Quandaries and Queries


Math Sage,
Let's say I have a list of different possible investements, and the list shows me my cost, and how much each investment will sell for. In order to compare the investments and put them in order of relative profitability, I would want to sort them by their profits as percentages of what? Also, if each investment had an equal probabilityof losing exactly 10% of the sell price before I sold would that have any relevance to the way I would calculate it?

Thanks for you help, and sorry for sending you a word problem with only one number in it. :-)




Hi Max,

This is a strange set of hypothesis - in particular, it is not clear whether the
sell price is above or below the buy price, or whether the probability of loosing 10% of the sell price is small, or is 1 (a guaranteed loss). So the conclusions could be widely different depending on these numbers. In some cases, you should not buy anything!

However, playing the mental game, it turns out a ranking of relative profitibility would be the same whether you took the 'profit' (sell - buy) as a percent of the buy price in every case, or as a percent of the sell price in every case. You are not trying to describe the profit, but to rank profits for several investments. The absolute numbers would be different, but the ranking would be the same.

Say you had two choices:

  1. Buy $20, sell $25 profit $5 profit % buy price 5/20 (100) = 25 Profit %sell price= 5/25(100) = 20

  2. Buy $40 sell $48 profit $8 profit % buy price 8/40 (100) = 20 Profit %sell price= 8/48(100) = 16.67

The ranking is unchanged by your choice of benchmark (buy price or sell price).

In general:

if (a-b)/a > (c-d)/c then (a-b)/b > (c-d)/d
This translates to 1 - b/a > 1-d/c then -b/a > -d/c then a/b > c/d then a/b -1 > c/d -1.

Walter Whiteley


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