Today I’ll talk about a term that I find crucial in money management and decision making in general: risk of ruin. It was briefly mentioned in a previous article on keys to money management, in which Mr Frugal and Mr Spendthrift were presented to the reader.
What is Ruin?
Let’s start by defining the term “ruin”. I’m considering ruin as the outcome in which a specific event makes you lose everything you have won until that point, making all your previous successful outcomes irrelevant. A classical example would be playing Russian Roulette. When you win, you get some reward. When you lose, you lose your life, which should be more valuable than everything you may have won playing this game before.
Even though the probability of losing, the risk of ruin, in a specific event or “game” could be very small, it becomes 100% if enough time passes. Eventually you shoot the gun and you meet the bullet, even if it just happens once every 1,000 times. And, when it happens, it won’t matter how much you won before.
The following graph presents this concept, the probability of this event occurring tends towards 100% the more times you play:
Are We Willing to Play this Game?
There are only three situations in which playing this kind of game makes sense:
- When you have no other choice (for example, when the options are going through a chirurgical operation in which you may die or just dying outright).
- When you don’t have skin in the game and others are facing the ruin when it occurs (“heads I win, tails you lose”).
- When the game has positive expected value and you can choose how much to bet.
The second scenario is very common, it can be seen very often in politics and financial markets. When someone with no morals is in a situation in which they benefit from the upside but they aren’t equally harmed from the downside (for example, they are just fired while you lose all your investment), they welcome volatility and aren’t scared of ruin. They are antifragile, at your expense.
An example of this would be when companies are bailed out. While citizens don’t participate in the upside that shareholders enjoy, they do participate in the losses. When the company fails, the ants get some of their hard-earned savings stolen, in order to save the grasshoppers.
Choosing How Much to Risk
For the remainder of the article, we are going to focus on the third scenario. We are going back to the Russian Roulette game, but with a few tweaks. Now, the game consists of you being able to bet money. When you win, you get back what you bet plus 20% extra. When you lose, you lose all your bet. The probability of losing is 10%. This could be a financial asset that gives 20% annual returns, but once every 10 years it “explodes” and you lose everything.
Should you play this game? First, let’s calculate the expected value (“EV”) of playing.
\[EV = {(P(W) * Quantity\;Won) – (P(L) * Quantity\;Lost)}\]
Where P(W) is the probability of winning and P(L) is the probability of losing.
Therefore; \[EV = (0.9 * 0.2) – (0.1 * 1) = 0.08\]
This means that, on average, every time you play, you win 0.08 times the quantity bet (8% of the quantity bet). This game, therefore, has positive expected value and you should play (if you don’t have a better use of that money).
However, how much should you bet? If you bet 100% of your money every time you play, there’s 100% chance that you end up hitting that negative scenario (even if it just happens 10% of the time) and you lose everything.
By risking too much, you have made a positive expected value game become a losing one. Finding profitable games, or investments, isn’t enough, you also have to know what’s the optimal percentage of your savings to risk, which depends on the payout structure of the investment (which are the possible scenarios and what’s the probability of each of them occurring).
How to Maximize Bankroll Growth
Let me introduce another concept, expected bankroll growth. This tells us at what rate our bankroll will increase after each bet. If you bet all of your money in something that has any probability over 0 of failing (which is almost everything in life), then the expected bankroll growth is negative, which means that it tends towards zero. The more you play, the more likely it is you lose everything.
If, instead, you bet an appropriate amount of money, your bankroll is expected to increase after each round. It tends towards infinite instead of zero.
What’s the optimal amount to bet? This is defined by the Kelly Criterion, which is the result of the following formula:
\[Kelly\;Criterion = P(W)\;-\;{{(1 – P(W))} \over {P(W) \over P(L)}}\]
In our game, this would mean:
\[Kelly\;Criterion = 0.9\;-\;{{(1 – 0.9)} \over {0.9 \over 0.1}} = 0.8889\]
To maximize our bankroll growth we should bet in every game 88.89% of our bankroll.
And our expected bankroll growth per game is \[0.8889\;*\;0.08 = 0.0711\]
After each bet, our bankroll increases by 7.11%, slightly under the expected value of 8%.
So what does all this mean? That diversification is needed. Or, in other words, “don’t put all your eggs in the same basket”. It doesn’t matter how profitable an investment is if you bet all your money on it, as inevitably you will end up losing everything.
While the risk of ruin can’t be removed at the particular investment level, it could be removed at the portfolio level by properly building a portfolio that maximizes its expected bankroll growth.
Correlation, an Essential Factor to Consider
When building a portfolio, it’s not enough to estimate the expected returns of each possible investment, but also the probability of each of them failing, and what can you expect to happen with your other investments when this happens. If your investments are highly correlated, which means that they rise and fall together, your portfolio is not properly diversified. You think you are safe when what you are doing is something very similar to betting everything on the same horse.
Imagine that, after the calculations we made before, you decide to invest 88.89% of your capital in that investment. And, with the rest, you go and invest it in something that is 100% correlated. So you think your portfolio is protected against the risk of ruin, and then you find out that when you lose, you lose in both places, as if you had simply invested 100% of your capital in the first one.
You want your portfolio assets to be uncorrelated. That means that when one of them goes wrong, the other ones don’t necessarily go wrong too. A good example of this is how a casino works. At the same time, they are placing several positive expected value bets, the outcome of each of them being independent. A roulette hitting black doesn’t affect the probability of the next roulette hitting black, the outcome in each game is uncorrelated.
Negative Correlation, the Icing on the Cake
It could get even better. You could have assets that are negatively correlated. That means that when one of them goes wrong, the other one goes well. Imagine there’s a coin-flipping game. You can bet both on heads and tails simultaneously. In each of those separate games, you get your money back plus 1% when you win and you just lose your bet when you lose (positive expected value of 0.005). As you win every time (either in one side or another of the bet), and the game has a positive expected value, you could risk all your capital in every roll. This could be the case of market-makers or casinos in some scenarios.
The more concentrated your portfolio is, the further you are from that situation. A portfolio that mostly invests in just one sector or just one country may do well when things are going well, but it’s going to do quite bad when things go bad. If it’s not properly diversified (or leveraged), you won’t just do bad, you will lose everything.
It often makes sense to add assets in your portfolio that have lower expected returns and even negative ones if that’s going to let you maximize the portfolio global returns and minimize the risk of ruin. For example, by adding puts options to a stock portfolio, you may be able to invest a higher percentage of your money in stocks (or even leverage), resulting in higher global returns than if you just invested less and kept some cash uninvested (as we were leaving 11.11% uninvested in the example game).
Adding Alpha Rock Capital to Your Portfolio
What would be the perfect asset to add to a portfolio? One that doesn’t just decrease the risk of ruin and volatility but that also increases returns. That may be the case if you add some Alpha Rock Capital shares to your portfolio. Even though most of the traditional markets did quite bad in 2020, our profits were considerably higher than before.
People were more willing to buy online now, and some of our products increased in demand tremendously. This trend has continued.
So, by having some Alpha Rock Capital shares, not only your returns would probably be higher (if you know of anything more profitable, please let us know, we are very interested), but it’s possible that this asset is not as correlated to the stock market as we thought. It’s too soon to confirm this, but so far that’s the case.
If you are interested in knowing more about Alpha Rock Capital, I would strongly suggest you check Antifragile, our monthly newsletter.
You can also reach us in our contact section if there is something you would like to discuss with us personally.