The Equity Risk Premium [Note to Self]

Readers: You can skip this one. I’m just jotting down some stuff related to the equity risk premium, though there may be something of interest for those interested in stocks and finance. But it’s written in a hurry.

In case you decide to read, here’s some quick background: The risk premium is the cornerstone of CAPM and thus of traditional valuation. They teach this in business school. (Warren Buffet thinks it’s kind of a joke.) It is also very confusing. (It’s actually very simple until you think about it. Then it gets confusing. Thus, the ongoing body of academic and industry research into the topic.) To get present (fair) value, you discount your forecast cash flows by the sum of the risk free rate plus the risk premium. Projects will have a life, so that’s like an annuity. A company’s cash flow forecasts can go in perpetuity or plug in a terminal value – you can see how silly this gets right away.

I think it was triggered by Janet Yellen’s confirmation testimony where she mentioned the high equity risk premium as the reason she doesn’t fear bubbly stock prices. Somehow I came across this paper (via Ritholtz) from some Fed researchers that demonstrated that a) the equity risk premium in early 2013 was historically high (which is favorable for stock returns) and that b) though it is really difficult to beat a simple “past is prologue –> use past equity premium average”, some of the risk premium models could add some bps to portfolio performance. (Of course this would be, ahem, before fees.)  Even then they point out that they did not share wide error bands with the readers and there could be survivorship bias in their method.

I also wondered if just about any post-WWII simple system that relied on any simple metric that hit extremes in 1973-1974, 1982, and 1999 wouldn’t do better than using a flat historical average in portfolio construction. In other words, perhaps all of those excess (sub-100) bps came from getting people overweight equities in 1974 and 1982 and underweight in 1999. That’s not a high hurdle.

But the thing that jumped out was their historical range of equity risk premium in the 1 – 5% range. That sounded low. And thus down the rabbit hole. Brealey and Myers, 1996, gives 8.4% nominal (over T-Bills), arithmetic. They also describe why to use arithmetic for projects instead of compound. Even then they were a little non-committal.

And then I came across this guy P Fernández. Man is this guy into the equity risk premium. He is Mr. Meta Research here and here. He shows a number of things. The most important are that a) there are different “equity risk premiums” – historical, expected, required, and implied and b) estimates vary widely as do which “flavor” is discussed in the literature. It goes from low double digits to low single digits. (Of course we can rely on the Siegel reference to be on the low end – at 2-3%.) More reason it just seems kind of useless and confusing even if conceptually it has some value. No wonder Buffet never embraced it.

Also, Aswath Damodaranð from Stern School of Business writes extensively on the subject.

Hussman does a take-down here and elsewhere (especially killing the “Fed Model” as a tool for prospective returns).

For one thing the “risk premium” should be against securities with similar duration to stocks, not the T-Bill.

Look, if I take the Fed paper’s risk premium of about 5% and add 0% for risk-free, I get 5%. That’s below lots of long-ish term earnings growth forecasts. If you set earnings growth at 5% then the perpetuity equation goes undefined (positive infinity style). Ditto for the growing annuity formula, but you at least I can re-derive as closed form when r=g to get PV = N*C/(1+r), where C = year one cash flow. Let’s say the average lifetime of an S&P500 stock is 50 years (with terminal value zero) and today’s profits at around $100. I’d get a fair value of 4,760. But I can come up with anything by tweaking things just a little. It’s nuts.


In his March 2013 memo Howard Marks of Oaktree Capital does an esoteric take down and build up of the equity risk premium (as in the full “it depends on what you mean by ‘is'” treatment) and goes ad hoc at the end to suggest that equity returns for the next few years might well exceed expectations of 6% annually – as of this writing, Nov. 18, 2013, he’s looking pretty wise with his experience+ad hoc model forecast. See and find it under 2013 “The Outlook for Equities”

The  Economist cites a paper that shows expected equity returns are weak, around 3%. Key take-away “If the ex ante ERP is so unstable, it provides no useful information for asset allocators, in his view.” Amen.

But secular stagnation / long term financial repression certainly adds a twist. This is because the thesis means a very extended period during which real interest rates must be held below zero to generate sufficient real growth and positive inflation. If we are in a long term regime of zero nominal rates and they get 2% growth and bump up to 3% inflation it seems like it would be highly supportive of stock prices (with added volatility). But the U.S. had a long period of financial repression after WWII and I don’t think (haven’t checked specifically for this post) that valuations were elevated or that returns were exceptional.

Larry Summers’ recent speech.

Krugman on Summers’ speech:

More on a higher inflation target from the Economist here and here.

This latter stuff is a separate topic really, but it nags on me w.r.t. stock valuation…

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