Problem Set 5
More Arbitrage
Bonds as commodities (Problem 1)
$1,017,408.41
7.00%
$1,000,000
NY
today
NY
90 days
7.50%
7.25%
NY
270 days
$1,055,739.13
Profit = $650.46
$1,055,088.67
1
Bonds as commodities (Problem 2)
$1,035,630.37
7.10%
$1,000,000
NY
today
NY
180 days
$1,035,758.04
7.50%
7.25%
NY
270 days
$1,055,088.67
Profit = $127.67
Bonds as commodities (Problem 3)
$1,017,408.41
7.00%
$1,000,000
NY
today
$1,017,634.17
7.15%
7.12%
Profit = $225.76
NY
90 days
NY
180 days
$1,035,732.50
2
Problem 4
•  Moving from 0% coupon to 6% coupon
Adds extra income of $6 per year
Adds $38.28 to price ($75.08 minus $36.80)
•  Moving from 6% coupon to 8% coupon
Adds extra income of $2 per year
Adds $3.92 to price ($79 compared with $75.08)
Therefore an extra $6 per year should cost three
times as much, $11.76
•  The 0% bond is a bargain
Problem 4
0
1
2
19
20
Sell
$300.32
$12
$12
$12
$412
Buy
$237.00
$12
$12
$12
$312
Buy
$36.80
0
0
0
$100
0
0
0
Net $26.52
0
NPV is clearly positive
3
Problem 4
Yield
11.60%
10.24%
10.00%
Risk (Convexity)
Problem 5
•  Moving from 6% coupon to 8% coupon
Adds extra income of $2 per year
Adds $9 to price ($76 compared with $67)
•  Moving from 8% coupon to 10% coupon
Also adds extra income of $2 per year
But, adds $12 to price ($88 compared with $76)
•  Therefore, the 10% bond is over-priced
(compared with the 8% bond)
4
Problem 5
0
1
2
19
20
Buy
$152.00
$8
$8
$8
$208
Sell
$67.00
$3
$3
$3
$103
Sell
$88.00
$5
$5
$5
$105
0
0
0
Net
$3.00
0
NPV is clearly positive
Problem 5
12.22%
Yield
12.10%
11.68%
Risk (Convexity)
5
Problem 6
Yield
8%
8%
7.75%
Risk (Convexity)
Problem 6
0
1
11
12
Sell
$181.36 $6
$6
$6
Buy
$90.61
$3
$3 $103
Buy
$88.35
$3
$3
Net
$2.40
0
0 $100 $3 $203 $3 $103
$3
14
13
15
16
$6 $206
$3
$3
$3 $103
NPV is always positive
6
Problem 7
8.5%
Yield
8%
8%
Risk (Convexity)
Problem 7
0
1
11
12
Buy
$174.00 $6
$6
$6
Sell
$90.61
$3
$3 $103
Sell
$88.35
$3
$3
Net
$4.96
0
0 $100 $3 $203 $3 $103
$3
14
13
15
16
$6 $206
$3
$3
$3 $103
NPV is always positive
7
Problem 8
Yield
8.50%
8.38%
8.00%
Risk (Convexity)
Problem 8
0
1
11
12
Sell
$178.88 $6
$6
$6
Buy
$88.44
$3
$3 $103
Buy
$86.35
$3
$3
Net
$4.09
0
0 $100 $3 $203 $3 $103
$3
14
13
15
16
$6 $206
$3
$3
$3 $103
NPV is always positive
8
Problem 9
Yield
8.5%
8%
8%
Risk (Convexity)
Problem 9
0
1
11
12
Sell
$178.88 $6
$6
$6
Buy
$90.61
$3
$3 $103
Buy
$85.70
$3
$3
Net
$2.57
0
0 $100 $3 $203 $3 $103
$3
14
13
15
16
$6 $206
$3
$3
$3 $103
NPV is always positive
9
Problem 10
Yield
8%
7.75%
7%
Risk (Convexity)
Problem 10
0
1
11
12
Buy
$181.36 $6
$6
$6
Sell
$90.61
$3
$3 $103
Sell
$93.95
$3
$3
Net
$3.20
0
0 $100 $3 $203 $3 $103
$3
14
13
15
16
$6 $206
$3
$3
$3 $103
NPV is always positive
10
Equities as commodities (Problem 11)
$ 1,500,000
CHF 1,725,000
ZUR
today
CHF 1.15
Spot 1500
Future 1575
Dividend 1%
R = 6%
CHF 1,776,799.41
ZUR
later
NY
today
=$1
CHF 1.14
=$1
CHF 1,812,600
Profit = CHF 35,800.59
NY
later
$ 1,590,000
What is not balanced?
Problem 12
•  Suppose you know Exxon will announce bad news
–  Beta is 0.95
–  Describe a no-money-in, hedged position designed to
benefit from the information
11
Problem 13
•  Suppose you know GM will announce bad news
–  Beta is 1.05
–  Describe a no-money-in, hedged position designed to
benefit from the information
Problem 14
Score
Prime
$
$
0
X
S
Primes get dividends plus
appreciation up to defined point
0
X
S
Scores get remaining
appreciation
What if Prime + Score > Stock?
12
JunkCo Arbitrage
Illustration of a Floating/Fixed Swap
Party
Variable
Variable
Underwriter
Fixed
Counterparty
Fixed
If net is positive, underwriter pays party. If net is negative, party pays underwriter.
JunkCo Arbitrage
Lender
Lender
T + 3%
JunkCo
11% Fixed
T-Bill
T-Bill
Underwriter
11% Fixed
AAA Corp
11% Fixed
T-Bill
Net for Underwriter:
• Net flows are zero
• Gains fees, future opportunities, &
goodwill
Net for JunkCo:
• Net is 14% fixed
• This is better than JunkCo could do by itself
After 1st year
Sinking
Fund
Net for AAA Corp:
• During 1st year, borrows at T-Note rate
• During remaining time, net flow is zero
• This is better than AAA could do by itself
13
JunkCo Arbitrage
How is this possible?
Answer: Quality gap is inconsistent
Junk
Quality Gap
Rate
AAA
Yield Curves
Maturity
Myron Labs Arbitrage
Variation on a currency swap
8% Fixed, £ Principal
8% Fixed, $ Principal
1
1
BT, £ Principal
BT, $ Principal 1st yr
£ Principal after 1st yr
Intermediary
Myron Labs
BT + 2%
Lender
£1,000,000
After 1st year
$2,000,000
$2,000,000
End of last year
£1,000,000
Advanced Devices
Lender
8% Fixed
BT-Bill
Volatility
After 1st year
Sinking
Fund, £
Dynamic Hedge
14
$5mm +
Appreciation
Fixed
BT
PEFCO
1% Coupon
Undisclosed
Flow
Appreciation
Appreciation
What happens to Tokyo Index?
Nikkei Put Warrants (Bringing
Dep
Public Market
Option Premium
At Beginning
Depriciation
At Maturity
Dep
Flow
Kingdom of Denmark
Flow
Goldman Sachs
innovation to retail)
Counterparty
SCPERS
$5 mm
Counterparty
PENs
15
App
App
Flow
Dep
Price
Public Market
Flow
Kingdom of Denmark
$5mm
+ App
Fixed
BT
1%
PEFCO
SCPERS
$5 mm
Goldman Sachs
Alternative Plan
Dep
Volatility
Dynamic Hedge
16