Is Your Mental Accounting Adding Up?


The faulty stock market perception can be illustrated with the following equations.
If you were to ask people what the average of 3 and 5 is, they typically respond as follows: (3 + 5 = 8)/2=4. The average is 4.

If you were then to ask them for the average of a negative 50 and a positive 50 they would do the equation the same way. So the typical investors assume that if they are getting positive returns and negative returns that they are still doing fine.

So what if you were then to ask them, “What is the impact of losing 50 percent one year and gaining 50 percent the following year? Back to your starting amount, right?” Actually, that would work out like this:

• $10,000 down 50 percent is $5,000
• Then up 50 percent is $7,500
• This is a 25 percent loss (13 percent annualized) after “offsetting” years.

Let’s look at an example in which the gaining percentage is greater than the losing one. A return of +66 percent followed by -50 percent would seem to add up to an 8 percent return. But actually:

• $10,000 up 66 percent is $16,600
• Then down 50 percent is $8,300
• +66 percent followed by -50 percent produces a negative 9 percent annualized return.

But look at the compounding gain of two 8 percent years:
$10,000 x 1.08 = $10,800 x 1.08 = $11,664

So, many people wrongly think that if they are getting a greater return than a loss, then they are doing well. But obviously that’s not true. Another misperception is just how deep a hole is created by losses. A 100 percent return would be necessary to offset a 50 percent loss. But a 300 percent return is required to offset a 66 percent loss. And then 400 percent for a 75 percent loss.

So, the next time you’re thinking about taking a risk, make sure you are doing an accurate mental accounting.

Posted on September 1, 2010
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