What Is Risk-Free Return?
Risk-free return is the theoretical return attributed to an investment that provides a guaranteed return with zero risks. The risk-free rate of return represents the interest on an investor's money that would be expected from an absolutely risk-free investment over a specified period of time.
Key Takeaways
- Risk-free return is a theoretical number representing the expected return on an investment that carries no risks.
- A risk-free return doesn't really exist, and is therefore theoretical, as all investments carry some risk.
- U.S. Treasuries are seen as a good example of a risk-free investment since the government cannot default on its debt.
- As such, the interest rate on a three-month U.S. Treasury bill is often used as a stand-in for the short-term risk-free rate, since it has almost no risk of default.
Risk-Free Return Explained
The yield on U.S. Treasury securities is considered a good example of a risk-free return. U.S. Treasuries are considered to have minimal risk since the government cannot default on its debt. If cash flow is low, the government can simply print more money to cover its interest payment and principal repayment obligations. Thus, investors commonly use the interest rate on a three-month U.S. Treasury bill (T-bill) as a proxy for the short-term risk-free rate because short-term government-issued securities have virtually zero risks of default, as they are backed by the full faith and credit of the U.S. government.
The risk-free return is the rate against which other returns are measured. Investors that purchase a security with some measure of risk higher than a U.S. Treasury will demand a higher level of return than the risk-free return. The difference between the return earned and the risk-free return represents the risk premium on the security. In other words, the return on a risk-free asset is added to a risk premium to measure the total expected return on investment.
How to Calculate
The Capital Asset Pricing Model (CAPM), one of the foundational models in finance, is used to calculate the expected return on an investable asset by equating the return on a security to the sum of the risk-free return and a risk premium, which is based on the beta of a security. The CAPM formula is shown as:
Ra = Rf + [Ba x (Rm -Rf)]
where Ra = return on a security
Ba = beta of a security
Rf = risk-free rate
The risk premium itself is derived by subtracting the risk-free return from the market return, as seen in the CAPM formula as Rm - Rf. The market risk premium is the excess return expected to compensate an investor for the additional volatility of returns they will experience over and above the risk-free rate.
Special Considerations
The notion of a risk-free return is also a fundamental component of the Black-Scholes option pricing model and Modern Portfolio Theory (MPT) because it essentially sets the benchmark above which assets that have risk should perform.
In theory, the risk-free rate is the minimum return an investor should expect for any investment, as any amount of risk would not be tolerated unless the expected rate of return was greater than the risk-free rate. In practice, however, the risk-free rate does not technically exist; even the safest investments carry a very small amount of risk.
FAQs
The formula for the risk-free rate of return is simple. It's based on what investors are willing to earn for taking no risk at all. The value of a risk-free rate can be figured out by subtracting the current inflation rate from the total bond yield. This would apply for the duration of the bond.
How do you calculate the risk-free return? ›
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.
What is the formula of risk-free? ›
Nominal Risk Free Rate Calculation Example
From those two assumptions, we'll enter them into the formula to calculate the nominal risk-free rate: Nominal rf Rate = (1 + 5.0%) × (1 + 3.0%) – 1.
How do you calculate expected return without risk-free rate? ›
The expected return is calculated by multiplying the probability of each possible return scenario by its corresponding value and then adding up the products. The expected return metric – often denoted as “E(R)” – considers the potential return on an individual security or portfolio and the likelihood of each outcome.
How do you calculate return risk? ›
Remember, to calculate risk/reward, you divide your net profit (the reward) by the price of your maximum risk. Using the XYZ example above, if your stock went up to $29 per share, you would make $4 for each of your 20 shares for a total of $80. You paid $500 for it, so you would divide 80 by 500 which gives you 0.16.
What is risk-free of return? ›
The risk-free rate of return is the interest rate an investor can expect to earn on an investment that carries zero risk. In practice, the risk-free rate is commonly considered to be equal to the interest paid on a 10-year highly rated government Treasury note, generally the safest investment an investor can make.
What is the simplest risk formula? ›
Risk is the combination of the probability of an event and its consequence. In general, this can be explained as: Risk = Likelihood × Impact.
What is an example of risk formula? ›
Risk is commonly defined as: Risk = Threat x Vulnerability x Consequence.
What is risk-free formula CAPM? ›
The capital asset pricing model (CAPM) formula states that the cost of equity—the expected return by common shareholders—is equal to the risk-free rate (rf) plus the product of beta and the equity risk premium (ERP). Where: Ke → Cost of Equity (or Expected Return) rf → Risk-Free Rate.
Is risk-free rate the same as required rate of return? ›
So when computing for required return on investment we start with a base rate which is known as risk free rate (minimum return any investment will yield), in simplest term we are referring to debt instruments issued by government as risk free rate (interbank rates) as they are backed by governments > government being ...
The expected return is calculated by multiplying the weight of each asset by its expected return. Then add the values for each investment to get the total expected return for your portfolio. Hence, the formula: Expected Portfolio Return = (Asset 1 Weight x Expected Return) + (Asset 2 Weight x Expected Return)...
How to calculate risk-free rate with beta and expected return? ›
To calculate the expected return on assets, you must utilize the CAPM formula: Expected return = risk-free rate + volatility/beta * (market return - risk-free rate).
What is the formula for risk-free rate and risk premium? ›
Now that you have determined the estimated return on an investment and the risk-free rate, you can calculate the risk premium of an investment. The formula for the calculation is this: Risk Premium = Estimated Return on Investment - Risk-free Rate.
How do you calculate risk-free beta? ›
Subtract the risk-free rate from the market (or index) rate of return. If the market or index rate of return is 8% and the risk-free rate is again 2%, the difference would be 6%. Divide the first difference above by the second difference above. This fraction is the beta figure, typically expressed as a decimal value.
