Chapter 11
What can you say about change in price using modified duration only and using modified duration and convexity
using duration only as an increase in bonds's YTM results in equivalent price change as a decrease in YTM of equal magnitude e Using both duration & convexity, an increase in bonds YTM results in a smaller price change than a decrease in yield of equal magnitude
Duration of perpetuity is...
(1+y)/y
How do you comprise a portfolio of zero coupon bonds and perpetuities to immunize a future obligation?
**slide 14
How does coupon rate affect duration?
higher coupons mean more cash flows sooner, which reduces the bond's duration
Holding other factors constant, a bond's duration and interest-rate sensitivity is ____ when a bond's YTM is ______
higher, lower
Generally, prices move more for ___ when ___ change
longer-term bonds when yields change
Characteristics of bonds which determine their price sensitivity to interest rates
1. bond prices and yields are inversely related 2. increase in bond's YTM results in smaller price change than yield decreases of equal magnitude 3. long-term bond prices are more sensitive to interest rate changes than short-term bonds 4. as maturity increases, sensitivity of bond prices to changes in yield increases at decreasing rate 5. interest rate risk is inversely related to bond's coupon rate; low-coupon bonds are more sensitive to interest rates 6. sensitivity of bond's price-to-yield change is inversely related to current yield to maturity
2 reasons why Marcaulay's duration is important
1. duration is a simple measure of the effective average maturity of the portfolio 2. it turns out to be an essential tool in immunizing portfolios from interest rate risk 3. duration is a measure of the interest rate sensitivity of a bond portfolio
Assume XYZ bond fund buys Bond A, Bond B, Bond C, and Bond D. Assume GGG bond fund buys Bond T, Bond U, Bond V, and Bond X. If you know both bond funds have the same duration, what can you tell me?
???
What determines duration?
If we wish to speculate on interest rates, duration tells us how strong a bet we are making -Conversely, if we wish to remain "neutral" on rates, and simply match the interest rate sensitivity of a chosen bond market index, duration allows us to measure that sensitivity and mimic it in our own portfolio.
Why do investors like convexity?
More convexity = greater price increases, smaller price decreases when interest rates fluctuate by larger amounts calculating the change in price with duration is only an approximation -the convexity adjustment increases our accuracy **convexity matters more for large changes in yields
A 9% coupon, 8-year maturity bond with annual payments, is selling at a YTM of 10%. It can be shown that the duration of this bond is 5.97 years. Would the duration of the bond be higher or lower if the bond made semiannual payments and why?
The duration would be lower on the semi-annual coupon bond -Duration measures the effective maturity of the bond, taking into account the timing of each payment -Since a semiannual bond makes payments earlier than the corresponding annual bond, the effective maturity is lower, which means the duration is lower.
If you use modified duration estimation vs. using modified duration and convexity rule to estimate change in prices, how would the answers differ?
answer from project****
Holding time and YTM constant, a bond's duration and interest-rate sensitivity is _____ when a bond's coupon price is ____
higher, lower
Holding the coupon rate constant, a bond's duration and interest rate sensitivity generally ____ with time to maturity
increase -long duration bonds generally have more duration risk
_______ bonds are more sensitive to interest rate movements than _______, thus in some sense, zero-coupon bonds must...
long-term bonds, short-term bonds must represent a longer term investment than an equal-time-to-maturity coupon bond
What does Marcaulay's duration tell us?
measures effective bond maturity and is the weighted average of the times (t) until each payment, where the weight is the present value of each cash flow as a % of the bond's price
What is immunization? Why is it important to many financial firms (give examples)
strategy to shield net worth from interest rate movements duration-matched assets and liabilities let the asset portfolio meet the firm's obligations despite interest rate movements -example: insurance companies with a future fixed obligation might consider immunization a reasonable risk management policy -if you match the duration of your bonds to the duration of your pension obligations, which are like a bond, then your portfolio is immunized. Fixed-income investors face two offsetting types of rate risk: price risk and reinvestment rate risk -if the portfolio duration is chosen to equal the investment horizon, these two effects will cancel out exactly and thus, the portfolio is immunized
What is convexity?
the curvature of the price-yield relationship -the rate of change of the slope of the price-yield curve, expressed as a fraction of the bond price -bonds with higher convexity = higher curvature in the price-yield relationship **slide 16
Zero-coupon bond's duration is...
time to maturity
Modified duration
used to get the percent change in price for a bond when bond yield's change -because the percentage change in the bond price is proportional to modified duration, modified duration is a natural measure of the bond's exposure to interest rate volatility