Chapter 23 7e Active Bond Portfolio Management Strategies

1



Chapter 23


Active Bond Portfolio Management Strategies


Learning Objectives
:
After reading this chapter, you will understand




the five basic steps involved in the investment management process



the difference between active and passive strategies



what t
racking error is and how it is computed



the difference between forward
-
looking and backward
-
looking tracking error



the link between tracking error and active portfolio management



the risk factors that affect a benchmark index



the importance of knowing the
market consensus before implementing an active
strategy



the different types of active bond portfolio strategies: interest
-
rate expectations
strategies, yield curve strategies, yield spread strategies, option
-
adjusted spread
-
based strategies, and individual

security selection strategies



bullet, barbell, and ladder yield curve strategies



the limitations of using duration and convexity to assess the potential performance
of bond portfolio strategies



why it is necessary to use the dollar duration when implement
ing a yield spread
strategy



how to assess the allocation of funds within the corporate bond sector



why leveraging is used by managers and traders and the risks and rewards
associated with leveraging



how to leverage using the repo market



















2


O
verview of the Investment Management Process


Regardless of the type of financial institution, the investment management
process involves the following five steps:


(1)

setting investment objectives

(2)

establishing investment policy

(3)

selecting a portfolio strategy

(4)

selecting assets

(5)

measuring and evaluating performance




(1)

Setting Investment Objectives


The
first step in the investment management process
is setting
investment
objectives
.


The investment objective will vary by type of financial institution.





(2)

Establi
shing Investment Policy


The
second step in investment management process
is establishing policy
guidelines for meeting the investment objectives.


Setting policy begins with the asset allocation decision so as to decide how
the funds of the institution sh
ould be distributed among the major classes of
investments (cash equivalents, equities, fixed
-
income securities, real estate,
and foreign securities).








3


(3)

Selecting a Portfolio Strategy


Selecting a portfolio strategy that is consistent with the objecti
ves and policy
guidelines of the client or institution is
the third step in the investment
management process
.


Portfolio strategies can be classified as either

(1)

active strategies
or

(2)

passive strategies
.


Essential to all active strategies is specifi
cation of expectations about the
factors that influence the performance of an asset class. Passive strategies
involve minimal expectational input.



(3) Hybrid strategies: “Indexing Plus”




Structured strategies: Use when liabilities drive the portolio’s

strategy (“Liability
-
driven strategies”






T
he choice
of

active, structured, or passive management depends on
:


(a)

the client or money manager’s view of the pricing efficiency of the
market


(b)

the nature of the liabilities to be satisfied




Pricing efficiency i
s taken to describe a market where prices at all times
fully reflect all available information that is relevant to the valuation of
securities.




When a market is price efficient, active strategies will not consistently
produce superior returns after adjust
ing for risk and transactions costs.





4


(4)

Selecting Assets


After a portfolio strategy is specified, the
fourth step

in the investment
management process
is to select the specific assets to be included in the
portfolio, which requires an evaluation of indiv
idual securities.




“Efficient” portfolios sit on the Markowitz efficient frontier of risky assets







(5)

Measuring and Evaluating Performance



Question: How well did the portfolio do?


Answer: Depends on how well the (passive) benchmark performed



Major
concept: How well your portfolio did should be measured relative
to how much risk you took to achieve that return. The risk of an
actively
-
managed bond portfolio is called
tracking error

(aka “active
risk”)


















5


C
alculation of Tracking Error


(1)

Compute the total return for a portfolio for each period.

(
2
)

Obtain the total return for the benchmark index for each period.

(
3
)


Obtain the difference between the values found in Step 1 and Step 2. The
difference is referred to as the active retur
n.

(
4
)


Compute the standard deviation of the active returns. The resulting value is
the tracking error.





The tracking error measurement is in terms of the observation period.




If monthly returns are used, the tracking error is a monthly tracking err
or.




If weekly returns are used, the tracking error is a weekly tracking error.


Portfolio A

Month in 2007

Portfolio

Return (%)

Benchmark Index

Return (%)

Active

Return (%)

January

-
0.02

-
0.04

0.02

February

1.58

1.54

0.04

March

-
0.04

0.00

-
0.04

April

0.61

0.54

0.07

May

-
0.71

-
0.76

0.05

June

-
0.27

-
0.30

0.03

July

0.91

0.83

0.08

August

1.26

1.23

0.03

September

0.69

0.76

-
0.07

October

0.95

0.90

0.05

November

1.08

1.04

0.04

December

0.02

0.28

-
0.26

Sum



0.041

Mean



0.0034

Variance



0.0086

Standard Deviation = Tracking error



0.0930
%

=0.000930

Tracking error (in basis points)



9.30






6



In contrast, for Portfolio B
,

the active returns are large, and thus, the monthly tracki
ng
error is large
—
79.13 basis points.


