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Unformatted text preview: Business 3059 Investment Management Lakehead University Midterm Exam Philippe Gr´ egoire Fall 2002 Time allowed: 1 hour 15 minutes. Instructions: Calculators are permitted. One 8 . 5 × 11 inches crib sheet is allowed. The marks awarded for each question are in brackets. Good luck! Part I: True or False . For FOUR of the following statements, say if the statement is true or false (2 points), and explain why (3 points). 1. Calculating a T-Bill yield using the bank discount yield method necessarily gives a lower value than if it is calculated with the bond equivalent yield method. True: Consider a T-bill that matures in n days and let P denote the current price of of the T-Bill, with a face value of \$1,000. For the return on this T-Bill to be positive, we need P < 1 , 000. The bond equivalent yield is then given by r bey = 1 , 000- P P × 365 n . On the other hand, the bank discount yield for this T-Bill is given by d = 1 , 000- P 1 , 000 × 360 n . 1 The bank discount yield can only be lower than the bond equivalent yield since d = 1 , 000- P 1 , 000 × 360 n = 1 , 000- P P × P 1 , 000 × 365 n × 360 365 = 1 , 000- P P × 365 n × 360 365 × P 1 , 000 = r bey × 360 365 × P 1 , 000 = r bey × P 1 , 013 . 89 | {z } < 1 < r bey . 2. A mutual fund never sells above its net asset value. False: A closed-end fund may either sell above or below net asset value. 3. Let R denote the nominal interest rate and let i denote the inflation rate. Then r = R- i is always a good approximation of the real rate of interest. False: This approximation is good only for small values of of R and i . For example, if R = 80% and i = 70%, then R- i = 10% whereas the exact real interest rate is 1+ R 1+ i- 1 = 1 . 8 1 . 7- 1 = 5 . 88%. 4. The profit made on a short sale is the mirror image of the profit that would have been made had the stock been bought and then sold. True: Let p denote the stock price at the time of the short sale and let p 1 denote the stock price when the osition is covered. Let d denotes the dividends that have been distributed to shareholders meanwhile. Since the short seller has to pay dividends to the stock lender, the profit from the short sale is p- ( p 1 + d ). If, instead, the stock had been bought and sold, the trader’s profits would have been p 1 + d- p , which is indeed the mirror image of the profit from the short sale....
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