8/8/2019 SAPM Final (3)

1/22

SAPMTHERE'S NO SUCH THING AS A SURE

THING, EVEN IN THE BOND WORLD

Prepared By:DEVESHREE RAUT

DEBJANI SINGHA

JAGRUTI CHAUHAN

8/8/2019 SAPM Final (3)

2/22

8/8/2019 SAPM Final (3)

3/22

EXAMPLE

5 Year Bond, Coupon Rate5%, FV Rs. 1000

1st Year 2nd Year 3rd Year 4th year 5thyear

(Interest) (Interest) (Interest) (Interest)

(Interest + Face Value)

Howtocalculate Duration:

8/8/2019 SAPM Final (3)

4/22

FACTORS AFFECTING BOND

DURATION1). TIME TOMATURITY:Consider 2 Bonds

A B

Face Value 1000 1000Interest Rate 5% 5%

Maturity 1 year10 year

Therefore, everyone would prefer BondA as itwillrepayits true cost quicklythan Bond B.

Hence, shorter duration maturity bond

8/8/2019 SAPM Final (3)

5/22

FACTORS AFFECTING BOND

DURATION

2).COUPON RATE

A Bonds paymentis the key factorin

calculating duration. Bonds withhigher

couponwillpaybackits originalcost

quickerthanthe loweryielding bonds.

Therefore, higher the coupon, the

lowerwill be the duration.

8/8/2019 SAPM Final (3)

6/22

UNDERSTANDING BOND DURATION

You may think a 30 year treasury is your

safest investment, but if you dont

understand the dynamics of Bond

duration you could be taking a big risk.

ONE RISK IN BOND MARKET= Interest Rate

Riskwhich is easy to determine through

the concept ofMODIFIEDDURATION.(1966, LarryFisher)

It is defined as the percentage change in

price for a 100 basis point change in

8/8/2019 SAPM Final (3)

7/22

MODIFIED DURATION

Itis the modified versionof theMacaulay Modelthataccounts forchange ininterestrates.

Fluctuatinginterestrates willaffect duration.

MODIFIED DURATIONFORMULA

MD = Macaulay Duration1 + YTM

no.of couponperyear

8/8/2019 SAPM Final (3)

8/22

EXAMPLE OFMACAULAY AND MODIFIED

Bettyhold a5year bond withaparvalue of 1000 and couponrate 5%.(Macaulay Duration).

Solution

1(50/1250)+2(50/1250)+3(50/1250)+4(50/1250)+5(50/1250)+5(1000/1250)= 4.6

years.

Continue with same Eg for ModifiedDuration.

Md=(4.55/ (1+0.05/1))= 4.33.

8/8/2019 SAPM Final (3)

9/22

EXAMPLE

2 bonds with similar maturity butwith differentcouponrates and

cash flowpatterns willhave

different duration.

1st Bond =5year maturity, 8.5%rate

,1000 face value , YTM=10%

2nd Bond =5year maturity,11.5%

rate,1000FV, YTM=10.6%.

8/8/2019 SAPM Final (3)

10/22

Duration of 8.5% Bond

YEAR CASH FLOW PV @ 10% BOND PRICE

PROPORTION

BOND

PRICE* TIME

1 85 77.27 0.082 0.082

2 85 70.25 0.074 0.149

3 85 63.86 0.068 0.203

4 85 58.06 0.062 0.246

5 1085 673.70 0.0714 3.572

943.14 1.000 4.252

8/8/2019 SAPM Final (3)

11/22

Duration of 11.5%Bond

YEAR CASH FLOW PV @ 10.6% BONDPRICE

PROPORTION

BOND

PRICE* TIME

1 115 103.98 0.101 0.101

2 115 94.01 0.091 0.182

3 115 85.00 0.082 0.247

4 115 76.86 0.074 0.297

5 1115 673.75 0.652 3.259

1033.60 1.0000 4.086

8/8/2019 SAPM Final (3)

12/22

COMPARISION OFBOTH THEBONDS

Durationof 1

st

bond=4.25

2 years Durationof 2nd bond=4.086years

Now, if we calculate the volatilityof boththe

bonds i.e. Modified Duration

Volatilityof 8.5% bond = 4.252/(1.100)= 3.87

Volatilityof 11.5% bond= 4.086/(1.106)= 3.69

Whichindicates that 8.5% bond has highervolatility.

