To Stay Sharpe Miss Right

With the US Open returning to the site of one of Tiger Woods’ greatest triumphs, it’s time to re-evaluate investing and portfolio construction from the perspective of Tiger Woods’ golf strategy. This time though instead of looking at the peak and maximizing return, we are going to explore errors and the affect they have on maximizing return per risk, aka the Sharpe Ratio.

Tiger’s Strategy

In the last post I showed how Tiger, when trailing by 2 at the 2019 Masters, decided to play away from the danger and take the safe route. Even though he was down, the situation didn’t call for aggression, it called for precaution, and the mindset of attacking later in the round when the overall conditions were more favorable.

This was absolutely the correct strategy for the time, and now we’re going talk about how a few holes later Tiger took a different approach and decided to attack.

Tiger on 16

A few holes later on the 16^th, Tiger is now leading by a shot.  The 16th is a another par 3, this time with water on the left.  So what does Tiger do? Do he play it safe again and just try and make par?

Nope.  Tiger hits his shot right next to the hole.

The slopes around the 16th hole are very different than those he faced at the 12th. Here the slopes in the green mean that even when he played somewhat safe out to the right, the ball would funnel back down towards the hole. 

Target the Forgiving Slopes

This flag is actually closer to the water than the shot he faced on 12, and he’s hitting a longer shot. On the most basic level, this is a more dangerous shot. But the slopes and wind are in his favor here and they were all against him on 12. But they are only in his favor if he uses them properly.

A shot hit directly at the flag, and a shot hit 20 feet to the right of the flag end up in almost the exact same spot.  A shot hit 20 feet to the left of the flag ends up in the sand or the water.  Big difference.

The penalty for missing left is much, much higher when aiming at the flag then when aiming to the right of the flag.

So Tiger here hit a safe shot which was still an attacking shot.¹  He understood the consequences of his misses, and chose to aim away from the target, knowing that if he hit his adjusted target, the end result would still be about the same as if he aimed at the flag.

Brilliant strategy which takes into consideration all the effect of his “misses” and slope of the land around the ultimate target. 

Now this strategy isn’t very novel for a PGA tour pro. Nearly everyone approaches this hole the same way Tiger did. But interestingly, few in the investing world takes on similar challenge the same way. They ignore the slopes around the target and aim at the flag.

Aim Right For Sharpe

In the last Tiger post, we talked about aiming left when the danger lurked off to the right.  Going past the peak leads to poor outcomes. The best case scenario is to make a decent return, but with high volatility.  Worst case is the volatility overwhelms the portfolio and you end up losing money.  Neither is good so we apply a factor of safety to the portfolio to make sure the investments don’t ever go past the peak.

This prior analysis was focused on maximizing return.  It acknowledges risk, in that you don’t want to invest in a portfolio which offers the same return for a bumpier, more volatile ride.  But there isn’t any thought on return/risk tradeoff here. It’s all about maximizing returns.

Many investors don’t aim to maximize their returns, but instead to maximize thier return/risk levels, aka their Sharpe Ratio.

Sharpe Ratio

The point of maximum Sharpe Ratio investing is also called the tangency portfolio and we discussed that concept in the post on the geometric frontier.  This is a very well defined point in investing and is one of the most often used “targets” in portfolio construction. 

The tangency point may be a good objective, but it’s a bad target, and focusing on it is equivalent to firing at the flag on the 16^th hole at the Masters on Sunday. 

Focus on the Slopes Around the Target

To understand why, we need to think again about errors.  If we know the returns, volatility, and correlation of our assets exactly then the tangency point will provide the maximum return per risk.  It gives us the highest Sharpe Ratio. But in real life we don’t know any of these things. They are all measurements, estimates, and guesses.  So where focusing on the peak and maximizing return makes “misses to the right” unfavorable, focusing on the tangency point and maximizing return/risk makes  “misses to the left” unfavorable.

This is actually very simple to see this graphically.  Here is an efficient frontier (it’s an arithmetic frontier as this shows the effect better than a geometric chart).²  The maximum slope here is 0.28. 

Now if we assume the misses are equal in both directions, then we see that a miss “to the right” hurts our Sharpe Ratio, but not by a large amount (purple line goes through the right edge of our range).  As risk increases, the frontier doesn’t pull back very quickly from the tangency line.  It’s a slow change, even though the portfolio may be more aggressive than was optimal.  The penalty in terms of Sharpe Ratio is low. 

On the right edge of the error bar (+or- 20% bonds/stocks ratio), you see a “Miss Right” Sharpe ratio of 0.254.  So less than perfect, but not much less.

This is similar to missing to the right of the flag at the 16^th hole at the Masters.  The slopes in the green mean a miss to the right leads to a shorter putt than you would expect.  So even though you “missed” right, the consequences of missing are small. The Sharpe Ratio is still pretty good.

But left is another story. 

Missing Left is Worse

The left side of the efficient frontier however, curls off faster, especially once you get out past the nose.  The Sharpe Ratio therefore degrades faster left of the tangency portfolio.  While a miss to the right is not overly penal, a miss to the left is very penal. 

Here the Sharpe Ratio at the end our error bar is much lower at 0.217.  The portfolio felt a greater return/risk impact by missing left than by missing right.  And notice, the penalty gets much, much worse if the errors get larger. The efficient frontier here is heading in the absolute wrong direction. Portfolios in this part of the frontier are no good and just as poor as those we saw past the peak when targeting returns.   