Portfolio B

Month in 2007

Portfolio

Return (%)

Benchmark Index

Return (%)

Active

Return (%)

January

-
1.05

-
0.04

-
1.01

February

2.13

1.54

0.59

March

0.37

0.00

0.37

April

1.01

0.54

0.47

May

-
1.44

-
0.76

-
0.68

June

-
0.57

-
0.30

-
0.27

July

1.95

0.83

1.12

August

1.26

1.23

0.03

September

2.17

0.76

1.41

October

1.80

0.90

0.90

November

2.13

1.04

1.09

December

-
0.32

0.28

-
0.60

Sum



3.42

Mean




0.2850

Variance




0.6262

Standard Deviation = Tracking
error




0.7913

%

=0.007913

Tracking error (in b
ps
)



79.13



The tracking error is unique to the benchmark used.



Exhibit 23
-
2 (
see Overheads 23
-
17 and 23
-
18
) shows the tracking error for the portfolios
using the Lehman Global Aggregate Index.



The monthly tr
acking error for Portfolio A (
in Overhead 23
-
17
) is 76.04 basis points
compared to 9.30

basis points when the benchmark is the Lehman U.S. Aggregate Index;
for Portfolio B (
in Overhead 23
-
18
), it is 11.92 basis points for the Lehman Global Index
versus 79.
13 basis points for the Lehman U.S. Aggregate Index.










7


Portfolio A


Month in 2007

Portfolio

Return
(%)

Benchmark
Index

Return (%)

Active

Return (%)

January

-
0.02

-
0.98

0.96

February

1.58

2.06

-
0.48

March

-
0.04

0.24

-
0.28

April

0.61

1.1
3

-
0.52

May

-
0.71

-
1.56

0.85

June

-
0.27

-
0.44

0.17

July

0.91

2.03

-
1.12

August

1.26

1.23

0.03

September

0.69

2.24

-
1.55

October

0.95

1.63

-
0.68

November

1.08

1.91

-
0.83

December

0.02

-
0.31

0.33

Sum



-
3.119

Mean




-
0.2599

Variance



0.5782

Standard Deviation = Tracking
error



0.7604

%

= 0.007604

Tracking error (in
bps
)



76.04


Portfolio B

Month in 2007

Portfolio

Return
(%)

Benchmark
Index

Return (%)

Active

Return (%)

January

-
1.05

-
0.98

-
0.07

February

2.13

2.06

0.07

March

0.37

0.24

0.13

April

1.01

1.13

-
0.12

May

-
1.44

-
1.56

0.12

June

-
0.57

-
0.44

-
0.13

July

1.95

2.03

-
0.08

August

1.26

1.23

0.03

September

2.17

2.24

-
0.07

October

1.80

1.63

0.17

November

2.13

1.91

0.22

December

-
0.32

-
0.31

-
0.01

Sum



0.26

Mean




0.0217

Variance




0.0142

Standard Deviation =
Tracking error



0.1192

%


= 0.001192

Tracking error (in
bps
)



11.92

8


Two Faces of Tracking Error




-

Backward
-

looking tracking error

(aka ex post tracking error)













-

Forward
-
lo
oking tracking error

(ex ante tracking error)









Risk Factors and Portfolio Management Strategies
: Like market risk
(beta), value, firm size, etc. for stock portfolios!


Exposure to systematic risk factors:







Exposures to non
-
systematic risk fact
ors:



9




Systematic risk factors:


(1)

Term structure risk factor



(2)

Non
-
term structure

risk factors:


(a)

Sector risk


(b)

Quality risk


(c)

Optionality risk


(d)

Coupon risk


(e)

MBS sector risk


(f)

MBS volatility risk


(g)

MBS prepayment risk

10


(3)

Non
-
systematic risk factors:


(a)

Issuer
-
spec
ific risk


(b)

Issue
-
specific risk




Determinants of Tracking Error


Once you have an idea of what kinds of risk your actively managed portfolio
is exposed to, you can generate an expectation of tracking error (assuming
that your exposures to these risks are
different than the benchmark portfolio)





Tracking error can be broken down to tracking errors related to all three
categories above, and to each of the subcategories (in the non
-
term
structure category)



Basic idea: If you want to outperform the benchmar
k, you must overweight
(or underweight) your portfolio based on over
-
exposure (or under
-
exposure)
to various systematic and non
-
systematic risk factors.


e.g.: Suppose you expect that interest rate volatility effecting prepayment of
MBS pass
-
through secur
ities is abnormally low (relative to market
expectations)…




Outcome: More reward, in exchange for greater risk (tracking error).













