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

Interest is a reward a borrower pays for using an asset, usually capital, belonging to a lender. It is compensation 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 that assets largely considered risk-free offer. 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 risk of a decrease in purchasing power validates the inflation risk premium.

Liquidity refers to the ease with which an investment can be converted into cash without significantly sacrificing market value. Liquidity risk premium refers to the additional return that an investor demands from any investment that cannot liquidate instantly for cash in the market.

Default risk describes a situation where a borrower may fail 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 an 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 an investor requires for assuming interest rate and reinvestment risk resulting from a longer investment 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 that assets such as corporate bonds largely considered risk-free offer.

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 that assets largely considered risk-free, such as government securities, offer.

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

Shop CFA® Exam Prep

Offered by AnalystPrep

Featured Shop FRM® Exam Prep Learn with Us

Subscribe to our newsletter and keep up with the latest and greatest tips for success

Sergio Torrico
2021-07-23
Excelente para el FRM 2 Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
diana
2021-07-17
So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts. The fun light-hearted analogies are also a welcome break to some very dry content. I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
Kriti Dhawan
2021-07-16
A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them. Thank you ! Grateful I saw this at the right time for my CFA prep.
nikhil kumar
2021-06-28
Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
Marwan
2021-06-22
Great support throughout the course by the team, did not feel neglected
Benjamin anonymous
2021-05-10
I loved using AnalystPrep for FRM. QBank is huge, videos are great. Would recommend to a friend
Daniel Glyn
2021-03-24
I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
michael walshe
2021-03-18
Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.