Market Timing Part 5: Equity Risk Premium Model

As we continue to roll out our market timing indicators, we have so far discussed four that we consider particularly useful for gauging long-term market trends.

Recall that we are not looking to time market inflection points perfectly; we are looking for near market entry and exit points. The first indicator released was our Triple Crossover Moving Average Model. The second indicator released was the well known Fed Model. The third and fourth models released were Graham's Classic and Modern Central Value Models. And this week we are going to release the Equity Risk Premium Model.

Methodology

The equity risk premium represents the additional return that investors require for holding stocks compared to long-term government bonds. The importance of the equity risk premium is that most analysts incorporate an estimate of it in their valuation models and in determining their required returns. When viewed in an American context, it reflects the investor’s expected excess return on the Standard & Poor's 500 against 10-year federal government bonds. When viewed in a Canadian context, it reflects the investor's expected excess return on the S&P/TSX against 10-year federal government bonds.

Estimating equity risk premiums can be a difficult task and differences in estimates frequently explain differences in market valuations. In practice, the most common method of estimating the equity risk premium is to calculate the average historical difference between the mean annual return on the S&P 500 (S&P/TSX) and the mean yield on 10-year government bonds. This method is favored by analysts principally because it is grounded in hard, verifiable data that allows them to form more objective expectations. Utilizing this method, however, does require that the analysts believe that excess returns are fairly stationary and that, on average, while excess returns may from time to time expand or contract, over the long term they will revert back to the mean.

The primary decision an analyst must make in using historical equity risk premium is whether the premium should be calculated as a geometric mean or an arithmetic mean. The geometric mean equals the compound annual excess return over the evaluation period. The arithmetic mean equals the sum of return differences divided by the number of years in the evaluation period. It is generally agreed that, in forecasting the premium one year ahead, an arithmetic mean is preferable. In forecasting the return over a longer time span, the geometric mean is preferable.

The results discussed here reflect historical return data on the indexes (excluding dividends) over the 1995-2015 period as well as average annual bond yields.

U.S. S&P 500 findings

Table 1: S&P 500 Return Properties 1995 to 2015

Figure 1: Box Whisker Plot Comparison

Table 2: Equity Risk Premium

Interpretation

Based on the historical record, we can draw the following conclusions: The historical arithmetic equity risk premium ranged from a low of -59% to a high of 39% with an average of 2.6%. The historical geometric equity risk premium averaged 1.5%. Note that these calculations exclude the impact of dividends. The average dividend yield on the S&P 500 averaged about 2.1% over the last 10 years. Assuming dividends remain at current levels, the size of the geometric and arithmetic equity risk premiums grow to about 3.6% and 4.7%.

Market timing rule

We do not generally rely on equity risk premiums to time the market directly. However, we sometimes track the historical S&P 500 return series in isolation to identify contrarian entry points. The statistical rule followed involves entering the market after a fall of at least one standard deviation below the historical mean return, with the best entry points in periods after a 2 or 3 standard deviation drop in returns. This indicator has not recently flagged any meaningful entry points in the U.S. market.

Figure 2: Return Series and 1 Standard Deviation Valuation Bands

Canadian S&P/TSX Findings

Table 3: S&P/TSX Return Properties

Figure 3: Box Whisker Plot Comparison

Table 4: Equity Risk Premium

Interpretation

Based on the historical record, we can draw the following conclusions: the historical arithmetic equity risk premium ranged from a low of -38% to a high of 27% with an average of 2.8%. The historical geometric equity risk premium averaged 1.4%. Note that these calculations exclude the impact of dividends. The average dividend yield on the S&P/TSX averaged about 2.3% over the evaluation period. Assuming dividends remain at current levels, the size of the geometric and arithmetic equity risk premiums grow to about 3.7% and 5.1%.

Market timing rule

We do not generally rely on equity risk premiums to time the market directly. However, we sometimes track the historical S&P/TSX return series in isolation to identify contrarian entry points. The statistical rule followed involves entering the market after a fall of at least one standard deviation below the historical mean return, with the best entry points in periods after a 2 or 3 standard deviation drop in returns. This indicator is currently signaling "entry" into the Canadian market.

Stay tuned

So far we have discussed five market timing indicators that we find particularly useful for gauging long-term market trends. We will build on this discussion further next week when we discuss the Shiller P/E model. Crossover points in this model have provided early warning signals of almost every major recession in the last 30 years.