S&P 500 10-Yr Expected Equity Risk Premium

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docneil88
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S&P 500 10-Yr Expected Equity Risk Premium

Post by docneil88 » Mon Mar 10, 2014 4:57 pm

Calculating S&P 500 10-Yr Expected Annualized Equity Risk Premium (ERP) over 10-Year US Treasury Bonds

Four Key Premises:

(1) The expected S&P 500 ERP over 10-Year Treasury Bonds is more important and relevant to a long-term investor than the expected ERP over 3-Month T-Bills.

(2) Because earnings are so volatile and cyclical from year to year, PE10 is more important and relevant to long-term investors than PE1 or any PE based on expected earnings. (Definition of PE10 from Wikipedia: "The cyclically adjusted price-to-earnings ratio, commonly known as CAPE or Shiller P/E, is a valuation measure usually applied to broad equity markets. It is defined as price divided by the average of ten years of earnings (Moving average), adjusted for inflation.")

(3)
UPenn Professor Jeremy Siegel wrote:...the earnings of a firm is based on real assets whose value will, over time, increase with the rate of inflation. Therefore the earnings yield is a real yield.

The historical data confirm this contention. In the United States, data of corporate profits go back to 1870 and the average P-E ratio during that period [from 1870 to April 2007] has been 14.4, leading to an average earnings yield of 6.9%. This is one-tenth percentage point above the average real return on equities, which is 6.8% over the period. [Source: https://web.archive.org/web/20080123071 ... vest/30733 ]
(4) Real yield on 10-year TIPS = Expected real yield on 10-year treasury bonds = Expected annualized real return on 10-year treasury bonds

The Variables:

(A) Expected annualized real return on the S&P 500 (including dividends) over the next 10 years = Expected yearly earnings yield on S&P 500 = Inverse of PE10 = 3.9% currently (source: http://www.multpl.com/shiller-pe/ ).

(B) Real yield on 10-year TIPS = Expected annualized real return on 10-year treasury bonds = 0.6% currently (source: http://www.bloomberg.com/markets/rates- ... -bonds/us/ ).

The Calculation:

(A) - (B) = 3.3% = S&P 500 10-Yr Expected Annualized ERP over 10-Year Treasury Bonds.

Historical Perspective:

From 1928-2013 the annualized ERP for the S&P500 vs. 10-year treasury bonds has been 4.62%, whereas from 1962-2013 the annualized ERP for the S&P500 vs. 10-year treasury bonds was 3.33% (source: http://pages.stern.nyu.edu/~adamodar/Ne ... stret.html ). Best, Neil

berntson
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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by berntson » Mon Mar 10, 2014 5:23 pm

This is a common observation, but the point of using something like PE10 is to smooth out economic cycles. It is unclear that the recent economic crisis was just part of the "cycle" in the relevant sense, so unclear how reliable PE10 is in such circumstances. My own preferred way for thinking about things is to use PE10 and PE1 to establish a range. In this case, the range is relatively narrow, giving us a 3.9% to 5% annualized equity premium. This compares to an average historic real equity premium of 5.9%.

But ultimately, I think it is not helpful for investors to think about returns in this sense. The important thing is what John Bogle calls fundamental returns, a shareholder's cut of the value that companies are actually adding to the economy. On top of this, there is speculative gain and speculative loss (roughly, gains or losses in the pe ratio). There is no reason to think that fundamental returns will be lower going forward. The main observation is that investors are now paying more than usual for stocks, so it's more likely that they will pay less for stocks (on an earnings adjusted basis) in ten years than more. That seems right.

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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by docneil88 » Mon Mar 10, 2014 5:38 pm

berntson wrote:This is a common observation, but the point of using something like PE10 is to smooth out economic cycles. It is unclear that the recent economic crisis was just part of the "cycle" in the relevant sense, so unclear how reliable PE10 is in such circumstances. My own preferred way for thinking about things is to use PE10 and PE1 to establish a range. In this case, the range is relatively narrow: 3.9% to 5% annualized real returns, or a 3.3% to 4.4% real equity premium. This compares to an average historic real equity premium of 5.9%.
Hi Berntson, I am sympathetic to also considering PE1 to some degree. For simplicity, I didn't add it to the mix in my calculations above. What time period does the 5.9% "average historic real equity premium" apply to? Is that an ERP relative to 3-month US treasury bills or to 10-year US treasury bonds? If you can provide a source, please do so. By the way, "real" ERP and non-inflation-adjusted ERP will end up being the same number. Best, Neil

steve_14
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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by steve_14 » Mon Mar 10, 2014 7:01 pm

No better or worse than any other guess about the very much unknown future. I use 6.5% nominal as my annual expected return number.

manwithnoname
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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by manwithnoname » Tue Mar 11, 2014 5:25 pm

Just what is the purpose of the OP?

Will it tell me how much I will earn over the next 10 years?

If no why bother with it.


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docneil88
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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by docneil88 » Wed Mar 12, 2014 2:00 pm

Thanks billjohnson for that excellent link. Here's a key chart from from the article (Shiller PE = PE10):
Image

Hi manwithnoname, One purpose of my post was to compare the current expected ERP (Equity Risk Pemium) with historical ERPs in order to gauge the relative attractiveness of S&P 500 equities vs. the 10 year treasury bond. As is often the case, the conclusion depends on which historical time period one thinks is most relevant; see my original post above.

As for expected annualized total return of S&P 500 over the next ten years, one method to figure that would be to take the current inverse of PE10 (3.8%) and add it to projected inflation. One way to project inflation is to take the 10-yr treasury bond yield and subtract the 10-year TIPS real yield: 2.72 - 0.52 = 2.2. So, 3.8 +2.2 = 6.0% expected annualized total return from the S&P 500 over the next 10 years.

Unfortunately, if one uses the Cliff Asness chart above, the current PE10 of over 25 indicates an average annualized real return on the S&P 500 of only 0.5% over the next 10 years. Add that to expected inflation of 2.2% and you get 2.7% expected annualized total return on the S&P 500 over the next 10 years. Best, Neil

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Re: S&P 500 10-Yr Expected Equity Risk Premium

Post by swaption » Wed Mar 12, 2014 4:24 pm

The purpose of using E10 is to normalize earnings. So let's assume that E1 was already normal, and that all of the prior 9 years were normal as well. In such a circumstance, theoretically there would be no problem using E1. So consider how in such a scenario the normal E1 would differ significantly from the E10. When you understand that, then you will understand why E10 is not appropriate for your calculation.

All of the above is true regardless of whether or not one drinks the PE10 kool aid (which I don't). Adding those considerations would only make it more wrong :happy

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