28 Jun HOW TO CALCULATE THE ARITHMETIC RETURN, GEOMETRIC RETURN, AND STANDARD DEVIATION
How to Calculate the arithmetic return, geometric return, and standard deviation
Rule: Complete the following 4 problems and each one is worth 20 points. The top 2 scores will be used to replace the lowest 2 scores in your Test 1 Problems.
1. You are given the returns for the following three stocks:
Year Stock A Stock B Stock C
1 8% 3% -24%
2 8 13 37
3 8 7 14
4 8 5 9
5 8 12 4
Calculate the arithmetic return, geometric return, and standard deviation for each stock. Do you notice anything about the relationship between an assets arithmetic return, standard deviation, and geometric return? Do you think this relationship will always hold?
2. You just sold short 1,000 shares of Jacobson, Inc., a fledgling software firm, at $96 per share. You cover your short when the price hits $86.50 per share one year later. If the company paid $.75 per share in dividends over this period, what is your rate of return on the investment? Assume an initial margin of 60 percent.
3. How many of the May contracts from the table below are currently open? How many of these contracts should you sell if you wish to deliver 155,000 bushels of corn in May? If you actually make delivery, how much will you receive? Assume you locked in the settle price. Suppose you sell 25 of the May corn futures at the high price of the day. You close your position later when the price is 475.275. Ignoring commission, what is your dollar profit on this transaction?
Corn 5,000 bushels
Contract Month Open High Low Settle Chg Open Int
Mar 455.125 457.000 451.750 452.000 22.750 597,913
May 467.000 468.000 463.000 463.250 22.750 137,547
July 477.000 477.500 472.500 473.000 22.000 153,164
Sep 475.000 475.500 471.750 472.250 22.000 29,258
4. Suppose youre evaluating three alternative MMMF investments. The first fund buys a diversified portfolio of municipal securities from across the country and yields 3.2 percent. The second fund buys only taxable, short-term commercial paper and yields 4.9 percent. The third fund specializes in the municipal debt from the state of New Jersey and yields 3.0 percent. If you are a New Jersey resident, your federal tax bracket is 35 percent, and your state tax bracket is 8 percent, which of these three MMMFs offers you the highest after-tax yield? Which MMMF offers you the highest yield if you are a resident of Texas, which has no state income tax?
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