all rights reserved dr david p echevarria 1 chapter 8 bond valuation and risk

Dr David P Echevarria 1All Rights Reserved

CHAPTER 8

BOND VALUATION AND RISK

2Dr David P EchevarriaAll Rights Reserved

BOND VALUATION

The value of any debt claim is equal to the sum of the discounted future cash flows. The discount [interest] for future cash flows is a function of the level of riskiness for a particular bond and is termed the Yield to Maturity (YTM).

Bond valuation model; 1. Vb = Coupon * PVIFA + Face Value *

PVIF


BOND VALUATION

A. Valuation of Bonds with Annual, Semi-annual, or quarterly Payments

1. Two cash streams are expect for each bonda. Couponsb. Face or maturity value

2. Coupons valued like an annuity 3. Face Value a single discounted future cash

flow

B. Methods for computing Bond Market Values

1. Bond Tables2. Financial Calculators (preferred)


BOND VALUATION

C. Impact of Interest Rate Movements on Bond Prices

1. Bond Prices move in the Opposite Direction to Interest Rates.

2. Bonds will sell at discounts or premiums or equal to Face values

3. Interest Rates move in the Same Direction as Inflationary Expectations

4. Interest Rates move in the Same Direction as Perceived Riskiness


BOND VALUATION

D. Factors Affecting Bond Price Interest Rate Sensitivity

1. The time remaining to maturity; direct relationship

2. The size of the coupon payments3. The frequency of coupon payments; i.e.,

annual, Semi-, quarterly, monthlyE. Measuring Sensitivity to Interest Rate

Movements: Duration1. As duration increases, the greater the

sensitivity to interest rate fluctuations2. Importance of determining the investment

horizon3. Key strategy for immunizing the yield on a

bond portfolio


HOMEWORK QUESTIONS

A. What 2 cash flows are associated with bond investments?

B. What effects do interest rate increases (decreases) have on;

1. Market values of bonds?2. Current yields?3. Yields to maturity?

C. What does it mean when a bond sells at par, at a discount, at a premium?

D. What information is necessary in order to make good bond investments?


BOND VALUATION

F. Determination of Bond Yields1. Yield to Maturity (YTM)2. Current Yield3. Tax treatment of gains and loses

a. Premiumsb. Discounts

G. Using Expectations to Manage Total Returns on Bond Portfolios

1. If you know were interest rates are going you know where bond prices are going

2. Riding the yield curve or betting on the movement of interest rates


BOND PORTFOLIO MANAGEMENT

A. Use of Duration as an Immunization Strategy"A portfolio of bonds is immunized from interest rate risk if the duration of the portfolio equals the desired investment horizon" Fisher and Weil

1. Requires a known investment horizon; when do you need the cash?

2. Involves periodic adjustment in portfolio composition; see #3 below

3. Increase in YTM after the position is set results in a decrease in duration and vice-versa (Reinvestment of cash flows at higher rates than original YTM)

4. Duration affected by calls, serial redemptions, and sinking fund provisions


Managing Bond Risk: Duration

YTM = 4.00%Par Value 1,000.00$ Price ($1,000.00)Coupon 4.00%

t CP PV(CP) t PV(CP)1 $40.00 38.46$ 38.46$ 2 $40.00 36.98$ 73.96$ 3 $40.00 35.56$ 106.68$ 4 $40.00 34.19$ 136.77$ 5 $40.00 32.88$ 164.39$ 6 $40.00 31.61$ 189.68$ 7 $40.00 30.40$ 212.78$ 8 $40.00 29.23$ 233.82$ 9 $40.00 28.10$ 252.93$

10 $1,040.00 702.59$ 7,025.87$ 1,000.00$ 8,435.33$

Dur = 8.43533161

YTM = 10.00%Par Value 1,000.00$ Price ($1,000.00)Coupon 10.00%

t CP PV(CP) t PV(CP)1 $100.00 90.91$ 90.91$ 2 $100.00 82.64$ 165.29$ 3 $100.00 75.13$ 225.39$ 4 $100.00 68.30$ 273.21$ 5 $100.00 62.09$ 310.46$ 6 $100.00 56.45$ 338.68$ 7 $100.00 51.32$ 359.21$ 8 $100.00 46.65$ 373.21$ 9 $100.00 42.41$ 381.69$

10 $1,100.00 424.10$ 4,240.98$ 1,000.00$ 6,759.02$

Dur = 6.7590238

10Dr David P Echevarria

Duration for a Zero Coupon Bond

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YTM = 10.00%Par Value 1,000.00$ Price ($385.54)Coupon 0.00%

t CP PV(CP) t PV(CP)1 $0.00 -$ -$ 2 $0.00 -$ -$ 3 $0.00 -$ -$ 4 $0.00 -$ -$ 5 $0.00 -$ -$ 6 $0.00 -$ -$ 7 $0.00 -$ -$ 8 $0.00 -$ -$ 9 $0.00 -$ -$

10 $1,000.00 385.54$ 3,855.43$ 385.54$ 3,855.43$

Dur = 10

Effects of Coupon Rates on Duration:As coupon rates increase, duration decreases and vice-versa.As YTM decrease, duration increases and vice versa.The duration for a zero-coupon bond is equal to its maturity.


BOND PORTFOLIO MANAGEMENT

B. Use of Derivative Securities as Hedges

1. Interest rate futures, as well as options on futures

2. May also involve currency hedges3. SWAP agreements may also be used

all rights reserved dr david p echevarria 1 chapter 8 bond valuation and risk

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