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**Risk Free Rate Of Return: Answered and Explained**

The risk free rate of return is the theoretical rate of return of an investment with zero risk. It represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time.

Investing is about putting money at risk in order to earn a return. In theory, the more risk an investor is willing to accept, the more returns he or she should expect to earn to compensate for the risk. However, in practice, the risk-free rate of return does not truly exist, as every investment carries at least a small amount of risk. To calculate the real risk-free rate, subtract the current inflation rate from the yield of the Treasury bond matching your investment duration. In this post, we will cover the basics of risk free rate of return and hopefully, by the end of it, you will have a clearer picture of the subject matter. Let’s get started.

# What is the Risk Free Rate of Return?

## Understanding the Risk-Free Rate Of Return

In Malcolm Kemp’s book* Market Consistency: Model Calibration in Imperfect Markets, *Chapter five states that the risk-free rate can mean different things to different people and a consensus towards its direct measurement doesn’t exist.

Another interpretation of the theoretical risk-free rate of return is aligned with Irving Fisher’s concept of inflationary expectations. This was described in his 1930 treatise *The Theory of Interest*. The treatise is based on the theoretical costs and benefits of holding currency. The Fisher model describes these with the help of two potentially offsetting movements:

- Expected increases in the money supply should result in investors preferring current consumption to future income.
- Expected increases in productivity should result in investors preferring future income to current consumption.

The correct interpretation of this is that the risk free rate can be positive or negative and the sign of the expected risk-free rate is an institutional convention in practice. An analogy to this can be found on page 17 of Tobin’s book, *Money, Credit and Capital. *This analysis supports the concept that the risk-free rate may not be directly observable in a system with endogenous money creation and where production decisions and outcomes are decentralized and potentially intractable to forecasting.

In theory, the risk-free rate is the minimum return an investor expects for any investment because he will not accept additional risk unless the potential rate of return is greater than the risk-free rate.

In practice, however, a truly 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 for U.S.-based investors.

Determination of a proxy for the risk-free rate of return for a given situation must take into consideration the investor’s home market, while negative interest rates can complicate the issue.

## Currency Risk

The three-month U.S. Treasury bill is a useful proxy because the market considers there to be virtually no chance of the government defaulting on its obligations. The large size and deep liquidity of the market contribute to the perception of safety. However, a foreign investor whose assets are not denominated in dollars incurs currency risk when investing in U.S. Treasury bills. The risk can be hedged via currency forwards and options but affects the rate of return.

The short-term government bills of other highly rated countries, such as Germany and Switzerland, can provide a risk-free rate proxy for investors with assets in euros or Swiss francs. Investors based in less highly rated countries that are within the eurozone, such as Greece or Portugal are able to invest in German bonds without incurring currency risk. On the other hand, an investor with assets in Russian rubles cannot invest in a highly rated government bond without incurring currency risk.

## Negative Interest Rates

The flight to quality and away from high-yield instruments amid the long-running European debt crisis has pushed interest rates into negative territory in the countries considered safest, such as Switzerland or Germany. In the United States, partisan battles in Congress over the need to raise the debt ceiling have sometimes sharply limited bill issuance, with the lack of supply driving prices sharply lower. The lowest permitted yield at a Treasury auction is zero, but that doesn’t stop bills sometimes trading with negative yields in the secondary market. And in Japan, stubborn deflation has led the Bank of Japan to pursue a policy of ultra-low, and sometimes negative, interest rates to stimulate the economy. Negative interest rates essentially push the concept of risk-free return to the extreme; investors are willing to pay to place their money in an asset they consider safe.

## How to Calculate Risk Free Rate of Return:

Two metrics to quantify how the market is valuing risks and rewards is to calculate the real risk-free rate.

The real risk-free rate takes the risk-free rate and incorporates inflation risk into the equation. Inflation is too often overlooked when assessing investment returns, but when high it can quickly erase actual wealth gains.

For example, if the stock market returns 8% in a given year but the inflation rate is 5%, the real return is a much less impressive 3%.

To calculate the real risk-free rate, subtract the current inflation rate from the yield of the

Treasury bond that matches your investment duration. If, for example, the 10-year Treasury bond yields 2%, investors would consider 2% to be the risk-free rate of return.

Treasury bonds are the most often cited proxy for the risk-free rate because they are backed by the full faith and credit of the U.S. government. If inflation stands at 0.5%, then the real risk-free rate would be 1.5%: The risk-free rate of 2% minus 0.5% inflation equals 1.5%.

In practice, this 1.5% real risk-free rate is the rate that investors expect to earn after inflation from a risk-free investment with a 10-year duration after inflation.

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