Lecture 5 - Managing Bond Portfolios

Question 1

Fixed Income Strategies

Answer 1

1) Passive
2) Active
3) Mixed

Question 2

Passive Fixed Income Strategies

Answer 2

• Bond Index Funds
• Immunization
• Cash flow matching & Dedication

Question 3

Mixed Fixed Income Strategies

Answer 3

Contingent Immunization

Question 4

Bond Index Funds

Answer 4

Bond indexes contain thousands of issues that are infrequently traded

Question 5

Immunization

Answer 5

A strategy that matches durations of assets and liabilities to make net worth unaffected by interest rate movements.

Question 6

Immunization Con

Answer 6

Must rebalance portfolio frequently

Question 7

Why must you rebalance your portfolio frequently during immunization?

Answer 7

Portfolio duration does not change linearly with time

Question 8

Cash Flow Matching & Dedication

Answer 8

A form of immunization, matching cash flows from a bond portfolio with an obligation.

A strategy where specific assets are set aside to cover future liabilities.

Question 9

Active Fixed Income Strategies

Answer 9

• Interest Rate forecasting
• Capturing bond mispricings

Question 10

Two parts of Interest Rate Forecasting

Answer 10

1) Interest Rate Forecasting
2) Horizon Analysis

Question 11

Horizon Analysis

Answer 11

Predicts the future yield curve to estimate the price of a bond after a specific holding period.

Question 11

Interest Rate Forecasting

Answer 11

• Decrease portfolio duration when increase in rates is anticipated
• Increase portfolio duration when decrease in rates is anticipated

Question 12

6 Bond Pricing Relationships

Answer 12

Price & Yield: When price goes up, yield goes down.

YTM Impact: Price drops less when yields rise than it gains when they fall.

Long Bonds: Longer bonds are more sensitive to rates.

Maturity: Sensitivity increases but slows down over time.

Coupon Rate: Higher coupons mean less sensitivity.

Yield Sensitivity: Higher yields mean less sensitivity.

Question 13

Substitution Swap

Answer 13

Exchange one bond for a nearly identical one (sell over valued, buy under valued)

Question 14

Intermarket spread swap

Answer 14

An exchange or sale of one bond for another with different terms

Question 15

Rate anticipation swap

Answer 15

When interest rates predicted to increase, PM will sell long duration bonds and buy short duration bonds

Question 16

Pure Yield Pick up Swap

Answer 16

Exchanging one set of bonds for another, intending to increase the yield received on those bonds.

Question 17

Tax Swap

Answer 17

Bond swap designed to exploit a tax advantage

Question 18

Type of Mixed Active/Passive FI Strategy

Answer 18

Contingent Immunization

Question 19

Contingent Immunization

Answer 19

If the portfolio exceeds the target return, the investor can actively manage it.

If the performance falls to the trigger level, the portfolio is immunized

Question 20

Duration

Answer 20

Duration measures how long it takes, in years, for an investor to be repaid a bond’s price through its total cash flows.

Question 21

What is the duration for zero coupon bonds

Answer 21

Duration = Maturity

Question 22

What is the duration for non-zero coupon bonds

Answer 22

Duration < maturity

Question 23

Change in Price (%)

Answer 23

∆P/P = - (D/1+y) x ∆y

Question 24

D

Answer 24

Macauley Duration

Question 25

Macauley Duration (D) Formula

Answer 25

= ∑ (t x CF)/P

Question 26

D*

Answer 26

Modified Duration

Question 27

D* = ?

Answer 27

D* = D/1 + y

Question 28

A bond has a three-year maturity, pays a 10% coupon, and that interest rates are 5%.

Find market price of bond:

Calculate the Macauley duration

Find Modified duration:

Answer 28

n=3; PMT=100; I/Y=5; FV=1000; COMP PV –> 1136.16

Macauley duration = ($95.24 * 1 / $1,136.16) + ($90.70 * 2 / $1,136.16) + ($950.22 * 3 )/ $1,136.16) = 2.753

Modified duration = 2.753 / (1 + 0.05) = 2.621

Question 29

Bond Convexity

Answer 29

Measures the change in duration as interest rates change

Question 30

Draw Bond Price Convexity Graph

Answer 30

See Slide 16

Question 31

Why do investors like convexity?

