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# Interest Rate as the Sum of Real Risk-Free Rate and Risk Premiums

Interest is basically a reward paid by a borrower for the use of an asset, usually capital, belonging to a lender. It is the compensation paid for the loss or value depreciation occasioned by the use of the asset. We could also describe it as the opportunity cost of alternative investments.

At the time of lending, the lender most likely has a portfolio of investment vehicles to choose from. As such, they must charge a premium for the ‘loss’ of the alternative investment opportunities. We express interest as an annual percentage, from which we can calculate monthly, quarterly, or semi-annual equivalents. The level of interest rate is a function of several risks.

Therefore, an interest rate is composed of a real risk-free interest rate plus a set of four premiums that represent compensation for bearing distinct types of risk:

\begin {align*} r & = \text {Risk free rate} + \text {Inflation premium} \\ & +\text {Liquidity premium} + \text {Maturity premium} \\ & + \text {Default premium} \end {align*}

Where $$r$$ is the interest rate.

## The Risk-Free Rate

The risk-free rate is the rate of return offered by assets largely considered risk-free. Such assets usually include government securities or local authority bonds. The real risk-free interest rate is the single-period return on a risk-free security assuming zero inflation.

Inflation risk is the loss of purchasing power of money as a result of the increase in prices of consumer goods. The inflation risk premium is the additional return that investors demand aside from the real risk-free rate. The inflation risk premium is validated by the risk of a decrease in purchasing power.

Liquidity refers to the ease with which an investment can be converted into cash without making a significant sacrifice to market value. Liquidity risk premium refers to the additional return that an investor demands from any investment that cannot be liquidated instantly for cash in the market.

Default risk describes a situation where a borrower may cease to repay borrowed funds as a result of bankruptcy. This might result in significant losses on the side of the lender. A default premium is the additional return required by the lender or investor from a borrower for their (lender’s) assumption of default risk.

Maturity risk premium is the additional return required by an investor for assuming interest rate risk and reinvestment risk of an investment that result from longer maturity timeline. Maturity risk premium increases with an increase in the maturity timeline. In other words, the longer the maturity timeline of an investment, the higher the maturity risk premium.

## Question

Which of the following statements is the most accurate about interest rates?

A. The risk-free rate is the rate of return offered by assets such as corporate bonds that are largely considered risk free.

B. Inflation risk describes a situation where a borrower may cease to repay borrowed funds as a result of bankruptcy.

Solution

You must add the four types of risks to the risk-free rate to come up with the overall rate of interest, r.

A is incorrect. The risk-free rate is the rate of return offered by assets largely considered risk free such as government securities.

B is incorrect. Inflation risk is the loss of purchasing power of money as a result of the increase in prices of consumer goods.

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