I wanted to discuss a potential new way to estimate the Equity Risk Premium. I run a lot of DCFs and so while calculating the discount rate through CAPM, having a good idea about the Equity risk premium is really helpful. Usually, there are 2 ways to estimate the Equity Risk Premium.

**1. The historical Equity risk premium**

You basically subtract the real risk-free rate from the historical stock return. The problem with this approach is that it’s historical and changing the time period you use for calculations changes the output. Furthermore, it may not incorporate the risk in the market at that very moment.

**2. Implied Equity Risk Premium**

This is a method that Aswath Damodaran talks about and uses. He basically uses the Gordon Growth Model. The Gordon Growth model has a few important inputs that are used to estimate the price of the stock/index. You need the

- Dividends and buybacks Paid
- Growth Rate for regular and terminal phase
- Cost of Equity

Now what Professor Damodaran assumes is that the current price of the index is the same as value given out by the model. That basically means that you have the price. He has the dividends and the growth rate and then he solves for the Cost of Equity. (This gives him the equity risk premium) . He does this for the United States and then he will add India’s country risk premium. That can be calculated using this formula.

(Default Probability on Sovereign Bonds)*(St Dev of Indian Stocks/ St Dev on Indian Bonds)

You can get these numbers on his website and he has videos on Youtube explaining the same.

**Now here is what I think maybe a quicker but rough method to estimate the same.**

Just like Equities, even bonds have had a risk premium. Corporate bonds have higher yields than Treasury bonds as they are riskier. The difference is the spread which can be looked at as a risk premium. The BAA Corporate Bond Spread is available on Fred.

For example, as of August 3rd, 2020, the BAA Spread is 2.58. We need to convert this premium to the equity premium. We can try to do this by looking at standard deviations. If we take the standard deviation for the SPY(US index) and the LQD(Investment Grade Corporate Bond ETF) we get 0.327 and 0.166 respectively giving us a multiplier of 1.96(0.327/0.166). So then we multiply the same with 2.58 to get a rough estimate of 5.07(2.58*1.96) as the ERP for the US.

Now that we have an Equity Risk Premium for the USA, we simply add India’s country risk premium, the same way Professor Damodaran does. Once we add that as of August 20th, the equity risk premium should be close to 8.5.

This method relies on the logic that risk in both the equity and bond markets usually increases together and hence if we know the bond risk premium we can attempt to estimate the equity risk premium. It is far from perfect but I thought it could be used to get a quick rough estimate.

Here is an article where I discuss all 3 methods in slightly more detail.