Bond Portfolio Management

Strategies

Alternative Bond Portfolio Strategies

1. Passive portfolio strategies2. Active management strategies3. Core-plus management strategy3. Matched-funding techniques4. Contingent procedure (structured active

management)

Passive Portfolio Strategies• Buy and hold

– A manager selects a portfolio of bonds based on the objectives and constraints of the client with the intent of holding these bonds to maturity

• Indexing– The objective is to construct a portfolio of bonds

that will equal the performance of a specified bond index (Match performance of a selected bond index)

– Performance analysis involves examining tracking error

Passive Portfolio Strategies

• Advantages to using indexing strategy– Historical performance of active managers– Reduced fees

• Indexing methodologies– Full participation– Stratified sampling (cellular approach)– Optimization approach– Variance minimization

Determinants of Price Volatility

Determinants of Price Volatility1. Bond prices move inversely to bond yields (interest rates)

2. For a given change in yields, longer maturity bonds post larger price changes, thus bond price volatility is directly related to maturity.

3. Price volatility increases at a diminishing rate as term to maturity increases

4. Price movements resulting from equal absolute increases or decreases in yield are not symmetrical

5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon

Determinants of Price Volatility

DURATION

It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows.

ZERO COUPON BONDVANILLA COUPON BOND

Duration• It is an important measure for investors to

consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations.

• It includes : present value, yield, coupon, final maturity and call features.

Duration

Developed by Frederick R. Macaulay, 1938

Where:

n = number of cash flows t = time to maturity C = cash flow i = required yield M = maturity (par) value P = bond price

Betty holds a five-year bond with a par value of $1,000 and

coupon rate of 5%. For simplicity, let's assume that the

coupon is paid annually and that interest rates are 5%.

What is the Macaulay duration of the bond?

= 4.55 years

Duration and Price Volatility

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

mYTM1

durationMacaulay duration modified

Where:

m = number of payments a year

YTM = nominal YTM

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

iDPP

mod100Where:

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

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

• Sinking funds and call provisions can have a dramatic effect on

a bond’s duration

Duration in Years for Bonds Yielding 6% with Different Terms

COUPON RATESYears toMaturity 0.02 0.04 0.06 0.08

1 0.995 0.990 0.985 0.9815 4.756 4.558 4.393 4.254

10 8.891 8.169 7.662 7.28620 14.981 12.980 11.904 11.23250 19.452 17.129 16.273 15.829

Source: 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.

Duration and Price Volatility• Longest duration security gives maximum price

variation• Active manager wants to adjust portfolio duration to

take advantage of anticipated yield changes– Expect rate declines (parallel shift in YC), increase average

modified duration to experience maximum price volatility– Expect rate increases (parallel shift in YC), decrease

average modified duration to minimize price decline

Convexity

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• 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

• 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

Convexity Calculation

Convexity adjustment to the percentage price change = C x change in yield squared x 100

To find the C in the equation, use this equation that has the same notation as duration:

C = V3 +V2 - 2(V1) / 2V1(change in yield) squared 

Total Price Change

Total Price change = (-duration x change in yield x 100)

+ (C x change in yield squared x 100)

Using the Stone & Co. bonds that had duration of 5.5, let's add a convexity of 93 and an increase of 150 bps in yield.

Active Management Strategies

Active Management Strategies• Potential sources of return from fixed income port:

1. Coupon income2. Capital gain3. Reinvestment income

• Factors affecting these sources:1. Changes in level of interest rates2. Changes in shape of yield curve3. Changes in spreads among sectors4. Changes in risk premium for one type of bond

Active Management Strategies• Interest-rate anticipation

– Risky strategy relying on uncertain forecasts– Ladder strategy staggers maturities– Barbell strategy splits funds between short duration and

long duration securities– Bullet strategies– Riding the YC.

• Valuation analysis– The portfolio manager attempts to select bonds based on

their intrinsic value

• Bonds rating, call feature, interest rate etc.• Buy the undervalued bond & sell the overvalued bonds• If bond rating is higher then interest is low and as result income is low

• Credit analysis

– Involves detailed analysis of the bond issuer to

determine expected changes in its default risk.

