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Chapter 11 Managing Bond Portfolios Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights...
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Transcript of Chapter 11 Managing Bond Portfolios Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights...
Chapter 11
Managing Bond
Portfolios
Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
11.1 Interest Rate Risk
11-2
Interest Rate Sensitivity1. Inverse relationship between bond price and
interest rates (or yields)
2. Long-term bonds are more price sensitive than short-term bonds
3. Sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases
11-3
Interest Rate Sensitivity (cont)
4. A bond’s price sensitivity is inversely related to the bond’s coupon
5. Sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling
6. An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a decrease in yield
11-4
Summary of Interest Rate Sensitivity
The concept: • Any security that gives an investor more money back
sooner (as a % of your investment) will have lower price volatility when interest rates change.
• Maturity is a major determinant of bond price sensitivity to interest rate changes, but
• It is not the only factor; in particular the coupon rate and the current ytm are also major determinants.
11-5
Change in Bond Price as a Function of YTM
11-6
Duration
1 2 3 4 5
$100 $100 $100 $100 $1100
Consider the following 5 year 10% coupon annual payment corporate bond:
• Because the bond pays cash prior to maturity it has an “effective” maturity less than 5 years.
• We can think of this bond as a portfolio of 5 zero coupon bonds with the given maturities.
• The average maturity of the five zeros would be the coupon bond’s effective maturity.
• We need a way to calculate the effective maturity.
11-7
Duration• Duration is the term for the effective maturity of a bond
• Time value of money tells us we must calculate the present value of each of the five zero coupon bonds to construct an average.
• We then need to take the present value of each zero and divide it by the price of the coupon bond. This tells us what percentage of our money we get back each year.
• We can now construct the weighted average of the times until each payment is received.
11-8
Duration Formula
icePr)ytm1(
CF
W
N
1tt
t
t
N
1tt tWDur
Wt = Weight of time t, present value of the cash flow earned in time t as a percent of the amount invested
CFt = Cash Flow in Time t, coupon in all periods except terminal period when it is the sum of the coupon and the principal
ytm = yield to maturity; Price = bond’s price
Dur = Duration
11-9
Year (T) Cash Flow PV @8%
CFT / (1+ytm)T % of Value PV/Price
Weighted % of Value (PV/Price)*T
1 $ 90 2 90 3 90 4 $1090
Totals
Calculating the duration of a 9% coupon, 8% ytm, 4 year annual payment bond priced at $1033.12,
$1,033.12 100.00% 3.5396 yrs
$ 83.33
77.16
71.45
$801.18
8.06%
7.47%
6.92%
77.55%
0.0806
0.1494
0.2076
3.1020
Duration = 3.5396 years
icePr)ytm1(
CF
W
N
1tt
t
t
N
1tt tWDur
11-10
Using Excel to Calculate Duration
Excel can be used to calculate a bond’s duration.
Usage notes:
•The dates should be entered using the formulas given
•If you don’t know the actual settlement date and maturity date, set the 6th term in the duration formulae to 0 as shown and pick a maturity date with the same month and day as the settlement date and the correct number of years after the settlement date.
•The par is not needed
11-11
More on Duration1. Duration increases with maturity
2. A higher coupon results in a lower duration
3. Duration is shorter than maturity for all bonds except zero coupon bonds
4. Duration is equal to maturity for zero coupon bonds
5. All else equal, duration is shorter at higher interest rates
11-12
More on Duration5. The duration of a level payment perpetuity
is ytmy ;y
y1Dperpetuity
11-13
Figure 11.2 Duration as a Function of Maturity
11-14
Duration/Price Relationship• Price change is proportional to duration
and not to maturity
P/P = -D x [y / (1+y)]
D* = modified duration
D* = D / (1+y)
P/P = - D* x y
D = Duration
11-15
11.2 Passive Bond Management
11-16
Interest Rate RiskInterest rate risk is the possibility that an investor does not earn the promised ytm because of interest rate changes.
A bond investor faces two types of interest rate risk:
1.Price risk: The risk that an investor cannot sell the bond for as much as anticipated. An increase in interest rates reduces the sale price.
2.Reinvestment risk: The risk that the investor will not be able to reinvest the coupons at the promised yield rate. A decrease in interest rates reduces the future value of the reinvested coupons.
The two types of risk are potentially offsetting.
11-17
Immunization• Immunization: An investment strategy
designed to ensure the investor earns the promised ytm.
• A form of passive management, two versions1. Target date immunization
• Attempt to earn the promised yield on the bond over the investment horizon.
• Accomplished by matching duration of the bond to the investment horizon
11-18
Terminal Value of an Immunized Portfolio over a 5 year Horizon
11-19
Figure 11.3 Growth of Invested Funds
11-20
Immunization
2. Net worth immunization
• The equity of an institution can be immunized by matching the duration of the assets to the duration of the liabilities.
11-21
Figure 11.4 Immunization
11-22
Cash Flow Matching and Dedication
• Cash flow from the bond and the obligation exactly offset each other
– Automatically immunizes a portfolio from interest rate movements
• Not widely pursued, too limiting in terms of choice of bonds
• May not be feasible due to lack of availability of investments needed
11-23
Problems with Immunization
1. May be a suboptimal strategy
2. Does not work as well for complex portfolios with option components, nor for large interest rate changes
3. Requires rebalancing of the portfolio periodically, which then incurs transaction costs– Rebalancing is required when interest rates move– Rebalancing is required over time
11-24
11.3 Convexity
11-25
The Need for Convexity
• Duration is only an approximation
• Duration asserts that the percentage price change is linearly related to the change in the bond’s yield– Underestimates the increase in bond prices
when yield falls– Overestimates the decline in price when the
yield rises
11-26
Pricing Error Due to Convexity
11-27
Convexity: Definition and Usage
2yConvexity2/1)y1(
yD
P
P
n
1t
2t
t2
)tt()y1(
CF
)y1(P
1Convexity
Where: CFt is the cash flow (interest and/or principal) at time t and y = ytm
The prediction model including convexity is:
11-28
Bond Price Convexity
11-29
Convexity of Two Bonds
11-30
Prediction Improvement With Convexity
11-31
11.4 Active Bond Management
11-32
Swapping Strategies1. Substitution swap
– Exchanging one bond for another with very similar characteristics but more attractively priced
2. Intermarket spread swap– Exploiting deviations in spreads between two market segments
3. Rate anticipation swap– Choosing a duration different than your investment horizon to
exploit a rate change.• Rate increase: Choose D > Investment horizon• Rate decrease: Choose D < Investment horizon
11-33
Swapping Strategies4. Pure yield pickup
– Switching to a higher yielding bond, may be longer maturity if the term structure is upward sloping or may be lower default rating.
5. Tax swap– Swapping bonds for tax purposes, for example
selling a bond that has dropped in price to realize a capital loss that may be used to offset a capital gain in another security
11-34
Horizon Analysis
• Analyst selects a particular investment period and predicts bond yields at the end of that period in order to forecast the bond’s HPY
11-35