Question Conventional Math: Misused Words

Jack walks into his financial advisor’s office and asks how his portfolio is doing. “Well, says the advisor, you’re up 60%!”  A year later, in the same office, with the same question, Jack is told he’s down 50% for that 2nd year. Jack says “so +60% – 50% = 10%, divided by 2 (years) = 5% average return.  “Okay, not too bad…”

Sarah walks into her financial advisor’s office and asks how to best invest $100,000. The advisor suggests some investment opportunities and they examine one that looks interesting. To explain the value, the advisor says “Over the last 25 years, the average return of this has been 7.34%…so, looking forward, using 7.34%…wait, let’s be conservative and use 6.34%…so, in 30 years, you would have $632,265.78!” Sarah certainly liked that number.

Harry, a 22-year-old in his first job, is told that he is being automatically enrolled in the 401(k) program.  To encourage participation, the conversation goes like this: “How old are you? 22? When do you think you’ll retire? 65? Okay…43 years, and you’re going to contribute $212 per paycheck.  The stock market has returned 7% over the last 25 years, so, using that, at age 65 you’ll have over $1,300,000!  How does that sound?”  Harry was thrilled.

At the end of their projected time periods, 30 and 40 years respectively, their numbers fell far short.  Why?

Because of the misinterpretation and misuse of the words “average,” “change,” “return,” and “straight-line projections.”  They are deceptively utilized, especially with your hard-earned dollars. 

For example, in the first scenario, if Jack invests $100 and it goes up 60% in year one, he has $160.  If it goes down 50% in year two, he loses $80 (50% of $160 = $80). Therefore, Jack has just $80 left.  He may be up 5% on average, but his account value is down 20%!  Here, using the word “average” is completely misleading.  There is no direct correlation between an average over the years vs. the actual dollar amount left in your account.

In the next two scenarios, only straight-line projections are used (“if you get 6.34% every year…”).  Has there been any time when the market was up exactly 6.34% for even just 2 years in a row?  No.  There is a critical part missing to the equation:

Volatility of the markets. 

Ignoring volatility both historically and with future projections causes actual dollar results to fall far short of expectations.

Think of it this way:  If you retired with a $1,000,000 portfolio in December 2000 and took $40,000 each year (a 4% drawdown) to pay your bills, how would you have felt paying $40,000 in the year when the market tumbled 34% in 2008 and your portfolio was only worth $660,000?  Neither the “historical average” nor the “straight-line projection” would help pay those bills, would they?  How long would it take to get back to $1,000,000, if ever?

“Average,” “change,” “return,” “straight-line projections,” and “volatility” are all poorly understood, even by the pros.  More to come about each of these…

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