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Right and Wrong

Updated: Jan 14, 2021

"If you throw 100 lit matches into a dynamite factory and live to tell the tale, it doesn't mean it was a good idea."

I’ve often heard the phrase “as an investor you’ll be wrong about 40-60% of the time”.


It’s one of those insidious phrases that sounds intelligent, but I think it does more harm than good. While it is true that you will be wrong a lot of the time, and that can exact a psychological toll if you’re not used to failing, the phrase is misleading.


It doesn’t matter how often you’re right and wrong. What matters is alpha generation – i.e. the magnitude of your wins netted against the magnitude of your losses.


To get a bit more technical, right and wrong can be expressed as probabilities. On their own, they’re not particularly useful. You need to consider the expectation: the probability multiplied by the payoff.


It doesn’t matter if you’re right 99% of the time, but the 1% of the time you’re wrong is a -80% catastrophe that wipes out most of your previous gains and more. By the metric of “% rightness”, you’re a hero. Acumen gleams from your eyeballs and alpha drips from your fingertips. By the metrics your investors care about, you’re at risk of making the acquaintance of a lynch mob, or worse, lawyers.


All this is to say that right/wrong rates alone are not particularly useful metrics. What really matters is the “right rate” multiplied by the gain, and the “wrong rate” multiplied by the loss, giving you an expected outcome. If it’s negative, you’ve got problems. This applies to both portfolio construction and individual positions.


The cautionary tale of Jacques

In one of my roles, I worked with a fellow who thought he was pretty good. We’ll call him Jacques Schenkel, because that’s his real name*.


Jacques had a post-announcement merger arbitrage idea. He presented it to the investment committee saying the stock traded at €7.80, the company had a takeover offer on the table for €8.00. The success or failure of the deal should be known within 6 weeks. That’s a 2.6% gain over the life of the investment, or a 25% annualised gain. Not a bad day at the office.


Or is it? Prior to the announcement, the target company traded at €6. This means that at €7.80, the market prices in a 90% chance the deal gets approved by regulators, the target’s shareholders and competition authorities (and various other deal terms too numerous to mention). For this to be a positive expected outcome investment, you need to believe the probability of approval is higher than 90%. So on a probability-weighted basis, it’s not that attractive.


Let’s put some numbers to it:


There are two problems here:

  1. The expected outcome is 0, so it doesn’t make sense to execute the trade

  2. If you’re wrong, you’d lose 23% in a very short time frame. The rather vicious mathematics of this means you’d need to subsequently generate +30% returns just to break even.


I was at the investment committee (IC) meeting when Jacques presented this idea. Jacques said he was highly confident the deal would go through.


IC: “Okay Jacques, if you had to turn your high confidence into a percentage, what would it be?”


J: “80-90%”


IC: “Okay…”


Let’s run that again with the low end of the probability range.



A negative expected outcome… so at best, you’d be indifferent and at worst, you’d expect to lose money.


So we’ve seen the problem for single trades, now lets take a look at portfolio-level impacts in two ways: compounding and exposure.


Compounding

Let’s assume our hypothetical portfolio only trades these merger arbitrage ideas. Let’s assume Jacques presents 10 similar trades (90% chance of upside, 2.6% return in upside, -23.1% in downside) throughout the year with the same payoffs and probabilities and we invest in all of them.

It’ll look something like this:

Jacques has been right 90% of the time yet delivered a negative return. The problem wasn’t how often he was right, it was the one time he was wrong. That combined with the effects of compounding mean even a €0 expected outcome investment can result in negative total returns. Get your running shoes on Jacques… the mob’s coming.


Or look at the inverse situation, Universa Investments (founded by one of Nassim Taleb’s former students). Universa can be boiled down to the use of options to bet on tail risks, a strategy that is right a handful of times a decade, i.e. they’re wrong ~99% of the time. Yet their returns are staggeringly positive: 76% p.a. since their 2008 inception (no that isn’t a typo). In the Feb/March meltdown of 2020 alone, they delivered +4,000% returns (also not a typo). Even though they’re wrong far more often than they’re right, the wrong trades are small losses, and the right trades are colossal winners.


Exposure management

Let’s look at this in terms of portfolio positioning using my own experience in 2020. In early February 2020, my portfolio was up about 5%, not bad, but nothing to write home about. At this time, I didn’t think covid was going to be a big deal in terms of economic impact. But I did think that if it became a big deal, it would have some pretty nasty consequences. The question I asked my self was not “will Coronavirus hurt the stock market” but “what probabilities and magnitudes of impact do I need to believe to stay invested”.


Let’s say the market continues to advance at its historic averages: somewhere between ~5-7% p.a. The market is already up ~1.4% this year, so by staying invested, I should expect further gains of ~1-2% over the next 3 months. What happens if covid does hit the market? Let’s say it results in a bear market, something like a 20-25% drop. What probabilities do you need to believe in for this to be a 0 expected outcome event? Let’s run the numbers.




So I’d need to believe there is only a 4-9% chance of covid impacting the market, to be indifferent about remaining invested. That’s an 91-96% chance that covid has no impact on markets – a near certainty. It’s here I started to think about reducing exposure. With no near-term catalysts for my positions, I thought it was time to take money off the table, and went to 70% cash in early February.


I’m not suggesting for a second that I called covid. What I’m saying is I didn’t need to. All you needed to understand was that there was a probability of disaster and it didn’t need to be that high for a rational person to reduce their exposure. In general, I'd recommend that people don't make calls ("X will happen", "Y is impossible") but instead assess expectations


Conclusion

So to summarise. How often you’re right and wrong doesn’t really matter in investing. The expectation is what matters (i.e. magnitude of each outcome multiplied by its probability). It's true rates can have psychological impacts on people, in which case, remember to invest your money in the stock market, not your ego. In fact, treat investment decisions as an opportunity for rapid feedback on your own development.


Stay tuned, in my next post I’ll be looking at a company that did very well in 2020 and what I think of it now.


* For the record, I’ve never worked with anyone called Jacques.


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