The risk-free rate of return is one of the most basic components of modern finance. Many of the most famous theories in finance - 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 use a risk-free asset as their base, there are limited other options.

This article looks at the risk-free security in theory and in reality (as a government security), evaluating how truly risk free it is. The model assumes that investors are risk averse and will expect a certain rate of return for excess risk extending from the intercept, which is the risk-free rate of return.

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 baseline where the lowest return can be found with the least amount of risk.

Figure 1
Copyright Ó 2008

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.
  • T-bills are sold at auction in a weekly competitive bidding process and are sold at a discount from par.
  • They don't pay traditional interest payments like their cousins, the Treasury notes and Treasury bonds.
  • They're sold in various maturities in denominations of $1,000.
  • 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 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.
  • 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 us very little about absolute risk - it only defines 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.
  • 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.

Although the U.S. government has never defaulted on any of its debt obligations, the risk of default has been raised during extreme economic events. The U.S. government can promise the ultimate security of its debt in unlimited ways, but the reality is that the U.S. dollar is no longer backed by gold, so the only true security for its debt is the government's ability to make the payments from current balances or tax revenues.

This raises many questions about the reality of a risk-free asset. For example, say the economic environment is such that there is a large deficit being funded by debt, and the current administration plans to reduce taxes and provide tax incentives to both individuals and companies to spur economic growth. If this plan were used by a publicly held company, how could the company justify its credit quality if the plan were to basically decrease revenue and increase spending? That in itself is the rub: there really is no justification or alternative for the risk-free asset. There have been attempts to use other options, but the U.S. T-bill remains the best option, because it is the closest investment – in theory and reality – to a short-term riskless security.

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 to the fact that the government exists in perpetuity by nature and have unlimited powers to raise funds both short- and long-term for spending and funding.

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