Does the market equity risk premium have a term structure?

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Dear Reader, this is probably one of the oldest discussions out there but it is indeed a very interesting one. Should the Market Equity Risk premium have a term structure / be dynamic? I'd like to start out with two quotes:

Of all the potential problems in estimating implied cost of capital, the lack of constancy of the
discount rate is probably the most under-researched in the literature."

(Lambert, 2009, p. 2)

"In an environment that allows for time-varying discount rates, instead of a static implied cost
of equity, there is a term structure of implied costs of equity capital."

(Callen and Lyle, 2014, p. 9)

Nowadays a lot of static/ backward-looking methods (like the CAPM and its variations) are used to estimate the market equity risk by extrapolating long-term averages assuming that the future premium will revert to its historical mean. But are those averages actually a good predictor for a future risk premium? Should a backward-looking average include the 2008 crisis event? How far should we go back? If we go back too far to smoothen out the crisis, is this old data even relevant for today's risk premia? Should we use data post-2008 crisis or would our data suffer from an insufficient sample size? Is it appropriate to use only data from the US equity market which has been the most successful capital market worldwide? Do other equity markets have sufficient and reliable stock data?

I stumbled upon a quite creative approach by Callen and Lyle (2014) about the calculation of a term-structure of equity market risk. In this paper, they tried to estimate the term structure based on synthetic futures contracts using current put and call options.

That leads us back to the question: Should the Equity Market Risk Premium have a term structure? I look forward to your comments.

Comments (6)

Dec 25, 2019

I don't know about a term structure, but the equity risk premium does change over time. 2018 was a great example of risk premiums rising across markets. I personally look at corporate bond yields over treasure yields as a proxy of equity risk premium. You could create a forward curve using the bonds. However, equities don't expire and you can't create a forward curve with one data point.

Dec 25, 2019

Thanks Jim Simons. In the above mentioned paper they construct an expected curve for equity risk by doing the following: (1) futures contracts with different maturities already contain predetermined price information for the years ahead. (2) since their is no current future market like this, the futures have to be synthetically constructed for each year using puts and calls with the same strike price. Two questions: (1) Do you think that the market equity risk premium should be forecasted as a term structure because different year inherent different expected risk profiles? (2) do you think the above mentioned method could be viable in practice?

Dec 25, 2019

By the way... This is the paper I am referring to (whoever is interested in studying it ): Jeffrey L. Callen and Matthew R. Lyle. The Term Structure of Implied Costs of Equity Capital. SSRN - Rotman School of Management Working Paper No. 1738401, 2014.

Dec 25, 2019

I agree that through should be a varying risk premium/ discount rate for companies. However, I can't see how futures even consider the risk premium. The future price = today's price - dividend yield + interest cost. It's an arbitrage, therefore the risk is hedge out and not considered.

Maybe you could theoretically extract a discount rate from the implied volatility of options but I'd rather just assume treasury rate + 2%, as it's simpler and more intuitive.

Dec 25, 2019

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Dec 26, 2019
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