Simplified: How do I find the risk-free?

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If you have taken part in a finance class or have completed some sort of finance related task there’s a high chance that you will have come across a term that is called the risk-free rate. Now I have been taught this concept many times myself, whether for the use in the calculations in the CAPM model or calculating the cost of debt, the risk-free rate is a very important addition to any model or calculation that you are preforming. Therefore, you would believe that it is also important to understand the exact definition of a risk-free rate and how you can find the risk-free rate in the real world. However, from my experience, from the majority of lessons that I’ve had about the risk-free rate have been very basic, short and usually was as simple as pointing at the 10-year US treasury rate. Let’s have a look at why this might not always be the case.

What is a risk-free rate?

In finance we usually have an expected return on a certain investment. Now whether the actual return meets this expected return will depend on the investment variance, how much the investment return is expected to deviate from what we expect the return to be. Now with a risk-free asset for the assumption to hold the expected return of the asset needs to be exactly the same as the actual return.

On a risk-free investment, the actual return is equal to the expected return. Therefore, there is no variance around the expected return.

Let’s take Apple and the 5-years treasury bill (a bond that is issued by the government that matures or ends its contract in exactly 5 years’ time). We expect the return of Apple to be 20% in 5 years based on our forecasts and 1.22% for the bond based on the yield it is providing right now (the numbers used are not actual market numbers). For my investment in this bond I am guaranteed to have the actual return be the expected return (in the real world this is not 100% true, but I’ll explain later).

As you can see there is no variance around the mean, the return will always equal the expected return. Therefore, we can say that this investment carries no risk. Compare this to your apple stock for which we expected a 5% return, the actual return varies a lot.

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Knowing this you can see that the return that I will actually get can be a variety and therefore this investment carries risk.

The characteristics of risk-free assets

The first and the most well-known factor is that there cannot be a default risk or a chance that the actual return is not equal to my expected return. This basically rules out any security issued by private or public institution as even the largest and most stable firm has a chance of default. In most currencies the security that is closest to default free is the government securities. This is because they control the printing of currency. I said ‘closest to default free’ because even governments sometimes refuse to honour what the previous regimes planned and borrow instead of print from other currency than their own. Also, there’s a small chance that they might not be able to pay (but very small).

Another important point that I’ve seen overlooked is the reinvestment risk. This basically means that the security that I invest in has a maturity that lasts the time horizon that is planned for my investment. So, for example, if I was looking to invest for five years, a 3-month T bill would not be suitable as I don’t know what the rate of it will be in 3 months; when I would have to re-invest. So, in this case a 5-year treasury bond would be the best risk-free rate. This also has its risk to a certain extent and to be precise we’d need to calculate the risk-free rate for each cash flow period. However, since this will cause very small changes to the computation of the cost of capital for the sake of simplicity and little added value, we don’t need to do this.

Finally, the most important characteristic that we have to follow is the currency. This means that the risk-free rate that we use in our models has to be consistent with the currency that is used in the cash flows implied. This is important to remember as the choice of the risk-free rate isn’t dependent on where the firm was domiciled but what currency the cash flows are generated in. This is because currencies will have differences in the risk-free rate due to the expected level of inflation. So, if I was valuing a company in GBP, I would look to use the UK government issued long term debt.

Real Risk-Free rates

Under high and unstable inflation, valuation can be done in real terms. Real terms mean making an adjustment to the expected level of inflation to remove its effects on the valuation. If you go along this route and use the real risk-free rate a few adjustments have to be made. Cash flows have to be estimated using a real growth rate (g minus inflation) and making sure that throughout the model no growth comes from price inflation. To be consistent the discount rates also have to be in real terms. So, how do you find a real-risk free rate? A standard approach is to minus the expected inflation from the nominal risk-free rate. So, reducing the US 10-year treasury yield by the level of inflation you expect in the future. Recently, there’s been an introduction of the inflation-indexed treasuries which basically offer investors a guaranteed real return. This will usually be stated as 3% + inflation. So, in this case if inflation was 2%, I would expect a return of 5%. The only problem with this security is that it is basically only done in the United States. A market where the expected inflation is low and stable. Market such as Venezuela where this type of security would come in very handy doesn’t actually exist. But that doesn’t mean me we can’t make use of it. As you will know there is friction and constraints to capital flowing through borders and markets. Therefore, the expected real return of the economy should be equal to the expected growth of the economy. Therefore, we can derive a real risk-free rate from this expected growth. If it’s an economy that has little friction in capital in/ outflows in regard to the US, then the US real risk-free rate can be used for this country as well.

Summary

When trying to figure out what the risk-free rate is there are three main points that you should follow to make sure you get the correct return:

1. Time horizon matters: Thus, the risk-free rates in valuation will depend upon when the cash flow is expected to occur and will vary across time. Avoid reinvestment risk.

2. Currencies matter: A risk free rate is currency-specific and can be very different for different currencies. (Why do risk free rates vary across countries? Inflation)

3. Not all government securities are risk-free: Some governments face default risk and the rates on bonds issued by them will not be risk-free.

Sometimes you want to remove the effects of volatile and high inflation, in this case a real risk-free rate can be employed.

Finally, it’s important to remember that the theoretical risk-free rate in the real world doesn’t actually exist but we can be smart and follow a set of rules to get as close to it as possible.


All opinions in this post are for non-professional investing and is solely my opinion. The value of investments will fluctuate, which will cause prices to fall as well as rise and you may not get back the original amount you invested. Past performance is not a guide to future performance. Only invest money that you are willing to lose.