Topic 12 Interest Rate Risk and Managing Bond Portfolios

Question 1

Macaulay’s Duration

Answer 1

-Measures time to get cash flows
-Weighted average of time takes to get each CF
-Weighted based on importance of cash flow today
givenForm=D=sum(t*pvt/bond value)

Question 2

3 rules of Macaulay’s duration

Answer 2

1) Duration increases as coupon rate decreases
2) Duration increases as yield decreases
3) Duration generally increases as maturity increases

Question 3

Modified Duration

Answer 3

D* and is given in years
-y denominator is per payment period rate
-Delta y is the yearly forecast for yield rate changes
-Decent for measuring sensitivity to changes in yields –in small changes accurate forecast

Question 4

4 problems of Duration

Answer 4

1) duration assumes a flat yield curve
2) Duration assumes parallel shifts in the yield curve
3) Duration is linear approx of convex relationship
4) Duration changes over time
-requires a rebalancing of portfolio

Question 5

Convexity

Answer 5

=rate of change of the slope of the yield curve expressed as a fraction of the bond price
-measures the curvature of the price vs yield curve
-measures rate of change in the modified duration
-convexity is always positive except for buyout agreements AND lenders like more relatively positive convexity

Question 6

Bond Management

Answer 6

How to protect the value of a bond portfolio with changing yields?
-have assets and liabilities that are affected by the interest rate changes
Solutions: Cash flow matching or Immunization using Duration

Question 7

Cash Flow Matching

Answer 7

Buy zero coupon bonds that provide payment at the exact time and same amount as liability
-multiperiod liabilities: match each liability with one discount bond
Advantage: simple and no need to rebalance
Disadvantage: securities may not exist, or may be too expensive

Question 8

Immunization

Answer 8

=Invest in a portfolio that has the same duration as the liability portfolio
-If interest rates change-> changes in prices of assets cancel out changes in prices of liabilities
Duration portfolio of assets = duration portfolio of liabilities

Question 9

How to immunize

Answer 9

1) Calculate duration of individual assets and liabilities
2) Duration of portfolio = VALUE WEIGHTED duration of securities in portfolio
3) Combine assets such that the asset portfolio duration = liability portfolio duration
4) Calculate present value of all liabilities
5) Find the amount of each security represented in asset in portfolio by the identity
-PV Liabilities = PV assets

Question 10

Issues with Immunization

Answer 10

Relies on duration
-assumes parallel shifts in rates ->only good for small changes in rates
thus need to rebalance as rates and duration changes-> costly bc of transaction costs

Question 11

Active Bond Management Strategies

Answer 11

-Gain from private knowledge of movement of interest rates or mispricing
–thus try to position a portfolio to gain from anticipated changes in future rates
1) Substitution swap- Select two almost identical bonds and believe there is mispricing
–purchase cheap bond and sell expensive bond
2) intermarket spread swap-select two bonds from different sectors in market and believe spread between sectors temporarily mispriced
3) Rate anticipation swap-believe rates will increase thus sell bond with longer duration and buy bond with lower
4) Pure Yield Pickup- Increase expected return by selling safe bond and purchasing one with higher risk