## What Is Risk-Free Rate?

### Definition of Risk-Free Rate

• The risk-free rate is the minimum rate of return on investment with theoretically no risk.
• Government bonds are considered risk-free because technically, a government can always print money to pay its bondholders.
• It is also the rate that provides an investor with some return and some compensation for future inflation.
• These two components are referred to as the real-risk free rate and the inflation premium.
• For practical purposes, the 10-Year U.S. Government Treasury bond can be considered the (nominal) risk-free rate.
• There is still a risk that the coupons payments a Treasury bondholder earns are reinvested at different, prevailing interest rates.
• Therefore, some people consider a more accurate risk-free rate to be a short-term U.S. Treasury Bill.
• But remember that when a short-term bond expires, the proceeds must be reinvested at the prevailing rate, so there is still reinvestment risk for a long-term investor.

### What Factors Influence the Risk-Free Rate?

• The general flexibility of the capital market due to supply and demand.
• Anticipated rate of inflation.

### How To Calculate the Risk-Free Rate?

• Subtract the inflation rate from the yield of the Treasury Bond matching the investment maturity.

((1 + Government Bond Rate)/(1 + Inflation Rate)) – 1

### Why is the Risk-Free Rate Important?

• It is the base rate for almost all interest rates and rates of return in a country.
• Used to calculate the cost of capital in the Capital Asset Pricing Model (CAPM).
• CAPM estimates the required rate of return on investment.

E(r) = Rf + ๐ฝ(Rm – Rf)

• Used in Modern Portfolio Theory, where investors are expected to maximize the risk-return trade-off.

### Digging Deeper

• Long-term investors in government bonds face two risks: Interest rate risk and reinvestment risk.
• Zero-coupon bonds can solve the problem of reinvestment risk because there is nothing to re-invest since there are no coupons paid.
• U.S. Government TIPS bonds were designed to compensate investors for inflation; hence they provide a real return.
• We can calculate the expected inflation rate as the difference between U.S. 10-Year U.S. Govt bonds and TIPS bonds.
• In global equity valuation, we often use the 10-Year Govt. bond of the country the stock is operating in.
• This is because these bonds tend to be most commonly available; hence, liquid, and that makes the interest rate more realistic.
• When a government prints money, it could cause the value of its currency to fall, so investors in another country’s government bonds are also taking on the currency risk.

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