The Bow Tie Chart - Relationship of Annualized Returns to Percent Returns

The bow tie chart plots the CTM annualized return against the corresponding CTM percent return for each buy and sell combination for a selected price series.

The following charts are based on the monthly closing prices of the Nikkei 225 from December 1989 to February 2003. There are monthly 12,720 buy and sell combinations for the period.

The pattern of the points is quite interesting. The bow tie pattern exists because all combinations of annualized and percent returns are grouped along iso lines of equal times held. The annualized returns for 161 months, the longest holding period, are in a nearly horizontal band for the entire range of percent returns. And the percent returns for the one month holding period are in an almost vertical band for the entire range of the annualized returns. Finally all the bands pass through zero. for both annualized and percent returns.

Notice the bands of data points of the longer holding periods tend to cluster (dark areas). This is because for a long price series CTM produces many more buy and sell combinations of relatively long duration than short duration.

The next two charts are close-up views of the first chart. There vertical scale includes annualized returns from -30% to 30%.

The next chart is the same as the previous chart except the background is black.