5. Suppose your friend tells you that tomorrow a certain stock will with go up t

Question

5. Suppose your friend tells you that tomorrow a certain stock will with go up to $10 (with probability 0.8) or will go down to $1 (with probability 0.2). Also suppose that the current stock price is $3 per share. If you buy 100 shares today, what is your expected profit tomorrow? What is the standard deviation of profit? 6. Suppose your friend has an investment for you: If you invest $999,480 there is a 50% chance the investment will mature to $2,000,000 but there is a 50% chance the investment will become worthless (i.e. you loose it all). Compute the expected profit from this investment and the standard dev . iation of your profit

Explanation / Answer

Q.5 Expected Profit on one stock = Pr(Profit) * profit value + Pr(loss) * loss value

= 10 * 0.8 - 1 * 0.2 = $7.8

Expected total profit = no. of shares * Expected Profit on one stock = 7.8 * 100 = $780

Standard deviation of profit per share = sqrt [(10 - 7.8)2 * 0.8 + (7.8 + 1)2 * 0.2] = 4.4

Standard deviation of total profit = 100 * 4.4 = $ 440

Q.6

Expected Profit = Pr(Profit) * profit value + Pr(loss) * loss value

= 0.5 * (20,00,000 - 999480) - 0.5 * (999480)

= 0.5 * 1000,520 - 0.5 * 999480

= $ 520

Standard deviation of profit = sqrt [(0 - 1,000,520)2 * 0.5 + (999480 -0)2 * 0.5]

= $1,000,000.14

(6) As we can see there is more expected profit in option 1 and standard deviation or here we can say risk is lesser than option 2 so we will choose option 1 here.

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