The risk-free interest rate is the theoretical rate of return of an investment with zero risk, including default risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a given period of time. The risk-free rate of return is one of the most basic components of modern finance and many of its most famous theories – the capital asset pricing model (CAPM), modern portfolio theory (MPT) and the Black-Scholes model – use the risk-free rate as the primary component from which other valuations are derived. The risk-free asset only applies in theory, but its actual safety rarely comes into question until events fall far beyond the normal daily volatile markets. Although it’s easy to take shots at theories that have a risk-free asset as their base, there are limited options to use as a proxy.
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.whereas, In practice 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.
The T-Bill Base
The risk-free rate is an important building block for MPT. As referenced in Figure 1, the risk-free rate is the base of the line where the lowest return can be found with the least amount of risk.
Risk-free assets under MPT, while theoretical, typically are represented by Treasury bills (T-bills), which have the following characteristics:
- T-bills are assumed to have zero default risk because they represent and are backed by the good faith of the U.S. government. (Read Why do commercial bills have higher yields than T-bills? to learn more.)
- T-bills are sold at auction in a weekly competitive bidding process and are sold at a discount from par. (Read Bond Market Pricing Conventions for more on how prices are determined.)
- They don’t pay traditional interest payments like their cousins, the Treasury notes and Treasury bonds.
- They’re sold in various maturities in denominations.
- They can be purchased by individuals directly from the government.
Because there are limited options to use instead of the United States T-bill, it helps to have a grasp of other areas of risk that can have indirect effects on risk-free assumptions.
Sources of Risk
The term risk is often taken for granted and used very loosely, especially when it comes to the risk-free rate. At its most basic level, risk is the probability of events or outcomes. When applied to investments, risk can be broken down a number of ways:
Absolute risk as defined by volatility: Absolute risk as defined by volatility can be easily quantified by common measures like standard deviation. Since risk-free assets typically mature in three months or less, the volatility measure is very short-term in nature. While daily prices relating to yield can be used to measure volatility, they are not commonly used. (For more insight, read The Uses And Limits Of Volatility.)
Relative risk: Relative risk when applied to investments is usually represented by the relation of price fluctuation of an asset to an index or base. One important differentiation is that relative risk tells very little about absolute risk – it only tells how risky the asset is compared to a base. Again, since the risk-free asset used in the theories is so short-term, relative risk does not always apply. (To learn more about degrees of risk, read Determining Risk And The Risk Pyramid.)
Default risk: What risk is assumed when investing in the three-month T-bill? Default risk, which in this case is the risk that the U.S. government would default on its debt obligations. Credit-risk evaluation measures deployed by securities analysts and lenders can help define the ultimate risk of default.
Conclusion
The risk-free rate is rarely called into question until the economic environment falls into disarray. Catastrophic events, like credit-market collapses, war, stock market collapses and dramatic currency devaluations, can all lead people to question the safety and security of the U.S. government as a lender. The best way to evaluate the riskless security would be to use standard credit evaluation techniques, such as those an analyst would use to evaluate the creditworthiness of any company. Unfortunately, when the rubber hits the road, the metrics applied to the U.S. government rarely hold up, due to the fact that they exist in perpetuity by nature and have unlimited powers to raise funds both short- and long-term for spending and funding.