Answer 31

1. Higher convexity gains more in price when yields fall
2. The more volatile interest rates, the more attractive
3. Bonds with greater convexity tend to have a higher price and/or lower yields

Question 33

New Financial Instruments

Answer 33

• Inverse Floaters
• MBS Derivatives

Question 34

Inverse Floaters

Answer 34

Bonds that pay a lower coupon if a specified interest rate increases

Question 35

MBS Derivatives

Answer 35

• Collateralized Mortgage Obligations
• Interest Only Strips
• Principal Only Strips

Question 36

A 10-year U.S. Treasury bond has a yield to maturity of 4.63% and a Macaulay duration of 8.25 years. If the market yield changes by 140 basis points, what is the percentage change in the bond’s price?

Answer 36

∆P/P = -D x ∆(1 + y)/1 + y)

Change in Price % = -D/(1+y) x (change in y) = -8.25/(1.0463) x .0140 = -.1104 = -11.04%

Question 37

Consider a 4%, 12-year bond with a yield to maturity of 5%. If the price of the bond changes by 8.5% when market yield changes by 96 basis points, what must be the bond’s Macaulay duration?

Answer 37

∆P/P = -D x ∆(1 + y)/1 + y)

Change in Price % = -D/(1+y) x (change in y)
.085 = - D /(1.05) x .0096
.085 = -D x .009143
-D = .085/.009143 = 9.30 years

Question 38

You predict that interest rates in Canada are going to continue to decrease until late 2025. Which bond should you choose?

Answer 38

You would prefer the bond with the longest duration – so that would be a bond with a long maturity and a low coupon

Question 39

A newly issued bond has the following characteristics:

Coupon Yield to Maturity Maturity Macaulay Duration
5% 8% 15 years 10 years

Calculate the modified duration

Answer 39

D* = D/1 + y
= 10/(1 + 0.08) = 9.26 years

Question 40

Explain why modified duration is a better measure than maturity when calculating the bond’s sensitivity to changes in interest rates.

Answer 40

Maturity only looks at the final cash flow of a bond, while modified duration also considers the size and timing of coupon payments and the interest rate (yield to maturity). Modified duration shows how much the bond’s price will change with a change in interest rates.

Question 41

What happens to modified duration if coupon increases?

Answer 41

Modified duration decreases since coupon payments increase so principal payment is less sensitive to interest rate changes

Question 42

What happens to modified duration if coupon decreases?

Answer 42

Modified duration increases because cash flows decreas so principal investment is sensitive to interest rate changes

Question 43

A 9-year bond has a yield of 10% and a duration of 7.194 years. If the market yield changes by 50 basis points, what is the percentage change in the bond’s price?

Answer 43

• D X ∆y = -(7.194/1.10) x 0.005 = -3.27%
  1 + y

Question 44

The historical yield spread between AAA bonds and Treasury bonds widened dramatically in 2008. If you believe the spread will soon return to more typical historical levels, what should
you do? This would be an example of what sort of bond swap?

Answer 44

Rate anticipation swap

Question 45

You predict that interest rates are about to fall. Which bond will give you the highest capital gain?

Answer 45

Zero Coupon, Long Maturity

Question 46

Long-term Treasury bonds currently are selling at yields to maturity of nearly 8%. You expect interest rates to fall. The rest of the market thinks that they will remain unchanged over the coming year. In each question, choose the bond that will provide the higher holding-period return over the next year if you are correct. Briefly explain your answer.

a. i. A Baa-rated bond with coupon rate 8% and time to maturity 20 years.
ii. An Aaa-rated bond with coupon rate of 8% and time to maturity 20 years.
b. i. An A-rated bond with coupon rate 4% and maturity 20 years, callable at 105.
ii. An A-rated bond with coupon rate 8% and maturity 20 years, callable at 105.
c. i. A 6% coupon noncallable T-bond with maturity 20 years and YTM = 8%.
ii. A 9% coupon noncallable T-bond with maturity 20 years and YTM = 8%.

