Investment Math
Tuesday, December 30th, 2008Quick – if an investment or portfolio loses 50% of its value, what percent return must you achieve just to reach parity (break even)? The answer is: 100% return. If you start with $100 and lose $50, you need a 100% return on the $50 you have left to get back to where you started. And so it works with the stock market, your IRA or your 401(k). Here is a more complete table:
|
Loss |
Return to Break Even |
||
|
10% |
11% |
||
|
20% |
25% |
||
|
30% |
43% |
||
|
40% |
67% |
||
|
50% |
100% |
||
|
60% |
150% |
||
|
70% |
233% |
||
|
80% |
400% |
||
|
90% |
900% |
||
|
99% |
9900% |
||
For number geeks, here is the formula: (1/(1-% Loss))-1
Some real life examples:
· A “balanced” portfolio of 60% US stocks (IWB) and 40% US bonds (AGG) has lost 21.8% of its value over the past year. Investors holding the portfolio need a 28% return to reach parity.
· The S&P 500 has lost 44.3% over the past year. The index must rise 80% to reach parity.
· The NASDAQ index, an indicator of technology stocks has lost 71% of its value since peaking at 5132.52 on March 10, 2000. Investors who bought at the peak need a 240% return to reach parity.
· The Japanese stock market (Nikkei 225) index has lost 77% of its value since peaking at 38,915.87 on December 29, 1989. Investors who bought at the peak need a 339% return to reach parity.
The point is that investors can little afford to follow popular strategies that result in huge portfolio drawdowns. Yet proponents of popular investment strategies like the Lazy Portfolios are proud of the fact that their buy-and-hold portfolios are “…beating the benchmark S&P 500 by anywhere from three to 18 percentage points.” Their logic is something like this: “The 8 Lazy Portfolios have lost “only” 21.86% to 39.80% in the past year – they all beat the S&P 500 Index!”
Applying simple “investment math” shows that it will take returns between 28%-66% for those portfolios just to break even. With math like that, you might as well go to a casino.