On Being a Contrarian

2024.12.22

LXXIX

The more you disagree with the average opinion, the more you stand to gain by being right where they are wrong.

Your Bet is Not Your Bet

One of the most interesting things I ever learned from financial markets was that no action you take or belief you hold operates or exists in a vacuum. 

In other words, if everyone already expects something to be true, and you do to, then your reward for it being true is low. 

Believing the contrarian view and being right has a higher reward than believing the consensus view and being right. Often times, if you factor out the cost to the ego, being contrarian and right has lower risk, too.

Not Like Us

Take some simple fair bets* on the outcome of an event–one thing happens, or another thing happens. For example, at the time of writing this, there are about 1:1 odds that Kendrick starts the Super Bowl halftime show by performing Not Like Us.**

The pricing of a fair bet tells you the average belief of the other participants who are betting. So, 1:1 odds means that roughly half of the betters think that Kendrick will lead his show with Not Like Us, and the other half don’t. 

If you agree with these odds and place the bet anyways, the expected return of your bet is 0%. To calculate this return, you multiply the probability of each outcome by its value, find out how much in excess of the investment this number is, and then convert it to a percentage on your original investment. 

((Not Like Us*.5*$200) + (Dif. song*.5 *$0) -$100) / $100 = 0%

If the odds are 50/50, and you believe they are right, you have no financial incentive to place the bet other than wanting to gamble. 

Now, if you think the odds are under pricing the probability that Kendrick plays Not Like Us as the first song, now you have a financial incentive to place the bet. Maybe you’ve analyzed his psyche deeply and are convinced that the probability of him playing this song first is 75%. Based on this belief, the expected return is a whopping 50%.

((Not Like Us*.75*$200) + (Dif. song*.25*$0) -$100 ) / $100 = 50%

Okay, so you might place that bet. But, now watch what happens if your belief stays the same and the odds in favor of not like us go up to 20:1? Maybe Kendrick has a rare tweet that increases the market’s certainty that he’ll play the song. Now, a correct bet of a $100 gives you $105 back, a 5% return.

But, if your belief is still that there is a 75% chance he plays the song, the expected value of the bet has now become negative.

((Not Like Us*.75*$105) + (Dif. song*.25*$0) -$100 ) / $100 = -21.25%

So, you can agree that the market is right about the event happening (you still think there is a greater than 50% chance he plays it), but still have a negative expected return if you bet. 

As the odds become more favorable for some event, your own certainty has to become higher to place the same bet.

Alternatively, you could now just bet against that same event you believe will happen and have a very positive expected return:

((Not Like Us*.75*0) + (Dif. song*.25*$2100) -$100 ) / $100 = 425%

Huh, there’s an asymmetry here… when your belief was 25% away from the 1:1 consensus odds, your expected return was 50%... now, when you’re less than 25% away from the 20:1 consensus, your expected return is 425%... 

Of course, your expected return isn’t worth shit until it’s dollars in the banks. That being said, we have some take aways:

1. You are not betting on an event, you’re betting against other people’s expectation of that event.

2. The magnitude of your reward for being right is directly proportional to not only how much you disagree the consensus belief, but also directly proportional to how strong the consensus belief is.

*The payout is proportional to the purported odds–if you bet $1 with 1:1 odds (50% chance), you get $2 back, or a 100% roi. If you bet $19 with 19:1 odds, you get $20 back, or a ~5.3% roi.

**The prop bet is not actually binary, you can bet on him playing a number of songs. The probability is also actually lower than 50%, the 50% “odds” are after fees. We ignore fees for simplicity.

Know what you’re betting against

These two notions of betting against expectations and your reward being effected by how contrarian you are map quite cleanly to financial markets.

It’s perfectly coherent to accept the fact that Nvidia is changing the world and will continue to make gobsmacking amounts of money while refusing to invest in the stock. 

By purchasing Nvidia now, you are not just betting on Nvidia, you are betting on Nvidia doing better than the current average expectation. 

The investment itself is important, but so is the current consensus on it’s value. You can make a lot of money on 2.5x YoY returns. But, every time that happens, your expected value for getting in now gets worse.* 

The stock market is not an inherently zero sum game, as would be the case with a true betting market. When you look at nosebleed price appreciation that outstrips business value creation, however, I would follow suit of Marks, Buffet, Munger, etc in the belief that it becomes more akin to zero sum as we are playing with speculating rather than betting on value creation. The Greater Fool Theory takes over and the “greatest fool” ends up “holding the bag.”** 

However, that also doesn’t mean you have to bet against a company like Nvidia, either. You can also go the other way, and buy companies that are worth a decent value but priced as if they are worth nothing. Here, the rewards for being right are disproportionately favorable, and the downside risk for betting against the market is considerably smaller than is the case when betting against an equity going up.

*If you trade momentum or otherwise exploit the greater fool theory, your roi may actually get better after price increases, as per Mandelbrot… as long as you sell before the momentum goes the other way.

**I have been the greatest fool before, and have evidence in the form of ownership of Canadian psychedelic companies.

Life is Like the Market

Now, I’m not clever enough to prove this, but I’d posit that these same two rules apply to a lot of other areas in life. We’ll succinctly formulate it as follows:

The Law of Contrarian Returns: The benefit you get from being contrarian and right goes up both as the strength of the consensus strategy increases and the degree to which you diverge from it increases.

Again, I can’t give you proof, but I can tell you I have substantial skin in the game on it, on many different levels. From the business I chose to start in college to the seemingly non sequitur of a business I am running now to the fact that I am even running a business and living at home with my parents instead of getting a real job out of school to my diet, I tend make a lot of contrarian decisions.

But don’t take it just from the conviction reflected in my actions—I’m young, naive, and perhaps overly ambitious. Instead, I’ll leave you with a few other examples that, the first two of which at least on the surface, support the claim. The third, on the other hand, is very mathematically sound and may be the strongest evidence for the claim there is.

• Anduril can brag about delivering machines ahead of schedule and under budget, which is utterly unheard of in the defense industry. 

• History remembers Martin Luther & his 95 Theses more than subsequent defectors from Catholicism or the ever expanding branches of Christianity, such as John Calvin or Joseph Smith.

• In an iterated multiplayer prisoner’s dilemma, it becomes disproportionately profitable to be a “hawk” when there are only “doves” and vice versa.

So, not only is it cool to be a contrarian, it can be profitable, too.

Merry Christmas,