ERP: Forward-Looking Estimates
Historical estimates of equity risk premia are a useful guide and are not to be discarded. But face it; history doesn't always repeat itself. Future equity premia will be based on other future values.
How do you think this could be applied to a market equity premium estimate?
No.
A simple average wouldn't be useful, and it would be quite time consuming as well.
Not quite.
Just think about how this formulation could be applied to the broad market without any significant change in the equation.
Absolutely!
Since the Gordon growth model leads to
$$\displaystyle r_e = \frac{D_1}{V_0} + g $$
for an individual stock, the market equity risk premium can be estimated as next year's total dividends divided by the price of the market, plus the expected dividend growth rate, and then minus the risk-free rate.
For example, a market is priced at 100 with current year dividends of 3, growing at 4%. With a risk-free rate of 2%, the Gordon growth model would suggest an equity risk premium of
$$\displaystyle \frac{3(1 + 0.04)}{100} + 4\% - 2\% = 5.12\% $$.
Consider how this would be related to the price to earnings (P/E) ratio of the market. What would this estimate of 5.12% assume about the market P/E?
That's right!
No. It would need to be constant.
Prices grow as earnings grow, since that's part of the return. But total returns will only grow as fast as earnings unless there's some expansion in the P/E ratio. Analysts will often consider whether the market P/E is at the "right" level, as there can't be any upward or downward trend there in the long run. Any expected change in the P/E will affect this estimated equity risk premium.
All of this leads to a forward-looking ERP estimate by subtracting the risk-free rate from both sides:
$$\displaystyle \text{ERP} = E \left( \frac{D_1}{V_0} \right) + E(g) - r_f $$
Which of these might be estimated with a difference of nominal and real yields?
Right.
This is just another way of getting at expected inflation, just as some analyst adjustment for market overvaluation or undervaluation might be applied to the expected repricing.
Actually, no.
This is real economic growth, which is widely estimated based on real economic factors.
No, any change in share issuance would be estimated based on the market and time period; but this isn't directly related to real and nominal yields.
Finally, one last way you might come up with an estimate of an equity risk premium is by asking other people. In this case, the range of experts' consensus can be from 2.5% to 6.0%, and it can be comforting to not get too far from the pack on estimates like this. But don't always let that be your guide; recency bias and confirmation bias may be at work here. After all, history doesn't always repeat itself.
To sum up:
[[summary]]
One way to look forward in this estimation is to use the Gordon growth model. Recall the form of intrinsic value or price estimation for a security.
$$\displaystyle V_0 = \frac{D_1}{r_e - g} = \frac{\mbox{Next Year's Dividend}}{\mbox{Required Rate of Return} - \mbox{Expected Dividend Growth Rate}} $$
If you solve for the required rate of return, you'll find that it's the dividend yield plus the earnings growth rate.
Sometimes, a macroeconomic model can be kind of fun, too.
The equity risk premium was already decomposed into a dividend yield ($$DY$$) and expected growth. The __Grinold-Kroner model__ breaks down growth into expected repricing (changes in P/E ratios), plus expected inflation ($$i$$), real economic growth ($$g$$) and expected percentage change in shares outstanding ($$\Delta S$$) so that smaller pieces of this can be estimated separately.
$$\displaystyle \text{ERP} = [DY + \Delta (P/E) + i + g - \Delta S] - E(r_f) $$
Use an average of _r_ for all stocks in the index
Subtract risk-free bond coupons from total dividends, and divide by price
Use aggregate dividends and the index price, subtracting a risk-free rate
That it's constant
That it's growing at 4%
$$i$$
$$g$$
$$\Delta S$$
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