Question

In: Finance

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

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.

Solutions

Expert Solution

=> 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


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