Last week we started our discussion of nine market timing indicators which, in our experience, provide the most effective and reliable signals of long-term trends.
Before continuing the discussion, it is important to emphasize that we do not advocate market timing in individual stock positions. These indicators are best used to time the market and can be executed through the use of exchange traded funds (ETFs) and, in particular, those that track the Standard & Poor's 500 and the S&P/TSX.
The first indicator discussed last week was our Triple Crossover Moving Average Model. This model (or system) is designed to give a read on the total amount of short-term and long-term momentum in the stock market. It can help investors see changes in the market and take action early on the upside/downside. The key to this system is that it requires persistent and pervasive movements in stock prices and trend lines to signal inflection points in the market and is meant to filter out day-to-day noise and focus only on the signals.
This week we're discussing the results of the "Fed Model."
Methodology
The Fed Model looks at the difference between the S&P 500 (and S&P/TSX) earnings yield and the 10-year government bond yield and assumes that investors will be indifferent between investing in equities and bonds when the difference between the two yields is zero.
Note that we do not use the Fed Model as a market timing indicator in the traditional sense. That is, we do not use it to measure in absolute terms whether bonds or equities are under or overvalued. We calibrate it to establish target weights for an “average risk” passive investor’s portfolio holdings when equities are outperforming or underperforming bonds. The model suggests that an "average risk" investor should hold a greater proportion of equities when the difference between the two yields is positive.
Similarly, an "average risk" investor should hold a larger proportion of bonds when the difference between the two yields is negative. A 50-50 split could be targeted in an increasing, decreasing or oscillating equity market if equities remain fairly valued on a relative-to-bonds basis.
Below we present Fed Model results for both the American and Canadian markets to determine recommended bond-equity allocations.
U.S. (S&P 500 findings)
As can be seen in the figure below, the S&P 500 is yielding 4.5% vs. 1.7% for long-term government bonds. Calibrated to the Fed Model, this calls for a portfolio equity allocation of 64% and a bond allocation of 36%. Based on these recommended allocations, equities are expected to clearly outperform bonds in the coming years.
Figure 1: Recommended Bond/Equity Allocation, January 1980 to April 2016
Table 1: Earnings Yield (EY), 10-Yr Bond Yield (TBY), Equity Allocation, Bond Allocation for Jan 1980 to April 2016
| Summary Statistics | %EY | %TBY | Equity | Bond |
| Mean | 5.9 | 6.4 | 47.5 | 52.5 |
| Variance | 6.6 | 10.6 | 118.5 | 118.5 |
| Std. Dev. | 2.6 | 3.3 | 10.9 | 10.9 |
| Skewness | 1.1 | 0.7 | 0.8 | -0.8 |
| Kurtosis | 4.3 | 2.8 | 2.8 | 2.8 |
| Median | 5.4 | 5.8 | 44.3 | 55.7 |
| Mean Abs. Dev. | 1.9 | 2.6 | 8.9 | 8.9 |
| Mode | 5.3 | 6.0 | 53.1 | 46.9 |
| Minimum | 0.8 | 1.5 | 26.7 | 22.6 |
| Maximum | 14.7 | 15.8 | 77.4 | 73.3 |
| Range | 13.9 | 14.3 | 50.7 | 50.7 |
| Count | 426 | 426 | 426 | 426 |
| Sum | 2522 | 2733 | 20243 | 22357 |
| 1st Quartile | 4.4 | 4.0 | 39.6 | 45.7 |
| 3rd Quartile | 6.7 | 8.3 | 54.3 | 60.4 |
| Interquartile Range | 2.3 | 4.3 | 14.7 | 14.7 |
Canada (S&P/TSX)
As can be seen in the figure below, the condition in Canada is slightly different than that in the U.S. The S&P/TSX is currently yielding 2.9% vs. 1.2% for long-term government bonds. Calibrated to the Fed Model, this calls for a portfolio equity allocation of 59% and a bond allocation of 41%. Similar to the U.S., based on these recommended allocations, equities are expected to outperform bonds in the coming years.
Figure 1: Recommended Bond/Equity Allocation, June 1980 to February 2016
Table 2: Earnings Yield (EY), 10-Year Bond Yield (TBY), Equity Allocation, Bond Allocation for June 1982 to February 2016
| Summary Statistics | %EY | %BY | Equity | Bond |
| Mean | 5.0 | 6.4 | 42.6 | 57.4 |
| Variance | 3.8 | 10.5 | 275.9 | 275.9 |
| Std. Dev. | 1.9 | 3.2 | 16.6 | 16.6 |
| Skewness | 0.2 | 0.4 | 0.0 | 0.0 |
| Kurtosis | 3.4 | 2.3 | 2.2 | 2.2 |
| Median | 5.0 | 5.7 | 42.4 | 57.6 |
| Mean Abs. Dev. | 1.5 | 2.8 | 13.6 | 13.6 |
| Mode | 3.8 | 2.0 | 42.4 | 57.6 |
| Minimum | 0.4 | 1.2 | 8.7 | 16.5 |
| Maximum | 12.7 | 16.4 | 83.5 | 91.3 |
| Range | 12.3 | 15.2 | 74.8 | 74.8 |
| Count | 405 | 405 | 405 | 405 |
| Sum | 2006 | 2602 | 17271 | 23229 |
| 1st Quartile | 3.7 | 3.9 | 31.4 | 43.9 |
| 3rd Quartile | 6.2 | 9.2 | 56.1 | 68.6 |
| Interquartile Range | 2.4 | 5.2 | 24.7 | 24.7 |
Conclusion
For an “average risk” passive investor, we recommend dividing your investment money between both bond and equity funds (or ETFs). Justification for increasing (decreasing) the proportion of funds allocated to equities depends on whether the equity market is under or overvalued on a "relative-to-bonds basis." As a general rule of thumb, it is suggested that investors divide their holdings equally 50-50 between the two asset classes when equity markets are relatively fairly valued. In this article, to answer the question of whether the markets are relatively fairly valued, we used a variation of the "Fed Model." For both the Canadian and American markets, model results point to the expected outperformance of the equity markets and recommend a portfolio allocation of approximately 60% equities and 40% bonds.
