Find the default risk premium for a debt security given the following information: inflation premium – 2.5 percent, maturity risk premium = 2.5 percent, real rate = 3 percent, liquidity premium = 1.5 percent, and nominal interest rate = 14 percent.
The Correct Answer and Explanation is:
Let’s start by defining the components and the formula involved.
Given:
- Inflation premium (IP) = 2.5%
- Maturity risk premium (MRP) = 2.5%
- Real rate (r) = 3%
- Liquidity premium (LP) = 1.5%
- Nominal interest rate (i) = 14%
Goal:
Find the default risk premium (DRP).
Key formula for nominal interest rate:
i=r+IP+MRP+LP+DRPi = r + IP + MRP + LP + DRP
This is based on the idea that the nominal interest rate on a debt security is the sum of the real rate plus all the risk and inflation premiums associated with the security.
Step 1: Write the formula with the known values.
14%=3%+2.5%+2.5%+1.5%+DRP14\% = 3\% + 2.5\% + 2.5\% + 1.5\% + DRP
Step 2: Sum the known premiums and the real rate:
3%+2.5%+2.5%+1.5%=9.5%3\% + 2.5\% + 2.5\% + 1.5\% = 9.5\%
Step 3: Solve for DRP:
DRP=14%−9.5%=4.5%DRP = 14\% – 9.5\% = 4.5\%
Answer:
The default risk premium is 4.5%.
Explanation
The nominal interest rate on a debt security reflects the compensation investors require to hold the security, taking into account various factors such as the time value of money, expected inflation, and risks related to the security. The real rate of interest (3%) reflects the return investors require over and above inflation, compensating for the opportunity cost of investing capital. The inflation premium (2.5%) accounts for the expected loss in purchasing power due to inflation during the investment period.
In addition, the maturity risk premium (2.5%) compensates investors for interest rate risk that increases with longer maturities. The liquidity premium (1.5%) reflects the ease with which the security can be sold without significant price concession—less liquid securities require higher premiums.
The default risk premium (DRP) is the extra return demanded by investors to compensate for the possibility that the issuer may fail to make interest or principal payments as promised. It reflects the credit risk of the borrower. The higher the chance of default, the greater this premium.
Given the nominal interest rate of 14%, which is relatively high compared to the sum of the real rate, inflation premium, maturity risk premium, and liquidity premium (totaling 9.5%), the difference of 4.5% is attributed to default risk. This indicates that investors perceive a significant chance of default or credit risk in this security.
Understanding the DRP is crucial for both investors and issuers because it affects borrowing costs and investment returns. A higher DRP means the issuer will pay more to borrow funds, while investors demand higher returns to compensate for greater risk
