document.write( "Question 1158324: Hi Professor:\r
\n" ); document.write( "\n" ); document.write( "I have a question related to the probability, a stock price is currently at $10, what will be the probability the stock price will be above $10 after 5 days? Assume the stock price will be randomly moved according to the following exact percentages: -3%, -2%, -1%, 1%, 2% and 3% (so there are total 6 different possible percentages movement and the movement are purely random among each day). \r
\n" ); document.write( "\n" ); document.write( "My approach to this problem is the following: there are total 6 different movement, and the total trials are 5 days, so the total permutations will be 6^5=7776, but I just can't continue the rest due to my limited math knowledge, could you help me out on this?\r
\n" ); document.write( "\n" ); document.write( "Thank you for reading my email and I am looking forward to hearing from you soon. \r
\n" ); document.write( "\n" ); document.write( "Alex
\n" ); document.write( "California\r
\n" ); document.write( "\n" ); document.write( "Hi Tutors:\r
\n" ); document.write( "\n" ); document.write( "Thank you for answering my questions above (at Answer 781251 ). \r
\n" ); document.write( "\n" ); document.write( "I think the answer (781251) just solved one of the permutation, what if the percentage change were repeatable negative percentages, these percentage changes are all independent, so it could have like: -3% every single days, or -3% for 3 days then another 2 days -2%, etc. I wanted to know what are the probability under all the permutations, what are the chances that the stock price at the end of 5th day will be above $10?\r
\n" ); document.write( "\n" ); document.write( "again, thanks
\n" ); document.write( "Alex \n" ); document.write( "

Algebra.Com's Answer #781251 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "If , , , . . . ,  are percentage rates increase/decrease, then the new price after a chain of changes is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "What is INTERESTING, after any chain of assigned changes, the value of the product of the growing/decreasing factors\r\n" );
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document.write( "DOES NOT DEPEND of their order in the chain.\r\n" );
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document.write( "It provides the answer in this case:  the final growing/decreasing factor is\r\n" );
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document.write( "    (1+0.03)*(1+0.02)*(1+0.01)*(1-0.01)*(1-0.02)*(1-0.03) = 0.9986.\r\n" );
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document.write( "Thus, after the chain of changes, you have finally DECREASE of the price by \r\n" );
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document.write( "   (1-0.9986)*100 =  0.14%,\r\n" );
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document.write( "I N D E P E N D E N T L Y   of the order of changes in the chain.    \r\n" );
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document.write( "  +----------------------------------------------------------------------------+\r\n" );
document.write( "  | So, after the given chain of changes, the final price of the stock will be |\r\n" );
document.write( "  |                                                                            |\r\n" );
document.write( "  |     10.00 - 0.0014*10.00 = 9.99 cents    (rounded to the closest cent)     |   \r\n" );
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document.write( "  | independently of the order of the pre-assigned changes.     ANSWER         |\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Quite unexpected result, isn't it ?\r
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\n" ); document.write( "\n" ); document.write( "But a correct one (!)\r
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