5 STEPS INVOLVED IN THE
MANAGEMENT INVESTMENT PROCESS
1. SETTING INVESTMENT OBJECTIVES 2. ESTABLISHING AN INVESTMENT POLICY
3. SELECTING A PORTFOLIO STRATEGY 4. SELECTING ASSETS
1.SETTING INVESTMENT OBJECTIVES
•Investment objective will vary by type of financial institution :
•Life insurance •Pension fund •Banks
2. ESTABLISHING AN INVESTMENT POLICY
•Setting asset allocation (cash, equities, fixed-income…)
•Regularly constraints (no bonds<BBB, limited in derivative instr…)
3. SELECTING A PORTFOLIO STRATEGY
•Forecast of future earnings, dividends
•Forecast of future interest rate volatility or yield spreads •For foreign bonds:
•Indexing : replicate the performance of the index (Trackers ETF)
•Core portfolio indexed with the balance managed
•Core portfolio indexed + low risk strategies : indexing plus
forecast of exchange rates
1..Active portfolio strategy
2..Passive portfolio strategy
4.IMMUNIZATION
WHO IS GOING TO MANAGE
WHICH WAY ?
•Pension fund manager ? Immunization strategy
•Mutual fund manager ? Active strategy
•Hedge fund manager ? Active strategy
•Insurance company ? Immunization strategy
•Index matcher mutual fund manager Passive strategy
4. SELECTING ASSETS
•Identifying mispriced issues (arbitrage)
•Select bonds according to : coupon, maturity, credit quality, callability..
5. MEASURING AND EVALUATING PERFORMANCE
•Compared to a benchmark
•Difference between performance and objective
Benchmark 1-year return = 2%
Portfolio manager exceeded by 200BP = 4%
Great job ?
ACTIVE PORTFOLIO
STRATEGY
What are the 3 sources of income from holding a bond :
•Coupon income
BOND VOLATILITY
AND
DURATION……..
PROPERTY 1: THE PERCENTAGE PRICE CHANGE IS NOT THE SAME FOR ALL THE BONDS.
PROPERTY 2 : FOR A LARGE CHANGE IN THE YIELD REQUIRED, THE PERCENTAGE PRICE CHANGE FOR A GIVEN BOND
DEPENDS ON ITS AND ON ITS .
PROPERTY 3 : FOR A SMALL CHANGE IN THE REQUIRED YIELD, THE PERCENTAGE CHANGE IN BONDS PRICES
IS ROUGHLY THE SAME.
VOLATILITY OF A BOND IS DETERMINED BY :
1. ITS COUPON
THE LOWER THE COUPON RATE, THE MORE/LESS VOLATILE THE BOND PRICE
THE LONGER THE TIME TO MATURITY, THE MORE/LESS VOLATILE THE BOND PRICE
MORE
WHAT WOULD AN INVESTOR WHO EXPECTS INTEREST
RATES TO FALL, LIKELY DO, REGARDING THE VOLATILITY
OF HIS BOND PORTFOLIO?
INCREASE IT……
HOW COULD HE INCREASE THE VOLATILIY OF HIS BOND PORTFOLIO?
DURATION
DURATION REPRESENTS THE NECESSARY LAP OF TIME FOR THE PRICE OF AN ASSET TO REACH ITS INITIAL VALUE THROUGH ITS DISCOUNTED CASH FLOWS
DURATION CAN BE SHOWN TO MEASURE THE SENSITIVITY OF A BOND PRICE TO CHANGES IN THE GENERAL LEVEL
DURATION vs CONVEXITY
10-year bond 5-year bond
20-year bond
Portfolio Duration= 7
DURATION
Measures only approximations for a small change in yield
yield Price
Actual price (convexity)
Y
Which bond is more convex ?
B
Which bond is more expensive ?
Using convexity in conjunction with duration is more accurate than using duration alone.
ACTIVE PORTFOLIO
MANAGEMENT
Factors affecting a portfolio’s return :
•Change in the level of interest rate
•Change in the shape of the yield curve
•Changes in the yield spreads among bond sectors •Changes in the option adjusted spread
•Changes in the yield spread for particular bond (risk premium)
Change in the level of interest rate
•The manager must determine whether his strategy and expectations of interest rates are the same as the markets.
•Forward rates are determined by what .
