Comm 324 --- W. Suo Slide 1. comm 324 --- W. Suo Slide 2 Active strategy Trade on interest rate...

comm 324 --- W. SuoSlide 1Slide 1

Managing Bond Managing Bond PortfoliosPortfoliosActive Management StrategiesActive Management Strategies


Active strategy Trade on interest rate predictions Trade on market inefficiencies

Passive strategy Control risk Balance risk and return

Managing Fixed Income Securities: Basic Strategies


Yield Curve Changes

It involves positioning a portfolio to capitalize on expected changes in the shape of the treasury yield curve

Type of shifts in the yield curve: Parallel shift: changes in the yields on all maturities are the same

yield change

short intermediate long

yield change


Yield Curve Change ...

Non parallel shifts Twist: flattening or steepening of the yields curve Slope of the yield curve is usually measures by the spread between

some long-term treasury and some short term treasury yields, e.g., 30 y over 12 year; 20 y over 2 y

yield change yield change

Flattening Steepening


Yield Curve Change ...

Butterfly shift Change in the humpedness of the yield curve: both the yields on

the short end and the long change in the same direction, while the yields with intermediate maturities change to an opposite direction

yield change yield change


Yield Curve Movement: Historical Facts

The three types of movements combined can explain more than 90% of the yield curve changes

They are not independent: downward shift usually combined the steepening of the yield

curve upward shift usually combined the flattening of the yield

curve


Yield Curve Strategy

Yield curve analysis is important if one has a portfolio consisting of many different maturities

Positioning a portfolio with respect to the maturities of the securities across the spectrum included in the portfolio

Common strategies: Bullet strategy: securities in the portfolio are concentrated

around one maturity Barbell strategy: concentrated around the extreme ladder strategy: evenly invested in securities with different

maturities


Example

Bullet portfolio (I): 100% of C Barbell portfolio (II): 50.2% of A, and 49.8% of B Duration:

I: 6.434; II: 0.502*4.005+0.498*8.882 = 6.434 Dollar convexity:

I: 55.4506; II: 0.502*19.8164+0.498*124.1702 = 71.7806 Yield:

I: 9.25%, and II: 0.502*8.50%+0.498*9.50% = 8.998%

Bond Coupon Mat Cash Pr Yield MD Dollar C’ty

A 8.5 5 100 8.5 4.005 19.8164

B 9.5 20 100 9.5 8.882 124.1702

C 9.25 10 100 9.25 6.434 55.4506


Example …

Yield difference: 9.25%-8.998% = 25.2 b.p. This is referred to as the cost of convexity: giving up yield

for better convexity Now suppose one has a 6-month investment horizon,

which portfolio should he choose: Same duration Yield (I) > Yield (II) Convexity (I) < Convexity (II)


Spread Trades

Consider the following bond that has a maturity on 5/15/2034

and the T-note with coupon 5.5% and matures on 11/30/2007

bid ask yield SD Acc Int PVBP

108.8405 108.903 7.96% 12/2/05 0.408654 1200.643

109.0806 109.1413 7.94% 12/3/05 0.432692 1204.999

109.8076 109.8701 7.88% 12/4/05 0.456731 1218.246

bid ask yield SD Acc Int PVBP

100.3735 100.4360 5.30% 12/2/05 0.03022 187.3602

1004664 100.5289 5.25% 12/3/05 0.04533 187.34

100.5967 100.6592 5.18% 12/4/05 0.06044 187.4086


Spread Trades

Yield Spread between 30 bond and the two year bond: 7.96%-5.30%=2.66%

What can one do if he believes that yield would be significantly increase (or the slope of the yield curve will increase) in a couple of days?

We don’t want to bear the risk of the yield curve having a parallel shift need to make the portfolio’s price risk to be zero:

In order for the spread to increase: yield for the 30 year increase relatively more than the 2 year note yield for the 30 year decrease relatively less than the 2 year note

How to setup portfolio to realize a profit based on one’s belief?

2 2 30 30n PVBP n PVBP


Spread Trades

Relative price would change: 30 year bond would be relatively cheaper than the 2 year note

short 30 year bond and long two year note Assume we want to short $100m par amount of 30 year

bond. To eliminate the parallel shift risk, we need to long

of par amount 2 year note Assume that the repo rate using the 2 year note as

collateral is 5%, and reverse repo rate using the 30 bond as collateral is 4.9%

302 30

2

1200.6435100 641

187.3642

PVBPn n

PVBP


Trading Spreads …

Trader Repo Dealer Trader

Deliver two year note

Borrow CashBuy 2 Y note

Borrow 30 Y bond

Post cash as collateral

Sell 30 Y bond

ON 12/2/05

Trader Repo Dealer Trader

ON 12/4/05Unwind the Position

Sell the 2Y note Buy 30Y Bond

Payback cash plus int

Collect 2Y note

Receive Cash plus int

Return 30Y bond


Summary: On 12/2/2005

Borrow enough cash to buy the $641m par 2Y note (and post it as collateral):

(100.4360+0.03022)*10,000*641= (643,988,470)

Borrow 30Y bond and sell it (then post the cash as collateral):(108.8405+0.408654)*10,000*100 = 109,249.154

Net Cash Flow: 0Note: usually repo dealers take haircut


On 12/4/04

Sell 2Y note: for the par amount $641m, (100.5967+0.0604)*10,000*641 = 645.212,011

Repay the repo dealer:643,988,470*(1+2*0.05/360)= (644,167,356)

Collect cash plus interest from the repo dealer:109,249,254*(1+ 2*0.049/360) = 109,278,894

Buy the 30Y bond to cover the short position:(109.8701+0.4567)*10,000*100 = (110,326,800)

Net: (3,251)


Spread Trades

Profit & loss depends on: bid-ask spreads repo rates

if the security that is long can earn a special repo rate, which is much higher, then the deal would have made money

haircut


Substitution swap Inter-market swap Rate anticipation swap Pure yield pickup Tax swap

Active Bond Management: Swapping Strategies


Yield Curve Ride

Maturity

Yield to Maturity %

3M 6M 9M

1.50 1.25 0.75

Comm 324 --- W. Suo Slide 1. comm 324 --- W. Suo Slide 2 Active strategy Trade on interest rate...

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