Bond Portfolio Management• Bond taxonomy

• Bond valuation

• Yields and Term-structures

• Bond risk and Duration

• Bond Portfolio Strategies– Passive strategies– Active strategies– Protective strategies

Bond = Long Term Debt from state, government or corporation-Contractual agreement

Primary Financial markets• Direct transfer• Through an investment banking house• Through a financial intermediary

Secondary Financial markets• Auction markets versus dealer markets (exchanges

versus the OTC market)• NYSE versus Nasdaq system: Differences are

narrowing

Bond issues…

Bond taxonomy• Bond = Long Term Debt from state, government or

corporation-Contractual agreement (Default = bankruptcy)• Face value or maturity value: Face amount; paid at maturity.

Assume $1,000.• Market value or proceed • Coupon or payment: Stated as interest rate. Multiply by par

value to get dollars of interest. Generally fixed.• Maturity: Years until bond must be repaid. Declines. (Issue

date: Date when bond was issued)• Yield or discount rate: opportunity cost of capital, i.e., the

rate that could be earned on alternative investments of equal risk. includes Default riskRisk that issuer will not make interest or principal payments

IndentureHard data:

• Term and amount of issue; date of issue and maturity

• Face value and Ask price

• Coupon and payment date

Soft data:

• Collateral and seniority; covenants (on dividends, asset restriction and financing restrictions)

• Sinking fund: Provision to pay off a loan over its life rather than all at maturity.Similar to amortization on a term loan. Reduces risk to investor, shortens average maturity.

• Call provision and call premium :Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds. Most bonds have a deferred call and a declining call premium.

Rating

What factors affect default risk and bond ratings?• Financial performance

– Debt ratio; TIE; Current ratios

• Provisions in the bond contract– Secured versus unsecured debt– Senior versus subordinated debt– Guarantee provisions– Sinking fund provisions– Debt maturity

• Other factors– Earnings stability– Regulatory environment– Potential product liability– Accounting policies

Bankruptcy• Two main chapters of Federal Bankruptcy Act:

– Chapter 11, Reorganization– Chapter 7, Liquidation

• Typically, company wants Chapter 11, creditors may prefer Chapter 7.• If company can’t meet its obligations, it files under Chapter 11. That

stops creditors from foreclosing, taking assets, and shutting down the business.

• Company has 120 days to file a reorganization plan.– Court appoints a “trustee” to supervise reorganization. – Management usually stays in control.

• Company must demonstrate in its reorganization plan that it is “worth more alive than dead.”

• Various groups of creditors vote on the reorganization plan. If both the majority of the creditors and the judge approve, company “emerges” from bankruptcy with lower debts, reduced interest charges, and a chance for success.

• Otherwise, judge will order liquidation under Chapter 7.

Liquidation• If the company is liquidated, here’s the payment

priority:1. Secured creditors from sales of secured assets.2. Trustee’s costs3. Wages, subject to limits4. Taxes5. Unfunded pension liabilities6. Unsecured creditors7. Preferred stock8. Common stock

• In a liquidation, unsecured creditors generally get zero. This makes them more willing to participate in reorganization even though their claims are greatly scaled back.

Quotation

Bond Valuation

PV=Present value of payments+ Present value of face value

Then,

PV=PMT x PVIFA(n x m, R/m)+ FV x PVIF(n x m, R/m)

Calculator:

FV I n PMT CPT PV

Excel:

Look at the functions PV, FV, PMT, Rate, NPER

……………..

Payments

Proceed

Face Value

Financial Asset Valuation applied to bonds

PV =

CF

1+ k ... +

CF

1+k1 n

12

21

CF

kn .

0 1 2 nk

CF1 CFnCF2Value

...

+ ++

PV=Present value of coupons + Present value of FV

Then, intuitively PV=PMT x PVIFA+ FV/FVIF

EXAMPLE 1: What’s the value of a 10-year, 10% coupon bond if kd = 10%?

V

k kB

d d

$100 $1,

1

000

11 10 10 . . . +

$100

1+ kd

100 100

0 1 2 1010%

100 + 1,000V = ?

...

= $90.91 + . . . + $38.55 + $385.54= $1,000.

++++

EXAMPLE 2: What would happen if inflation fell, and kd

declined to 7%?

10 7 100 1000N I/YR PV PMT FV

-1,210.71

If coupon rate > kd, price rises above par, and bond sells at a premium.

INPUTS

OUTPUT

M

Bond Value ($)

Years remaining to Maturity

1,372

1,211

1,000

837

775

30 25 20 15 10 5 0

kd = 7%.

kd = 13%.

kd = 10%.

A bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if I is 10%, 13%, or 7%?

Example 3

A bond has 5 years to maturity and a coupon rate of 10%. Interest rates are compounded semi-annually

Joe thinks that such bond is expected (as of now) to return 12%, Cindy thinks it should yield 8%, and for Charles it must return 10%.

