Question

2. Start with $0 in your account.

a) Short XYZ at $100 and use some of the cash to buy a 95 strike call, investing the rest in zero coupon bonds.

b) Construct profit and payoff graphs for this position (ignoring stock borrow fees).

c) Instead, borrow enough cash to buy the 95 strike put.

d) Construct profit and payoff graphs for this position. (Assume you pay interest r on your loan.)

d) How do your graphs from b) and d) compare?

e) How does your answer to d) change if you include a stock borrow fee of 0.25% on the $100 of XYZ stock you borrowed?

Answer 1

	a)	Price of stock at expiration=S
		Assume stock borrowing cost =$0
		Short XYZ at$100
		Long (Buy) $95 strike Call
		Assume Call Price =$6
		Remaining cash available=(100-6)=$94
		Payoff for shorting =94-S
		Payoff on long $95 strike call=(S-95)
		If S> 95
		Payoff on long $95 strike call=0
		If S< 95 or S=95
		S	A	B	C=A+B
		Price at expiration	Payoff on Shorting	Payoff on Long Call	Profit
		$90	$4	$0	$4
		$91	$3	$0	$3
		$92	$2	$0	$2
		$93	$1	$0	$1
		$94	$0	$0	$0
		$95	($1)	$0	($1)
		$96	($2)	$1	($1)
		$97	($3)	$2	($1)
		$98	($4)	$3	($1)
		$99	($5)	$4	($1)
		$100	($6)	$5	($1)
		$101	($7)	$6	($1)
		$102	($8)	$7	($1)
		$103	($9)	$8	($1)
		$104	($10)	$9	($1)
		$105	($11)	$10	($1)
		BORROW $1 to buy $95 put
		Payoff on put:
		If Price at expiration =S
		Payoff =(95-S) if S< 95
		Payoff=0 if S>95 or S=95
		Amount tobe returned with interest=1.05
		Interes=5%
		S	A	B=A-1.05
		Price at expiration	Payoff	Profit
		$90	$5	$3.95
		$91	$4	$2.95
		$92	$3	$1.95
		$93	$2	$0.95
		$94	$1	($0.05)
		$95	$0	($1.05)
		$96	$0	($1.05)
		$97	$0	($1.05)
		$98	$0	($1.05)
		$99	$0	($1.05)
		$100	$0	($1.05)
		$101	$0	($1.05)
		$102	$0	($1.05)
		$103	$0	($1.05)
		$104	$0	($1.05)
		$105	$0	($1.05)
		STOCK BORROWING FEES OF 0.25%
		S	A	B	C=A+B-0.25
		Price at expiration	Payoff on Shorting	Payoff on Long Call	Profit with stock borrowing fees
		$90	$4	$0	$3.75
		$91	$3	$0	$2.75
		$92	$2	$0	$1.75
		$93	$1	$0	$0.75
		$94	$0	$0	($0.25)
		$95	($1)	$0	($1.25)
		$96	($2)	$1	($1.25)
		$97	($3)	$2	($1.25)
		$98	($4)	$3	($1.25)
		$99	($5)	$4	($1.25)
		$100	($6)	$5	($1.25)
		$101	($7)	$6	($1.25)
		$102	($8)	$7	($1.25)
		$103	($9)	$8	($1.25)
		$104	($10)	$9	($1.25)
		$105	($11)	$10	($1.25)
							Profit.C $5.00 $4.00 $3.00 $2.00 Profit.C $1.00 $0.00 $88 $90$92 $9 $96 $98 $100 $102 S104 ▼- $106 ($1.00) ($2.00) 10 ($1.05)