L17 - Management of Interest-Rate Risk

Question 1

How do interest rates affect bond pricing?

Answer 1

• First order effect: Bond prices and yields are negatively related
• Maturity matters: Prices of long-term bonds are more sensitive to interest-rate changes than short-term bonds
• Convexity: An increase in a bond’s YTM results in a smaller price decline than the price gain associated with a decrease of equal magnitude in the YTM.
  
  • – A zero with YTM of 5% costs 95.24
  • – If YTM goes up by 1%, the price changes to 94.34 (down by 0.90)
  • – If YTM goes down by 1%, the price changes to 96.15 (up by 0.91)
• Effect is larger for longer maturity

Question 2

How do you calculate Duration?

Answer 2

• Speed at which the bond is paid back in full

Question 3

What is the duration of a 3-year coupon bond with a coupon rate of 8% and a YTM of 10% ?

Answer 3

Question 4

Facts about Duration?

Answer 4

• Higher yield reduces the PV of all payment buy more so for more-distant ones
• Thus, a higher fraction of the bond’s value comes from its earlier payment
• This implies shorter average waiting time –> lower interest rate risk

Question 5

What are the two risks that arise from a change in the interest rate on an underlying asset?

Answer 5

• Investors and financial institutions are subject to interest-rate risk, for instance,
  
  • – homeowner: mortgage payments
  • – bank: short-term deposits and long-term loans
  • – pension fund: owns bonds and must pay retirees
• A change in the interest rate results in:
  
  • 1. price risk
  • 2. re-investment risk
• Want to construct a portfolio which is insensitive to interest-rate changes

Question 6

What is Cash-flow matching?

Answer 6

• A way of controlling for interest rate risk
• Match exactly the cash-flows of assets and liabilities:
  
  • – Then the portfolio is risk-free, in particular,
  • – it has no interest-rate risk.
  • – Can in principle be done using, for instance, zero-coupon bonds
• Problems with cash-flow matching:
• – it can be difficult to find securities that enable a perfect match
• – the needed securities may be illiquid and have high transactions costs

Question 7

What is Duration Matching: immunisation?

Answer 7

Question 8

Example of Immunsation?

Answer 8

Question 9

Problems with immunisation?

Answer 9

• Requires rebalancing
• It is an approximation that assumes:
  
  • – flat term structure of interest
  • – only risk of changes in the level of interest; not in the slope of the termstructure or other types of shape changes

Question 10

What is convexity?

Answer 10