Interpreting Interest Rates

The interest rate “r” is usually referred to most commonly as the required rate of return or the discount rate. Interest rates can be broken down into five major components using the following formula:

interest rate components

where:

r-sub-f = risk free rate
i = inflation premium
d = default risk premium
L = liquidity premium
m = maturity premium

Suppose you wanted to purchase a $1,000 bond, what is the required return that you should expect on the bond given the individual components above?

At the very least, you should expect to earn the nominal risk-free rate which is the product of the risk-free rate and the expected rate of inflation. Assume that short term treasuries are yielding 2%, and the expected rate of inflation is 3%. What is the nominal risk-free rate?

On an additive basis, we can calculate the nominal risk free rate as follows:

nominal risk-free rate = risk-free rate + inflation

However, the convention used by the CFA Institute is multiplicative rather than additive. Let’s calculate the nominal risk-free rate using this method:

nominal risk-free rate = (1 + risk-free rate)(1 + inflation) – 1

Based on the numbers above, the market has determined that the nominal risk-free rate, given the current yield on risk-free bonds and the projected rate of inflation, should be 5.06%.

From here, values need to be assigned for default risk, liquidity risk, and maturity.

Default risk adds a premium based on the probability of default of the borrower. These probabilities are typically reflected by the credit ratings of the borrower. Credit rating agencies assign credit ratings which classify bonds as being either investment grade, or high yield (junk). The further you go down in credit rating the higher the premium for default risk should be.

Liquidity risk is determined by how quickly or how long it would take to liquidate the bond on the open market prior to maturity. Thinly traded bonds with low volume would require a higher liquidity premium.

Lastly, the maturity premium is determined by the amount of time that needs to elapse before the bond matures and you receive you principal back. The longer the maturity, the greater the maturity premium should be.

If we assume that the premiums assigned for default risk, liquidity risk, and maturity are 0.20%, 0.50%, and 2.00% respectively, we can now calculate the total required rate of return or discount rate as follows:

where; nominal risk-free rate = 5.06%, default risk prem = 0.20%, liq prem = 0.50%, maturity prem = 2%

Understanding the components of interest rates components is critically important when attempting to determine the required rate of return on fixed income securities.

Typically, bond rates are quoted as a nominal risk-free rate plus some spread. In this case, the spread represents the default, liquidity, and maturity risks.

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