11


Active Portfolio Strategies





Now that you know what the risk factors are
,

h
ow
do you
judge how much
exposure to

take to these factors?





(1)

Interest
-
Rate Expectations Strategies

(or,
exposure to term
-
structure
risk
)



Such swaps are commonly referred to as
rate anticipation swaps

–

pegged to
interest rate forecasting. If investors think rates will fall, they swap i
nto
bonds of longer duration. If rates are expected to rise, they swap into shorter
duration.




Big question: How accurate are guesses about shifts in the yield curve (i.e., future
interest rates)?





What kind of portfolio you pick depends on the typ
e of shift in the yield curve
--

parallel (up / down), pivoting (flatter / steeper), or changes in humped
-
ness (more
humped / less humped
, these are called “butterfly shifts”
)


Most common are:




Parallel
-
Down combined with steepening








Parallel
-
Up combi
ned with flattening


12


Yield Curve Strategies




Yield curve strategies
involve positioning a portfolio to capitalize on
expected changes in the shape of the Treasury yield curve.



In a
bullet strategy
, the portfolio is constructed so that the
maturities of
t
he securities in
the portfolio are highly concentrated at one point on the
yield curve.







In a
barbell strategy
, the maturities of the securities in the portfolio are
concentrated at two extreme maturities.








In a
ladder strategy

the portfolio is
constructed to have approximately
equal amounts of each maturity.





Duration and Yield Curve Shifts



Key point: We learned in Chapter 4 that price sensitivity to interest rate
movements can be estimated with modified duration (D*). Therefore, the
port
folio duration (weighted average of individual durations) summarizes
the sensitivity of the portfolio’s value to interest rate movements.


Question: What interest rates are we talking about? Suppose that a three bond
portfolio made up of 5y, 10y, and 20
y bonds has a portfolio duration of 4:


The portfolio’s value will change by 4% if the yield on five
-
, 10
-
, and 20
-
year
bonds all change by 100 basis points. That is, it is assumed that there is a
parallel yield curve shift
.


13


Analyzing Expected Yield Curve

Strategies



Key point: Bond portfolios with the same duration may react very differently to
different typ
es of shifts in the yield curve
. This is because d
uration is only an
approximation

of

the price reaction. We also need to consider
convexity

(Chp 4
)
.



Example

of Bullet vs. Barbell
:



Bond

Coupon (%)

Maturity

(years)

Price Plus

Accrued

Yield to

Maturity (%)

Dollar

Duration

Dollar

Convexity

A

8.50

5

100

8.50

4.005

19.8164

B

9.50

20

100

9.50

8.882

124.1702

C

9.25

10

100

9.25

6.434

55.4506




Main
ideas:


(1)

Dollar duration of the bullet (all C) is equal to the dollar duration of the
barbell (A+C)



(2)

Dollar convexity of the barbell > bullet





What is the value of each portfolio in 6 months?



Three yield curve shift scenarios:
(1) Parallel shift up/dow
n ; (2) Flattening;

and
(3) S
teep
e
ning:


(1)

Parallel shift (Column 1): small
shift

vs. large

shift
: Bullet outperforms

for
small changes in rates






14


(2)

Flattening (Column 2): Barbell is always better

(Bullet underperforms)

for
any scenario










(3)

Steepening

(Column 3): Bullet
is
better except for “
large
” changes in y
ields









Overall Conclusion:



S
uppose that a portfolio manager with a six
-
month investment horizon has a
choice of investing in the bullet portfolio or the barbell portfolio.



Which one s
hould
they

choose? The manager knows that (1) the two
portfolios have the same dollar duration, (2) the yield for the bullet portfolio is
greater than that of the barbell portfolio, and (3) the dollar convexity of the
barbell portfolio is greater than that

of the bullet portfolio.




Answer:
T
his information is not adequate in making the decision. What is
necessary is to assess the potential total return when the yield curve shifts
.

15


What if you expect no change in the yield curve?

