Computing the Spread 1

‘In some seasons, trend following is good; in others, reversing is good. The problem is how to differentiate the two seasons in advance.’

Victor Niederhoffer

The Education of a Speculator

The Spread is the difference in performance between relative-strength leaders and relative-strength laggards.As we saw in the previous lesson, this difference changes over time.During strength-following markets, the Spread expands. The opposite is true during contrarian markets, when the Spread contracts.

Computing the Spread requires computation of the periodic relative strength of each target in a selected universe of stocks. Here are the steps:

1.Determine a universe of stocks. A target universe should contain no less than 30 to 40 stocks.There is no maximum number of stocks.This universe should be well diversified, including stocks from a wide list of sectors and groups.

Ideally, stocks chosen for the purpose of computing the Spread will be a fair sample of the broad market. It is important to choose stocks on some basis not related specifically to relative strength or to price performance more generally.Selection based on price performance will not provide the cross-section of relative-strength performance essential to producing a useful Spread.

Caution: If the universe is not diversified, the Spread will tend to contract indefinitely.This is so because issues which are too closely related tend to behave similarly. If the universe included only, say, bank stocks, the Spread would tend to contract chronically because traders specializing in bank stocks arbitrage disparities by buying relatively weak and selling relatively strong issues which stray too far from the mean. Like sheep dogs, arbitrageurs keep similar stocks herded closely together. This sets up a chronic reversion to the mean and causes the Spread to contract indefinitely.

2. Compute the daily percentage changes of each stock for 100 days. Any period may be used as a basis to construct The Spread. I have found that a 100-day computation picks up important shifts in the Spread while filtering out minor noise.

3. Compute the daily percentage changes of the benchmark for 100 days. This is accomplished by averaging the daily changes of all stocks in the universe. Put another way, the daily percentage change of the benchmark is the average daily percentage change of the universe of stocks. For purposes of calculating the Spread, the benchmark is always an average of all stocks in the selected universe.

4. Compare the performance of each stock to the performance of the benchmark over the same time period. Leaders and laggards are determined by comparing the sum of each stock’s 100 daily changes to the sum of the benchmark’s 100 daily changes. To do this, divide the sum of the 100 daily changes for each stock, plus one, by the 100-day sum for the benchmark, plus one:

Sum of Target’s 100 Daily Changes + 1
Sum of Benchmark’s 100 Daily Changes + 1

Suppose the sum of 100 daily changes for the target is .269, and that the sum of benchmark’s percentage changes over the same period is .212. To calculate the target’s 100-day relative strength, substitute these values in the formula shown above:

Computing the Spread

This formula yields the periodic relative strength of the target, as of the 100th day. With an RS greater than 1, this target is stronger than the benchmark (the relative strength of the benchmark is always 1).

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