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Unformatted text preview: Solution to Problem Set 1 Investments Prof. Pierre-Olivier Weill 1. (a) Allowing you to reinvest at 1% per day means that you are earning compound interest on your initial $100 investment. The formula for P growing to F for one year at a compound rate r per annum is: F = P parenleftbigg 1 + r n parenrightbigg n where n is the number of compounding periods per year and hence r/n is the rate per compounding period. We are given r/n = 1% per day and are asked to calculate the annual yield. This is equivalent to asking for the effective annual rate. EAR = (1 + . 01) 250- 1 = 11 . 0321 Multiplying by 100 puts this into percentage terms: 1103.21% per annum. Looked at another way, investing $100 in the hedge fund produces $100(1 + . 01) 250 = $1203 . 21 at the end of one year. (b) If the hedge fund manager insists on putting your daily 1% earnings into a zero-interest bearing checking account, then you will earn only the daily rate (1%) multiplied by the number of days, or, 1% × 250 = 250% Notice that this is equivalent to the annual percentage rate (APR) calculation:...
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This note was uploaded on 02/04/2010 for the course ECON 106v taught by Professor Miyakawa during the Spring '08 term at UCLA.
- Spring '08