He had a winning ticket! In the ensuing days he learning of his winning one jackpot lumpsum would be $500,000. This was after taxes, and he knew what he was going to do with part of the money at it was going to be: buy a new car; pay off his college loans; and send his grandmother on a all paid trip to HI. A couple of days later he was sitting around with his friends Josh and Peyton, all are fraternity brother and Business majors. They sat around and thinking how much his retirement fund would be worth in 30 years.
If you invest (p) for dollars and (n) for year at a annual interest rate of (i) percent (n) years you would have p(1 + i)n dollars. So they figured if they invested $250,000 for 30 years in an investment with a 10% return in 30 years he would have $4,362,351, that is ($250,000 + 0.10)30).
But after he was thinking they were thinking they figured it was unlikely he would find and investment that would produce a return of precisely 10%
each and every year for the next 30 year. So they assume he would find an investment with an return of 17.5% seventy percent of the time and a return or (actually a loss)-7.5 thirty percent of the time. Such an investment should produce an average annual return 0.7(17.5%) + 0.3(-7.5) = 10%. Josh felt certain that Patrick could still expect his $250,000 to grow to $4,362,351 in 30 yrs because $250,000 (1 + 0.10)30 = $4,362,351.
Peyton thought Josh was wrong. Peyton said Patrick should see a 17.5% in 70% of the 30 years (0.7)30 = 21 yrs)and a -7.5% return in 30% of the 30 years (0.3(30 = 9 yrs). So, according to Peyton, Patrick should have $250,000 (1 + 0.175)9 = 3,664,467 after30 yrs.
But that's $697,884 less than what Josh says Patrick should have. Josh assumes Peyton is wrong because the "good" return of 17.5% would ocur in each of the 21 years and the "bad" return -7.5 would ocur in each of the last 9 years. But Peyton counteracted the argument by saying that the order of the good or bad return doesn't matter.
Patrick is really confused. So what do you think? Who is right, Josh or Peyton? Can you explain why? Thanks
Josh is correct and Peyton is wrong. Peyton is making a fundamental mistake of assuming that the returns in different years are dependent (conditional).
When we say good or bad return, this is for a particular year and returns received in every year are independent of ...
Quantitative analysis for decision analysis is examined.