Answer 46

In each case, choose the longer-duration bond in order to benefit from a rate decrease.
a. ii. The Aaa-rated bond has the lower yield to maturity and therefore the longer duration.
b. i. The lower-coupon bond has the longer duration and greater de facto call protection.
c. i. The lower coupon bond has the longer duration.

Question 47

A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted change in price using the duration concept?

Answer 47

Bond price decreases by $80.00, calculated as follows:
10 × 0.01 × 800 = 80.00

Question 48

A bond with annual coupon payments has a coupon rate of 8%, yield to maturity of 10%, and Macaulay duration of 9 years. What is the bond’s modified duration?

Answer 48

9/1.10 = 8.18

Question 49

When interest rates decline, the duration of a 30-year bond selling at a premium:

Answer 49

Declines

Question 50

If a bond manager swaps a bond for one that is identical in terms of coupon rate, maturity, and credit quality but offers a higher yield to maturity, the swap is:

Answer 50

A substitution swap

Question 51

Which bond has the longest duration?

i. 8-year maturity, 6% coupon.
ii. 8-year maturity, 11% coupon.
iii. 15-year maturity, 6% coupon.
iv. 15-year maturity, 11% coupon.

Answer 51

iii. 15-year maturity, 6% coupon.

Question 52

You are the manager for the bond portfolio of a pension fund. The policies of the fund allow for the use of active strategies in managing the bond portfolio. It appears that the economic cycle is beginning to mature, inflation is expected to accelerate, and in an effort to contain the economic expansion, central bank policy is moving toward constraint. For each of the situations below, state which one of the two bonds you would prefer.

Briefly justify your answer in each case.

Government of Canada (Canadian pay) 4% due in 2014 and priced at 98.75 to yield 4.50% to maturity.
or
Government of Canada (Canadian pay) 4% due in 2024 and priced at 91.75 to yield 5.19% to maturity.

Texas Power and Light Co. 5½ due in 2019, rated AAA, and priced at 90 to yield 7.02% to maturity.
or
Arizona Public Service Co. 5.45 due in 2019, rated A–, and priced at 85 to yield 8.05% to maturity.

Commonwealth Edison 2¾ due in 2018, rated Baa, and priced at 81 to yield 7.2% to maturity.
or
Commonwealth Edison 93/8 due in 2018, rated Baa, and priced at 114.40 to yield 7.2% to maturity.

Shell Oil Co. 6½ sinking fund debentures due in 2023, rated AAA (sinking fund begins September 2010 at par), and priced at 89 to yield 7.1% to maturity.
or
Warner-Lambert 67/8 sinking fund debentures due in 2023, rated AAA (sinking fund begins April 2017 at par), and priced at 89 to yield 7.1% to maturity.

Bank of Montreal (Canadian pay) 5% certificates of deposit due in 2012, rated AAA, and priced at 100 to yield 5% to maturity.
or
Bank of Montreal (Canadian pay) floating-rate note due in 2016, rated AAA. Coupon currently set at 3.7% and priced at 100 (coupon adjusted semiannually to .5% above the 3-month Government of Canada Treasury bill rate).

Answer 52

a. Choose the short maturity (2020) bond.

b. The Arizona bond likely has lower duration. The Arizona coupons are slightly lower, but the Arizona yield is higher.

c. Choose the 9 3/8 % coupon bond. The maturities are approximately equal, but the 9 3/8 % coupon is much higher, resulting in a lower duration.

d. The duration of the Shell bond is lower if the effect of the earlier start of sinking fund redemption dominates its slightly lower coupon rate.

e. The floating rate note has a duration that approximates the adjustment period, which is only six months, thus choose the floating rate note.