Risky business

1. Risky business

As we discussed, risk is a product of both the likelihood of an occurrence and the severity of its consequences. It's important to note, though, that these calculations are simply estimations of the total amount of risk. Such models rely on probabilities; they are not guarantees.

2. Bring the noise

In statistics, we define noise as unexplained variation in the data. The plot you can see represents a prediction, the same kind you have made using the FORECAST() function. The light gray outline around our prediction line illustrates the error for a given observation. You can see that the error tapers toward the middle of the plot, where we have more data and therefore more certainty.

3. Random numbers

One way to test our predictions under various conditions is actually to introduce noise into our dataset. For example, we could slightly modify the data we use in our predictions to see how our predictions hold up. One way to do this is to multiply our data by small randomized numbers to make small modifications. We can generate random numbers using the RANDBETWEEN() function. This function takes an upper bound and a lower bound and generates a random number between the two.

4. Random numbers

For example, calling the RANDBETWEEN() function with low and high values of -100 and 100 will give you a number in between. Depending on the range and scale of the data, modifying the data by a factor of 100 may be too much noise. Consequently, we may want to divide the random number we generate to a more appropriate factor. For example, we could divide our random number (which will fall between negative and positive 100) by 50 to cap the variation we'll introduce to a factor of 2.

5. Too random?

One thing to note, the RANDBETWEEN() function will return a new value each time you edit the cell. So if you want to keep your random numbers the same, you'll need to copy your numbers and paste them as values to keep them fixed.

6. Adjusting data

Once we have our multipliers, we can multiply by the original data and add this product to the original data. In the example of the risk we calculated, we would multiply our random number by the original risk, and add this product to the original risk. This would adjust our total risk accordingly. This comes with a problem, though. Larger negative multipliers can actually result in negative risk. This can skew our results. We can solve this using the MAX() function. For example, we can take the MAX() between 0 and the original value plus the multiplied value. This will set a lower limit of 0 and will avoid skewing our data.

7. Framing effect

In addition to statistical noise, our brains also introduce noise into how we evaluate risk. That is, we perceive risks differently based on how they are explained. This is called framing effect. In the 1980s, behavioral economists studied how people respond differently to the same odds presented in different ways. Let's give you the same test. Let's say you have two options. In the first option, I say I'll give you $250. Sounds pretty good, right? For the second option, I say you have a 25% chance of winning $1000 and a 75% chance of winning nothing. Would you take the risk of winning big, or would you take the sure bet of $250? If you are like 84% of the people experimented on, you would prefer $250 in your pocket to the chance to strike it rich.

8. Framing effect

But what if we flipped things around? What if I told you that you either had to pay me $750 or you could have a 75% chance of losing $1000 and a 25% chance of walking away owing nothing. Which would you choose? In this instance, nearly 90 percent of people chose to take their chances in the hopes they would owe nothing, even though the risk is the same from the standpoint of risk and probability.

9. Framing effect

So what does this suggest about how we perceive risk? It suggests we are loss-averse. We hate to part with money or resources of any kind. We are psychological hoarders, in a sense. This affects how we perceive and act on risk.

10. Let's practice!

Now let's turn up the noise in the exercises that follow.

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