Fin550 fin560 3. Suppose that an investor holds a share of Sophia common stock, currently valued at $50. She is concerned that over the next few months the value of her holding might decline, and she would like to hedge that risk by supplementing her hol

Q3

Current value	$50	Answer
a.	b.
Deruivative positions	1 .	A short position in a forward option with a exercise price of $50
1	Expiratigon date Sophia	Short forward (k=$50)	Initial short
Short position with contract price	$50	Stock price ($)	payoff=max(0,s-50)	Forward premium	Net profit	1 .	Short Forward
2	put option	25	$25	$0	$50	$25
Long position in exercise price	$50	30	$20	$0	$50	$20
Front end premium expense	$3.23	35	$15	$0	$50	$15
3	Call option	40	$10	$0	$50	$10
Short position with exercise price	$50	45	$5	$0	$50	$5
front end premium receipt	$5.20	50	$0	$0	$50	$0
Answer	55	($5)	$0	$50	($5)
3 .	F0, T = Call-Put + PV(strike)	60	($10)	$0	$50	($10)
c.	$50 = 5.20-3.23 +PV($50)	65	($15)	$0	$50	($15)
PV= ($50-5.20+3.23)/50	70	($20)	$0	$50	($20)
75	($25)	$0	$50	($25)
PV =	$1.041
2	A long position in a put option with a exercise price of $50 and a front-end premium expense of $3.23.
S= F/(PV factor)	Expiratigon date Sophia	Short forward (k=$50)	Initial long put
$50 = F/(1.041)	Stock price ($)	payoff=max(0,50-s)	put premium	Net profit	2 .	Long Put
F =	52.05	25	$25	($3.23)	$46.77	$25
30	$20	($3.23)	$46.77	$20
The contract price $52.05 are not the same because the put and the call option are not the same. If the call and the put are together the price will be zero.	35	$15	($3.23)	$46.77	$15
40	$10	($3.23)	$46.77	$10
45	$5	($3.23)	$46.77	$5
50	$0	($3.23)	$46.77	$0
55	$0	($3.23)	$51.77	($5)
60	$0	($3.23)	$56.77	($10)
65	$0	($3.23)	$61.77	($15)
70	$0	($3.23)	$66.77	($20)
75	$0	($3.23)	$71.77	($25)
Expiratigon date Sophia	Short call (k=$50)	Initial short
Stock price ($)	payoff=max(0,s-50)	Call premium	Net profit	3 .	Short put
25	$0	$5.20	$30.20	$25
30	$0	$5.20	$35.20	$20
35	$0	$5.20	$40.20	$15
40	$0	$5.20	$45.20	$10
45	$0	$5.20	$50.20	$5
50	$0	$5.20	$55.20	$0
55	($5)	$5.20	$55.20	($5)
60	($10)	$5.20	$55.20	($10)
65	($15)	$5.20	$55.20	($15)
70	($20)	$5.20	$55.20	($20)
75	($25)	$5.20	$55.20	($25)

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

20-10

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

50

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

75

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

20-10

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

50

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

75

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

20-10

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

50

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

75

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 -5 -10 -15 -20 -25

payoff=max(0,50-s) 25 30 35 40 45 50 55 60 65 70 75 25 20 15 10 5 0 0 0 0 0 0

payoff=max(0,s-50) 25 30 35 40 45 50 55 60 65 70 75 0 0 0 0 0 0 -5 -10 -15 -20 -25

