Annualized Returns and Time Held

This article discusses how annualized returns and holding period are related The analysis plots annualized returns and holding periods in years for all Complete Trading Model (CTM) buy and sell combinations for the:

The price chart shows the price pattern or the S&P 500 from July 1982 to March 2003.

The next chart shows the annualized returns for all CTM trades for the S&P 500 for the period.

Each data point represents the annualized return and corresponding holding period for one CTM trade. So there are 30,876 data points on the chart.

The vertical axis of the chart shows the annualized return in percent. The horizontal axis shows the numbers of years the investment was held - the difference in years between the buy date and sell date. Since the period starts in July 1982, a full one-year holding period represents a sale in July 1983, a full 2-year holding period is for a July 1984 sale and a sale at the peak in March 2000 corresponds to a 18 year holding period.

The red horizontal line separates the winning trades (above the line) from losing trades (below the lone). Of the 30,876 CTM trades, 93% were winners and 7% were losers, with the losing trades occurring for a holding period of six or less years.

The returns for the short-term holding periods on the left side of the chart are extremely variable. The returns go from a -94.5 percent loss to a 310 percent. These extreme annualized returns result from large percentage loses or gains that occur in a few weeks or months. When the value is annualized, it explodes to a large number. These large annualized returns are not too important because they do not occur frequently.

The next macro pattern is that returns tend to converge toward a somewhat narrower band that fluctuates around the median annualized return of 12.21 percent as the holding period increases.

The next chart displays a higher resolution so you can discern many more individual data points.

The close-up view shows the data points for all winning trades with annualized returns from zero to 30 percent. This magnified view displays sharper detail of the data point patterns than the previous chart.

Notice the dense arc pattern of data points from eight to 19 years held. In this band the concentration of data points (dark area) shows an increase in annualized returns from holding periods 8 to fifteen years and then a decrease in returns. These patterns coincide with increasing and decreasing prices of the S&P 500.

Another very important pattern is that for a given holding period the range of returns varies greatly. Look at the 15-year holding period and see the returns are from seven to 15 percent. Variation in returns is apparent for all holding periods. This large range tells us the large gains result from those trades that were purchased at low prices during a dip. And the low gains result from purchases at higher prices at intermediate tops. Therefore, not all investors get the same returns for the same holding periods.

If you hold the annualized return constant and examine a range of holdings periods, you'll see that you can achieve the same return for many holding periods. For example, you can get a 10 percent annualized return for almost any holding period. This tells us that you can get a like return using a buy and hold strategy or executing a quick trade.

The last pattern is the decline of returns after the 17-year holding period on the right side of the chart. This decline happens because of the drop in the S&P since 2000. As the holding period increased, the effect of lower selling prices reduced the return for the buy and holders.

The Nikkei 225 peaked in December 1989 and since then the index has been on the downside. Its long-term declining price pattern serves as a stark contrast to the S&P 500 18-year upside.

The next chart shows the annualized returns plotted against time held for the 12,720 CTM trades.

Losing trades outnumbered winning trades by 10,433 (82.1%) to 2,277 (17.9 %). The horizontal red line separates the winning and losing trades. The median annualized return was -6.13 percent. The overall pattern of data points the chart is similar to the pattern of all annualized returns for the S&P 500.

The greatest variation in returns occurs for the brief holding periods and returns tend to converge around the median return as holding period increases. The right-hand tip of the data points is turning down as prices continue to decline.

The close-up view shows the the annualized returns from -20 percent to 20 percent.

Notice the three dark areas of data points that appear as downward sloping bands. These areas represent concentrations of declining returns due to buying at intermediate tops and declining prices. In contrast to these bands notice the numerous thinner upward sloping dark bands that fan out from left to right. These concentrations of data points represent returns for buy/sell combination that were bought on dips in price.

Conclusions

The following list summarizes the findings of the CTM annualized returns and holding period analysis.

Short-term returns are extremely variable and difficult to predict. Returns can be very high or almost a total loss.
Long-term returns tend to converge on a median return value so they are predictable. But long-term investing doesn't necessary mean ever-increasing returns.
Returns vary greatly for a given holding period. Therefore, not all investors will make the same returns for the same holding period.
Holding periods vary for a given return. Therefore, short-term traders can make the same or more money than long-term investors.