Quantitative methods and the CFA

Hello, and welcome to our talk today about quantitative methods and the CFA or Chartered Financial Analyst exam. Now, I'm Professor Michael McDonald. I'm a Professor of Finance at Fairfield University in Fairfield, Connecticut. Today I want to talk to you at a high level about what it is you need to know in order to pass the quantitative methods section on the CFA level 1 exam.

To begin with, for the CFA exam, you'll certainly need to be very familiar with a variety of different investment statistics out there. In the investments world, one of the most important topics is statistics. The reality is that investors measure their performance using a variety of different kinds of statistics, and so the CFA puts a heavy emphasis on this. Indeed, if you're going to work in the finance industry at all, independent of the CFA, you need to have a strong understanding of statistics and how they work. This includes things like descriptive statistics versus inferential statistics, the concept of populations versus samples, different types of measurement scales, quantitative versus qualitative variables, etc.

The concept of investment statistics begins with different measures of central tendency. Now, this is just a fancy way of talking about a concept we're all familiar with anyway, averages. The simplest form of average is just the arithmetic average. We add up all of a particular variable and then divide by the number of that variable. Said differently, we sum up the variable and then divide by the count for that. If we wanted to understand, for instance, the average height in a room, we'd add up everybody's height, divide by the number of people in that room. But an alternative metric for averages is what's called the weighted average or sometimes weighted mean. This is going to put a weight on each individual observation and its representation within the group overall. Where you frequently see this in the investments field is as it relates to market capitalizations. For instance, we might look at the market cap weighted return. Apple having say, a one trillion dollar market cap, would get a lot bigger weight than, say, if we had a hypothetical company, Joe's Hot Dogs. Joe's Hot Dogs had a $10 million market capitalization, so we weigh each company based on their market capitalization and then account for their return overall. Related to this, we also have a concept called the geometric mean. Now, the arithmetic mean, or just the average tells us in essence, what is the typical return look like for an average stock out there? The geometric mean would tell us instead, how fast is the return on those stocks growth over time? How fast is the value of that stock growing if we hold it for 10 years? The geometric mean, in other words, gives us a way to understand the average rate of growth. That's very important in the investments world, so you want to understand the difference between these. They're calculated very differently. The geometric mean is our final value divided by our initial value raised to the 1 divided by n, all minus 1. That n is the number of observations or number of years in most cases, that we're looking at this. Where you most often seen geometric mean is, calculating say, the average return on a mutual fund or a hedge fund, or the average return on the stock market or something like that.