## Summary

- The S&P 500 index level contains important information about investors' required risk adjusted returns.
- Today's implied risk adjusted return expectation may be low, but that doesn't make it wrong.
- Investors can easily construct their own required risk adjusted return benchmark.

Is the widely followed S&P 500 equity index -- tradeable via the SPDR S&P 500 ETF Trust (NYSEARCA:SPY) -- wildly overvalued at its current price of 2,000? Well, that depends upon your assumptions about earnings and dividend growth and your risk adjusted required rate of return.

Let's look at the values of the implied parameters based upon the current level of the S&P 500. The index currently sports a 2% dividend yield which is directly observable. That means an investor will collect approximately 40 index points per annum by holding the index (2,000 *.02). The long-term average of dividend growth at S&P component companies is 5%, which is also directly observable. The implication is that investors must have an approximate expected risk adjusted required rate of 7% to justify an index value of 2,000. The math is simple: 2,000 = 40/(x-.05). Solving for x yields 7%. That is the implied risk-adjusted required return that the average investor hopes to earn by holding a long position in the S&P 500 index.

If you think that the expectation of 7% risk-adjusted return is reasonable to bear equity risk, then you should be comfortable with the current valuation. However, the valuation appears stretched unless you trust that the dividend yield or growth rate of dividends will increase, or you are willing to lower your required rate of return.

Is seven percent a reasonable expectation of risk-adjusted returns to bear equity risk? Frankly, it seems low based upon historical experience. To estimate a fair risk adjusted required rate of return, we need to turn to the Capital Asset Pricing Model or CAPM. Here again, your assessment of a sensible required rate of return is based upon the values of two parameter estimations: the long-term average of risk-free rate and estimation of the equity risk premium. We assume Beta is one since we are examining a very broad and diversified index.

Estimating the long-term average of the risk-free rate is straight forward. Simply take the ten-year average rate of the 10y nominal U.S. Treasury. That's about 3%. Now add an estimate of the equity risk premium to the risk-free rate, and you have a sound approximation of a fair required rate of return. Longer term estimates of the equity risk premium vary widely, but many academics have settled on a range between 5% -7%. So let's call it 6% - which gives us a required rate of return of 9% (3%+6%). That's higher than the current implied risk adjusted required rate of return (7%) derived from today's S&P 500 price.

Let's say that you believe that the required rate of return of 7% is not enough compensation to bear equity risk and that 9% is a more justifiable expectation. You would then conclude the S&P 500 is overvalued by about 50%! Again the math is modest: p = (40/ (.09-.05)), solving for p produces an index level of 1,000. That's a full 1,000 points lower from today's price.

The above analysis is obviously highly stylized and simplified. We use it to support the essence of our thesis that investors should estimate their required rates of return or, at a minimum, at least be mindful of the market's implied rate of return. A practitioner's main criticism with this approach is that both the ERP and the CAPM required rate of return tend to use backward-looking historical data. Many will argue, rightly in our view that in a world of quantitative easing, manipulated yield curves and implied state support of many industries such as banking that the past is a poor reflection of what may lie ahead. Nonetheless, investors may find it useful to benchmark their expectations of a fair required rate of return versus others and that which is implied in current pricing

The table above, complements of Duff and Phelps, indicates their estimate of the current required rate of return should be 9% (5% +4%), the same as ours although the values of our parameters differ from theirs. Notice that Duff and Phelps use a normalized 20y UST rate as their proxy for the risk-free rate. The current 20y yield is closer to 2.90%. So you can certainly craft your estimate of the required rate of return based upon parameter values you are most comfortable using.

Conclusion

The S&P 500 is neither overvalued nor undervalued at its current price. The price simply reflects consensus expectations about forward earnings and dividends growth, multiples, interest rates and a fair required rate of return. All these variables are either directly observable or have easy to use empirical based models for parameter estimation. Investors can and should evaluate their expectations against others and market implied realities. Consensus expectations and your own can be too high or too low. They can be overly optimistic or unduly pessimistic- but the price of the S&P 500 is right.