Exercise 1. Imagine you have $5000 you want to invest. Swift corporation\'s stoc

Question

Exercise 1. Imagine you have $5000 you want to invest. Swift corporation's stock is currently selling for $100. The stock price will either go up to S120 or go down to $90 with equal probability. Consider the following potential strategies a Invest all $5000 in the stock. b Borrow S5000 from your broker. Invest all $10000 in the stock. From the proceeds, pay the broker back the $5000 owed (no interest) c Put the 85000 in a risk free T-bill that gets 2 percent. d Short sell $5000 of stock. Put all S10000 in T-bills that earns 2 percent For each of those strategies: What are all possible payoffs? ·What are the possible returns? What is the expected return? What is the variance of the returns?

Explanation / Answer

A) If you invest all $5000 in stocks which costs $100 each , you would get 50units of stock.

Now there can be two situations:- Either price will go up or dowm.

If price shoots up to $120. There will be a profit of $ 20/ unit.

I.e 20*50 = $1000 profit. (:Payoffs)

But if price plunge down to $ 90 , there will be a loss of $ 10/unit

i.e 50*10 = $500 loss (Payoffs)

Expected return from this strategy with equal probability is

1000(0.5) + (-500) (0.5) = $250

Possible returns if price goes up or goes down is $1000 and $(500) respectively.

B) If we borrow $5000 from broker. Now from $10000 with stock price be $100 we will get 100 units.

So if price goes up to $120 there will be profit of $20 / unit = $2000. But if price goes down there will be loss of $10 / unit = $1000.

Possible return if price goes up to $120

100*120 = $12000

Pay $5000 to broker i.e $12000-5000 = $7000

$7000 - 5000(our investment) = $2000 net profit.

But if price goes down to $90

90*100 = 9000

Pay $ 5000 to broker

$9000 - 5000 = $4000

Now, $4000- 5000 (our investment ) = $-1000 net loss.

Expected returns

2000(0.5) + (-1000)(0.5) = 0

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