed upward. In other words, if B400 tends to produce returns that are skewed to the upside, a high standard deviation is precisely what you should want it to have.
Here it is worthwhile exploring other statistical measures of return distributions such as skewness and kurtosis. We will do so in a separate newsletter as we continue to explore ways to measure B400’s performance.
Coefficient of Variation and Sharpe Ratio
Two more measure worth introducing here in our risk conversation are Coefficient of Variation (CV) and Sharpe Ratio. CV is a fancy way of labeling how much risk you’re getting (using standard deviation as a measure of risk) for every unit of return. It is calculated by simply dividing standard deviation by the mean. For example, also over the last 10 years through November 30, B400 has a CV of 1.83; in other words, 1.83 units of standard deviation for every unit of return. Too high you say? Its benchmark, DJUSTSM, which is also the broadest measure of the overall U.S. stock market, produced, over the same time period, 2.44 units of “risk” for every unit of return. The S&P 500 produced 2.69 units of “risk” per unit of return. Over a longer time period, since 2000, which encompasses the dot-com meltdown, the results are eye opening. The coefficient of variation for B400 over this time period was 1.82 compared to 4.64 for DJUSTSM and 5.72 for the S&P 500. Their average annual return of 4.3% and 3.3% compared to B400’s 12.0% no doubt explain this.
The Sharpe Ratio is pretty much the inverse of the coefficient variation and a staple in investment performance measurement but with a twist: it incorporates, wisely we would say, the so-called risk-free rate of return. Historically the U.S. T-bill has been used as a proxy for the risk-free rate but given today’s rock-bottom rates we’ll use the current yield on the 10-Year Treasury instead, or 2.85% as of last night. The Sharpe Ratio thus subtracts the risk-free rate from the instrument’s historical rate of return and divides the result by the period’s standard deviation. Going back to our 10-year example, we get a Sharpe Ratio of 0.44 for B400 compared to 0.28 and 0.23 for the Dow Jones U.S. Total Stock Market Index and the S&P 500 Index, respectively (since this is the inverse of CV, the higher the number, the better). Translated, this means that B400, as measured by the Sharpe Ratio, produced in the last 10 years 0.44 units or return per year in excess of the risk-free rate per unit of risk. DJUSTSM and SPX produced 0.28 and 0.23 units respectively.
Let’s Settle In the Middle
Conspiracy theorists might argue that part of B400’s returns in the last 10 years have been back-tested. Indeed, to clarify, all B400 data prior to August 2007, when Dow Jones Indexes took over the calculation of the index, is back-tested data (today B400 is calculated and disseminated by NYSE). Everything since is based on live, published data. Therefore, before we conclude today’s missive, we would like to summarize the index’s standard deviation, coefficient of variation and Sharpe Ratio using five-year figures.
During the last five years, again through November 30, 2013, the CV for B400 (or the amount of risk per unit of return) was 0.74 compared to 0.70 and 0.69 for DJUSTSM and SPX, respectively. Based on this, B400 doesn’t look so superior. When we look at the Sharpe Ratio, the numbers are almost identical, with 1.21 for both B400 and DJUSTSM and 1.22 for the S&P 500. It would seem, then, that over the last five years B400 has produced an identical amount of return in excess of the risk-free rate per unit of risk than these two benchmarks. Advantage gone, right? Well, why not think about it this way: If you have an index (B400) that produces virtually the same amount of risk per unit of return (see CV), but which outperforms, on average, over the last five years, what many consider the stock market’s benchmarks by 6.1 (DJUSTSM) and 7.2 (SPX) percentage points, respectively, which one would you prefer to follow?
Below we have included annual returns for the indexes mentioned in this newsletter as well as three, five and 10-year measures of mean returns, standard deviation, coefficient of variation and Sharpe Ratio.
Annual Returns (Price-Only)
| Year | B400 | DJUSTSM | S&P 500 |
| 2000 | 14.6 | -11.9 | -10.1 |
| 2001 | -1.8 | -12.1 | -13.0 |
| 2002 | -10.7 | -22.1 | -23.4 |
| 2003 | 43.8 | 29.4 | 26.4 |
| 2004 | 22.6 | 10.7 | 9.0 |
| 2005 | 11.0 | 4.6 | 3.0 |
| 2006 | 11.6 | 13.8 | 13.6 |
| 2007 | 5.1 | 3.8 | 3.5 |
| 2008 | -40.0 | -38.4 | -38.5 |
| 2009 | 39.1 | 25.7 | 23.5 |
| 2010 | 22.6 | 15.3 | 12.8 |
| 2011 | -0.4 | -0.9 | 0.0 |
| 2012 | 13.8 | 13.9 | 16.1 |
| 2013* | 37.2 | 27.7 | 27.8 |
*Through November 30, 2013
Returns Between 2000 and 2013
| Index | Mean Return | StdDev | Sharpe Ratio | CV |
| B400 | 12.0 | 21.9 | 0.42 | 1.82 |
| DJUSTSM | 4.3 | 19.7 | 0.07 | 4.64 |
| S&P 500 | 3.3 | 19.1 | 0.03 | 5.72 |
5-Year Returns
| Index | Mean Return | StdDev | Sharpe Ratio | CV |
| B400 | 22.5 | 16.5 | 1.21 | 0.74 |
| DJUSTSM | 16.4 | 11.4 | 1.21 | 0.70 |
| S&P 500 | 15.3 | 10.5 | 1.22 | 0.69 |
10-Year Returns
| Index | Mean Return | StdDev | Sharpe Ratio | CV |
| B400 | 12.3 | 22.4 | 0.44 | 1.83 |
| DJUSTSM | 7.6 | 18.5 | 0.28 | 2.44 |
| S&P 500 | 6.7 | 18.0 | 0.23 | 2.69 |
