bottom up and top down approach
07 Sep 2008
Apr
02
Price of risk (equity risk premium) - reader question
by David Harper, CFA, FRM, CIPM
I received this question about the equity risk premium (EPR) from a reader of an article I wrote for Investopedia.com on How to calculate the equity risk premium:
David, I would be interested in knowing what method of calculating equity risk premium you believe is better and why. Also, other than earnings based and dividend based, are there any other methods. Thanks, Paul
For my FRM candidate customers, please note the equity risk premium (EPR) is related to the following learning outcome (LO) in the 2008 FRM: Explain the price of risk, the quantity of risk (beta), and equilibrium theory.
The price of risk is the equity risk premium (ERP, where we treat equities as the same thing as the total market) and the quantity of risk is beta in the capital asset pricing model (CAPM). So, the EPR is the price of risk and it's the difference between the market (broad equity) return and a risk-less return.
You can measure ERP historically (flawed) or with forward-looking expectations
You can either measure ERP historically or build it with forward-looking expectations. About forward-looking procedures, as I wrote in the original article, there are demand-side models or supply-side models. A demand-side model starts with risk (e.g., volatility of equities) and tries to figure the return that investors collectively deserve for bearing the risk; it is consistent with referring to the ERP as the price of risk because it prices return as compensation for risk. Supply-side starts with profit-producing engines--public companies in the economy--and tries to figure out how much value they can create for shareholders; it comports with emphasizing the ERP as an excess return. So these are the three approaches, but I personally only find the supply-side approach persuasive:
- The historical approach measures actual return difference between equities and riskfree bonds. I find it ineffective, unless adjusted, for the reasons below.
- The forward: demand-side models take a risk metric (e.g., volatility of equities) and uses a risk function to estimate the ERP. That is, given a risk aversion function, it asks, what is the return expected for a given volatility? It seems like much academic work has been done in this vein but I find it unpersuasive as you need to specify an investor utility function that feels arbitrary.
- I like the forward: supply-side approach because it recognizes that investors' collective returns, over the long run, must be a function of (and limited by!) the flows generated by their owned assets.
Historical ERP estimates
Jeremy Siegel is known for his careful study of the historical ERP; see Stocks for the Long Run. I haven't read his updated view, but his long term data showed a 7% real returns for stocks; e.g., so if the long-term real risk-less yield is, say, 2%, you'd get something like a 5% ERP (7% real return for stocks - 2% real return for riskfree bonds = 5% ERP).
But I think the practice of extrapolating a long-run historical ERP (e.g., 1920- or 1960- to today) forward has been effectively disproved. My original article was informed by this excellent paper by Robert Arnott and Peter Bernstein. This is the best piece I've read on the topic. Arnott and Berstein show that historical data is infected by certain events that cannot repeat. They give three or four, but these two are compelling: first, the drop in real bond returns over the last 75 or so years was a unique one-time shock; second, more importantly, the rise in equity valuation multiples (in particular over the 1980 to 2000 bull) is unlikely to repeat.
Put another way, if you want to use a historical average (average real equity minus average real bond returns), you have to select the length of the period. Different periods get different results, unless maybe you go really long run. Then you have to make a clumsy argument for why that selected period will repeat going forward, at the same time you know that the ERP varies over time anyway! Measurement precision in historical data does not justify claims of accuracy projected into the future.
Forward: supply side approach
This approach is just like asking of a single stock, given an earnings base and growth prospects, what is my expected return? Except you ask the question of stocks collectively (the market).
1. Earnings yield
Maybe the easiest way to answer this question is with the earnings yield (E/P) which is the inverse of the P/E ratio. If a normalized P/E is 15x, then a normalized earnings yield is about 6.7% (1/15). I sort of like the simplicity of this and Siegel has said that it holds up remarkably well in the data. (A couple of technical notes: One, unlike the dividend yield approach below, you do not get to add a growth term to this. Growth is already implicit in the E/P. Second, technically if your replacement cost of capital is less than the market value of equity, your yield could be greater than this, but I would just drop this out.)
2. Better: dividend yield plus growth
But I think Arnott and Bernstein run the best procedure (attached again). They improve on earnings by using dividends, so you've got:
Real equity return = dividend yield + expected real dividend growth rate + valuation change (expansion in price/dividend multiple) + error
You also see the following similar formula often (where growth in earnings is used instead of growth in dividends)...
Real equity return = dividend yield + expected earnings growth rate + valuation change (expansion in price/dividend multiple) + error
...but I think the Arnott paper shows why the latter formula is inferior (although if the payout rate is constant, they should be the same)
The valuation change is the wildcard that arguable makes a range ERP more honest: how can you anticipate multiple expansion or contraction? The authors drop this term; if you don't, you have to justify why there ought to be multiple expansion (why equities are currently undervalued). That reduces to:
Real equity return = dividend yield + expected real dividend growth rate
So, this to me seems the most reasonable. It's concrete and conservative. Note Arnott is really instructive in estimating the growth rate: the dividend growth rate is less than economic growth because it shares growth with entrepreneurs and managers! Overall economic growth (e.g., GDP) is not shared lockstep by shareholders in existing enterprises. Current owners only participate in productivity growth. They are diluted in two ways. First, innovation dilutes them because new companies don't create value generally for public company owners. Second, managers dilute them with stock options and restricted stock (and equity-like cash incentives, for that matter). So you end up with an even more conservative estimate:
Real equity return = dividend yield + [expected GDP growth or per capita GDP growth - haircuts for dilution]
That's my choice. Of course, subtract the long-term riskless rate from this to get the ERP (I don't really know what folks are doing for this currently, is the TIPS yield good?). I hope that is helpful.
Comments
Thank you, Mr. Harper. Your 2 articles in Investopedia and this answer on reader question really helped me to write a course work on theme “Analysis of methods of calculating of risk premiums for heterogeneous risk portfolio”
Rafail Gabdullin
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