Inherently Dangerous Activities, Part 1
On Climbing, Investing, and Risk
I spend my weekends confronting fear and risk on the rock faces of New England, which is a phrasing that my mother would probably not approve of. Risk is bad! Why would you purposefully seek out a risky activity? Is it really worth the adrenaline rush? On one level, it’s an intensely personal question. We all make choices every day that involve some level of risk — we drive to work, we eat fatty foods, we finally work up the courage to talk to that cute barista. What separates an acceptable risk from an unacceptable one?
I spend my weekdays confronting fear and risk in front of a computer screen in an office tower in Boston; my mother is much more relaxed about that. I model the risks and returns of financial assets for institutional investors — my job is to think carefully about risk, and for better or worse that carries over to my hobbies.
The goal of this post is to think about risk in the context of two inherently dangerous activities — climbing and investing. Which risks are worth taking, and which are best avoided?
Compensated vs. Uncompensated Risk
One useful way to think about risk is to think about what you gain from embracing a given risk. In investing circles, risks are sometimes divided into two categories — compensated and uncompensated. 
One classic compensated risk is the “equity premium,” or the excess return achieved by holding stocks instead of a risk-free asset. Stocks are risky — sometimes they go up 20% in a year, sometimes they go down 50%. Over a long historical period, however, the average return to equities has been almost 10%. By holding equities, you are compensated for bearing that risk with, on average, a 10% gain each year. 
On the other hand, not every risk comes with a positive expected return. A classic example in this category is lack of diversification. Say you have two assets with an expected return of 10% and standard deviation of 20%. If you put all of your money into one asset, that’s what you’ll get. If you split your money between the two, however, you’ll still have a 10% expected return but the standard deviation of that return will drop. The extra risk you take on by concentrating your assets is uncompensated. 
Make sense? Great! Now let’s move into the horrifying real world where PEOPLE TAKE UNCOMPENSATED RISKS ALL THE TIME! Go to any climbing area in the country and you will see people needlessly endangering themselves. They don’t wear helmets, they build shoddy anchors for their rope, and they trust inattentive belayers who literally hold their partners’ lives in their hands.
This is not to say that climbers are risk-loving daredevils. No more than investors are risk-seeking gamblers. Instead, we universally make bad choices by accepting easily avoidable risks while recoiling from the more salient, unavoidable ones. Every climber feels a tingle of fear when dangling high above the ground. However, the risks that climbers take for the same experience can vary dramatically. The smartest climbers and investors demand compensation.
A Systematic Approach
“Climbing is inherently dangerous.” Yeah, I get it. However, the vast majority of climbing accidents are not inherent to the sport at all. The vast majority of accidents are tragically avoidable.
Rappelling accidents are one of the most frequent causes of injury and death. On a rappel, the climber uses a friction device on the rope to lower herself back to the ground. There are several steps, but most rappels are quite similar:
1. The climber attaches the rope to the rock with some sort of anchor.
2. The climber attaches herself to the rope with a friction device.
3. The climber descends the rope in a controlled manner until she reaches the ground, or the next anchor.
Done correctly, this process is extremely safe and straightforward. Mess up any one step and it could kill you — and it has, many times, even for the most experienced climbers. If you don’t check the integrity of an anchor, it could break and kill you. If you set up your friction device incorrectly, it won’t hold and it will kill you. If you lose control of the rope while descending, you’ll go into free fall and it will kill you. If you misjudge the distance and accidently rappel off the bottom of your rope — you get the idea.
The only way to reliably solve this problem is with a systematic approach. Risk-aware climbers check the integrity of fixed gear. They tie knots in the bottom of the rope so they can’t rappel off the ends. They double or triple-check their connections before committing to a system. They use a backup hitch that will stop them if they lose control. These are low-cost precautions, and a risk-aware climber will take them every time.
Similarly, a systematic approach can save you from the most common investing mistakes. The point of this approach is not to eliminate all risk — there are few, if any, rewards in the financial world that don’t come with risk. The point is to eliminate risks that don’t come with any reward. An undisciplined investor may be enthusiastic and make a big bet one day, but take her money out of the market the next day after seeing a loss. A systematic investment strategy sets well-defined rules for responding to events in the market, and then follows those rules. Each investor is in a unique situation, but the best advice is quite similar:
1. Build an appropriate portfolio.
2. Identify how and under what circumstances you’ll change that portfolio
3. Don’t do anything else!
The best rules take risk where it is well compensated and shun risk where it is not. As in our climbing example, messing up any of the steps above can lead to unfortunate consequences.
The Efficient Frontier
I would be remiss if, in a discussion of climbing and risk, I didn’t talk about Alex Honnold. Alex is one of the strongest climbers in the world, and he is far and away the best free soloist. He recently completed an ascent of Yosemite’s 3,000 ft. El Capitan without a rope or any safety gear. A fall at any point would have meant certain death. Alex is a master of risk management.
Commentary on Alex’s ascent fell into one of two categories: he was either a reckless daredevil with a death wish, or a superhuman machine who feels neither fear nor weakness. Alex controlled every possible aspect of his climb — he soloed larger and larger routes each year, he climbed his particular route on El Capitan with a rope many times, he sought alternate paths around the areas that were just too insecure to climb without a backup. Even then, his climb was risky — the rock he was holding onto could break off in his hands. His feet could slip on a patch of water or dirt or a leaf he didn’t see. Climbers above him could dislodge a rock and knock him off his stance. Many climbers at Alex’s skill level would have decided that this was still too much risk to accept. Nevertheless, Alex was operating at the efficient frontier.
In finance, the efficient frontier relates to the trade-off between risk and reward. When off of the efficient frontier, we can either increase the expected reward or reduce the risk without having to trade off between the two. This applies equally to the helmet-less climbers in an area known for loose rock and the investor who takes on more risk by holding an undiversified portfolio. Once on the efficient frontier, we can only increase the expected reward by increasing the risk.
A related concept, and one that is easier to think about, is “risk budgeting.” The idea is that we choose an acceptable level of risk, and then try to maximize our reward while staying within this budgeted level of risk. If we remove an uncompensated risk — say, by double-checking our rappel setup — we can accept a new risk with much greater rewards. Alex was able to accept the unavoidable risks of soloing El Capitan because he mitigated the avoidable ones.
Not everyone has Alex’s risk budget. However, everyone can operate at the efficient frontier. The biggest risk, after all, is taking no risk at all.
 Sometimes you’re even paid to sell risks. The gambling industry is weird.
 This is an approximate average return for US equities over the last ~100 years. But, jeez, please don’t take these numbers too seriously. Definitely don’t take this as a statement about forward-looking returns.
 The actual risk depends on the correlation of the assets and the relative weights in your portfolio. We’re calculating the standard deviation of a sum of random variables — if we weight them equally and they are perfectly correlated, the standard deviation is still 20%. If they are uncorrelated it drops to 14% and if they are perfectly negatively correlated, it drops to 0% — money for nothing!