## “Risk free” rates and discount rates for DCF models

In the discussion to the Piquadro valuation, I quickly mentioned that the concept of “risk free” rates is a difficult concept at the moment.

Let’s have a quick look at the “academical” world:

**CAPM**

If we look at the CAPM (no matter if one beliefs this or not) we can see that the risk free rate of return plays an important role there. First, it is the basis return on needs to achieve with any investment, secondly it also influences the equity risk premium.

**Risk free rate of return**

The definition of the risk free rate itself is quite “fishy”. Investopedia for example states:

Investopedia explains ‘Risk-Free Rate Of Return’

In theory, the risk-free rate is the minimum return an investor expects for any investment because he or she will not accept additional risk unless the potential rate of return is greater than the risk-free rate.In practice, however, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. Thus, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate.

This is of course not really applicable for any serious long term investor. Damodaran has a nice paper about “risk free rates” here.

His major points are as follows:

The first is that

there can be no default risk. Essentially, this rules out any security issued by a private firm, since even the largest and safest firms have some measure of default risk. The only securities that have a chance of being risk free are government securities, not because governments are better run than corporations, but because they control the printing of currency. At least in nominal terms, they should be able to fulfill their promises. Even this assumption, straightforward though it might seem, does not always hold up, especially when governments refuse to honor claims made by previous regimes and when they borrow in currencies other than their own.

So this is important: **No default risk !!!** So it is wrong for instance to use current yields of Italian Govies for valueing Italian stocks, as considerable default risk is embedded in current spreads. The “country” risk could/should be embedded into the equity risk premium, not into the risk free rate. A hypothetical Italian company with 100% of its business in Germany for example, should only get a very small country risk charge if any.

A second point is the following:

There is a second condition that riskless securities need to fulfill that is often forgotten. For an investment to have an actual return equal to its expected return, there can be no reinvestment risk.

In theory, one should discount annual cash flows with the respective annual risk free rates. With a flat yield curve, this is not so important but for steep yield curves the differences can be significant. However in practice Damodaran recommends using the **duration of the cash flows **of the analysed investment as proxy for the risk free rate. As the best proxy if we don’t want to do this, he recommends the 10 year rate.

For the EUR, he recommends specifically the following:

Since none of these governments technically control the Euro money supply, there is some default risk in all of them. However, the market clearly sees more default risk in the Greek and Portuguese government bonds than it does in the German and French issues. To get a riskfree rate in Euros, we use the lowest of the 10-year government Euro bond rates as the riskfree rate; in October 2008, the

German 10-year Euro bond rateof 3.81% would then have been the riskfree rate.

With regards to **currencies** he says this:

Summarizing, the risk free rate used to come up with expected returns should be measured consistently with the cash flows are measured. Thus, if cash flows are estimated in nominal US dollar terms, the risk free rate will be the US Treasury bond rate. This will remain the case, whether the company being analyzed is a Brazilian, Indian or Russian company. While this may seem illogical, given the higher risk in these countries, the riskfree rate is not the vehicle for conveying concerns about this risk. This also implies

that it is not where a project or firm is domiciledthat determines the choice of a risk free rate,but the currency in which the cash flowson the project or firm are estimated.

The most common mistake with currencies is usually to use current exchange rates for future cashflows which then results in a preference for projects in countires wiht high nomnal rates.

About **Inflation**, he is not really clear in my opinion. He argues basically, inflation does not matter because we get the same result if we use yields of inlfation linked bonds combined with inflation adjusted growth rates.

Especially the current situation, where we see **negative real yields in many markets**, one could argue about his appoach. A negative real yield means for an investor, that the “risk free” nominal asset would have a guaranteed loss in real purchasing power over the investement horizon.

Consider for instance the UK: 10 year gilts run at 2.158% yield, this would be the proxy for the risk free rate. Current inflation runs at 5%, UK 10 year implied inflation from inflation linked bonds is around 3%.

So if I would use the 10 year gilt as proxy as the risk free rate, I woul dalready accept a loss of -1% p.a. in real terms p.a. or almost -3% p.a. based on current inflation rates.

I think this topic might justify even a doctorate thesis, but in my opinion, one could go the following pragamatic way:

Proxy for risk free rate: ** Higher of 10 year risk free Govie Yield in currency or inflation ).**

So in the case of the risk free rate for an Italian company I would compare:

a) 10 year risk free EUR rate = 10 year bunds = 1.89%

b) Inflation: Currently =3.4%

I would the use the **higher of the two rates, 3.4 %**. This would be a pragmatic way to avoid unnecessary country risk premium and still make sure, the risk free rate does not imply a guaranteed loss in real terms.