•For those managers whose benchmark is a bond index , adjusting their portfolio’s duration must be done with regard to the index’s duration.
•A portfolio’s duration can be changed by bonds in the portfolio for new bonds that will achieve the target portfolio
duration
•Abusive use of interest rate options and futures by portfolio manager to cover inferior performance.
swapping
YIELD CURVE STRATEGIES
•Yield curve strategies involve positioning a portfolio to
capitalize on expected changes in the shape of the yield curve
Shifts in the yield curve :
Parallel shift in the yield curve
Parallel Shifts
Y IE D L C H A N G EST INTERM. LT
MATURITY 0
UPWARD PARALLEL SHIFT
Y IE D L C H A N G E
ST INTERM. LT
MATURITY
0
TWISTS SHIFTS
Y IE D L C H A N G E 0ST IM LT
BUTTERFLY SHIFTS
Y IE D L C H A N G E 0ST IM LT
Short rates up Intermediate rates Long term rates
Flattening yield curve
Yield spread between LT rates and ST rates has increased/decreased ? decreased
Steepening yield curve
The maturity of the securities in a portfolio will have an important impact on the total return of the portfolio.
What maturity paper will most likely affect the return of your portfolio in the short term? Long duration paper
For ST horizon, the spacing of maturities in the portfolio will have a significant impact on the total return.
3 STRATEGIES
•BULLET STRATEGY
•BARBELL STRATEGY
BULLET STRATEGY
Yrs 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
•Spikes indicate maturing principal •Bullet concentrated around 10 years
BARBELL STRATEGY
Yrs 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
LADDER STRATEGY
Yrs 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
YIELD CURVE STRATEGIES
BOND COUP. YEARS
PRICE YTM
DUR. CONV
A
8.5
5
100
8.50
4.005
19.816
B
9.5
20
100
9.50
8.882
124.17
BOND COUP. YEARS
PRICE YTM
DUR. CONV
A
8.5
5
100
8.50
4.005
19.816
B
9.5
20
100
9.50
8.882
124.17
Percentage price change due to duration : duration x %
Percentage price change due to convexity : 1/2 x convexity x ( %)2 Approximating Percentage Price Change using Duration and Convexity
Mention spread analysis Short 5 year treasury
Long 10 year strategy if curve steepens
For a 200BP decrease in interest rate , Bond B would vary by :
Duration : 0.02 x 8.88 = 17.6%
Convexity : ½ x 124.17 x 0.022 = 2.48%
17.6% + 2.48% = 20.08%
For a 200BP increase in interest rate , Bond B would vary by :
Duration : -0.02 x 8.88 = -17.6%
Convexity : ½ x 124.17 x 0.022 = 2.48%
-17.6% + 2.48% = -15.12%
BULLET PORTFOLIO BARBELL PORTFOLIO
2 PORTFOLIOS
100% Bond C
50.2% Bond A
49.8 % Bond B
What is the duration of the bullet portfolio?
6.434
What is the duration of the barbell portfolio?
0.502 (4.005) + 0.498 (8.882) = 6.434
What is the dollar convexity of the bullet portfolio? 55.4506
What is the dollar convexity of the barbell portfolio?
0.502 (19.816) + 0.498 (124.17) = 71.784
Convexity
barbell> Convexity
bulletWhich portfolio is more volatile ?
For 2 portfolios with the same duration, the greater the
convexity, the better the performance of a bond,
when yield changes.
What is the dollar yield to maturity of the bullet portfolio? 9.25%
What is the dollar yield to maturity of the barbell portfolio?
0.502 (8.50%) + 0.498 (9.50%) = 8.998%
ANALYSIS CONCLUSION
•Same duration = 6.434
•Yield
bullet> Yield
barbell•Convexity
barbell> Convexity
BulletChosing the barbell portfolio is refered to The Cost of Convexity
…...6-MONTH HORIZON
(hand out)
Which portfolio (bullet or barbell) should a portfolio manager choose with a 6-month investment horizon ?
PARALLEL SHIFT
•When yield changes by more than 100BP, the barbell portfolio outperforms the bullett portfolio (and vice versa)
Even with parallel shift in yield curve 2 portfolios with the same
duration will not give the same performance Different convexity
With all other things beeing equal, the market pays more for
PARALLEL SHIFT
•If the yield changes by less than 100BP (up or down), the bullet portfolio will provide a better total return.
