Managing Interest Rate Risk Flashcards
fixed-income investments are exposed to
interest rate risk
Interest rate risk: values are impacted by changes in interest rates
Properties for relationship between bond prices & yield (interest rates):
- bond prices and yield are inversely related
- increase in yield produces a smaller price change than same size decrease in yield
- as term of bond increases, price becomes more sensitive to yield changes
- sensitivity of bond prices to yield increases at a decreasing rate as maturity increases
- lower coupon bonds are more sensitive to changes in yields
- sensitivity of bond prices to yield are inversely related to yield
Duration & uses
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
Macaulay’s duration
weighted average of lengths of time to future cash flows
Modified duration
based on Macaulay’s, it is measure of duration that is used in practice
-If rates are continuous, Modified duration equals Macaulay’s duration
Properties of Duration
- duration of zero-coupon bond = its time to maturity
- duration decreases as coupon rate increases
- duration generally increases as maturity increases
- 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 - duration of perpetuity = (1+y)/y
Convexity
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.
investors like bonds with higher convexity
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)
Accounting for this convexity will improve
the accuracy of the approximation:
ΔP/P = -(D*)Δy + 0.5Convexity(Δy)^2
Callable bond & convexity
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
Effective Duration
The future cash flows of callable bonds are unknown so effective duration needs to be used.
Effective duration = -(ΔP/P) / Δr
passive investors believe
that bond prices are fair and therefore rather than searching for underpriced bonds, main goal is to control risk of fixed income portfolio
Passive Bond Management
- indexing
- immunization
- cash flow matching
indexing
Creating a portfolio that resembles the composition of a market index.
Problems associated with forming this portfolio (indexing)
- 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
Immunization
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
when immunizing, we need to keep in mind
that duration is not constant
- it will change as the rates change
- it will fall as time passes.
in order to keep it immunized, it is necessary to
to rebalance the portfolio: rebalancing involved realigning portfolio to produce a duration = horizon length
Practical limitations of immunization
- need to rebalance as interest rates change
- will need to rebalance as time changes
Immunization problems
- 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
Optimal strategy, given no constraints, for immunizing the liability
- 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
Cash Flow Matching/ Dedication
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.
advantages and disadvantages of cashflow matching
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
Active management
portfolio manager tries to gain additional value by actively selecting bonds that he believes will provide better returns than a benchmark index.
2 sources of value in active management
- interest rate forecasting: increase portfolio duration if rate declines are expected
- identification of relative mispricing
4 types of bond swaps
- 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
Mortgage Backed Securities, MBS
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
Mortgage-backed derivatives
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
can hedge risk of increasing interest rates by taking an offsetting position in
interest rate futures (Treasury bond contract)
Price value of a basis point
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)
Hedge ratio
Hedge ratio (H) = PVBP Portfolio / PVBP hedge vehicle
H = number of future contracts required to offset portfolio’s exposure to interest rate fluctuations
