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Prior to the roll, we know the number of outcomes, we know what the outcomes are,

Â and we know that the probability of each outcome is one sixth.

Â In the second type of uncertainty,

Â we don't know the probabilities of the outcomes.

Â And in fact, we might not even know what the possible outcomes are.

Â In other words,

Â there is total uncertainty, in the sense that there is nothing measurable.

Â For example, it is very difficult to assess the probability that

Â an idea becomes a successful business.

Â This is a very complex problem that depends on way too many factors and

Â sources of uncertainty.

Â And this is why you often hear that successful entrepreneurs are not the ones

Â that have one great idea, but actually the ones that have lots of ideas.

Â In risk analysis, we are interested in the first type of uncertainty.

Â That is, the one for which we either know or

Â we can estimate the probability of each outcome.

Â The reason is simple, this type of uncertainty is the one that we can

Â measure, and therefore we're able to create models to assess risk.

Â These models take into consideration that some

Â elements are not known with certainty.

Â For instance, let's consider profit,

Â which is probably the most fundamental mathematical model in business.

Â Profit is calculated as the difference between revenue and cost.

Â Let's suppose that we know exactly how much everything is going to cost

Â to make a unit of a product that we want to sell.

Â It's not a very realistic assumption, but let's just go with it.

Â To make it simple, we're also going to assume that the single source of

Â revenue for this business is what we collect from the selling of this product.

Â If we're the ones determining the price of the product,

Â then all we need to do to calculate profit is to multiply

Â the number of units sold by the price per unit, and then subtract all the cost.

Â Calculating profit is very simple once we know how many units we have sold.

Â But if we want to do some planning based on future revenues, then things get a bit

Â more complicated, because we need to be able to estimate demand.

Â If we take a very simplistic approach, we might just say that demand

Â is going to stay steady, and therefore we will estimate

Â future demand with just the average demand that we have observed so far.

Â And this could work well in environments where things don't change much.

Â The reality is that in most situations,

Â things don't stay exactly the same from one period to another.

Â We must consider variability, and

Â it is precisely this variability, the one that produces uncertainty.

Â What we want the models to be able to capture is uncertainty

Â that is related to elements that include some level of randomness.

Â We want to extract historical patterns that can help us assess risk.

Â As we mentioned earlier, the key is to be able to determine all outcomes and

Â the probabilities.

Â For example, would you invest in a stock that is expected to double its

Â price within a year?

Â Well this seems like a pretty good opportunity.

Â But the key word here is expected.

Â Expected values don't tell you anything about the range of outcomes and

Â their probabilities.

Â With this limited information we simply don't know what the risk is.

Â Decisions involve risk and

Â attitudes toward risk vary from one person to another.

Â Some can tolerate more, and some less.

Â But we all need to have a way of measuring the amount of risk involved.

Â Risk analysis can be done at several levels of complexity.

Â At the very basic level, we could do a best case, worst case analysis.

Â Let's suppose that we have a spread sheet model in which some cells represent data

Â with uncertainty.

Â For example, we could have some cells that represent uncertain demand.

Â For the base case, we plug in the most optimistic values in each of these cells.

Â We can then see what happens to the outcome cell.

Â In the worst case scenario, we plug in the most pessimistic values for

Â the uncertain cells.

Â And once again, we check what happens to the output cells.

Â This is easy to do, but it doesn't give us information about the distribution of

Â all possible outcomes between the best and the worst cases.

Â Take a look at these distributions of values between the best and the worst.

Â All of these distributions have the same best and worst outcomes, and

Â even the same average outcome, but they certainly don't look alike.

Â The bell shape distribution tells us that the average is the most likely outcome,

Â and the values deviate above and below the average with the same probability.

Â The distribution in the form of a U tells us that the average almost never happens

Â and that it's as likely to get the worst possible outcome as it is to get the best.

Â Most people would associate this distribution to a risky situation.

Â The other two distributions have long tails indicating that extreme

Â values do not happen often, but they could happen with a small probability.

Â These distributions illustrate that examining only the best and

Â the worst possible outcomes is a limited analysis that ignores

Â a lot of valuable information.

Â You now might be wondering well,

Â then how can we get the values in between the best and the worst?

Â And the answer is Monte Carlo Simulation, a predictive analytics tool.

Â The name of this methodology comes from the famous casino in Monaco, and

Â it has a very interesting story that dates back to the experiments that took

Â place during the development of the atomic bomb.

Â Here of course,

Â we are going to focus on a more peaceful application of this technique.

Â And easy way of describing how Monte Carlo Simulation works, is by assuming

Â that we have expression model in which some of the cells contain certain values.

Â For example, suppose that the green cells are the ones with the uncertain values,

Â and that the orange cell is the outcome.

Â For most models, if we use expected values for

Â the green cells, we obtain an expected value for the orange cell.

Â We can also plug in the worst and the best estimates for the green cells, and

Â observe the best and the worst estimates for the orange cell.

Â In general, any set of values for the green cells generates a value for

Â the orange cell.

Â This is known as what-if analysis.

Â If we plug in a lot of values for the green cells, and

Â then store all the resulting values for

Â the orange cell, we could create a picture of all possible outcomes.

Â This picture is what we have been calling a distribution.

Â Plugging in a lot of numbers to create a distribution is very tedious,

Â and not only that, if we are the ones choosing these input values,

Â we're bound to introduce our own biases in the process.

Â And this is why we use Monte Carlo Simulation.

Â The method requires that we make assumptions about

Â how the values of the uncertain cells behave.

Â For instance, do the uncertain values follow a uniform distribution?

Â Or a normal distribution?

Â We will see that these assumptions are typically based on both experience and

Â historical data.

Â The quality of the model will depend on how reasonable these assumptions are.

Â But once we feel comfortable with the assumptions about the uncertain values,

Â the method will produce valuable information about the outcomes.

Â It is really exciting that, thanks to advances in personal computing and

Â software, we get to use a tool that, not long ago,

Â was only available to those with advanced programming skills and powerful computers.

Â