YIELD SPREAD
STRATEGIES
•Positioning a portfolio to capitalize on change in yield spreads
between sectors of the bond market
CREDIT SPREAD
•Credit spread between Treasury and non-Treasury in a declining or contracting economy.
widens or narrows Widens why?
Less revenues for companies debt repayment problems less credibility
IMPORTANCE OF
DOLLAR
DURATION
P = 80 Dur = 5
P = 90 Dur = 4
A B
For a 100BP change, Bond A will vary by 5% that is $40
Suppose that a portfolio manager owns $10 million of par value of Bond A and Bond B which has a market value of $8 million
$9 million The dollar duration of Bond A per 100BP change in yield for the $8 million market value is $400 000 that is 5% x $8 million
•Suppose that the portfolio manager wants to exchange Bond A that it owns in his portfolio for Bond B
•He needs to keep the same interest rate exposure (same duration) for Bond B that he currently holds for Bond A
What quantity of Bond B must he purchase to keep his dollar
Duration the same ?
1. If he buys $10 million of par value of Bond B and therefore $9 million of market value of Bond B(90% of face value),
the dollar change for a 100 BP change in rates would be only $360 000
2. If he purchases $10 million of market value of Bond B, the dollar change for a 100BP change in rates would be $ 400 000
Because Bond B is trading at 90, $11.1 million of par value
Mathematically….
Let:
$DA = dollar duration per 100BP change in yield for Bond A for the market value of Bond A held
MDB = Modified duration for Bond B
MVB = Market value of Bond B
Then the following equation sets the dollar duration for Bond A equal to the dollar duration of Bond B :
MDB
THE USE OF LEVERAGE
•A portfolio that does not contain any leverage is called an
unlevered portfolio.
•A portfolio that contains leverage is called a levered portfolio.
Why use leverage in any investment ?
DURATION OF A
LEVERAGED PORTFOLIO
•Portfolio of $100 million invested in a bond with a duration of 10
•Borrows $300 million and invest it in the same bond
What if rates change by 100BP ? Changes by $40 million
The portfolio manager is interested in his equity ($100 million), not the levered part of his investment.
The proper way to measure the portfolio’s duration is relative to the unlevered amount of equity because the the manager is concerned with the risk exposure relative to his equity
Speculating on Interest Rates
•A portfolio manager who wants to speculate on an increase in interest rates will buy/sell interest rate futures .
sell
• 3 advantages of using futures : 1. Lower transaction cost
Controlling the interest rate risk
of a portfolio
•Interest rate futures can be used to adjust the of a portfolio.duration
•Suppose a portfolio manager wishes to increase the duration of his portfolio from 5 years to 10 years using futures.
How many contracts should he buy/sell? buy
(DTarget - Dinitial ) Pvalue
Approximate # of contracts =
BOND
A
BOND
B
BOND
C
FV
$2 000 000 $3 000 000 $5 000 000
DUR
9
10
12
100
100
100
The portfolio manager expect a decrease in interest rate.
•What should he do regarding duration ?
•He wishes to modify the duration of his portfolio by 20%
How many futures contracts should he buy/sell knowing that
the contract trades at 103 ? (20-year 8% coupon bond yielding 6% has a modified duration of 13)
Di =10.8 Buy 17 contracts
HEDGING USING
INTEREST RATE FUTURES
If rates are expected to go up, and a portfolio manager wishes to hedge his long position in bonds, he would interest rate futures.
short
•How many contracts should he short ?
Par value to be hedged Hedge ratio x
Par value of contract
Duration of bond to be hedged Hedge ratio =
Duration of hedging instrument
If the bond to be hedged is more volatile than the hedging instrument,
more/less of the hedging instrument will be needed. more
Par value to be hedged Contract amount = Hedge ratio x
BOND
A
BOND
B
BOND
C
FV
$2 000 000 $3 000 000 $5 000 000
DUR
9
10
12
PRICE
90
110
100
Portfolio Value = 10,1Million
Duration : (9 x 17,82%) + (32,68% x 10) + (12 x 49,50%) =10.82
Consider porfolio’s value of $95 million (par value $100 million).
Volatility of the portfolio is 16% and the volatility of the contract is 13%. How many contracts should be bought/sold to hedge the portfolio?
