Interest Rate Risk: Definition, Formula & Models

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  • 0:02 What Is Interest Rate Risk?
  • 0:49 Bond Valuation Basics
  • 1:53 Reinvestment Rate Risk
  • 3:16 Can Risk Be Avoided?
  • 6:46 Lesson Summary
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Lesson Transcript
Jay Wagner

Jay holds a Masters of Business Administration

Expert Contributor
Steven Scalia

Steven completed a Graduate Degree is Chartered Accountancy at Concordia University. He has performed as Teacher's Assistant and Assistant Lecturer in University.

Interest rate risk is really the risk of two different events (price reduction and reinvestment rate reduction) caused by a change in interest rates. Interest rate risk affects bond investments, but the good news for bond investors is that it can be mitigated or eliminated.

What Is Interest Rate Risk?

Interest rate risk is one of five types of risk that are not specific to the firm that affect the return on investments in stocks and bonds. Unlike the other four types, interest rate risk has a significant effect only on bonds. If the required return, the return the market demands on the investment, is higher or lower than the bond's coupon rate, the rate on which interest payments are based, the price of the bond adjusts to provide the market's required return. As a result, if interest rates change, bond prices also change and bond investors can unexpectedly gain or lose money. Reinvestment rate risk, the risk that the investor won't be able to reinvest the money received from a bond at the same rate, is another form of interest rate risk.

Bond Valuation Basics

Let's say that a company issues bonds with a $1,000 par value that have a 6% coupon rate and will pay interest semiannually for 10 years (20 semiannual periods). The value of a bond at any given time is the present value of the interest payments plus the present value of the repayment of the par value, so if the market is demanding a 6% return on bonds of similar risk, the value of the bond is $1,000.

If you invested when the bonds were issued, you paid $1,000, you're happy with a 6% return, and you plan to hold the bonds for the full 10 years, you're in great shape. However, what happens to your return if, six months later, the market starts demanding 6.5% on this bond? Instead of remaining a nice steady $1,000, the price changes to $964.97 to reflect the new required return. If you have to sell the bond at this time for any reason, your return on the investment for the six months you held the bond is -1.01%; you lost money!

Reinvestment Rate Risk

In reinvestment rate risk, the concern isn't price, but rather the ability to reinvest the money received from a bond at the same rate. In this case, lower interest rates push the required returns on bonds down. As a result, investors must either settle for the lower return or expose themselves to increased risk in order to earn the same return.

The market interest rate is really the sum of five factors: the risk-free interest rate, the default risk premium, the inflation risk premium, the liquidity risk premium, and the interest rate risk premium. The four risk premiums are different for different levels of risk, and for now we'll assume that they don't change.

Previously, we saw that an increase in interest rates causes the price of a bond to fall. The reverse is also true: if interest rates fall, bond prices increase. With that in mind, let's say that the Federal Reserve starts buying Treasury bonds in an effort to force their price up and their return down, thus lowering the interest rate by lowering the risk-free rate. With the exception of inflation, Treasury bonds are considered to be essentially risk free. Not only will the prices of Treasury bonds increase, all bond prices will increase, and it will be impossible to reinvest the money you had in bonds into new bonds at both the same return and the same level of risk.

Can Risk be Avoided?

Interest rate risk will always be present to some degree in bond investments, but there are some ways to mitigate the risk. Zero coupon bonds are a form of bond that makes no interest payment and pays back its face (par) value at maturity. If we assume that a zero-coupon bond with a par value of $1,000 that matures in 10 years is selling to yield 7.5%, its price at issue will be $485.19.

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Additional Activities

Interest Rate Risk - A Practical Exercise:

The following exercise is designed to help students apply their knowledge of the interest rate risk in real-life scenarios.


Imagine if you are a wealthy investor that manages his or her own money. Below are a variety of independent scenarios that can occur to your investments in the coming year. For each scenario, determine whether this is an example of (1) interest rate risk, (2) reinvestment rate risk, or (3) an interest rate risk mitigation strategy. Hint: The answer can also be none of these options!

See below.

1You purchase the interest rate futures contract at the beginning of the year at the cost of $700 per contract.
2Your current coupon payment of $500 per bond (5% coupon) can only yield 2% in other securities that have a similar risk level.
3Interest rates have fallen due to a sudden recession. Your bonds have increased in value by 10%!
4You have bonds denominated in foreign currency, and that currency has just weakened significantly.
5At the beginning of the year, prime interest rates rise since inflation has picked up. Your bond has lost 10% of its value!


See below.

1Interest rate risk mitigation strategy
2Reinvestment rate risk
3Interest rate risk
4Not applicable (currency risk)
5Interest rate risk

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