Interest Rates and the Equity Risk Premium: Conflicting Evidence

# What should happen to the equity risk premium as rates change?


# What should happen to the equity risk premium as rates change?












Suppose I set forward-looking expected returns for capital markets using a dividend discount model framework, under which expected return for equities is the sum of dividend yield, expected trend growth and a valuation change. I use this expected return to estimate the current risk premium on equities by subtracting the current risk free rate (proxied by say the 10 year T bond rate).

Now I am interested in what happens to this estimated risk premium if rates increase. While of course the estimated risk premium will be lower if I hold the return on equity constant, I would expect the components of the equity return to change if the interest rate environment shifts. For example, dividend yields tend to be strongly correlated with the level of rates, returns might be lower if debt costs increase, etc.

What would be some ways to estimate this relationship and more accurately characterize how equity risk premiums should change if interest rates change?

## Answer by AK88 (score 3, accepted)

https://quant.stackexchange.com/a/50202

There does not seem to be a clear relationship between interest rates and equity risk premiums. Damodaran (2019) has a great paper that goes into details of equity risk premiums. In this work, he writes:

> In much of valuation and corporate finance practice, we assume that the equity risk premium that we compute and use is unrelated to the level of interest rates ... But is this a reasonable assumption? How much of the variation in the premium over time can be explained by changes in interest rates? Put differently, do equity risk premiums increase as the risk free rate increases or are they unaffected? To answer this question, we looked at the relationship between the implied equity risk premium and the treasury bond rate (risk free rate). As can be seen in figure 13, the implied equity risk premiums were highest in the 1970s, when interest rates and inflation were also high. However, there is contradictory evidence between 2008 and 2018, when high equity risk premiums accompanied low risk free rates.

Duarte and Rosa (2015) have discussed multiple variants of equity risk premiums, including the DDM framework. While their main objective was to compare and contrast the models, they also highlight that:

> The ERP in 2012 and 2013 reached heightened levels—of around 12 percent—not seen since the 1970s.

This is in line with the previous study. Furthermore,

> There are two reasons why the ERP can be high: low discount rates and high current or expected future cash flows ... We conclude the ERP is high because Treasury yields are unusually low. Current and expected future dividend and earnings growth play a smaller role. In fact, expected stock returns are close to their long-run mean.

I looked at Ang and Bekaert (2007) and thought that they were looking at interest rate predictability by dividend:

> Table 5 reports that the long sample for the U.S. shows a positive effect of the dividend yield on future interest rates. The effect is economically small ... we view the relationship between dividend yields and future interest rates as economically important because interest rates are a crucial component of a present value relation. From the present value relation (5), we expect a positive relation between dividend yields and future discount rates. The interest rate enters the discount rate in two ways. The discount rate is the sum of the risk free rate and the risk premium and enters these two components with opposite signs. It is the first component that gives rise to the positive relation.Although not statistically significant, the positive sign of interest rate predictability by dividend yields is robust.

I wonder if the reverse is true.

Overall though, I do not think that the relationship between the interest rates and equity risk premiums is straightforward to capture. This is more an art than a science and involves lots of subjective judgement. Hope you will find the papers useful and let us know your thoughts!