Exercise 1. Imagine you have 500 dollars you want to invest for two periods. Swi

Question

Exercise 1. Imagine you have 500 dollars you want to invest for two periods. Swift corporation's stock is currently selling for $10. In each of the two periods, the stock price could either go up one dollar or down one dollar with equal probability $12 50% $11 50% 50% $10 $10 50% 50% $9 50% $8 a Suppose you invest all S500 dollars in the stock. How many shares to you have? How much money do you have at each final node? What is the expected value of your investment after the two periods? What is the variance of your investment after two periods? b Suppose that you invest $1000 dollars in the stock using your margin account. How many shares to you have? How much money do you have at each final node? What is the expected value of your investment after the two periods? What is the variance of your investment after two periods? Comment on the two investing options.

Explanation / Answer

A) Number of stocks for $500 = 50

Expected value = 50(0.5x0.5x12 + 0.25x10 + 0.25x10 + 0.5x8)

= 50 (3 + 2.5 +2.5 + 2)

= $500

Variance = (12x50 - 10x50)2x 0.25 + 0+ 0 + (8x50 - 10x50)2x0.25

= 10000x0.25 + 10000x0.25

= $5000

B) Expected outcome when $1000 is invested = $1000

Variance =  (12x100 10x100)2x 0.25 + 0+ 0 + (8x100 - 10x100)2x0.25

= 40000x0.25 + 40000x0.25

= $20,000

C) The variance is high in case of option b. Expected outcome is same as the investment in both cases. Its preferable to invest in option A as it is less risky (subjected to less variation from expected value)

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