Managing Interest Rate Risk

Question 1

fixed-income investments are exposed to

Answer 1

interest rate risk

Interest rate risk: values are impacted by changes in interest rates

Question 2

Properties for relationship between bond prices & yield (interest rates):

Answer 2

1. bond prices and yield are inversely related
2. increase in yield produces a smaller price change than same size decrease in yield
3. as term of bond increases, price becomes more sensitive to yield changes
4. sensitivity of bond prices to yield increases at a decreasing rate as maturity increases
5. lower coupon bonds are more sensitive to changes in yields
6. sensitivity of bond prices to yield are inversely related to yield

Question 3

Duration & uses

Answer 3

measure of average maturity of financial instrument’s cash flows

several uses in fixed income portfolio management:

summary statistic of effective average maturity

helps immunize portfolios from interest rate risk

measures interest rate sensitivity

Question 4

Macaulay’s duration

Answer 4

weighted average of lengths of time to future cash flows

Question 5

Modified duration

Answer 5

based on Macaulay’s, it is measure of duration that is used in practice

-If rates are continuous, Modified duration equals Macaulay’s duration

Question 6

Properties of Duration

Answer 6

1. duration of zero-coupon bond = its time to maturity
2. duration decreases as coupon rate increases
3. duration generally increases as maturity increases
4. duration decreases as yield to maturity increases
   - As interest increases, the more distant payments receive more discounting than the closer ones so portion of the total PV (future payments) associated with the closer payments therefore increases, reducing the duration
5. duration of perpetuity = (1+y)/y

Question 7

Convexity

Answer 7

The graph of the change in bond price to change in yield is convex

duration approximation always understates the bond value because according to -D*Δy, graph of change in bond price to change in yield should be a straight line

• it understates the increase when yields fall
• it overstates the losses when yields rise.

Question 8

investors like bonds with higher convexity

Answer 8

because as convexity increases, a bond appreciates more when yield fall and depreciates less when yield rise (increase in bond price from a given decrease in interest exceeds the decrease in price from the same increase in interest)

Question 9

Accounting for this convexity will improve

Answer 9

the accuracy of the approximation:

ΔP/P = -(D*)Δy + 0.5Convexity(Δy)^2

Question 10

Callable bond & convexity

Answer 10

can be recalled by issuer if its price reaches a certain level

• convexity is different to that of a regular bond because callability option places a ceiling on price to which it can rise
• when yield falls enough, value of bond is compressed to call price
• shape of curve at this region is said to have negative convexity
• negative convexity is unfavorable to investors as an increase in interest rates produces a larger price decline than price increase produced by an equivalent decrease in interest rates

Question 11

Effective Duration

Answer 11

The future cash flows of callable bonds are unknown so effective duration needs to be used.

Effective duration = -(ΔP/P) / Δr

Question 12

passive investors believe

Answer 12

that bond prices are fair and therefore rather than searching for underpriced bonds, main goal is to control risk of fixed income portfolio

Question 13

Passive Bond Management

Answer 13

• indexing
• immunization
• cash flow matching

Question 14

indexing

Answer 14

Creating a portfolio that resembles the composition of a market index.

Question 15

Problems associated with forming this portfolio (indexing)

Answer 15

• The index could consist of 000s of securities
• The composition of the bond index changes more often than that of the stock index. Bonds are dropped from index as their maturities fall under a year and new bonds are added to index as they are issued
• due to difficulties, stratified sampling is utilized
• involves stratifying bond market into several classes; percentage of bonds in index that fall into each class is then calculated and the portfolio manager creates a portfolio with representation from each cell

Question 16

Immunization

Answer 16

strategies used to protect the portfolio from interest rate fluctuations

process where investor creates portfolio with duration equal to investment horizon

-> price risk and reinvestment risk will cancel out

Question 17

when immunizing, we need to keep in mind

Answer 17

that duration is not constant

• it will change as the rates change
• it will fall as time passes.

Question 18

in order to keep it immunized, it is necessary to

Answer 18

to rebalance the portfolio: rebalancing involved realigning portfolio to produce a duration = horizon length

Question 19

Practical limitations of immunization

Answer 19

• need to rebalance as interest rates change
• will need to rebalance as time changes

Question 20

Immunization problems

Answer 20

• it is based on a measure of duration that makes the assumption that the yield curve is flat
• only effective for parallel shifts of yield curve
• inappropriate in an inflationary environment

Question 21

Optimal strategy, given no constraints, for immunizing the liability

Answer 21

• Cash flow matching: match the cash flows of the assets and liabilities
• Very difficult to find the right combination of bonds that would produce an aggregate cash flow that would match that of the liability

Question 22

Cash Flow Matching/ Dedication

Answer 22

Due to the problems of immunization, portfolio managers may consider alternatives:

• Cash Flow Matching: buy a zero which will make a payment that exactly matches the future cash obligation.
• Dedication Strategy: Purchase a combination of coupon paying bonds and/ or zeros to match a series of obligations.

Question 23

advantages and disadvantages of cashflow matching

Answer 23

Advantages include: -automatically immunizes the portfolio from changing interest rates -rebalancing will not be necessary

Disadvantage: -hard to implement because they impose strong constraints on the bonds that can be selected

Question 24

Active management

Answer 24

portfolio manager tries to gain additional value by actively selecting bonds that he believes will provide better returns than a benchmark index.

Question 25

2 sources of value in active management

Answer 25

• interest rate forecasting: increase portfolio duration if rate declines are expected
• identification of relative mispricing

Question 26

4 types of bond swaps

Answer 26

• Substitution swap: exchange of a bond for an almost identical substitute, due to a belief that the 2 bonds are temporarily mispriced
• Intermarket spread swap: could be pursued if the investor believes that the yield spread between two sectors is temporarily out of line.
• Rate anticipation swap: move to longer duration bonds if you forecast that rates will decrease
• Pure yield pickup swap: increase returns by moving to a higher yield bond

Question 27

Mortgage Backed Securities, MBS

Answer 27

mortgagors that sell mortgage loans to federal agencies which then go on to combine several and resell as MBS

• one of risks to investors is that homeowner has right to prepay the loan at any time
• may do this if interest rates reduce as they can take out a loan at a lower rate and then use proceeds to pay off original loan
• MBS can be viewed as being callable

Question 28

Mortgage-backed derivatives

Answer 28

created from MBS

Mortgage-backed derivatives help investors manage interest rate risk.

A CMO segments the cash flow stream from MBS into different tranches with different effective durations

• different tranches have different levels of risk: lower have principal repaid before the higher so different tranches have different effective durations
• investors can use these investments to modify their portfolio duration

Question 29

can hedge risk of increasing interest rates by taking an offsetting position in

Answer 29

interest rate futures (Treasury bond contract)

Question 30

Price value of a basis point

Answer 30

Price value of a basis point (PVBP) is the sensitivity of the value of the unprotected portfolio to changes in interest rate

PVBP = Change in portfolio value / Predicted change in yield (in basis points)

Question 31

Hedge ratio

Answer 31

Hedge ratio (H) = PVBP Portfolio / PVBP hedge vehicle

H = number of future contracts required to offset portfolio’s exposure to interest rate fluctuations