What is the Risk Free Rate?
The Risk Free Rate (rf) is the theoretical rate of return received on zero-risk assets, which serves as the minimum return required on riskier investments. The rate should reflect the yield to maturity (YTM) on default-free government bonds of equivalent maturity as the duration of the projected cash flows.
How to Calculate Risk Free Rate (Step-by-Step)
For corporate valuations, the majority of risk/return models begin with the presumption that there is a so-called “risk free rate”.
The yield on a risk-free asset – most commonly the 10-year Treasury bond in the US – is the minimum rate of return expected on investments with “zero risk” and the starting point upon which many valuation models build.
Despite the fact that the return expected by investors is considered to be risk-free, it is important to remember that the risk-free rate is a mere simplification, as all investments carry some degree of risk.
However, government-issued bonds are logically about as close to being risk-free as an asset could get, as governments could simply print more money if necessary.
As a result of being secured by a central government, the probability of default on such bond issuances is practically zero – and therefore, government bonds are viewed as the safest asset class that investors could place their capital in.
The risk-free rate should ideally match the duration of the forecast period of the cash flows, however, the limited liquidity and data for the longest maturity government-issued bonds have made the current yield on 10-year US treasury notes the preferred risk-free rate proxy in the U.S.
Risk Free Rate Formula (rf)
To expand further on the risk-free rate, there are two different types to consider:
- Real Risk-Free Rate
- Nominal Risk-Free Rate
The reasoning behind these two concepts is related to the inclusion (or exclusion) of the rate of inflation.
The real risk-free rate is the required return on zero-risk financial instruments with the rate of inflation taken into account.
The relationship between the real and the nominal risk-free rate is depicted by the following equation:
The nominal risk-free rate refers to the yield on a risk-free asset without the effect of inflation.
If the projected cash flows are discounted in nominal terms (i.e. reflects expected inflation), the discount rate used should also be nominal.
Risk-Free Rate in Capital Asset Pricing Model (CAPM)
The risk-free rate has a significant role in the capital asset pricing model (CAPM), which is the most widely used model for estimating the cost of equity.
Under the CAPM, the expected return on a risky asset is estimated as the risk-free rate plus an approximated equity risk premium. The minimum returns threshold factors in the beta of the specific asset (i.e. systematic, non-diversifiable risk) and the average return of the stock market.
The risk-free rate serves as the minimum rate of return, to which the excess return (i.e. the beta multiplied by the equity risk premium) is added.
The equity risk premium (ERP) is calculated as the average market return (S&P 500) minus the risk-free rate.
The equity risk premium helps investors evaluate potential investments based on the “extra” return that they are receiving for the incremental risk above the rf rate.
In effect, the risk-free rate has broad implications on how investors allocate their capital based on prevailing market conditions.
Risk Free Rate vs. Discount Rate
The risk-free rate assumption is also a key input in the estimation of the weighted average cost of capital (WACC) of a company.
The CAPM estimates the cost of equity based on the risk-free rate of return and the additional risk (and required return) associated with the investment. But the cost of debt can also be estimated by adding a certain spread based on the risk profile (i.e. default risk premium) of the company to the risk-free rate.
If the risk-free rate increases, there will be increased pressure on the equity risk premium to compensate investors more for the amount of risk undertaken (and vice versa).
Since investors can receive higher returns from risk-free assets, riskier assets are expected to result in higher returns to meet the new standards set by the market for the returns of riskier assets.
All else being equal, lower risk-free rates result in lower discount rates, which directly causes higher valuations of equities.