Bonds by Alan Brazil
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Transcript of Bonds by Alan Brazil
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8/3/2019 Bonds by Alan Brazil
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Goldman, Sachs & Co.
Alan Brazil
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Goldman, Sachs & Co.
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Assumptions: Coupon paid every 6 months, $100 of
principal paid at maturity, government guaranteed
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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?
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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
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20
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80
100
120
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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
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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
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Higher coupon, higher price, but is it high enough?
Higher coupon, longer maturity, lower price, why?
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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
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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
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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
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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
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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
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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
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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
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It had better be a dead heat otherwise you have anarbitrage opportunity
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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
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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