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November 12th, 2012, 11:09 AM  #1 
Newbie Joined: Oct 2012 Posts: 13 Thanks: 0  Profitability of an Investment
PLEASE DON'T BE TURNED OFF BY THE TOTAL WORDS IN THE PROBLEM. IT ISN'T THAT BAD. This is a step above the problem listed here as "Is this a good investment?" Please see it for more information. I think I have right answers to the problems listed below, but I don't know how to write them exactly in mathematical notation. I hope you can help. Here is the longworded problem, which will not produce a longwinded answer: In a particular market, there are a large number of securities with independent and identically distributed returns. For each such security, the percentage returns from one day to the next are themselves independent. A portfolio manager is considering two possible strategies: Strategy 1: Invest everything in one security and hold it for many days. Strategy 2: Invest in a large number of securities whose returns are independent and identically distributed for a single day and then sell. a.) Suppose that strategy 1 is deemed profitable in the sense that the average accumulation per day is greater than the amount invested. Should we expect strategy 2 to be profitable as well? My answer: Yes, because, in the first instance, we hare a geometric case and, in the second case, we have an arithmetic case. b.) Suppose that strategy 2 is deemed profitable in the sense that the average accumulation per day is greater than the amount invested. Should we expect strategy 1 to be profitable as well? My answer: No, because the second is arithmetic, and the geometric will not necessarily be greater than 1. c.) Suppose that strategy 1 is deemed unprofitable. Should we expect strategy 2 to be unprofitable as well? My answer: No, because you can lose money in the geometric sense and not in the arithmetic sense, which only accumulates for one day. d.) Suppose that strategy 2 is deemed unprofitable. Should we expect strategy 1 to be unprofitable as well? My answer: Yes, because if you lose money in one day, you're likely to lose it over a period of several days. 
November 20th, 2012, 01:07 PM  #2 
Newbie Joined: Oct 2012 Posts: 13 Thanks: 0  Re: Profitability of an Investment
Will someone reply to this, please?

November 20th, 2012, 04:27 PM  #3 
Senior Member Joined: Aug 2008 From: Blacksburg VA USA Posts: 346 Thanks: 6 Math Focus: primes of course  Re: Profitability of an Investment
well, nothing I read in the problem relates profitability between the 2 strategies or between individual securities. So, for a,b,c,d I answer "cannot be determined". Obviously these next numbers are not "independent" but they only illustrate a sample scenario where only the strategy 1 is profitable, but each security has similar distribution. (The formatting will not match my original after posting but hopefully it's bearable) Time RETURN Period Sgl Secur SecurityA SecurityB SecurityC SecurityD SecurityE 1 1.00% 7.00% 7.00% 6.00% 5.00% 4.00% 2 0.00% 6.00% 7.00% 7.00% 6.00% 5.00% 3 1.00% 5.00% 6.00% 7.00% 7.00% 6.00% 4 2.00% 4.00% 5.00% 6.00% 7.00% 7.00% 5 3.00% 5.00% 4.00% 5.00% 6.00% 7.00% 6 3.00% 6.00% 5.00% 4.00% 5.00% 6.00% 7 2.00% 7.00% 6.00% 5.00% 4.00% 5.00% OR, maybe I missed the entire concept 
November 20th, 2012, 04:29 PM  #4 
Newbie Joined: Mar 2012 Posts: 25 Thanks: 0  Re: Profitability of an Investment
Those two strategies have the same expected value, but #2 has a lower variance. Since the avarages will be the same, and if your definition of a good investment is greater than zero expected value, then #1 is good if and only if #2 is; same for being bad. However daily expected value > 0 doesn't mean that it's a good investment over the long run, so I'm confused by your question. 
November 21st, 2012, 08:46 AM  #5 
Newbie Joined: Oct 2012 Posts: 13 Thanks: 0  Re: Profitability of an Investment
Sorry, but I don't understand either of your replies. This question has to do with compounding over one day versus over many days. One day is likely to be arithmetic, and compounding over many days will lead to a geometric distribution. However, I don't know how to put that into writing. Kiuhnm, can you help a brother out?

December 18th, 2012, 11:35 PM  #6 
Newbie Joined: Dec 2012 Posts: 3 Thanks: 0  Re: Profitability of an Investment
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