In our US study, we divided the S&P 500 index into deciles based on each companies upside to model price. The first decile portfolio contained the 50 companies out of the 500 that had the greatest upside while the 10th decile contained the 50 companies with the least upside (greatest downside) to model price. The test period covered 9-years from December 31, 1994 to December 31, 2003, portfolios were re-balanced monthly and returns were capital gains only with no transaction or management fees assessed.

The average monthly returns for the deciles are shown in the bar chart below. As can be readily seen, returns fall in an almost uniform pattern from decile 1 to decile 10 indicating that portfolios with greater upside to model price outperform portfolios with less upside. Also included in the chart is the return for the S&P 500 index for this time period.

We also looked at the volatility of the portfolios to determine their risk. As seen on the chart below, the volatility (as measured by the standard deviation of monthly returns) follows a U-shaped pattern across the deciles with the top and bottom deciles being more volatile than the middle deciles. If the model price is a relevant measure of value, then this is what we would expect as the top and bottom portfolios, being the most mis-priced, would have the greatest volatility as the market brings their value back in line with the market. In fact, the middle deciles had volatility similar to the index, as were their returns, suggesting that those portfolios made up of companies with little upside or downside to their model price had return and volatility characteristics similar to the index. In other words these portfolios would seem to be properly priced.

The results provide evidence that being invested in the top decile portfolios led to greater returns than the overall index, but also showed that investors would have had to incur greater volatility. Were the greater returns enough to compensate investors for the greater volatility? One way to answer this is to measure the return per unit of risk (dividing the average return by its standard deviation). In the graph below we show this measure for the decile portfolios and the index.

The chart shows that the returns for the top decile portfolios were enough to compensate investors for the added volatility of the portfolios, as the return/risk ratio is greater than that of the S&P 500 index. Also the relationship has a general downward slope as we move across the deciles (although not uniformly so) as the bottom decile portfolios not only suffered from low returns, but also from greater volatility.