• Internal & external Factors affect the credit rating of

the company such as financial ratios, inflation, etc.

• Higher the risk higher the return.

Active Management Strategies

Active Management Strategies• High-Yield Bond Research

– Several investment houses such as Merrill Lynch, First Boston, Lehman Brothers, etc., have developed specialized high-yield groups that examine high-yield bond issues and monitor high-yield bond spreadsAve. Cumul. Default Rates Corp Bonds

Years Since IssueRatings 5 10AAA 0.08% 0.08%AA 1.20% 1.30%A 0.53% 0.98%BBB 2.39% 3.66%BB 10.79% 15.21%B 23.71% 35.91%CCC 45.63% 57.39%

Active Management Strategies• Yield spread analysis

– Assumes normal relationships exist between the yields for bonds in alternative sectors

• Factor affecting yield spread:-– Business cycle– Volatility in the market interest rate

• Bond swaps

Bond Swaps• Involve liquidating a current position and

simultaneously buying a different issue in its place with similar attributes but having a chance for improved return.

Pure Yield Pickup Swap– Swapping low-coupon bonds into higher coupon

bondsSubstitution Swap– Swapping a seemingly identical bond for one that is

currently thought to be undervalued

Bond Swaps (Cont.)Tax Swap

Swap in order to manage tax liability (taxable & munis)

Swap strategies and market-efficiency

Bond swaps by their nature suggest market inefficiency

A Global Fixed-Income Investment Strategy

Factors to consider– The local economy in each country including the

effects of domestic and international demand

– The impact of total demand and domestic monetary

policy on inflation and interest rates

– The effect of the economy, inflation, and interest

rates on the exchange rates among countries

Core-Plus Bond Portfolio Management

• This involves having a significant (core) part of the portfolio managed passively in a widely recognized sector such as the U.S. Aggregate Sector or the U.S. Government/Corporate sector.

• The rest of the portfolio would be managed actively in one or several additional “plus” sectors, where it is felt that there is a higher probability of achieving positive abnormal rates of return because of potential inefficiencies

Matched-Funding Techniques• Dedicated Portfolios Dedication refers to bond portfolio

management techniques that are used to service a prescribed set of liabilities– Pure Cash Matched Dedicated Portfolios‑

• Most conservative strategy– Dedication With Reinvestment

• Cash flows do not have to exactly match the liability stream

Matched-Funding Techniques

• Immunization Strategies– A portfolio manager (after client consultation)

may decide that the optimal strategy is to immunize the portfolio from interest rate changes

– The immunization techniques attempt to derive a specified rate of return during a given investment horizon regardless of what happens to market interest rates

Immunization Strategies

• The process intended to eliminate interest rate risk is referred to as immunization

• Components of Interest Rate Risk– Price Risk– Coupon Reinvestment Risk

Classical Immunization• Immunization is neither a simple nor a

passive strategy• An immunized portfolio requires

frequent rebalancing because the modified duration of the portfolio always should be equal to the remaining time horizon (except in the case of the zero-coupon bond)

Classical Immunization

• Duration characteristics– Duration declines more slowly than term to

maturity, assuming no change in market interest rates

– Duration changes with a change in market interest rates

– There is not always a parallel shift of the yield curve

– Bonds with a specific duration may not be available at an acceptable price

Matched-Funding Techniques

• Horizon matching – Combination of cash-matching dedication and

immunization– Important decision is the length of the horizon

period

Contingent Procedures

• A form of structured active management– Constrains the manager if unsuccessful

• Contingent immunization– duration of portfolio must be maintained at

the horizon value– cushion spread is potential return below

current market– safety margin– trigger point

Implications of Capital Market Theory and the EMH on Bond Portfolio Management

• Bonds and Total Portfolio Theory• Bonds and Capital Market Theory• Bond Price Behavior in a CAPM Framework• Bond-Market Efficiency