What is the bond value for each individuals?

Solution• Variables:FV=1000; m=2; n=5PMT=%C x FV/m=10% x 1000/2=$50 • For Joe: PV=50 PVIFA(10,6%)+1000/FVIF(10,6%)=926.7• For Cindy:PV=50 PVIFA(10,4%)+1000/FVIF(10,4%)=1081.2• For Charles:PV=50 PVIFA(10,5%)+1000/FVIF(10,5%)=1000

• Then, At maturity, the value of any bond must equal its par value.

• The value of a premium bond would decrease to $1,000.

• The value of a discount bond would increase to $1,000.

• A par bond stays at $1,000 if kd remains constant.

Bond Properties• Par, Premium and Discount

• Bond prices and yield are inversely related

• Bond prices and maturity are inversely related

• Bond prices and coupon are positively related

If YTM > %COUPON

YTM = %COUPON

YTM < %COUPON

Price Price<1000 Price =1000 Price>1000 Bond sold

At discount At par At premium

Yields• Reinvestment rate=Yield• Calculating yield: calculator or excel• Approximation:

• Yield Components: Economic forces + issue characteristic

“Nominal” Rate = Risk-free rate + Risk

Real rate + Inflation + Risk

Rm PMT

FV PV

nFV PV

.

2

EXAMPLE 4: Questions

• What is the assumption behind the YTM, when valuing bonds?

• How does “poor business performance” affect a corporate bond value?

EXAMPLE 5: What’s the YTM on a 10-year, 9% annual coupon, $1,000 par

value bond that sells for $887?

90 90 90

0 1 9 10kd=?

1,000PV1 . . .PV10

PVM

887 Find kd that “works”!

...

10 -887 90 1000N I/YR PV PMT FV

10.91

V

INT

k

M

kB

dN

dN

1 11

... +INT

1+ kd

887

90

1

1000

11 10 10

k kd d

+90

1+kd

,

Find kd

+ + + +

++++

INPUTS

OUTPUT

...

Example 6: Find YTM if price were $1,134.20.

10 -1134.2 90 1000N I/YR PV PMT FV

7.08

Sells at a premium. Because coupon = 9% > kd = 7.08%, bond’s value > par.

•Relationship between coupon rate and kd?

•Relationship between price and kd?

•Price at maturity?

INPUTS

OUTPUT

Example 7: A 10-year, 10% semiannual coupon,$1,000 par value bond is selling for$1,135.90 with an 8% yield to maturity.It can be called after 5 years at $1,050. What’s the bond’s nominal yield to call (YTC)?

Note: In general, if a bond sells at a premium, then coupon > kd, so a call is likely. Then, expect to earn:YTC on premium bonds.;YTM on par & discount bonds.

10 -1135.9 50 1050 N I/YR PV PMT FV

3.765 x 2 = 7.53%

INPUTS

OUTPUT

Example 8

• A bond yields 10%. It has 20 years to maturity and pays 6% coupon annually.

• 1) How much will you accumulate in 5 years if you reinvest your coupon at 2%?

• 2)What is the realized yield to maturity?

Example 8 (continued)1) find the future value of the coupons over 5 years

and add the value of the bond 5 years from today:

FV(Coupon):

60 pmt, 2 I, 5 n, Compute FV=312.24

Then get the PV(bond in 5 years:

60 pmt, 10 I, 15 n, 1000 FV, Compute PV=695.76

In sum, you will accumulate $1008 after 5 years

Example 8 (continued)

2) Here, you know you will accumulate 1008 in 5 years. First, figure what you paid for the bond initially:

60 pmt, 10 I, 20 n, 1000 FV, Compute PV= 659.46

Then, if you invested 659.46 initially and received 1008 5 years later, then you must have returned:

-659.46 PV, 5 n, 1008 FV, Compute i=8.9%

How do you make money on a bond?

Current yield =

Capital gains yield =

= YTM = +

Annual coupon pmtCurrent price

Change in priceBeginning price

Exp totalreturn

Exp Curr yld

Exp capgains yld

EXAMPLE 9: Find current yield and capital gains yield for a 9%,

10-year bond when the bond sells for $887 and YTM = 10.91%.

Current yield = = 10.15%. $90 $887

YTM = Current yield + Capital gains yield.

Cap gains yield = YTM - Current yield = 10.91% - 10.15% = 0.76%.

What four factors affect the cost of money?• “Nominal” Rate =Risk-free rate + Risk Premium

=Real rate + Inflation + Risk PremiumProduction opportunitiesTime preferences for consumptionRiskExpected inflation

k = k* + IP + DRP + LP + MRP.DRP = Default risk premium.

LP = Liquidity premium.

MRP = Maturity risk premium.

