Listing Category: Quantitative Methods

Time Value of Money: Using Timelines

Much of finance centers around the idea of the time value of money: a dollar (or euro, or yen, or pound, or yuan, or franc, or won, or ruble, or bhat, or rupee, or whatever) today is worth more than a dollar (or euro, or . . . well, you get the idea) tomorrow, because…

Yield Measures

There are a variety of conventions for measuring the yield (or return) on an investment; you need to know the definitions of each of these yield measures and how to convert from one yield measure to another (to facilitate comparison of various investments).

Student’s t-Distribution

The Student’s t-distribution has an interesting history. It was published by a gentleman who worked for Guinness Breweries in Dublin, Ireland, who used it for statistical tests on the ingredients for Guinness beer; apparently Guinness preferred that their employees publish under pseudonyms, so this gentleman (William Sealy Gosset), chose “Student” as the name under which he published his papers.


Skewness of a probability distribution is a measure of its asymmetry; the higher the (absolute value of the) skewness, the more asymmetric the distribution. Symmetric distributions have skewness of zero. The formula for the skewness of a sample is:

Sample Standard Deviation

In comparing the formulae for the standard deviation of a population and the standard deviation of a sample:

Normal Distribution

The normal (or Gaussian) probability distribution is arguably the most important continuous distribution used in probability and statistics; it is certainly the most important continuous probability distribution appearing in the CFA curriculum. There are several reasons for its prominence:

Nominal vs. Effective Interest Rates

The ideas behind nominal and effective interest rates are fairly simple, but you need to be sure that you understand the differences, and that you know which convention is used for which common rate quotes. At the heart of the difference is the idea of compound interest, so let’s start there. Throughout this article, we’ll measure time in years, so unless specified otherwise, interest will be quoted as an annual rate.


Kurtosis is generally viewed as a measure of peakedness of a probability distribution (how tall the center of the distribution is compared to, say, a normal distribution); the taller (and thinner) the center peak, the higher the kurtosis. Another way of describing kurtosis is as a measure of how fat the tails (extreme ends, positive and negative) are compared, again, to a normal distribution; the fatter the tails, the higher the kurtosis.

Hypothesis Testing – Step 7: Make a (Business) Decision Based on the Results of the Test

While I realize that most of the people reading this series of articles all the way to the end will happily engage in the first six steps of hypothesis testing simply for the sheer joy of testing hypotheses – there are some of you who secretly wish that you could get a job where you could get paid for doing nothing more than formulating and testing hypotheses all day long – in the real world we have to accept the harsh truth that, having made a decision regarding the null and alternative hypotheses, we must now make a business decision based on the outcome of the test.

Hypothesis Testing – Step 6: Make a Decision Regarding the Null and Alternative Hypotheses

Having gotten through the difficult steps, we’re at the easiest one of the bunch: compare the calculated test statistic to the critical value(s) and determine whether the test statistic lies in the rejection region or the acceptance region. If the former, we reject the null hypothesis in favor of the alternative hypothesis; if the latter, we fail to reject the null hypothesis.