Characterizing Financial Risk – Historic Simulation and Modeling

One Asset, One Time Period

Imagine purchasing an asset today for $50 that you will sell tomorrow. You purchase the asset because you believe it will increase in value tomorrow (lets say you expect it to increase in value by 2%), but you also know its value tomorrow is uncertain—it may go up by more than 2% or it may actually lose value. Because you realize this, you decided you want to understand what risk you are taking by purchasing the asset.

First you might ask: what is the probability that I will actually lose money on this investment? If there is a chance you will lose money, you then might wonder: what is the worst lost I could suffer? The answers to both of these questions are not simple. In order to answer them you have to characterize the set of possible returns. In other words, you need to characterize the risk of the asset. In order to do this task you need both data and assumptions. It is important to know when you are making assumptions and the strengths and weaknesses of your data.

Continuous Distribution

As a first cut, you might ask someone familiar with the asset to give a best possible gain and a worst possible loss. Say the numbers you get are -8% (loss) and 12% (gain). Remember that you believe the mean return is 2%. If you assume that each of the outcomes between -8% and 12% are equally likely, you can draw a uniform distribution like below:

Now you can answer the questions posed at the start. The probability that the asset will lose value is the area under the curve between x-axis values of -8 and 0. This is 0.40 (a 40% chance of loss). The worst-case loss is -8% of $50 or $4. Therefore, under your assumptions, by purchasing this asset you are accepting a 40% chance of any size loss and a 5% chance of a $4 loss (which also happens to be the worst