BOND PORTFOLIO MANAGEMENT

PRESENTED BY: JUANITA ANN MATHEW

ROLL NO. 52

INVESTMENT MANAGEMENT PROCESS

• Setting investment objectives• Establishing investment policy• Selecting a portfolio strategy• Selecting assets• Managing and evaluating performance

1. Setting investment objectives

• For institutions such as banks and thrifts– dictated by nature of liabilities

• For Pension Funds– to generate sufficient cash flows to meet pension obligations

• For Life Insurance Companies– the basic objective is to satisfy obligations stipulated in

policies and generate profits• For Mutual Funds

– Objectives are set forth in the prospectus– No specific liabilities

2. Establishing investment policy

• Asset allocation decision: cash equivalents, equities, fixed- income securities, real estate, and foreign securities

• Considerations– Client and regulatory constraints– Tax and financial reporting implications

3. Selecting a portfolio strategy

– Passive• rests on the belief that bond markets are semi-strong

efficient• current bond prices viewed as accurately reflecting all

publicly available information• Involves minimal expectational output e.g. Indexing

– Active• rests on the belief that the market is not so efficient• some investors have the opportunity to earn above-average

returns• Involves forecasts of future interest rates, future interest

rate volatility, or future yield spreads.

3. Selecting a portfolio strategy (contd.)

– Enhanced Indexing/ Indexing Plus• A primarily indexed portfolio but employ low-risk strategies to

enhance the indexed portfolio’s returns

– Structured Portfolio Strategies• Used to fund liabilities. • To achieve the performance of a predetermined benchmark

– To satisfy single liability (Immunization)– To satisfy multiple future liabilities (Immunization, Cash flow matching, horizon

matching)

– Contingent Immunization• Manager follows active strategy to point where trigger point is

reached• Switch made to passive strategy to meet minimum acceptable return

4. Selecting assets

• For e.g. In Active strategy – identifying mispriced assets

• Based on bond characteristics like coupon, maturity, credit quality, options embedded.

• Attempts to create an efficient portfolio

5. Managing and evaluating performance

• Involves measuring the performance and evaluating the performance to some benchmark e.g. Merrill Lynch Domestic Market Index.

Five Bond Pricing Theorems

• For a typical bond making periodic coupon payments and a terminal principal payment– THEOREM 1

• If a bond’s market price increases• then its yield must decrease• conversely if a bond’s market price decreases• then its yield must increase

Five Bond Pricing Theorems

• For a typical bond making periodic coupon payments and a terminal principal payment– THEOREM 2

• If a bond’s yield doesn’t change over its life,• then the size of the discount or premium will decrease

as its life shortens

Five Bond Pricing Theorems

• For a typical bond making periodic coupon payments and a terminal principal payment– THEOREM 3

• If a bond’s yield does not change over its life• then the size of its discount or premium will decrease• at an increasing rate as its life shortens

Five Bond Pricing Theorems

• For a typical bond making periodic coupon payments and a terminal principal payment– THEOREM 4

• A decrease in a bond’s yield will raise the bond’s price by an amount that is greater in size than the corresponding fall in the bond’s price that would occur if there were an equal-sized increase in the bond’s yield

• the price-yield relationship is convex

Five Bond Pricing Theorems

• For a typical bond making periodic coupon payments and a terminal principal payment– THEOREM 5

• the percentage change in a bond’s price owing to a change in its yield will be smaller if the coupon rate is higher

Duration

• Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective

• A composite measure considering both coupon and maturity would be beneficial

Duration (contd.)

price

)(

)1(

)1(

)(

1

1

1

n

tt

n

tt

t

n

tt

t CPVt

i

Ci

tC

D

Developed by Frederick R. Macaulay, 1938

Where:

t = time period in which the coupon or principal payment occurs

Ct = interest or principal payment that occurs in period t

i = yield to maturity on the bond

Problem on Macaulay’s DurationUndiscounted Cash Flow

Time PV Factor Present Value PV*T

-100 0

10 1 1/1.10 10*1/1.10 9.09

10 2 1/1.10^2 10*1/1.10^2 16.53

10 3 1/1.10^3 10*1/1.10^3 22.54

10 4 1/1.10^4 10*1/1.10^4 27.32

110 5 1/1.10^5 110*1/1.10^5 341.51

100 416.99

Problem (contd.)

• Macaulay’s Duration

17.4100

99.416

price

)(1

n

ttCPVt

D

Characteristics of Duration

• Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments– A zero-coupon bond’s duration equals its maturity

• An inverse relation between duration and coupon• A positive relation between term to maturity and

duration, but duration increases at a decreasing rate with maturity

• An inverse relation between YTM and duration

Duration in Years for Bonds Yielding 6% with Different Terms

Term to maturity

0.02 0.04 0.06 0.08

       

1 0.995 0.990 0.985 0.981

5 4.756 4.558 4.393 4.254

10 8.891 8.169 7.662 7.286

20 14.981 12.980 11.904 11.232

50 19.452 17.129 16.273 15.829

Modified Macaulay’s Duration

• An adjusted measure of duration can be used to approximate the price volatility of a bond

mYTM

1

DurationMacaulay Duration Modified

Where:

m = number of payments a year

YTM = nominal YTM

Problem on Modified Macaulay’s Duration

79.31

0.101

4.17m

YTM1

DurationMacaulay Duration Modified

Duration and Price Volatility

• Bond price movements will vary proportionally with modified duration for small changes in yields

• An estimate of the percentage change in bond prices equals the change in yield time modified duration

iDP

P

mod100

Where:P = change in price for the bondP = beginning price for the bond

Dmod = the modified duration of the bondi = yield change in basis points divided by 100

Duration and Price Volatility

Where:P = change in price for the bondP = beginning price for the bond

Dmod = the modified duration of the bondi = yield change in basis points divided by 100

58.7

279.3100100

100 mod

P

P

iDP

P

Duration and Price Volatility

• Longest duration security gives maximum price variation

• Duration is a price-risk indicator

Convexity

• Modified duration approximates price change for small changes in yield

• Accuracy of approximation gets worse as size of yield change increases– WHY?– Modified duration assumes price-yield relationship of

bond is linear when in actuality it is convex.– Result – MD overestimates price declines and

underestimates price increases– So convexity adjustment should be made to estimate of %

price change using MD

CONVEXITY

• The relationship between convexity and duration

YTM

P

0

Convexity (contd.)

• Convexity of bonds also affects rate at which prices change when yields change

• Not symmetrical change– As yields increase, the rate at which prices fall becomes

slower– As yields decrease, the rate at which prices increase is

faster– Result – convexity is an attractive feature of a bond in

some cases

Convexity (contd.)

• The measure of the curvature of the price-yield relationship

• Second derivative of the price function with respect to yield

• Tells us how much the price-yield curve deviates from the linear approximation we get using MD

REFERENCES

• Bond Markets, Analysis, and Strategies– Frank J. Fabozzi

• L. Fisher and R. L. Weil, "Coping with the Risk of Interest Rate Fluctuations: Returns to Bondholders from Naïve and Optimal Strategies," Journal of Business 44, no. 4 (October 1971): 418. Copyright 1971, University of Chicago Press.