Measurement of Interest Rate Risk

Here are some notes on the measurement of interest rate risk:

  • Duration: Duration is a measure of the sensitivity of a bond’s price to changes in interest rates. It is calculated as the weighted average of the time to maturity of the bond’s cash flows, with the weights being the present values of the cash flows. A bond with a longer duration is more sensitive to interest rate changes than a bond with a shorter duration.
  • Convexity: Convexity is a measure of the curvature of a bond’s price-yield curve. It is calculated as the second derivative of the bond’s price with respect to interest rates. Convexity measures how much the price of a bond changes for a given change in interest rates, taking into account the fact that the price-yield curve is not linear. A bond with more convexity is more sensitive to interest rate changes than a bond with less convexity.
  • Value at Risk (VaR): Value at risk (VaR) is a measure of the maximum loss that an investment portfolio can expect to incur with a given level of confidence over a given time horizon. VaR can be used to measure interest rate risk by calculating the VaR of the portfolio’s assets and liabilities under different interest rate scenarios.

Here are some MCQs on the measurement of interest rate risk:

  1. Which of the following is not a measure of interest rate risk?
    • Duration
    • Convexity
    • Value at risk (VaR)
    • Standard deviation
  2. If interest rates rise, what is the likely impact on the duration of a bond?
    • The duration will rise.
    • The duration will fall.
    • The duration will remain unchanged.
  3. If interest rates rise, what is the likely impact on the convexity of a bond?
    • The convexity will rise.
    • The convexity will fall.
    • The convexity will remain unchanged.

Answers:

  1. The answer is (d). Standard deviation is not a measure of interest rate risk. It is a measure of the volatility of an investment’s returns.
  2. The answer is (a). If interest rates rise, the duration of a bond will rise. This is because the present value of the bond’s cash flows will fall, which will make the bond more sensitive to interest rate changes.
  3. The answer is (a). If interest rates rise, the convexity of a bond will rise. This is because the curvature of the bond’s price-yield curve will become more pronounced, which will make the bond more sensitive to interest rate changes.