“Riding the Yield Curve
”



Example:
Suppose you are considering a 6% annual coupon bond with FV=100.
Using the spot rates below (i.e. the yield curve), these are the prices that 6% bonds
with maturities up to 5 years would trad
e at. You expect these rates to hold next
year for
each maturity, too:


Maturity (years)

spot rate (%)

Bond price

1

3.90

102.021

2

4.50

102.842

3

4.90

103.098

4

5.25

102.848

5

5.60

102.077





If you have a 1
-
year horizon, what is the ret
urn from buying the 5
-
year bond

and
selling it in 1 year
, comp
ared to buying the 1
-
year bond
?


(1)

Buy now at 102.077

(2)

Sell in one year at the 4
-
year rate (5.25%)


102.848

(3)

Receive income = 6

(4)

Return = [(102.848
–

102.077) + 6] / 102.077 = 6.633%


Compare to return from buying the 1
-
year bond:


[100
–

102.021) + 6] / 10
2.021 = 3.90%!





What does the
pure
expectations theory have to say about this?
There
s
hould not be a better return to investing in a series of 1
-
year bonds, vs.
investing in the 5
-
year bond.






However:
If there is a “liquidity premium” for LT bonds, ex
pectations
theory will not hold perfectly


steep increasing yield curve might mean
that expected returns on long
-
term bonds are higher than on short
-
term
bonds over a given horizon.



16


A
sset allocation
among

sectors


Intermarket spread swap
:



(1)

Credit Sprea
ds




(2)

Spreads related to callability






Individual Security Selection Strategies



Substitution swap:



(1)

Is bond currently under
-
priced?




(2)

Is the rating expected to improve (so that price will increase)?




(3)

Is your guess about prepayment speed different
than the market’s?












17


A
sset allocation
within

sectors


Example: You are deciding how to allocate funds across ratings sectors (i.e.,
consider credit sectors as sub
-
classes of the credit
sector
)


Chapter 7:
The following ratings transition matrix
s
how
s

that
, historically,

ratings
increases

are less likely than ratings
decreases
:




Aaa

Aa

A

Baa

Ba

Bb

C or D

Total

Aaa

91.90

7.38

0.72

0.00

0.00

0.00

0.00

100.00

Aa

1.13

91.26

7.09

0.31

0.21

0.00

0.00

100.00

A

0.10

2.56

91.20

5.33

0.61

0.20

0.00

100.00

Baa

0.00

0.21

5.36

87.94

5.46

0.82

0.21

100.00


First, modify this matrix based on current economic conditions
.


Now, g
iven
your

expected ratings transition matrix, calculate an
expected
incremental return

for each credit quality sector as follows:


(1)

Estimate what the spread over Treasuries will be for all ratings at the end of
your horizon




(2)

Estimate the price change for upgraded and downgraded bonds based on the
new spreads



(3)

Compute the total return for u
pgraded and downgraded bonds based on the
price change from (1) and the coupon interest



(4)

Calculate the expected incremental return for the credit quality sector by
weighting the returns by the probability as given in the ratings transition
matrix

18


Example:



Initial

Spread

Horizon

Rating

Horizon

Spread

Return over

Treasuries

(bp)

Transition

Probability

(%) =

Contribution to

Incremental

Return (bp)

30

Aaa

25

38

1.13

0.43

30

Aa

30


30

91.26

27.38

30

A

35


21

7.09

1.49

30

Baa

60

–
㈴

〮㌱

–
〮〷

㌰

䉡

ㄳ1

–
ㄴ1

〮㈱

–
〮㌱

m潲瑦潬o漠f湣牥浥湴m氠let畲渠u癥爠rrea獵物e猠s′㠮㤰




The 28.9 bp incremental return (or, expected return of Aa bonds relative to
Treasuries) using an initial spread of 30 bp is given below in Row 2. The table
also gives incremental re
turns for other ratings classes for other initial spread
levels. For example, if you start with an initial spread of 35 bp
s

for Aa bonds
(instead of 30 used above), then the portfolio incremental return would be 31.4 bp
s

using the process as above.




Ini
tial

Spread

Incremental

Return

Initial Spread

Incremental

Return

Aaa

25

24.2

30

28.4

Aa

30

28.9

35

31.4

A

35

31.1

45

37.3

Baa

60

46.3

70

39.9

Aaa

35

31.7

45

34.6

Aa

40

30.3

55

34.8

A

55

37.9

75

42.7

Baa

85

21
.9

115

27.4