Aim Right to Stay Sharpe

Here’s an example of how this works mathematically.

The tangency portfolio in this example is 60% Asset #1 , 40% Asset #2.  What happens when we acknowledge our estimates of standard deviation for Asset #2 are incorrect and will be higher or lower than the 20% volatility we expect?²

You can see that when the volatility is lower than expected, the portfolio benefits by “aiming right” and holding more of Asset #2.  When volatility is higher than expected, you end up worse by holding more of Asset #2.  But if your misses are equally higher and lower, the average Sharpe Ratio ends up higher by aiming “away” from the actual maximum Sharpe Ratio portfolio.³

Different Greens

Now other golf greens provide an advantage somewhat similar to the 16^th at the Masters, although the 16th does so in a very obvious way.  But not every golf hole provides this benefit.

One obvious example is the 17^th at the TPC Sawgrass, which is fully surrounded by water.

This hole is essentially an island.  Aiming away from water on one side just makes it more likely to go in the water on the other side.  Aiming anywhere beyond the middle may be the most risky, least rewarding, approach.⁴  There is a limit to how far you can aim right. Therefore the golfer must know the hole they are playing, as no hole is the same.

Different Frontiers

For investing, I believe the benefit to aiming right of the tangency portfolio is nearly always true to some degree when targeting maximum return/risk. But the amount varies depending on the market.  Many markets look similar to the example provided above, but not all of them.

Some look like this:

Unlike the previous examples, these two assets are positively correlated. The benefit to missing right here is far less obvious. It technically still exists, but it’s very small. Furthermore, aiming too far right may end up being detrimental. So the market you’re in determines the benefit of “missing right”.

You must always be aware of the type of market you’re playing today.

What About Multiple Assets.

Now this example is very clear with two assets. The possible portfolios are linear up and down the frontier (see the previous charts).

The error line becomes a multi-dimensional “splotch” with multiple assets, and therefore gets more complicated than our nice clean linear example.  

But the overall concept remains.  If you are aiming for a maximum Sharpe ratio portfolio, errors mean you should never aim for the actual tangency point. 

The curving slopes of the efficient frontier mean that some errors are penalized far more than others. Therefore it makes sense to tilt your portfolio slightly towards the riskier asset(s). How much you should do this depends on how accurate you believe your estimates are, and the current conditions of the market. 

Approaching portfolio construction this way may turn your portfolio into a Tiger Woods Portfolio. 

Don’t Aim At The Flag

Tiger Woods has said he almost never aims at the flag and he adjusts his aiming point based on the conditions during the round.

The strategy in golf requires the expert player to often aim away from the ultimate target.  Nearly every shot is “missed” in golf, and because the course is full of slopes and hazards, not every miss is treated the same.  Some misses are rewarded.

The best golfers in the world use these slopes to thier advantage, aiming for places where the slopes help their misses, not punish them.

Investing is full of similar slopes in the form of return/risk ratios. These slopes are not uniform in shape and size.  Investors may target a maximum Sharpe Ratio portfolio, but we all know the target is elusive and the best we can hope for is to get near it. Therefore it’s best to use the slopes to our advantage where possible and aim slightly away from the target for optimal realized returns.

Follow Tiger’s lead: be aggressive firing to your spot, don’t aim at the flag⁵, and aim right to stay Sharpe.

1-At one level, there is another lesson here that even when leading–if the conditions are favorable–you should still attack. Tiger still had two difficult holes to play. In his last Masters win in 2005, Tiger bogied the last two holes.  So just because he’s leading now, there isn’t any reason that will stay that way at the end.

Prior success doesn’t mean difficult times aren’t ahead. So if the opportunity is there you need to try and take advantage of it. Tiger only ends up winning by one shot, so looking back in hindsight he needed the birdie on 16 to win. 

2- These charts use the following asset properties:

Asset 1- 7% return, 10% standard deviation
Asset 2- 10% return, 20% standard deviation
Correlation -0.4
Risk Free Rate of 6%

3-Lets take this to a deeper level. As usual, I tried to simplify the concept as much as possible.  This example works with Asset #2, but it doesn’t work the same with Asset#1.  Variation in some of the input properties makes tilting towards Asset #1 a better choice. So the ultimate question becomes which estimates do you have more confidence in, and which are more likely to be wrong?  My experience is more volatile assets are harder to accurately predict than less volatile assets.  Therefore I expect my estimates of Asset #2 to be “most” wrong.  If for some reason you believe Asset #2’s is easier to predict than Asset #1, then the math here actually reverses, and you should aim left. 

The big picture here is to understand that because our estimates are wrong, the optimal target is not the target we traditionally think of.  You are better off aiming away from the traditionally defined optimum point than you are going right at the flag.

4-For those that know this hole well, internally it does have slopes which can help move the ball towards the hole.  However to use them properly, you need to be professional level confident in the size of your misses.  This is an example of how understanding the accuracy of your predictions really matters.  If you have good estimates with smaller errors you could use these slopes, but if you have average estimates with larger variances, trying to use these slopes is probably still too risky because of the closeness of the water.

5-It’s also important to not aim at the hole on putts. Let’s hope this week provides a tournament even half as entertaining as the last US Open at Torrey Pines.