### Risk-Free Rate of Return Definition

The risk-free rate of return is the optimum rate of return on an investment with zero risk of default or loss. Restated, it is a hypothetical rate of interest that an investor would expect from an investment without incurring any risk. That means the investor is assured to get the principal amount and a minimal return over a specified period of time.

### A Little More on What is the Risk Free Rate of Return

In reality, every investment carries a certain amount of risks, and a risk-free rate of return does not exist. Even the safest investments have a small number of risk factors attached to it.

In the U.S., the interest rate on the three-month Treasury bill is considered to be risk-free. It provides the comparative basis for determining a risk-free rate of return. It is a theoretical number, as it is possible for even the governments to default on their securities (thought the chances are almost nil).

The investor’s domestic market is an important factor that needs to be considered while determining a proxy for the risk-free rate of return. Negative interest rates further complicate the issue.

The U.S Treasury bill is an effective proxy for the U.S. Investors; but that might not be the case for investors whose assets are not denominated by dollars. For them, it incurs currency risk when investing in the U.S. Treasury bills. The perception of US Treasury safety depends on the large market size and its deep liquidity. For the non-U.S. investors, the rate of return might get affected even after hedging the currency risk via currency forwards and options.

Short-term government bills of highly-rated countries allow risk-free investment to the investors based in less highly-rated countries with the same currency. Those short-term bills serve as the proxy for the risk-free rate of return for them. As members of the European Union employing the Euro currency, investors based in Greece or Portugal can invest in highly rated German bonds without incurring currency risk; but, the investors with Russian rubles won’t be able to avoid that risk while investing in the German bonds.

The lowest allowed yield at a Treasury auction is zero. In certain situations, however, the bills might be traded with negative yields in the secondary market. In the U.S. debates regarding the need of raising the debt ceiling sometimes limit the issuance of treasury bills. The lack of supply reduces the prices drastically. The situation may lead to negative real interest rates (a situation where the bond returns less than the present value of cash considering inflation).

Sometimes during persistent deflation, the governments are forced to follow a policy of very low-interest rates that may even become negative, in order to rejuvenate the economy. In such situations, investors tend to invest their money in the assets they consider to be the safest.

### References for Risk-Free Rate

- https://en.wikipedia.org/wiki/Risk-free_interest_rate
- https://www.investopedia.com/terms/r/risk-freerate.asp
- https://investinganswers.com/financial-dictionary/investing/risk-free-rate-return-5133
- http://www.businessdictionary.com/definition/risk-free-rate-of-return.html

**Academic Research on Risk-Free Rate**

The equity premium puzzle and the **risk**–**free rate **puzzle, **Weil, P. (1989). Journal of Monetary Economics, 24(3), 401-421. **

**This study examines the effects for general equilibrium asset pricing of a set of Kreps-Porteous unexpected utility preferences characterized by a constant intertemporal elasticity of substitution and a constant, although unrelated, coefficient of relative risk aversion. The results suggest that relaxing the parametric restriction on tastes imposed by the time-additive expected utility specification does not seem to solve the Mehra-Prescott (1985) equity premium puzzle.**

The equity premium and the **risk**–**free rate**: Matching the moments, **Cecchetti, S. G., Lam, P. S., & Mark, N. C. (1993). Journal of Monetary Economics, 31(1), 21-45. **This paper investigates the ability of a representative agent model with a time-separable utility to discuss the first and second moments of the risk-free rate and the return to equity. The results indicate that the first moments of the data can be matched for an extensive range of preference parameter values, but the model is not able to generate the first and second moments of returns that are statistically close to those in the sample.

A monetary explanation of the equity premium, term premium, and **risk**–**free rate **puzzles, **Bansal, R., & Coleman, W. J. (1996). Journal of Political Economy, 104(6), 1135-1171. **

**This article creates and estimates a monetary model which explains various puzzling features of observed returns on equities and default-free bonds. The primary feature of the model is that some assets aside from money can play an essential role in facilitating transactions that impact the rate of returns they offer.**

Equity-premium and **risk**–**free**–**rate **puzzles at long horizons, **Daniel, K., & Marshall, D. (1997). Macroeconomic Dynamics, 1(2), 452-484. **

**This research presents two consumption-based models which are time-separable utility and the habit model of Constantinides. It also estimates a vector ARCH model that includes the pricing kernel and the equity return and uses the fitted model to assess the effects of the model for the equity premium and the risk-free rate.**

Explanations for the instability of equity beta: **Risk**–**free rate **changes and leverage effects, **DeJong, D. V., & Collins, D. W. (1985). Journal of Financial and Quantitative Analysis, 20(1), 73-94. **

**This research attempts to bridge the gap that currently exists between the theoretical and empirical literature on the instability of equity beta. It utilizes alternative variable parameter regression models to determine whether highly leveraged firms show higher equity beta instability than firms with lower leverage.**

Financial innovation, precautionary saving and the **risk**–**free rate**, **Elul, R. (1997). Journal of Mathematical Economics, 27(1), 113-131. **

**This study investigates the implications brought about by the theory of precautionary saving for the effect of financial innovation on the riskless interest rate. The theory states that when marginal utility is convex, the availability of uninsured risk in the economy can result in more significant savings leading to a lower equilibrium interest rate than the usual case.**

Market Risk Premium and **Risk Free Rate **used for 51 countries in 2013: a survey with 6,237 answers, **Fernandez, P., Aguirreamalloa, J., & Linares, P. (2013). **** **This article presents the statistics of the Risk-Free Rate and the Equity Premium or Market Risk Premium (MRP) used in 2013 for 51 countries. The survey in the article focuses on Required MRP. The article also presents the Risk-Free rate utilized and the comments from both the people who use MRP and those who don’t.

On the calculation of the **risk free rate **for tests of asset pricing models, **Vaihekoski, M. (2009). **This paper contains an explanation of issues in calculating risk-free rates from the money market instruments, most importantly for tests of asset pricing models and event studies. More attention is given to situations in which the maturity of the money market instrument is not the same as that of other assets under investigation.

The capital asset pricing model’s **risk**–**free rate**, **Mukherji, S. (2011). ** ** **This is an investigation of the market and inflation risks of treasury securities with distinct maturities over distinct investment horizons. The results suggest that mean real returns, volatility as well as market and inflation risks of treasury securities increase with the maturity period. The results also indicate that treasury bills are better proxies for the risk-free rate than longer-term treasury securities despite the investment horizon.

The equity premium and the **risk free rate**: A cross country, cross maturity examination, **Canova, F., & De Nicoló, G. (1995). **** **This article investigates the relationship between the equity premium and the risk-free rate at three separate maturities by using post-1973 data for a panel of seven OECD countries. It also conducts simulations using a standard consumption-based CAPM model and proves that the basic features of Mehra and Prescott’s puzzle remain no matter the period, the investment maturity and the country under consideration.

Determining the **risk free rate **for regulated companies, **Lally, M. (2002). Preparado para ACCC (The Australian Competition and Consumer Commission). **This paper explores various issues regarding the risk-free rate in terms of determining the cost of capital for regulated entities in Australia. It also attempts to identify the appropriate method to use for forecasting inflation for the purpose of setting the allowed output price in the first year. It also investigates the period over which the risk-free rate should be averaged when determining the rate to be used.