Error Drag: A Lesson in Strategy from Tiger Woods

If Tiger Woods was a investment manager, he would dominate investing just as he dominates golf.

Golf is often called a game of misses. Even a professional doesn’t hit most shots to their target. Therefore they try to manage each shot so that the bad ones don’t ruin the round.

2019 Masters

Re-watching Tiger Woods’ Masters win a couple months ago remined me of his brilliant play on the twelfth in the final round.

Going into the hole Tiger’s down two.  The leader, Francesco Molinari, just hit it in the water right before him, partially because he didn’t judge the wind properly. 

Tiger is the best golfer in the last 40 years, and probably ever.  If he focused solely on making birdie here, he probably does so 4 times out of 10.  With a birdie, he takes the outright lead. 

I’ve played tournament golf.  I can tell you how tempting it would be to attack at this moment.  I can only image how tempting it would be to attack with Tiger’s skills. But what does Tiger do?

He aims way left and plays safe. He didn’t just play somewhat safe, he played very safe. Tiger confirmed later in an interview this was in fact his intention.

I doubt anyone in the field aimed as safely.  He took away any chance of making birdie and any change of holding the lead himself after the hole.  Tiger hit the most conservative shot possible, ensuring a large miss didn’t hurt him.

Why?

Tiger knew the danger in attacking and aiming at the flag. Wind is key input into a golf shot. Sometimes the direction and speed of the wind is difficult to judge, which was the case here.

He saw the leader Molinari go in the water, and he saw Brooks Koepka go in the water 10 minutes earlier. Tiger knew the outcome of his shot was more uncertain than normal.  He didn’t believe the risk of attacking, even in the slightest, was worth the potential downfall.

The water to the right and short of the flag was simply too penalizing. A miss to the left wasn’t penalizing. So Tiger aimed left because he knew he couldn’t properly judge the wind and his shot might not end up where he aimed.

Consequences of Errors

Golf is often pretty clear at telegraphing the penalty for misses. Water on one side is more penalizing than the open green to the other. The consequences of the misses are rarely equal.

In the last post, I discussed why you might aim away from the target — the maximum return. I explained how the error in measurements and estimates ensure you will not hit the target — the top of the return curve. The charts implied a miss left and a miss right were symmetrical around the top. But are they really? Are the impacts of errors to the “left” the same as errors to the “right”?

Are there hidden water hazards in the investment world?

Example

To keep this simple, let’s pretend our estimates for standard deviation are either 10% above or below true volatility. We’ll leave return and correlation errors out for now and just assume they are accurate. What does this error do to the portfolio returns?

We’ll use an example similar to the one from mixing two risky assets (read the post to learn more about using this method to find the maximum geometric return).

Asset #1 forecast:
6% Return
20% Standard Deviation

Asset #2 forecast:
10% Return
30% Standard Deviation

The assets are uncorrelated.

Target Portfolio

Mixed with the method shown, the portfolio holding 5/13 = 38% of asset #1, and 62% of asset #2 maximizes growth at a 6.46% geometric return.

So now we have our portfolio. Let’s find out what happens to this 38%/62% portfolio when the estimates are wrong.

Error of Over-Estimating Standard Deviation

First let’s examine the effect of over estimating the standard deviation. What if the true standard deviations are 10% and 20% for each asset respectively?

The entire curve changes since the volatilities are lower. The maximum return is actually found in only owning asset #2. Our 38/62 portfolio isn’t at the top any longer. It is too conservative for the true distribution. But at least it’s not past the peak; you can’t find another portfolio with a higher geometric return and lower standard deviation.

Happily, the portfolio does perform better than our estimates projected, with a return of 7.64%. Therefore, all else being equal, overestimating standard deviation leads to better realized results than projected. This is a good error.

Under-Estimating Standard Deviation

What if the error falls the other way and our inputs underestimate the true standard deviation? What if real volatility is 30% and 40% respectively?

