How good are we at odds?

Let’s take an example, if the weatherman said this morning, “There is a 30 percent chance of rain.” Would you take out an umbrella or not?

We can take home two lessons from this assumption.

1. How do we make decisions?

Considering that in this city rainfalls are no longer tied to predefined seasons, and that the cost of carrying an umbrella is low, you would surely carry it. You might not regret carrying a light umbrella.

If the decision involves an expenditure, we should take into account: How much does the umbrella cost? How much would it affect me to get wet? How much do I trust that estimate?

Furthermore, the umbrellas’ prices would most likely be affected by other variables such as the impact of supply and demand, immediacy, among others.

As we highlight through this mundane example, every day we make decisions without delving much into all the variables, viscerally or instinctively. This kind of automatic reactions are the ones we should scrutinize, whenever the stakes are high due to the relevance of the possible outcomes.

Perhaps, instead of rain we are referring to an emergency scenario, probably the price to pay for aid isconsiderably higher compared to an umbrella, and it might be the case that a 30 percent chance of occurrence is simply not as tolerable.

2. How do we judge the forecaster?

Following on with our example, suppose that it did indeed rain that day. In such a case, many may think that the meteorologist is bad, and erred in his forecast. We tend to simplify, and a lot of people think that a probability of less than 50 percent implies that it won’t rain at all, while aiming for something greater than 50 percent is certainty. Some people use uncertainty bands between 40 and 60, or 30 and 70, and assume that whatever lies beyond these barriers is certainty.

As a matter of fact, the afore mentioned 30 percent means that, historically, the coincidence of certain observed meteorological variables has resulted in rain 30 percent of the time. It would be fair to assume that the meteorologist is not very accuratet, if, after observing one hundred “30%” forecasts, the event did not match expectations. In other words, if out of a 100 times that he forecasts a 30% probability of rain, it rains many more than 30 times..

Over the past 90 years, the S&P Index for the US market, throughout over 22,356 daily observations, has averaged annual returns of 7.4 percent. If we interpret that, on one-year horizons, the average yield is 7.4 percent, it sounds interesting, but this is just an average. It would also be necessary to consider the variance, that is, how far the observations can move away from said average.

Another interesting fact is that in over 7,000 observatios negative returns have been posted almost 32 percent of the time. While history shows that positive returns show up twice as often, it never hurts to carry an umbrella.

What kind of umbrella?