Now suppose that the test came out positive for you. What is the chance that you have the disease ? Is it close to 0.1%, 1%, 10% or 100% ?
Ray Dalio is the founder of Bridgewater Associates - the largest hedge fund in the world with nearly $122 billion in management. Since its origin in 1975, the fund has seen several ups and downs. Notably, it was one of the few hedge funds which returned +12% in 2008. How did Dalio manage such a return when S&P was down 37% for the year ?
A picture emerges from Maneet Ahuja’s book “The Alpha Masters”.
Dalio creates universal investment and management principles by learning from history. He analyzes how different countries, cultures, and people around the world react to different incidents like debt or oil shocks, for example, and figures out the variables that affected the different outcomes. Stripping away all the variables let Bridgewater arrive at universal laws for doing business. “If you’re limiting yourself to what you experienced, you are going to be in trouble. . . . I studied the Great Depression. I studied the Weimar Republic. I studied important events that didn’t happen to me.”
Dalio explains, “As risk at a particular period of time increases or decreases, it is either going to have a positive or a negative effect on certain markets and in various magnitudes.” For example, when dealing with bad economic conditions and higher default risks, Treasury bonds would have a positive beta, and equities would have a negative beta. And each instrument has various betas to it.“You can go back to Argentine stocks and certain emerging currencies,” Dalio says. “They all have various betas that we can see and adjust according to changes in the global risk environment. As a result, we pay attention to those things in structuring the portfolio. It’s a computer system that’s constantly updated.”
Let us ignore what Dalio does exactly. We simplify the model and assume that whatever Bridgewater does has an accuracy of 99%. This in my opinion is a very high accuracy rate for *any* model.
Did you solve the toy problem I posed at the beginning of the article ? If you haven’t please give it a serious thought before reading further.
The answer is 0.1% i.e., even if the test came out positive, there is a very small chance that you have the disease.
Let me explain. Consider a sample of 100,000 people. You expect 1 person in this sample to have the disease. If we test each and every individual in this sample using our test - it will come out positive for 1% of the healthy 99,999 individuals. This is a total of 999.99 false positives. So, you expect that nearly 1,000 people will test positive even when they do not have the disease. In this sample, only one person has the disease. Hence, the test gives at least 1,000 false alarms in a sample of 100,000 people.
If you tested positive, then what is the probability that you are the 1 out of 100,000 individual who has the disease ? It is at most 1/1,000 because of the 1,000 false alarms; which is a 0.1% chance of having the disease.
What happens if the disease is less rare ? If the disease occurs in 1 out of 10,000 people then the chance that you have the disease increases to 1%. For 1 out of 1,000 it stands at 10% and for 1 out of 100 it is nearly 100%.
Consider a situation in which Dalio’s model predicts an imminent major collapse in some market. If the event is sufficiently rare then with very high probability the model is wrong about the prediction.
If the event is not rare, then the prediction might be correct and useful. A major obstacle though is to calculate the rarity of an event. Can one claim that 2008 crisis was a rare event ? If yes, how rare ? Is it 1-in-10 or 1-in-100,000 ? How about the 9-11 attack on the World Trade Center or the World War 1 ? How rare are those ?
In hindsight, these events might be explainable but that does not mean that they were explainable while they were unfolding. The 1987 crash was short lived and the market was back to the peak in 1989. The internet bubble crash took nearly 5 years to reverse and immediately the market plunged back and is yet to recover completely.
Most of the time Dalio’s crisis indicator will say that it does not see an imminent major event. In these cases, most of the time the model will be right. But we don’t exactly need a model to tell us that the status is going to be “quo”. We need it when there is a risk of something drastic happening.
In case, the event which is going to happen is quite rare, whatever that means, the model is useless.
If the event is not a rarity then the model might be right. But unless it is completely mundane prediction like the rates are going to go up - the rarity of an event is nearly impossible to estimate correctly. Even predicting the direction the rates will go is close to impossible. Think of the rarity of 9-11 on Sep 8, 2009. Think of World War 1 and World War 2. Who thought that the interval between them will be only 20 years and then there will be no world wars until 2012 ? Can you predict the rarity of World War 3 ?
It is highly unlikely that anything usable comes out of the model Dalio has. Probably the only thing one can do is to get out of the corresponding market if the model raises an alarm. With very high probability it will be a false one, but at least you might be true in 0.1% of the cases and avoid huge losses. I am not sure how useful you think this strategy is. For me, Dalio’s model is quite expendable.
I will be happy to hear diverging opinions.