This curve looks very different. It almost has a point, and the slopes on either side of the peak are steeper. This portfolio is too aggressive for the true volatility. It needed more of asset #1. The 38/62 portfolio is past the true peak. Not ideal.

Underestimated returns become worse from the original estimate. Now the portfolio experiences a 4.76% return. This is a bad error.

Consequences are not Equal

Notice the positive consequences do not counteract the negative ones.

The errors in your favor (overestimated) helped the portfolio by 1.18%. The errors not in your favor (underestimated), hurt the portfolio by 1.71%.

Errors which move the portfolio “past the peak” hurt the portfolio returns more than errors to the left.

The errors are convex in their consequences.

If the errors are balanced (just as many misses left as right), the realized returns will end up less than expected. In this case they would be:

+1.18% – 1.71% = -0.53%

The errors may cancel out, but the consequences to not. They make realized returns worse. I call this “Error Drag”

Leverage Magnifies Error Drag

Now this portfolio isn’t one you necessarily want to leverage. But by leveraging it, we can see that leverage magnifies the estimation error.

2X leverage doubles the error. 3X leverage triples the error. But the error’s effect on portfolio return isn’t linear, therefore the leverage amplifies this impact on returns even more.

The more leverage used, the more the errors negatively influence returns. The curve becomes more and more convex, making the portfolio suffer further under leverage.

Leverage already convexly impacts portfolios through volatility drag. But leverage also impacts returns by magnifying error drag. Another reason why leverage can be very dangerous. If you’re using leverage, you should aim further away from the peak, more conservatively.

Aiming Left Improves Returns

This leads to an interesting observation. Aiming left of the peak return, away from the target, actually increases realized returns.

Let’s say you moved the allocation 5% to the left and used a 43%/57% portfolio instead.

This portfolio projects a slightly lower geometric return of 6.448%. By moving to the left, the two error portfolios (+/- 10%) produce a 7.538% return and a 4.849% return.

Now for the sake of simplicity, let’s say a miss left, and a miss right have equal likelihood of occurring. Interestingly, you end up with a higher geometric average (the one that matters) when employing a more conservative portfolio.¹

This is a bit counterintuitive right? By aiming away from the theoretical best spot, you end up with the better realized return. The actual top isn’t at the top when the inputs have errors.

Miss in the Correct Spots

Tiger Woods is an absolute master at evaluating the risk and reward of a situation. His 2019 Masters final round presents a master class on strategically managing misses. Take this interview question after he won:

Tiger begins his answer saying that he felt good. That he had all the shots. It was there. And then at the 27:00 mark he “kept telling himself to miss the ball in the correct spots”. Think about that contrast. He knows he’s on. You could say he feels hot. And yet he’s worried about his misses.

Miss the ball in the correct spots.

Tiger Woods.

Investing is about managing risk and reward. It’s about missing correctly. It’s about seeing the hidden water hazards waiting to ruin your portfolio and navigating around them.² Tiger understands these concepts so intuitively, which is why I believe Tiger would dominate investing if that was his chosen profession.

As we continue down this path examining input errors, let’s think about Tiger Woods and remember to build portfolios that strategically miss in the correct spots.

Part 3 to follow.

1- I understand that the difference shown in the example is tiny. But this is a simplified example meant to demonstrate a very complicated mathematical point. This analysis only looks into standard deviation errors. Correlation also has a similar convex effect as volatility, which was demonstrated here.

In real life errors often can be much worse than 10% and have fat tails. In March of this year many people held portfolios built for 16% annualized stock volatility, when the true volatility reached 80%. That’s a big error. A big miss on the wrong side. Even Geometric Balancing, with frequent rebalancing and input monitoring was off by 20%+ during this time. Thankfully it was aiming left.

2-Most of the hazards are “right”. But as we get deeper into this, you’ll see there are hazards of getting too conservative as well and deeply underperforming.