What the equity risk premium is not...

Today's Financial Times had an article titled "What the equity risk premium tells us today" authored by Jason Voss of the CFA Institute.  I had high hopes for the article, but unfortunately it makes two fundamental errors.

1. The article defines the equity risk premium as the difference between the earnings yield on stocks and the 10 year treasury yield.  The earnings yield on stocks is the inverse of the P/E ratio.  It is designated as E/P.

ERP = E/P - 10 year ytm

This is incorrect.  The equity risk premium is the amount by which investors expect the return on stocks to exceed the return on riskless bonds.  Roughly computed it would be the expected return on the S&P 500 less the treasury rate.  Edit: The formula as shown above is merely a very rough method of estimating the ERP.  It implicitly assumes stocks pay all excess cash as dividends, grow at a constant rate, don't require external financing, and exist in a world of zero or unchanging inflation.  For all practical purposes, this is a not a realistic method of estimating the ERP.  Far better methods exist.

To compute the equity risk premium one must try to extract the premium implied by the current level of a market index (such as the S&P 500).  I won't do it here because Aswath Damodaran does an excellent job of it each month on his site.  Aswath estimates the current premium to be about 5.20%.   We can also estimate what the realized risk premium is by looking at the past difference between stock returns and bond returns.  Depending on what time frame you look at, this number is about 6%.

So why is this article interested in the difference between E/P and the treasury rate?   Well what is really going on here is that Mr Voss is invoking the long discredited (and I thought dead and buried) "Fed Model".  (Note: despite the name, the Fed Model has nothing to do with the Fed).   The Fed Model argues that the earning yield on stocks should be about equal to the yield to maturity on bonds.  If E/P is greater than the YTM on bonds, then stocks are cheap.  If E/P is less than the ytm on bonds, then stocks are expensive.

This appears to be the argument that is being made in the article.  But let's be really clear here - despite its simplicity, the Fed Model makes no sense whatsoever and this represents the second mistake in the article.  The Fed Model is garbage for at least two reasons:

1. Stocks are real assets, bonds are nominal assets.  When inflation is high the ytm on bonds will be higher, but the E/P ratio for stocks should be unaffected because both the numerator and the denominator are measured in real dollars.  This means that the Fed Model is very easily distorted by inflation.  In fact the reason that it is positive now is precisely because inflation is so low.

2.  E/P is not a valid measure of return.  E/P is merely the accounting earnings over price - a number easily manipulated that doesn't reflect the true cash flow of the firm and certainly does not come close to measuring the return of a stock.

I've posted on the Fed Model before - its a flawed model because it compares apples to oranges.