Treasury: IP, MRPCorporate: IP, DRP,

MRP, LP

Term Structure of Interest Rates• Relationship between term to maturity and yield to maturity

for a sample of bonds at a fixed point of time. • Referred to as the “yield curve.” • Issues differ only in their maturities--Treasury instruments• 3 shapes (Normal,Flat,Inverted)• 3 underlying theories, relating to the different supply and

demand pressures in different maturity sectors:– Expectation (expected to earn on successive investments in ST

bonds during the term to maturity of a LT bond)– Liquidity (investors prefer the liquidity of ST bonds but will buy

LT bonds if the yields are higher)– Market segmentation (yields curve reflects the investment policies

of financial institutions who have different maturity preferences)

Corporate yield curves are higher than for Treasury bond. However, corporate yield curves are not necessarily parallel to the Treasury curve. The spread between a corporate yield curve and the Treasury curve widens as the corporate bond rating decreases.

0

5

10

15

0 1 5 10 15 20

Years tomaturity

Interest Rate (%)

5.2%5.9%

6.0%Treasuryyield curve

BB-Rated

AAA-Rated

U.S. Yield Curve Inverts Before Last Five Recessions(5-year Treasury bond - 3-month Treasury bill)

-6

-4

-2

0

2

4

6

8% GDP Growth/Yield Curve

% Real annual GDP growth

Yield curve

?RecessionCorrect 2 Recessions

Correct

RecessionCorrect

RecessionCorrect

RecessionCorrect

Data though 12/20/00

Bond Risks

• Interest rate risk dichotomy:– Price risk or price volatility

– Reinvestment risk or “ending wealth” volatility

• If interest rates are expected to increase; bond price will decrease and ending wealth will increase.

• interest rates are expected to decrease; bond price will increase and ending wealth will decrease.

Bond risk…

• As Coupon is greater, Price sensitivity to yield decreases.

• As Maturity gets greater, Price sensitivity to yield increases.

• A bond with high yield is less sensitive to a change in interests than a bond with low yield.

• Bond risk = Price risk and reinvestment risk

• Q: with an expected change interest rates, which bond would you pick?

EXAMPLE 10:Effect of Maturity on Bond Price Volatility

Maturity (years) 1 5 10 30

Par 1000 1000 1000 1000

initial coupon 8% 8% 8% 8%

initial yield 8% 8% 8% 8%

Initial value 1000 1000 1000 1000

drop in yield 6% 6% 6% 6%

New price $1,018.87 $1,084.25 $1,147.20 $1,275.30

Bond volatility 1.89% 8.42% 14.72% 27.53%

increase in yield 10% 10% 10% 10%

New price $981.82 $924.18 $877.11 $811.46

Bond volatility -1.82% -7.58% -12.29% -18.85%

EXAMPLE 11:Effect of Coupon on Bond Price Volatility

Maturity (years) 10 10 10 10

Par 1000 1000 1000 1000

initial coupon 5% 7% 9% 11%

initial yield 8% 8% 8% 8%

Initial value $798.70 $932.90 $1,067.10 $1,201.30

drop in yield 6% 6% 6% 6%

New price $926.40 $1,073.60 $1,220.80 $1,368.00

Bond volatility 15.99% 15.08% 14.40% 13.88%

increase in yield 10% 10% 10% 10%

New price $692.77 $815.66 $938.55 $1,061.45

Bond volatility -13.26% -12.57% -12.05% -11.64%

Some Trading Strategies…

• If market rates are expected to decline, bond prices will rise you want bonds with maximum price volatility. – Maximum price increase (capital gain) results from long

term, low coupon bonds, low yield

• If market rates are expected to rise, bond prices will fall you want bonds with minimum price volatility. – Invest in short term, high coupon bonds to minimize

price volatility and capital loss, high yield.

EXAMPLE 12: Evidence of reinvestment risk (8% coupon, 25 years, 8% yield, semi-annual). How does the ending wealth change if interest rates increase by

1%ANS: ≈+15%)

Price sensitivity and Duration Measures

Duration: the weighted average time to full recovery of principal and interest payments.

)R(

)R(D

P

P

1

1

Characteristics of D

• D = term to maturity for a zero coupon bond.

- D < term to maturity for a coupon bond

- D as coupon

- D as Term to maturity

- D as YTM

Duration Strategies• (Dm) = Modified duration =Duration/(1+yield/m)…just a shortcut

– Example 13: Given a bond that pays semi-annual coupons with a duration of 6 years and a yield of 8%, what will the percentage change in price be if market rates are expected to rise by 50 basis points?

– ANSWER: P/P = 6/(1+8%/2) x .5% = 2.88%

• Some basic duration strategies:– If decline in rates is expected, buy a long duration bond.

