Estimating Risk Free Rates

Estimating Risk free Rates

Models of risk and return in finance start off with the presumption that there exists a risk

free asset, and that the expected return on that asset is known. The expected return on a

risky asset is then estimated as the risk free rate (i.e., the expected return on the risk free

asset) plus an expected risk premium. In practice, however, there are two major issue that

we have to consider when estimating risk free rates. The first relates to the definition of a

risk free security, and the characteristics such a security needs to possess. The second

applies when there are no risk free assets, and examines how best to estimate a risk free

rate under these conditions. We attempt to deal with both these issues in this paper.

The Risk free Rate

Most risk and return models in finance start off with an asset that is defined as

risk free, and use the expected return on that asset as the risk free rate. The expected

returns on risky investments are then measured relative to the risk free rate, with the risk

creating an expected risk premium that is added on to the risk free rate. But what makes

an asset risk free? And what do we do when we cannot find such an asset? These are the

questions that we will deal with in this paper.

What is a risk free asset?

To understand what makes an asset risk free, let us go back to how risk is

measured in finance. Investors who buys assets have a return that they expect to make

over the time horizon that they will hold the asset. The actual returns that they make over

this holding period may by very different from the expected returns, and this is where the

risk comes in. Risk in finance is viewed in terms of the variance in actual returns around

the expected return. For an investment to be risk free in this environment, then, the actual

returns should always be equal to the expected return.

To illustrate, consider an investor with a 1-year time horizon buying a 1-year

Treasury bill (or any other default-free one-year bond) with a 5% expected return. At the

end of the 1-year holding period, the actual return that this investor would have on this

investment will always be 5%, which is equal to the expected return. The return

distribution for this investment is shown in Figure 1.

This investment is risk free because there is no variance around the expected return.

Requirements for an Asset to be Risk free

Under what conditions will the actual returns on an investment be equal to the

expected returns? In our view, there are two basic conditions that have to be met. 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 fulfil 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.

Returns

Probability = 1

Expected Return

Figure 1: Returns on a Riskfree Investment

There