Risk Free Rate- Logic behind Assumptions

The cost of Equity is given as

 Ke = Rf + Beta* ( Rm-Rf)
Rf = Risk free rate
Rm= Expected return from the market
Here, Risk Free rate is rate at which there lies no variance around the expected return rate. It means that on a risk free asset, the actual return is equal to the expected return. For any investment to become risk free it must satisfy two conditions which are as follows:-
1.No Default risks
2.No Reinvestment risks
The first condition states that it shouldn’t carry unwanted risks i.e. Business risks, financial risks or any other risks whereas second one states that there should not be any risk associated with the reinvestment of the money in the same assets.
Besides these the other two things that one must keep in his mind while taking assumptions for risk free rate is that time horizon matters , which means it is always better to take risk free rate of that assets for the current period rather than from any historical data. It also states that it is always better to take risk free rate for that asset whose time period of maturity matches with the time period of your valuation. Suppose you want to do valuation for a company by taking cash flow for 10 periods, then it is better to take 10 years Treasury bond rate as Rf rather than 6 months treasury bill rate because reinvestment risk is attached with 6 months treasury bill. Secondly, not all government securities are risk free.so, before using any Government securities rate as risk free rate kindly check the risk associated with it. For example, most of the analysts in the world uses U.S. Treasury bond as risk free rate but after 2008 crisis Moody has downgraded U.S. bond ratings from Aaa grade. So, we can’t take it as risk free rate rather we must subtract its credit spread associated with its bond ratings to get Rf.
One can calculate risk free rates in three ways
Risk free rates when valuation is done in local currency:-When we want to do valuation for a company in local currency then the best way to calculate the risk free rate is to subtract the Credit spread from the local government bond rate. Now, the question arises, why we subtract the credit spread? And the answer to this question is that as discussed above not all Government securities are risk free rather they have some inherent risks which is calculated by Credit Rating agencies and is given in the form of Credit spread. Hence, once we subtract that credit spread we will get the Rf. The credit spread arises because of various economic, social, political, legal etc. risks associated with a country. Hence, as an investor I will invest in those bonds when I will be getting the premium and that premium is calculated in the form of credit spread by the rating agencies.
Risk Free rate in Real term:-When you are doing valuation in real term then take the government inflation indexed bond as risk free rate or if such rate is not available then take the normalized value of the growth rate of country as risk-free rate.
Stable currency denominated bond can be used as risk free rate but it must be issued by the country whose currency you think is stable. For ex- Dollar ( Though Moody has downgraded the rating of U.S. bond but still people all over the world uses it), Euros.
One thing that we must keep in mind is that the risk free rate varies across currencies, therefore we use stable currency denominated bond as risk free rate. The reason behind difference in the risk free rate for different currencies is that every currency is associated with the economy of its host country and hence any downslides in the economy affect its stability. Hence, risk free rate varies across the currency depending upon the stability of its host country. (Please note that there are many other issues attached with the stability of the currency)
[The article has been written by Alok Kumar Agrawal. He has completed his PGDM from IIM Shillong in Finance. ]

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Pranjal Gangurde

Thanks for insightful article! Most of the B school students take government bond rate as risk free rate while doing valuation of company. As you discussed about credit spread, where should one find it? As it depend on economic ,social, political factors, it will keep changing accordingly. So,how one should keep track of credit spread?

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