– If rates are expected to rise, buy a short duration bond.• Some limitations on duration strategies:

– Percent change estimates using modified duration are good only for small-yield changes.

– Callable bonds

RDP

Pmod

Passive Bond Portfolio StrategiesBuy-and-Hold Strategy• Investor selection based on quality, coupon and maturity• Match maturity with investment horizon• Modified buy and hold

Indexing Strategy• Money managers can’t beat the market“If you can’t beat

them, join them.”• Difficulties:

– Tracking error - difference between the portfolio’s return and the return for the index.

– You must know characteristics and composition of the various indexesIndexes change over time.

Active Bond Strategies• Active management strategies » Interest Rate Anticipation (Valuation

Analysis, Credit Analysis, Yield Spread Analysis, and Bond Swaps)• Riskiest

– If i is expected to increase, preserve capital– If i is expected to decrease, make capital gains

• Objectives are achieved by adjusting the portfolio’s duration (maturity).– Shorten duration if rates are expected to

• Play the Reinvestment advantage card and get Cash flow ASAP (liquidity)

– Lengthen duration if rates are expected to • Play the Interest rate card lower coupons and play on an increase in bond

prices

• Q: What is the duration of a portfolio of bonds?• A: The weighted average duration of each bond in a portfolio—I.e.,

ni

iii DWD

1

Matched Funding Techniques: Dedicated Portfolios

What are they? Bond portfolio management technique used to service a specific set of liabilities

Pure-Cash Matched Dedicated Portfolio • Cash flows from all sources exactly match up in timing and size with

the liability schedule.

• Can be achieved by buying a series of zero coupon Treasury securities.

• Total passive strategyDedication with Reinvestment• Cash flows don’t exactly match the liability schedule, also cash flows

received earlier are reinvested at a relatively low interest rate.• Advantages: (1) Allows for wider set of bonds to be considered; (2)

Lower net cost of the portfolio; (3) Safety equivalent to with pure cash-matching.

• Potential problem: Early redemption

Matched Funding Techniques: Immunization Strategies

• Immunization: Attempt to generate a specified rate of return regardless of what happens to market rates during an investment horizon.

• Immunization is a process intended to eliminate interest risk; it is achieved if the ending wealth of a bond portfolio is the same regardless of whether interest rates change

• Example 14: Assume a 6 year strategic asset allocation horizon and market rates on 6% coupon bonds is 6%.– Strategy one: Maturity (cash) Matching Strategy

• A manager has a portfolio of bonds with an average maturity of 6 years. The average coupon rate of the portfolio is 6%.

– Strategy two: Duration Matching strategy=portfolio immunization• A manager has a portfolio of bonds with an average maturity of 7 years. The

average coupon rate of the portfolio is 6%. The average duration is about 6 years.

– Q: What happens if interest rates increase or decrease suddenly by 1%

Example 14…continuedInterest rates unchanged or R=6%

Strategy 1: FV=PMT x FVIFA + 1000=60 x 6.975 +1000=$1,418.5

Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF=

=60 x 6.975 +60 x .943 + 1000/1.06=$1,418.5

Decrease of 1% or R=5%

Strategy 1: FV=PMT x FVIFA + 1000=60 x 6.802 +1000 =$1,408

Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF

=60 x 6.802 +60 x .952 + 1000/1.05=$1,417.6

Increase of 1% or R=7%

Strategy 1: FV=PMT x FVIFA + 1000=60 x 7.153 +1000=$1,429.2

Strategy 2: FV=PMT x FVIFA + PMT x PVIFA +1000/FVIF

=60 x 7.153 +60 x .935 + 1000/1.07=$1,419.9For strategy 2: At t=6 years, bonds have 1 year left of life!

Conclusion:

Applications: • immunize the bond portion of your strategic allocation• Immunize a future cash outflows (pension funds, insurance

companies)• Not as easy as it sounds (rebalancing, duration drift,

unavailability…)

Strategy 1 Strategy 2

R=6% 1,418.5 1,418.5

R=5% 1408 1417.6

R=7% 1429.2 1419.9

%change (-1%) -0.07% 0%

%change (+1%) 0.08% 0%

Example 15: Questions

• You immunize a 4-year investment by purchasing a coupon bond with a duration of 4 years. If interest rates do not change, is your bond still immunized one year after?

• What if you purchased a 4-year zero coupon bond?

• Horizon matching combines cash matching and immunization to Provide protection against unequal interest rate changes

– » Short term end is set up as a cash matching portfolio

– » Longer term end is duration immunized

– » Roll out occurs when the time horizon is pushed out one year further into the long term time horizon

• Contingent immunization allows for active portfolio management while assuring a minimal return by creating a Cushion spread ( difference between market rates and the minimum that investors are willing to accept.)Immunize a specific return; play with the cushion!

Matched Funding Techniques: Horizon Matching and contingent immunization