Which of these is the interest rate that would exist on a default-free security

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Abstract

This paper uses an intertemporal general equilibrium asset pricing model to study the term structure of interest rates. In this model, anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices. Many of the factors traditionally mentioned as influencing the term structure are thus included in a way which is fully consistent with maximizing behavior and rational expectations. The model leads to specific formulas for bond prices which are well suited for empirical testing.

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Econometrica publishes original articles in all branches of economics - theoretical and empirical, abstract and applied, providing wide-ranging coverage across the subject area. It promotes studies that aim at the unification of the theoretical-quantitative and the empirical-quantitative approach to economic problems and that are penetrated by constructive and rigorous thinking. It explores a unique range of topics each year - from the frontier of theoretical developments in many new and important areas, to research on current and applied economic problems, to methodologically innovative, theoretical and applied studies in econometrics.

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The Econometric Society is an international society for the advancement of economic theory in its relation to statistics and mathematics.

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Econometrica © 1985 The Econometric Society
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Abstract

A bond subject to default risk trades at a higher interest rate than a comparable default-free bond in order to compensate investors for expected loss resulting from reduced or delayed promised payments; the difference between the yields to maturity on the two bonds is called the default yield premium. Bonds with the same default yield premium, however, may differ in regard to the timing of their reductions in payment. Each time pattern of cash payments translates into a different duration value for a given stochastic process of default-free interest rates. Failure to take this time pattern into account when computing durations of non-default-free bonds will result in misspecification of risk exposure. For instance, the duration of a bond that defaults on the first coupon will differ from the duration of a bond that defaults on the last payment, even if both bonds have the same default yield premium and initial maturity. Early defaulters will have durations that are consistently longer than their simple, unadjusted macaulay durations, while later defaulters will have consistently shorter durations. Furthermore, the error from not taking the stochastic process of default into account will be larger, the greater the default yield premium. More common than outright default is the situation where the issuer delays coupon and principal payments but eventually pays them in full some time after default. All default-adjusted durations for these bonds will exceed their corresponding unadjusted durations, with the size of the adjustment increasing with term to maturity and exceeding the length of the delay in payments.

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The Financial Analysts Journal aims to be the leading practitioner journal in the investment management community by advancing the knowledge and understanding of the practice of investment management through the publication of rigorous, peer-reviewed, practitioner-relevant research from leading academics and practitioners.

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Building on two centuries' experience, Taylor & Francis has grown rapidlyover the last two decades to become a leading international academic publisher.The Group publishes over 800 journals and over 1,800 new books each year, coveringa wide variety of subject areas and incorporating the journal imprints of Routledge,Carfax, Spon Press, Psychology Press, Martin Dunitz, and Taylor & Francis.Taylor & Francis is fully committed to the publication and dissemination of scholarly information of the highest quality, and today this remains the primary goal.

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Financial Analysts Journal © 1988 CFA Institute
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What Is the Risk-Free Rate of Return?

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

The so-called "real" risk-free rate can be calculated by subtracting the current inflation rate from the yield of the Treasury bond matching your investment duration.

Key Takeaways

• The risk-free rate of return refers to the theoretical rate of return of an investment with zero risk.
• 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 inflation rate from the yield of the Treasury bond matching your investment duration.

Risk-Free Rate of Return

Understanding the Risk-Free Rate of Return

In theory, the risk-free rate is the minimum return an investor expects for any investment because they will not accept additional risk unless the potential rate of return is greater than the risk-free rate. Determination of a proxy for the risk-free rate of return for a given situation must consider the investor's home market, while negative interest rates can complicate the issue.

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 (T-bill) is often used as the risk-free rate for U.S.-based investors.

The three-month U.S. Treasury bill is a useful proxy because the market considers there to be virtually no chance of the U.S. 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, offer a risk-free rate proxy for investors with assets in euros (EUR) or Swiss francs (CHF). Investors based in less highly rated countries that are within the eurozone, such as Portugal and Greece, are able to invest in German bonds without incurring currency risk. By contrast, an investor with assets in Russian rubles cannot invest in a highly rated government bond without incurring currency risk.

Negative Interest Rates

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 Germany and Switzerland. 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 bills sometimes trade 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.

Why Is the U.S. 3-Month T-Bill Used as the Risk-Free Rate?

There can never be a truly risk-free rate because even the safest investments carry a very small amount of risk. However, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate for U.S.-based investors. This is a useful proxy because the market considers there to be virtually no chance of the U.S. government defaulting on its obligations. The large size and deep liquidity of the market contribute to the perception of safety.

What Are the Common Sources of Risk?

Risk can manifest itself as absolute risk, relative risk, and/or default risk. Absolute risk as defined by volatility can be easily quantified by common measures like standard deviation. Relative risk, when applied to investments, is usually represented by the relation of price fluctuation of an asset to an index or base. Since the risk-free asset used is so short-term, it is not applicable to either absolute or relative risk. Default risk, which, in this case, is the risk that the U.S. government would default on its debt obligations, is the risk that applies when using the 3-month T-bill as the risk-free rate.

What Are the Characteristics of the U.S. Treasury Bills (T-Bills)?

Treasury bills (T-bills) are assumed to have zero default risk because they represent and are backed by the good faith of the U.S. government. They are sold at a discount from par at a weekly auction in a competitive bidding process. They don't pay traditional interest payments like their cousins, the Treasury notes and Treasury bonds, and are sold in various maturities in denominations of $1,000. Finally, they can be purchased by individuals directly from the government.

What is the risk

What is the real risk

What is the risk

What is the current risk