V. 22:6 (24-31): Zigzag And One Rank Compared by Norman J. Brown

V. 22:6 (24-31): Zigzag And One Rank Compared by Norman J. Brown

Try this to switch mutual funds.

The zigzag indicator has long been used to pick out the peaks and troughs of the price changes (rate of change, or ROC) of stocks and mutual funds. However, such an indicator typically cannot be used as an investing tool for switching funds. This is because the process of confirming the peaks or troughs with a following trough or peak will introduce excessive delays.

OVERCOMING THESE DELAYS

These delays can be overcome if you set the zigzag filter level below the smallest ROC of the fund being investigated. For example, assume all ROCs are greater than +/-0.01% and that the zigzag filter is set to 0.01%. Then any peak formed by one or more up days is immediately confirmed by any subsequent down day, as that down value always exceeds the filter level.

To confirm this approach, I applied zigzag with various filter levels to the Fidelity mutual fund FSPTX over a period of 10 years, 1993–2003. The data in Figure 1 shows that as the filter value becomes smaller, the parameters converge at a filter threshold of 0.01%, just as anticipated. Since the peaks/troughs are determined as they occur, the delay (Q command in FastTrack) is 0/0. If the delay is increased by one day (so you can take action with a buy or sell), the annualized return drops from 718.5% to 36.4%.

What is the significance of these two returns? The first one is the maximum possible return of FSPTX if the investor buys and sells on each day at precisely the right time — seldom, if ever, possible. If the zigzag investor buys on the following day, however, the resulting (very nice) 36.4% return is what you would get using the “one rank” (OR) method, described in my earlier articles (see suggested reading). The bias and S/Y, or yearly switching rate, are also the same. The mathematically inclined may be interested to know that the 718.5% works out to 1.58% return per up day. This value is referred to as “average up return” in my earlier articles, where I pointed out that value is a direct function of the standard deviation (STD). This is an important parameter of risk that I will discuss later.