Question

An investor buys a collared stock. The current price of the stock is 200. The collar has strike prices 200 and 210 and is zero cost. The collar expires in 6 months.

The stock pays a dividend of 1 every 3 months. The next dividend is payable in 1 month.

The annual effective risk free interest rate is 4%.

Let S be the price of the stock at the end of 6 months.

Determine the range of S for which the collared stock generates a positive loss

Answer 1

	a	INITIAL INVESTMENT FOR BUYING STOCK	200
	b	Present Value of first dividend after one month=1/(1+(0.04/12))	0.9966777
	c	Present Value of Second dividend after 4 months=1/((1+(0.04/3)	0.9868421
	D=a-b-c	Net Present Value of Investment=	198.02
		Payoff from Buying Put at strike=200
		Payoff=Max.((200-S),0)
		Payoff from Writing CALL at strike=210
		Payoff=Min.((210-S),0)
		THERE WILL BE LOSS IF S IS LESS THAN 202
			S	A	B	C	D=A+B+C	E=D/1.02	F=E-198.02
			Price at expiration	Amount from selling stock	Payoff from Buying Put	Payoff from Writing Call	Total Amount received	Present Value of Total amount	Net Present Value of Gain/(Loss)
			190	190	10	0	200	196.08	-1.94
			191	191	9	0	200	196.08	-1.94
			192	192	8	0	200	196.08	-1.94
			193	193	7	0	200	196.08	-1.94
			194	194	6	0	200	196.08	-1.94
			195	195	5	0	200	196.08	-1.94
			196	196	4	0	200	196.08	-1.94
			197	197	3	0	200	196.08	-1.94
			198	198	2	0	200	196.08	-1.94
			199	199	1	0	200	196.08	-1.94
			200	200	0	0	200	196.08	-1.94
			201	201	0	0	201	197.06	-0.96
			202	202	0	0	202	198.04	0.02
			203	203	0	0	203	199.02	1.00
			204	204	0	0	204	200.00	1.98
			205	205	0	0	205	200.98	2.96
			206	206	0	0	206	201.96	3.94
			207	207	0	0	207	202.94	4.92
			208	208	0	0	208	203.92	5.90
			209	209	0	0	209	204.90	6.88
			210	210	0	0	210	205.88	7.86
			211	211	0	-1	210	205.88	7.86
			212	212	0	-2	210	205.88	7.86
			213	213	0	-3	210	205.88	7.86
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