BOND PORTFOLIO MANAGEMENT PRESENTED BY: JUANITA ANN MATHEW ROLL NO. 52
Dec 24, 2015
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.