Question

An investor has $20,000 to invest and is bullish on the common shares of Omega Corp, a public corporation.

The stock is trading at $25 and the risk-free rate is 1% compounded semi-annually. The following European options on Omega's stock are currently available: C all Strike Term Premium Put Strike Term Put Premium

$25 6 months $2.50 $25 6 months $2.00

$28 6 months $1 .75 $22 6 months $1 .10

$30 6 months $1.25 $18 6 months $0.75

$35 6 months $0.20 $15 6 months $0.40 Devise a strategy for the investor that capitalizes on their view but contains less risk and more potential reward

than holding the stock alone, assuming the stock price will be either $32.00 or $17.00 in 6 months' time.

table that illustrates how your strategy produces a smaller loss at $17 but a larger profit at $32, than holding the

stock alone.

Answer 1

=> If the investor purchases the stock for $25,

Profit if the stock ends at $32 = 32-25 = $7

Loss if stock ends at $17 = 17-25 = -$8

=> The investor must buy 2 call options of strike price $25 and sell 2 call options of strike price $35.

Investment per unit for strategy = 2.5*2 - 0.2*2 = $4.6

Profit from the strategy, if the stock price ends at $32 = 2*(32-25) - 4.6 = $9.4

Loss from the strategy, if the stock price ends at $17 = -$4.6

Stock price at maturity	2 Long calls strike $25	2 Short calls strike $35	Net payoff
15	-5	0.4	-4.6
16	-5	0.4	-4.6
17	-5	0.4	-4.6
18	-5	0.4	-4.6
19	-5	0.4	-4.6
20	-5	0.4	-4.6
21	-5	0.4	-4.6
22	-5	0.4	-4.6
23	-5	0.4	-4.6
24	-5	0.4	-4.6
25	-5	0.4	-4.6
26	-3	0.4	-2.6
27	-1	0.4	-0.6
28	1	0.4	1.4
29	3	0.4	3.4
30	5	0.4	5.4
31	7	0.4	7.4
32	9	0.4	9.4
33	11	0.4	11.4
34	13	0.4	13.4
35	15	0	15
36	17	-2	15
37	19	-4	15
38	21	-6	15