L11 - Managing Bond Portfolios

Question 1

What is Interest Rate Risk?

Answer 1

• As the interest rate rises (falls), bondholders experience capital loss/gain.
• Therefore, the sensitivity of bond price to changes in interest rate is of great concern to investors.
• Different bonds have different sensitivity to changes in interest rate (interest rate risk)
  
  • General principle: If the bondholder has to wait a long time to receive most of the promised payments, this bond is subject to high interest rate risk.

Question 2

What Bond features can affect interest rate risk exposure?

Answer 2

• looking at the scale we want to balance the payments –> the closer the balance is to the maturity time we say it has a longer average waiting time for payments to receive most of the interest payments and is subject to very high interest rate risk
• we compare all cashflows at their PV

Question 3

What is the coupon effect?

Answer 3

• How does coupon rate affect exposure to interest rate risk?
  
  • Higher coupon rate means a higher fractions of value is tied to coupons rather than the final payments of par value –> center of the balance is closer to the left
  • More earlier-payments –> short average waiting time –> lower interest rate risk
  • For lower coupon bonds, investors must wait longer to receive most of the payments –> higher interest rate risk

Question 4

What is the YMT effect?

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

How can you calculate Macaulay’s Duration?

Answer 5

• Helps calculate Interest rate Risk

Question 6

How can you calculate Interest Rate Sensitivity of bond?

Answer 6

If you multiply the duration equation by P you convert it from percentage change into a dollar amount

Question 7

How can you calculate modified duration?

Answer 7

Question 8

What are the Rules of Duration?

Answer 8

1. Duration is shorter than maturity for all bonds except zero coupon bonds. Duration of a zero-coupon bond equals maturity
2. .Holding time to maturity and YTM constant, duration is higher when coupon rate is lower
3. .Holding coupon and YTM constant, duration generally (but not always) increases with time to maturity.
4. .Holding coupon and time to maturity constant, duration is lower when YTM is higher.
5. .Duration of a perpetuity is ( 1 + y ) / y.

Question 9

How do you calculate Portfolio Duration?

Answer 9

Question 10

When is the Duration approximation not very accurate?

Answer 10

• When there is a large change in the interest rate
• Duration is a local concept

Question 11

Why is Duration a local concept?

Answer 11

• Due to convexity, the relationship between bond price, and yield is not linear (think of macro bond and interest rate graph)
• The Duration approximation is a linear relationship between ΔP and Δyield
  
  • ΔP/P = -D*Δy
• Duration rule is a good approximation for only small changes in bond yields

Question 12

How can you measure Convexity?

Answer 12

Question 13

How does can convexity affect the price change on a bond?

Answer 13

• convexity is also not symmetrically as a large fall in yield causes a greater decline in price rather than a large rise in yield
• If a bond has large convexity, the magnitude of a price increase due to yield decrease is greater than the magnitude of price decrease due to yield rise
• Convexity is a highly desirable feature when the interest rate is very volatile.

Question 14

Why is Duration important?

Answer 14

• It measures interest rate risk –> approximate price change when the yield changes
• Useful in risk management
  
  • –Asset-liability management (ALM): match the durations of a firm’s assets and liabilities
  • –Or hedge the interest rate risk of an investment

Question 15

What are the two passive bond portfolio strategies?

Answer 15

• Indexing: have the same risk-reward profile as the bond market index to which it is tied
• Immunization: seek to establish a portfolio with virtually no interest rate risk

Question 16

What are the two active management strategies?

Answer 16

Interest rate forecasting

–Identification of relative mispricing within the fixed-income market

Question 17

What is the Bond Index Strategy?

Answer 17

• Major bond indices:–Barclays Capital Aggregate Bond Index, Salomon Broad Investment Grade Index,etc.•Bond indices contain thousands of issues, many of which are infrequently traded.
  
  • –Difficult to purchase the securities at a fair market price
  • •Bond indices change their constituent bonds frequently
    
    • –Bonds are continually dropped from the index as their maturities fall below certain level (i.e. 1 year), and new bonds are added when they are issued.
• •Therefore, bond index funds hold only a representative sample of the bonds in the actual index.

Question 18

What is bond immunisation?

Answer 18

• Immunization is a way to control interest rate risk.
• •Widely used by pension funds, insurance companies, and banks, since these institutions often have a mismatch between asset and liability maturity structures
  
  • .–For example, banks’ liabilities are short-term deposits (Short-duration), but their assets are long-term loans or mortgages (long duration).
  • –If there is a sudden increase in interest rate, banks may have a liquidity problem.
    
    • Value of long-term assets remain the same but short-terms (liabilities) can change a lot
• •Result of immunization: Value of assets will track the value of liabilities regardless of changes in interest rate.

Question 19

DO FROM IMMUNISATION EXAMPLE!

Answer 19

1:19-1:57