Bonds by Alan Brazil

8/3/2019 Bonds by Alan Brazil

1/86

Goldman, Sachs & Co.

Alan Brazil


2/86


1

Assumptions: Coupon paid every 6 months, $100 of

principal paid at maturity, government guaranteed


3/86


2

Debt is a claim on a fixed amount of cashflows in the future A mortgage loan

Equity is a claim on a fixed percentage of cashflows in the

future A share of GS

What's the difference?


4/86


3

0

20

40

60

80

100

120

140

160

180

200

10 50 90 130

170

210

250

290

330

370

410

450

490

530

570

610

650

690

730

770

810

850

890

930

970

Revenue

Probability

All cashflows can be divided into certain and uncertaincashflows

Certain

First $260 Uncertain


5/86


4

0

20

40

60

80

100

120

140

160

180

200

10 50 90 130

170

210

250

290

330

370

410

450

490

530

570

610

650

690

730

770

810

850

890

930

970

Revenue

Probability

Debt gets the first set of cashflows, equity gets theremainder

Debt:

First $200

Equity:

You Get 10% of the Remainder


6/86


5

0

20

40

60

80

100

120140

160

180

200

10

100

190

280

370

460

550

640

730

820

910

100

Revenue

Probability

0

20

40

60

80

100

120140

160

180

200

10

100

190

280

370

460

550

640

730

820

910

100

Revenue

Probability

0

20

40

60

80

100

120140

160

180

200

10

100

190

280

370

460

550

640

730

820

910

100

Revenue

Probability Highly Rated

Higher

Yield


7/86


6

Higher coupon, higher price, but is it high enough?

Higher coupon, longer maturity, lower price, why?


8/86


7


9/86


8

The typical terms of a debt obligation is broken down intotwo components

You receive principal in N years

And every year until then you receive a coupon payment This coupon is a percentage of the principal


10/86


9

Remember what that was

The lump sum of $100 was the principal

The $6 was the coupon payment

$6 = 6% of $100

You get $6 every year for ten years,then a lump sum payment of

$100 in ten years


11/86


10

Seems like a reasonable price Total of at least $160

You get a total of $60 (6 times 10) over 10 years

You also get your money back in ten years Problems

You dont get to use you $100 for ten years

Giving me $60 over ten years may not be enough


12/86


11

Lets say you were going to pay B for the first set of cashflows

But instead you are offered whats behind door number 2:

You can invest risk free at R% every year for the next tenyears

Well call this the rolling strategy

You roll your investment as it matures every year


13/86


12

Rolling Strategy Assume you invest B in this rolling strategy, and reinvest

each year the entire amount

After Year 1: $B (1 + R)1

Year 2: $B (1 + R)2

Year 3: $B (1 + R)3

.

.

Year 10: $B (1 + R)10


14/86


13

Assume you pay B and you reinvest the interim cashflows atR as well

The first coupon is worth more in ten years due toreinvestment

Year 1 you get $6In year 2, after reinvesting at R, you get 6(1 + R)

In year 3, you get 6(1 + R) (1+R) = 6(1 + R)2

.

.By year 10, this grows to 6(1 + R)9


15/86


14

Year 1 Cashflow In ten years: 6(1 + R)9

Year 2 Cashflow in ten years: 6(1 + R)8

Year 3 Cashflow in ten years: 6(1 + R)7

.

.

Year 10 Cashflow in ten years: 6 + 100

Total Cashflows in ten years,

10

100 + 6 (1 + R)10-i

i=1


16/86


15

It had better be a dead heat otherwise you have anarbitrage opportunity

10

B (1 + R)10 = 100 + 6 (1 + R)10-ii=1

Cashflow at the end of ten years

of both strategies must be the same

Rolling Value in Ten Years = Cashflow One in Ten Years


17/86


16

You can retire in a few years and skip the rest of this course For example if

Then borrow B dollars at R and buy the first security at B

No cost and you cash out in ten years Do this a bunch of times and your making real money

10

B (1 + R)10

Bonds by Alan Brazil

Documents