Q5

answer
Trading price	$42	a.	Share price	Payoff to Buyer of call option	Payoff to sellter of call	b.	Share price	Payoff to Buyer of put option	Payoff to sellter of put
Expiration date	6	months	$20	($3.90)	$3.90	$20	$18.55	($18.55)
Exercise price	$40	$25	($3.90)	$3.90	$25	$13.55	($13.55)
Market price	$30	($3.90)	$3.90	$30	$8.55	($8.55)
Put	$1.45	$35	($3.90)	$3.90	$35	$3.55	($3.55)
Call	$3.90	$40	($3.90)	$3.90	$38.55	$0.00	($0.00)	Break even
$43.90	$0.00	$0.00	Break even	$40	($1.45)	$1.45
Risk free holding period return	4%	$45	$1.10	($1.10)	$45	($1.45)	$1.45
Annual rate	8%	$50	$6.10	($6.10)	$50	($1.45)	$1.45
$55	$11.10	($11.10)	$55	($1.45)	$1.45
Answer	$60	$16.10	($16.10)	$60	($1.45)	$1.45
c.
Share price	Payoff to Buyer of call option	Payoff to sellter of call	Share price	Payoff to Buyer of put option	Payoff to sellter of put
Call-Put = S-PV	$20	($3.90)	$3.90	$20	$18.55	($18.55)
$3.90-$1.45 ≠$42-(40/1.04)	$25	($3.90)	$3.90	$25	$13.55	($13.55)
$30	($3.90)	$3.90	$30	$8.55	($8.55)
$3.54	$35	($3.90)	$3.90	$35	$3.55	($3.55)
$40	($3.90)	$3.90	$40	($1.45)	$1.45
The call parity will not hold for a European style contract because 3.54 is not equivalent to $2.45 difference.	$45	$1.10	($1.10)	$45	($1.45)	$1.45
$50	$6.10	($6.10)	$50	($1.45)	$1.45
$55	$11.10	($11.10)	$55	($1.45)	$1.45
$60	$16.10	($16.10)	$60	($1.45)	$1.45

Call option

Payoff to Buyer of call option 20 25 30 35 40 43.9 45 50 55 60 -3.9 -3.9 -3.9 -3.9 -3.9 0 1.1000000000000001 6.1 11.1 16.100000000000001 Payoff to sellter of call 20 25 30 35 40 43.9 45 50 55 60 3.9 3.9 3.9 3.9 3.9 0 -1.1000000000000001 -6.1 -11.1 -16.100000000000001

Put option

Payoff to Buyer of put option 20 25 30 35 38.549999999999997 40 45 50 55 60 18.55 13.55 8.5500000000000007 3.55 2.886579864025407E-15 -1.45 -1.45 -1.45 -1.45 -1.45 Payoff to sellter of put 20 25 30 35 38.549999999999997 40 45 50 55 60 -18.55 -13.55 -8.5500000000000007 -3.55 -2.886579864025407E-15 1.45 1.45 1.45 1.45 1.45

Call option

Payoff to Buyer of call option 20 25 30 35 40 43.9 45 50 55 60 -3.9 -3.9 -3.9 -3.9 -3.9 0 1.1000000000000001 6.1 11.1 16.100000000000001 Payoff to sellter of call 20 25 30 35 40 43.9 45 50 55 60 3.9 3.9 3.9 3.9 3.9 0 -1.1000000000000001 -6.1 -11.1 -16.100000000000001

Put option

Payoff to Buyer of put option 20 25 30 35 38.549999999999997 40 45 50 55 60 18.55 13.55 8.5500000000000007 3.55 2.886579864025407E-15 -1.45 -1.45 -1.45 -1.45 -1.45 Payoff to sellter of put 20 25 30 35 38.549999999999997 40 45 50 55 60 -18.55 -13.55 -8.5500000000000007 -3.55 -2.886579864025407E-15 1.45 1.45 1.45 1.45 1.45

Q8

call	put	Answer
Stock price	$3.18	$3.38	a.
exercise price	$60	$60
Expiration date	6	months
T-bill	$97.00
face value	$100

$60

-$60

0

Payoff

Sum of T-bill, call and put

T-bill

Stock price

Call

$60

Put

Q9

Portfolio price	$55,000,000
Time	4	months
Options
Buy a protective put
Selll a covered call
Bid	Ask
Call	$2.553	$2.573
Put	$1.297	$1.317

Q10

a.	Stay long with the stock
Keep the put long and
Kepp the call short