```Math 420 – Spring 2016
Problem Set 9
1. The bid and ask prices of stocks A and B are as follows:
Stock
Bid
A
99.50
100
B
75.25
76
Ted buys one share of stock A and sells two shares of stock B. The broker's commission is 0.3%. What
is his net cash flow?
2. Rob bought 100 shares of stock on March 1 and sold them 6 months later. The bid and ask prices
are as follows:
Stock
Bid
Mar 1 60.25
60.50
Sept 1 68.50
68.75
The broker's commission was X%. Rob's gain was 767.75, ignoring interest. Find X.
1
Math 420 – Spring 2016
Problem Set 9
3. John short sells a stock for 10,000. The proceeds of the sale are retained by the lender. John must
deposit 5,000 with the lender as collateral. He earns 6% effective on his haircut. At the end of one year,
he closes his short position by buying the stock for 8,000 and returning it o the lender. A dividend of
500 was payable one day before he covered the short. What was John's effective rate of interest on his
investment?
4. The bid and ask prices for a stock are as follows:
Stock
Bid
Feb 1
60.25
60.50
Aug 1 68.50
68.75
a) Chris enters into a short sale on Feb 1 for 100 shares. He covers his short position on Aug 1. The
broker's commission is \$10 per transaction. What is Chris's profit/loss?
b) Chris must deposit a haircut equal to 50% of the proceeds received from the sale of stock. Market
rate of interest is a nominal rate of 8% compounded semiannually, but the short rebate is only 5%
compounded semiannually. A dividend on this stock of \$0.40 per share was payable on March 31 and
\$0.50 per share was payable on June 30. What is Chris's profit/loss on the short sale?
2
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