The Risk-Free Rate explained.
The Risk-Free Rate is a theoretical interest rate of return that carries zero risk. Although technically all investments carry some level of risk, investors want a way to measure the rate of return against other safer alternatives to ensure that the payoff to risk-reward is in their favour.
The Risk-Free rate is an important formula used for valuation and modelling work. It helps to calculate the Cost of Equity, Weighted Average Cost of Capital as well as the risk premium. The 10-Year treasury bond or 3-month treasury bill in the investor’s home country are often used as the RFR. All though unlikely a government can default on this, it is still considered the safest zero risk-free rate of return.
Investors can also use fixed deposits and other forms of safe investment vehicles where the rate of return is known and guaranteed over a certain period. I’d tailor to each investor’s own risk-free alternatives.
For example, I recently locked away some cash in a term-deposit with a major bank for a period of 12 months. The interest rate was 5% which is now my RFR. This is better than the 10-year government bond or 3-month yield on a treasury bill returning only 4.25%.
The idea behind this RFR is that investors want to understand opportunity cost when looking at investment ideas. As investors’ opportunity cost is everything, they want to know why they should invest and take a considerable risk with the potential loss of capital if the return is only a couple of percent higher than that of a zero-risk opportunity.
What is the Risk-Free Rate formula?
The formula behind the two concepts is due to the inclusion (or exclusion) of the rate of inflation. The real risk-free rate is the required return on zero-risk financial products taking into account inflation.
When discussing risk-free interest rates, we’re talking about two different approaches: the real risk-free interest rate and the nominal risk-free interest rate. They are quite easy to understand; just like our working calculations for the Inflation-adjusted return, the Real Risk-Free rate considers the effects of inflation, while the Nominal risk-free rate does not.
Real RFR Formula
- Real RFR = (1 + Nominal rf Rate) Γ· (1 + Inflation Rate)
- Nominal rf Rate = The return yield on a risk-free asset without the effect of inflation.
- Inflation Rate = The CPI of the country you reside in or the country the investment is based in.
Nominal RFR Formula
- Nominal RFR = (1 + Real rf Rate) x (1 + Inflation Rate) – 1
How to use the RFR?
The RFR is the minimum return investors expect for any investment. Why would investors accept additional risk unless the rate of return is greater than something with zero risk?
Let’s dive into a simple example showing how we can calculate each of the risk-free rates. Using the given rates below.
Real rf Rate = 6.2%
Inflation Rate = 2.8%
| Risk-Free Rate (rf) | Rate |
|---|---|
| Real Risk-Free Rate | 6.2% |
| Inflation rate | 2.8% |
| Nominal rf Rate | 9.17% |
| Nominal rf Rate | 9.17% |
| Inflation Rate | 2.8% |
| Real Risk-Free Rate | 6.2% |
Our working calculations are displayed below to show how the inputs are used.
Nominal rf Rate (1 + 6.2%) Γ (1 + 2.8%) β 1 x 100 = 9.17%
Real rf Rate (1 + 9.17%) Γ· (1 + 2.8%) β 1 = 6.2%
In another example, let’s evaluate an opportunity from an inflation perspective to see if our capital can keep up with a loss in purchasing power. We find a new fixed interest account returning 4.25% for 12 months. We know the 10-year bond yield is 4% and we think 0.25% is good for a similiar zero risk instrument.
However, inflation hit 7.25% and rising in the US and other Western countries. So if we take this into consideration the Real rf Rate is 4% – 7.25% = – 3.25%. With this in mind we would be loosing 3.25%.
In Summary…
Although the risk-free rate is a theoretical concept, understanding and calculating the real risk-free rate is crucial for investors. Knowing if an investment can preserve capital and combat inflation is significant. Valuing investments, especially when seeking opportunities that can keep up with inflation and provide greater returns than zero-risk instruments, is also important.
The RFR is a valuable tool for researching an investment to determine if it makes sense in the current low-interest-rate and high-inflation economy.
A rising risk-free rate of return has two opposing views from the business and investor’s perspectives. Investors view it as a sign of a stable government and high returns on investment. However, businesses may find it stressful as they must meet investors’ expectations of higher returns from riskier assets when the RFR is higher.
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