You are a well known hedge fund manager in Wall Street circles. One of your weal
ID: 3224100 • Letter: Y
Question
You are a well known hedge fund manager in Wall Street circles. One of your wealthy clients has $1 million dollars to invest in XYZ stocks. Currently, XYZ stocks are trading at $2 per share. You tell your client that in one week the stock will be trading at $1 or $4 per share with equal probability. (a) If your client's objective is to maximize the expected balance in his brokerage account at the end of the week, what advice would you offer to your client? (b) If your client's objective is to maximize the expected number of shares at the end of the week, what advice would you offer to your client?Explanation / Answer
(A)
Expected profit per share on xyz = expected value of stock in 1 week - current stock value
= (1/2)*4 + (1/2)*1 - 2 = 2+1/2-2 = $0.5 per share
to maximize the balance, we advice buying all stocks at the begining of week only, investing all $1 million to get 0.5 million stocks
(B) here we have a choice, we can buy some stocks now and some stocks at the end of the week by using the remaining money
suppose we spend x fraction of 1 million now on stocks, and buy # of stocks = x/2 * 1 million
at the end of week, either the price would have doubled or halved, that means with the remaining (1-x)*1 million , we can buy at $4 per stock or $1 per stock
==> with probability (1/2), we can buy (1-x)*1 million / 4 stocks
and with probability we can buy (1-x)*1 million stocks
Total expected stocks = x/2*1 million + (prob = 1/2)* (1-x)*1 million / 4 + (prob=1/2) *(1-x)*1 million
= (5-x)/8
hence we see that expected total shares varies negatively with x, hence we minimize x
For this case, we can take minimum x = 0
The advice we give is dont buy any shares now and spend all the money at the end of week
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