Compound Interest Returns and Your Portfolio

A member recently asked us about the performance we report for the AAII stock screens. He specifically inquired about the difference between the cumulative returns of the AAII stock screens and the monthly returns. The answer is tied to one of the key investing concepts.

The returns reported for AAII stock screens are representative of an equally weighted portfolio of the stocks passing the screen at the start of each month. These hypothetical portfolios are held for a single month and then are completely reconstituted. If one were to add up the returns for each individual month, they would end up with a different cumulative return than the hypothetical portfolio realized.

To keep things simple, let’s assume a portfolio with a starting value of $1,000 returned 10% each year for 10 years. If you simply added the returns of the individual years together, the return would seem to be 100% (10 years × 10% = 100%). The actual cumulative 10-year gain is rather 159%.

The reason has to do with the concept of compound interest. After the first year, each subsequent year realizes gains on the original starting balance of $1,000 plus the gains on top of the cumulative gains already realized. You make money on the dollars you saved and on the extra dollars you realized through capital gains, reinvested dividends and interest received.

(The exact opposite occurs for debt such as credit card balances. Each month the loan is not paid off, future interest is charged on the amount you borrowed and any increase in the balance resulting from interest charges. Hence, the term “interest on interest.”)

Those who are able to stay invested over long periods of time benefit the most from compound interest. Relative to the amount invested, gains on gains are initially small. Invest $1,000, earn a 10% return and your gains on gains during the second year will be $10. (The math is 10% of the previous year’s gain of $100.) Keep the $1,000 invested, earn a 10% return for 10 years and your gain on gains in year 10 will be $594. This is why Albert Einstein is credited for calling compounding the eighth wonder of the world. (Whether he did is a subject of debate.)

Real-world returns aren’t steady; they fluctuate. Sometimes they are small, sometimes they are large (woo hoo!) and sometimes they are negative (d’oh!).

To account for these swings, the geometric mean instead of the arithmetic average is used.

Here’s an example from AAII’s Stock Investor Pro stock screening and database program to explain the return calculations. They represent the returns for one of the Graham screens for the years 1998 through 2004: –27%, 14%, –4%, 44%, 6%, 44% and 26%. An arithmetic average shows an annual return of 14.8%. The geometric mean is lower, at 12%.

In 1998, a hypothetical portfolio following the screen lost 27%. This reduced the value of a $1,000 portfolio to $729. The portfolio realized a positive return of 14% in 1999 but the gain was realized on 1998’s ending balance of $729. So, the portfolio ended 1999 with a value of $834 or approximately 16% below its starting value of $1,000. Arithmetic averages don’t properly account for the impact going from positive to negative returns (or vice versa).

Whenever a percentage loss is realized in a portfolio, a bigger percentage gain is required to get back to breakeven. Lose 10% and you’ll need a gain of nearly 12% to make it back. This is why some investors—such as William O’Neil—call for using stop-limit orders on stocks to keep losses from growing too big.

The risk of stop-limits is that what you do with the proceeds may not lead to a higher return than you would have achieved if you hadn’t sold. At the portfolio level, tactically shifting into cash requires getting back into the market before a big rebound has taken place. Making the wrong decision after being “stopped out” can cause you to lock in your losses.

Because the stock market has risen over time and the biggest benefit from compound interest is realized over the long term, there is a big argument for keeping dollars invested that are not needed for shorter-term withdrawals. Corrections and bear markets are never fun, but the stock market does rebound and go on to set new record highs. The percentage gains from the rebounds are larger than the percentage losses from the declines.

As far as drops in individual stocks and other securities are concerned, you can minimize the impact through diversification. A large drop in one stock can be sustained if the other portfolio holdings rise. The key is to hold enough stocks to prevent any single holding from tanking your portfolio.