One of the big challenges of risk management is that some of the methods for treating risk can be quite expensive. So plan is a concern about the high error rates that exist within a manual process. You can see our investment in new computer systems to automate that process and reduce the errors, but the cost is high. Another example might be the question of whether to purchase insurance to transfer a particular risk to another party. Again, the cost is substantial. So how can you know whether the cost is justified? How can you build a business case for this expenditure? Quantification of risks addresses these problems, helping managers decide whether they can justify expenditure to treat risk. Without this justification, it's often really difficult to convince senior leaders to make significant investments in risk management. So you could say quantification is part of our influence skill set. In this video, I'm going to give you an example of how you can quantify risk and build a business case for investing in risk management. I've opened up the spreadsheet for this lesson, and I'm starting out in the data and analysis sheet. In columns A to C, I have a history of loss data for a particular event type. This is my risk event database. In 2008, there were five loss events. I have the date recorded for each one, and the impact expressed in dollars. In columns F through to H, I've calculated the number of loss events for the year. The sum of all the loss events and the average impact of each loss event in that year have also been calculated. This is repeated for every year through to 2018. Across 11 years, I have 50 events. The average number of events per year is 4.5, but there's quite a bit of variation. In 2013, there were only two events, and in 2017, there were eight events. The average losses from this risk type in a year is just under 200,000. Of the 11 years for which we have data, the highest loss in 2015 was 422,000. On the face of it, it appears that this is a significant risk, and some form of treatment may be justified. But one of the problems we have is that the data sample is quite small, with only 50 events across 11 years. In statistics, we need much larger samples to produce robust inferences. If there were more data, might we observe even more extreme outcomes? This is where Monte Carlo Analysis comes in. We can simulate a large dataset consistent with the limited data we have a new set to help us understand the more extreme cases. I'll demonstrate how we could estimate losses that will only be exceeded in one out of 20 years, that is, with 95 percent confidence, or one out of a 100 years with 99 percent confidence, and so forth. Once we know the extent of potential losses, we'll be in a much better position to judge what kind of investment in risk can be justified. In a separate video for degree learners only, I'll explain exactly how to conduct the Monte Carlo Analysis. But for now, let's suppose that you have the results of this analysis, the model numbers expressed in thousands of dollars. The Monte Carlo Analysis tells us the expected loss in a typical year is a 113,000, this is the median or the 50th percentile. The loss with 95 percent confidence that will be exceeded in only one in 20 years is 1,042,000. The loss with 99 percent confidence that will be exceeded in only one in a 100 years is 2,798,000. The same information is expressed here in a diagram showing the distribution of losses. The most likely outcomes involve relatively modest losses, but there's a small probability of a significant loss. In other words, it's a heavily skewed distribution, and this is common for many types of operational risk. So what could you do with this information? Let's come back to the issue of equity capital. You remember from Week 4 that equity capital is a crucial buffer to protect businesses against risk. You could say that capital is the ultimate mitigate control that will protect the firm in the event of a serious financial loss. The amount of capital we need for the business will depend on risk appetite. So let's say that the board determines that the risk of insolvency in any year should be no more than one percent. In that case, the business will need sufficient capital to cover losses to 99 percent confidence. For this particular risk type, that equates to 2,798,000. Actually, the amount of risk capital needed for this particular risk type is 2,798,000 less the expected loss of a 113,000 or 2,685,000. We can deduct the expected loss because that part of the loss distribution is handled differently through earnings. A resilient business will set its pricing margins to ensure that profits are enough to cover not only costs, but also the expected losses in a typical year. Risk capital is needed only to cover the losses beyond what occurs in a typical year as shown in the diagram. We assume that in this business, the cost of equity capital is 10 percent per annum. So now for the really important bit, how can we use this information to make a better risk management decision? So let's suppose that it's possible to treat this risk either with insurance, or new controls, or systems. But the cost of the treatment is pretty expensive at $200,000 a year. Based on quantitative modeling, we believe that if the treatment were implemented, the distribution of losses would be quite different as shown in this table. In this example, the effect of the treatment is to reduce expected losses by 53,000, or a 113 minus 60,000. The reduction in the risk capital is 2,685,000 minus 440,000, giving 2,245,000. Now, with a cost of capital at 10 percent, this gives an annual saving of 224,500. So the overall annual saving is 53,000. In other words, the saving in expected losses plus the saving in capital, 224,500, giving a total of 277,500. Recalling that the treatment costs $200,000 a year, it's clear that investing in the treatment makes good business sense, the benefit outweighs the cost. This analysis will be the basis of a strong argument, this is likely to be very influential. Hopefully, this makes the power of risk quantification really clear.