Is this approach reasonable for calculating the expected US equity risk premium?

Schiller P/E10 is about 30. Earnings yield is the inverse, or E10/P, so 3.3%. But we then need to multiply by 1.075 to adjust for lag, so adjusted to 3.6%.

Longest TIPS is 30 years, and is presently yielding about 1% real.

Difference is 2.6%, which is the expected equity risk premium using long-TIPS as the baseline.

## Present US equity risk premium

### Re: Present US equity risk premium

I'm not an expert, but I was under the impression that the risk-free rate is based on short-term, guaranteed investments (i.e. short-term treasuries or insured CD's), which would be about 1.25% nominal.

### Re: Present US equity risk premium

Sammy,

It seems to me like one reasonable way to estimate future returns and then the equity risk premium, though

I’m still working through these concepts myself. There's probably some logical mistakes below.

Expected returns:

For a one page argument why we might accept earnings yield as a return estimate, see Appendix A to the “Appendix” here: https://www.aqr.com/library/aqr-publica ... et-classes

Another way to estimate future returns is to use the Gordon Model where expected return = starting dividend yield + expected earnings growth. Research Affiliates uses this here: http://www.researchaffiliates.com/Asset ... ities.aspx Click on an asset to see yield and growth.

AQR uses two methods.

First method, found near the top of p3 of the appendix, is to replace dividend yield with .5/CAPE, or half the earnings yield. (CAPE is adjusted for lag as in your post.) Historical payout ratio isn’t far from 50%, so it’s like using dividends and pretending the payout ratio didn't change. Assuming reinvested earnings make the same returns as the stock market, it shouldn’t matter if earnings go to dividends, buybacks, or investment.

This method can produce a very different prediction than your method, if 1/CAPE isn’t close to twice the earnings growth rate. I don’t know what to think about that.

I post AQR's second method here: viewtopic.php?t=220734#p3402185

Another possibility is a linear or nonlinear regression on historical 10 year returns vs starting CAPE. The prediction might look like r = a + b*CAPE. Unlike the other methods, I don't know of a good data source for this.

It seems to me like one reasonable way to estimate future returns and then the equity risk premium, though

I’m still working through these concepts myself. There's probably some logical mistakes below.

Expected returns:

If reinvested earnings can be expected to return as much as the stock market does then it shouldn’t matter if earnings are given to you as dividends or reinvested in the company. Either way, the earnings yield is your expected return. Similar for earnings used for reorgs like mergers. For earnings used for stock buybacks, you can simply sell the portion of shares bought back, so they are much like dividends. Changes in buyback rates might change the growth rate of earnings per share, but that’s a relatively small component of your formula.Sammy_M wrote:Schiller P/E10 is about 30. Earnings yield is the inverse, or E10/P, so 3.3%. But we then need to multiply by 1.075 to adjust for lag, so adjusted to 3.6%.

For a one page argument why we might accept earnings yield as a return estimate, see Appendix A to the “Appendix” here: https://www.aqr.com/library/aqr-publica ... et-classes

Another way to estimate future returns is to use the Gordon Model where expected return = starting dividend yield + expected earnings growth. Research Affiliates uses this here: http://www.researchaffiliates.com/Asset ... ities.aspx Click on an asset to see yield and growth.

AQR uses two methods.

First method, found near the top of p3 of the appendix, is to replace dividend yield with .5/CAPE, or half the earnings yield. (CAPE is adjusted for lag as in your post.) Historical payout ratio isn’t far from 50%, so it’s like using dividends and pretending the payout ratio didn't change. Assuming reinvested earnings make the same returns as the stock market, it shouldn’t matter if earnings go to dividends, buybacks, or investment.

This method can produce a very different prediction than your method, if 1/CAPE isn’t close to twice the earnings growth rate. I don’t know what to think about that.

I post AQR's second method here: viewtopic.php?t=220734#p3402185

Another possibility is a linear or nonlinear regression on historical 10 year returns vs starting CAPE. The prediction might look like r = a + b*CAPE. Unlike the other methods, I don't know of a good data source for this.

### Re: Present US equity risk premium

Not for Equity Risk Premium. The question it posses is this: What extra return do you need to invest in stocks instead of safe risk free investment. The time frame posed in this question is long term. We need to compare apples to apples. If stocks are a long term investment then we need to compare it to another long term investment. Every textbook or academic article I have seen uses the nominal 10 year Treasury.venkman wrote:I'm not an expert, but I was under the impression that the risk-free rate is based on short-term, guaranteed investments (i.e. short-term treasuries or insured CD's), which would be about 1.25% nominal.

### Re: Present US equity risk premium

In my opinion, the expected value of the equity risk premium should be the historical average risk premium for global stocks going back as long as reliable data is obtainable. Other methods of calculation are more market-timing, in my opinion. Note that I intentionally said "global" - one should look at equities as a global market.

The caveat is that there is a high standard deviation to the average premium. That is the issue with "expected values" - they don't show how likely it is to be far below the average. Generally, one prepares for the chance of these scenarios by having exposure to non-equity (i.e. bond) markets. Long duration bond holdings may allow for interest rate risk (and credit risk in corporates) to contribute meaningfully to total return while not wagering the entire portfolio on the equity risk premium. (Of course, short-term bonds and cash are also needed for safety).

The risk premium must be a premium over "something". Consider use of a reasonable, global risk-free rate, such as an average of the LIBOR and the Federal funds rate.

The caveat is that there is a high standard deviation to the average premium. That is the issue with "expected values" - they don't show how likely it is to be far below the average. Generally, one prepares for the chance of these scenarios by having exposure to non-equity (i.e. bond) markets. Long duration bond holdings may allow for interest rate risk (and credit risk in corporates) to contribute meaningfully to total return while not wagering the entire portfolio on the equity risk premium. (Of course, short-term bonds and cash are also needed for safety).

The risk premium must be a premium over "something". Consider use of a reasonable, global risk-free rate, such as an average of the LIBOR and the Federal funds rate.