3. (4 points) A stock is currently traded at So -$50. The one-month European cal

Question

3. (4 points) A stock is currently traded at So -$50. The one-month European call option on the stock with strike K = $50 is being sold for $2. If an investor has $1000 to spare, he/she can invest in i) 20 shares of the stock, or (ii 500 shares (5 contracts) of the option. (a) If the stock goes up to $55 after one month, what are the returns of investment choices (i) andi) respectively? choices (i) andi) respectively? shares of the call, such that (b) If the stock stays at $50 after one month, what are the returns of investment (c) Consider the third choice for investment: you buy shares of the stock, and 50a + 25 = 1000 Notice that = 20, 0 correspond to choice (i), and = 0, -500 corre- spond to choice (ii). Explain what would happen to the returns in above two scenarios if you choose > 20,

Explanation / Answer

a)
i)
Returns=(20*55-1000)/1000=10%
ii)
Returns=(500*max(55-50,0)-1000)/1000=150%

b)
i)
Returns=(20*50-1000)/1000=0%
ii)
Returns=(500*max(50-50,0)-1000)/1000=-100%

c)

i)

For a>20 and b<0, lets say a=25 then b would equal -125..returns=(25*55-125*max(55-50,0)-1000)/1000=-25%

or. returns=(a*55+(500-25a)*5-1000)/1000=(1500-70a)/1000 If a<21.42857 returns will be negative

For a<0 and b>500, lets say a=-20 then b would equal 1000..returns=(-20*55+1000*max(55-50,0)-1000)/1000=490%

or. returns=((20-0.04b)*55+b*5-1000)/1000=(3.8b+100)/1000 If b>500 returns will be more than 200%

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