If YTMincrease by 1%, this willresultin 3.87%

8/8/2019 SAPM Final (3)

13/22

PRESENT VALUE(IN RUPEES)

DISCOUNT RATE(In%)

5 YEAR BOND 10YEAR BOND PERPETUALBOND

5 1216 1386 2000

10 1000 1000 1000

15 832 749 667

20 701 581 500

25 597 464 400

8/8/2019 SAPM Final (3)

14/22

WHATCOULDBE THE REASON?

The reason forthis differential

responsiveness is not difficultto

understand.

Incase of 10 year bond, one would

get just Rs.100 evenif interestrate

rises to say 15percent.Incase of 5

year bond, one canatleast sellthe

bond after5years and reinvest

moneytoreceive Rs.150 forthe next

five years.

8/8/2019 SAPM Final (3)

15/22

WHAT IS PORTFOLIO DURATION?

A portfolio's durationis equal

tothe weighted average of

the durations of the bonds in

the portfolio. The weightis

proportionaltohow muchofthe portfolioconsists of a

certain bond.

8/8/2019 SAPM Final (3)

16/22

EXAMPLEPortfolio Duration =w1D1 + w2D2 ...+ wkDk

Let's take 3 bonds:

6,000 market value of ABC ltd 7%of 10 with durationof

5.5

3,400 market value of XYZ 5%or 15with durationof 7.8

1,535,market value of CDS 9%or 20 with durationof 12

Total market valve of 10,935.

Solution:

Firstlet's find the weighted average of each bond:

ABC LTDweighted average is 6,000/ 10,935=.548

XYZ LTDweighted average is 3,400 / 10,935 =.311

CDS LTDweighted average is 1,535/ 10935, =.14

Sothe PortfolioDuration =.548(5.5) + .311(7.8) + .14 (12)=

8/8/2019 SAPM Final (3)

17/22

LIMITATION OFTHE PORTFOLIO

DURATION ME

ASURE

Eachof the bonds inthe

portfolio mustchange bythe100 or50bps, orthere must be

aparallel shiftinthe yield

curve forthe durationmeasure to be useful.

8/8/2019 SAPM Final (3)

18/22

EFFECTIVE DURATION

The modified duration formula discussed aboveassumes thatthe expected cash flows willremainconstant, evenif prevailinginterestrates change; this is alsothe case foroptionfree fixedincome securities.

Onthe otherhand, cash flows from securitieswith embedded options orredemption featureswillchange wheninterestrates change.

Forcalculatingthe durationof these types ofbonds, Effective Durationis the mostappropriate.

EG CALLABLE BONDS.

8/8/2019 SAPM Final (3)

19/22

WHAT ISCONVEXITY?

Why durationis inaccurate in measuringthe effectofyield changes onprice?

Durationand YTMare inverselyrelated.

As yields rise, duration falls. Thus, the nextyield

increase has less of anegative effectonprice since

durationis lower.

As yields fall, durationrises. Thus, the nextyield

decline has more of apositive effectonprice sincedurationis higher.

Usingthe duration method tocalculate the new

price of a bond followingayield change negative

orpositive will, therefore, be inaccurate (and

8/8/2019 SAPM Final (3)

20/22

The more Convex a Bond, the

more attractive. Bond A has a higher convexity than Bond B,

which means that all else being equal,Bond A

will always have a higherprice than Bond B as

interest rates rise or fall.

8/8/2019 SAPM Final (3)

21/22

WHAT IS NEGATIVECONVEXITY?

Foranoncallable bond, there is aninverserelationship between durationand yield.

Negative convexity means thatas marketyieldsdecrease, duration decreases as well.

Since this is anunfavorable characteristicof a bond,investors demand ahigheryield.

Negativelyconvex bonds (suchas callable corporate

and mortgages)thus yield more thanotherwiseequivalentnoncallable, orpositivelyconvex, bonds.

Investors expecting stabilityinyields are attractedto such bonds.

8/8/2019 SAPM Final (3)

22/22

THANK YOU