### What does it mean to be a good stock picker? Part 2

**BOTTOM LINE UP FRONT: A slugging percentage above 1.65x demonstrates stock picking skill for an active manager.**

In the previous post, we explained that comparing an active manager to a randomized version of an active manager was the best way to measure their stock selection skill. We discussed why constructing our random portfolio using absolute return or benchmark adjusted returns was flawed. This resulted in the use of an equal-weighted benchmark (equivalent to a monkey throwing darts in a more normalized time period*). We started with Batting Average and will continue our analysis with Slugging Percentage.

**Slugging Percentage**

Slugging percentage is a measurement of the average winner divided by the average loser. If I have a batting average of 50% and a slugging of 1.0x, then my fund will generate a 0.0% return (50% of stocks make +20% and 50% make -20%). Anything greater for either of those metrics and the returns turn positive. If you can find winners that go up twice as much as losers, you need only have a batting of 33.3% to result in a return of 0.0%.

To demonstrate skill, a manager needs a slugging percentage* of 1.65x. This may seem high, but we must understand that the market demonstrates persistent positive skew (a straightforward way to think of positive skew is that more stocks go up more than 100% than go down more than 100%). This positive skew is also one of the major reasons that the batting average of the randomized portfolio we calculated in the previous post, 37.8%, seems so low.

If a manager has a 40% batting average (better than 37.8%) and 1.8x slugging percentage (better than 1.65x), they are demonstrating skill in two categories: both in picking winners and picking winners that go up much more than their losers. This is a good start, but how good is 40% and 1.8x?

The next step would be to Monte Carlo random portfolios and determine the probability of getting a 40% batting and 1.8x slugging portfolio. In fact, the ideal method would be to:

- - Match manager time period and industry;
- - Randomly select longs at the ratio of manager long positions;
- - Randomly select shorts at the ratio of manager short positions;
- - Randomly assign weights to Monte-Carlo’d portfolios using position
- size ranges;
- - Assess the gross exposure of an individual manager; and
- - Build a distribution of portfolios with those standardized
- characteristics to determine the probability of achieving a
- similar portfolio.

With that, you can perform significance tests and take samples from different periods to determine the persistence of skill.

We may explore this concept in the future, but in the interim, the simple approach above is a shortcut method to help elucidate the idea of comparing managers to random as a way of measuring manager skill.

**SLUGGING PERCENTAGE FORMULA:** (if positive: average (return of stock - return of the average stock in the index) / if negative: average (return of stock – return of the average stock in the index)*

*THE RANDOMNESS EQUATION: **Equal Weighted Batting Average of ACWI * Slugging Percentage of ACWI + (1-Equal Weighted Batting Average of ACWI * Denominator of Slugging Percentage of ACWI = The Randomness Equation*

37.8% * 165% + 62.2% * -100% = 0.0% Return – The Randomness Equation