Internal consistency of risk free rate and MRP in the CAPM

In fact, we know from earlier studies that the expected risk premium on the
market as well as conditional betas are not constant (Keim and Stambaugh
(1986), Breen, Glosten, and Jagannathan (1989)), and vary over the business
cycle (Fama and French (1989), Chen (1991), and Ferson and Harvey (1991)).
41. Fama and French (1989) 8 cited by Jaganathan and Wang conclude:
Our tests indicate that expected excess returns (returns net of the one-month
Treasury bill rate) on corporate bonds and stocks move together. Dividend
yields, commonly used to forecast stock returns, also forecast bond returns.
Predictable variation in stock returns is, in turn, tracked by variables commonly
used to measure default and term (or maturity) premiums in bond returns. The
default-premium variable (the default spread) is the difference between the yield
on a market portfolio of corporate bonds and the yield on Aaa bonds. The term-
or maturity-premium variable (the term spread) is the difference between the
Aaa yield and the one-month bill rate.
3.2. MRP will often move in the opposite direct into the risk free rate
42. Moreover, there is a general consensus that the market risk premium tends to move in
the opposite direction to the risk free rate – especially for material changes in the level
of the risk free rate. For example, Lettau and Ludvigson 9 find that the risk premiums
tend to move in the opposite direction to the de-trended government bond rate.
43. Amongst other findings, they found a strongly statistically significant negative
relationship between the de-trended US bill rates and the change in the log excess
return (the variable they introduce akin to the MRP). Such a negative relationship held
true without controlling for other potential variables that might affect risk premiums (i.e.
a simple correlation suggested that the risk premiums rose 2.1% for every 1%
reduction in the de-trended risk free rate). When Lettau and Ludvigson included
controls for other variables they still found that when the de-trended risk free rate fell
the risk premiums tended to rise by the same amount as the fall in the de-trended risk
free rate.
44. Reflecting this negative relationship, Smithers and Co, advisers to the UK economic
regulators, have recommended that the cost of equity not be varied based on
variations in the risk free rate:
Given our preferred strategy of fixing on an estimate of the equity return, any higher
(or lower) desired figure for the safe rate would be precisely offset by a lower
8 Fama and French, 1989, Business Conditions And Expected Returns On Stocks And Bonds, Journal of
Financial Economics
9 Lettau, Martin and Sydney Ludvigson, 2001, “Consumption, Aggregate Wealth and Expected Stock Returns,”
Journal of Finance 56 (3), pp. 815—849.
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