Claritas Curriculum Review: Quantitative Concepts

I know 99% of you are looking at the chapter subject, quantitative concepts, and are shuddering right now. MATH! Ugh!
As a reborn numbers junkie myself, I can understand your apprehension. I always hated math in school but have grown to really enjoy it since studying for the CFA exams. Math is one of the only true absolutes in life. In all the mystery and chaos of our daily gamble, you know that 2 +2 will always equal 4. I kinda like that assurety.
Try to open yourself to the material and embrace it as a way to make yourself a better professional in an area where others will surely neglect. The section is important for the Claritas Investment Certificate and is one of the five chapters in Module 3 that account for 20% of your exam score.

Time Value of Money


There are two ideas at play here. First, everyone would rather have money now rather than later so most people want some kind of return to sacrifice current spending power. Second, the timing of when you receive the money is important to how much value it has now.
There is a lot of definition material here but it is all inter-related so try to get the overall concept first and everything should fall into place. Understand the difference between simple interest and compound interest.
Compound interest is a very important concept and just means that you will receive interest in the future for interest payments you receive now so it is worth progressively more money. The calculation is super easy on most calculators. Simply type in the interest rate (1+rate) and hit the yx key then the number of periods to compound and times the initial dollar amount.
Once you have the difference between simple and compound interest, the definitions for Annual Percentage Rate (APR) and Effective Annual Rate (EAR) become clear. Remember, the EAR is effectively the money you will be paying or receiving since it is the more accurate compounded rate.
Net Present Value is probably the most important concept in finance. An investor/financier needs to know how much an asset is worth in today’s dollars to be able to make funding decisions. As with any net figure, it is the difference between the total present value and the initial cost. Be sure you understand the process, i.e. why each year’s cash flow is discounted by a rate to find the present value, but you can do this calculation quickly and easily on the calculator.
Annuities and Mortgages are conceptually the same thing. The only difference is who receives the money and makes payments. In mortgages, you receive money to buy a house and make regular payments in the future. In an annuity, the bank receives the initial payment and promises to make payments to you in the future. Really the only difference is that annuities may be structured to pay off for an indefinite period.
Each mortgage payment includes a portion of interest and a repayment of the initial loan, so eventually the amount is paid off.

Descriptive Statistics


I think a lot of the terms here are unnecessary jargon. “Data set” just means the numbers you’ve collected for your analysis. Much of the chapter is like this but there are a few very important words and concepts.
Central tendency is just the best number that describes a group of numbers. Understand the difference between the “mean or arithmetic mean” and the “geometric mean.” The arithmetic mean is the simple way you learned in school, adding everything up and dividing by the number of occurences. Geometric mean is the average of the compounded return for each occurrence.
Median and mode are very important but pretty easy concepts. Remember, median is the middle number (or an average of the two middle numbers) while the mode is the number that happens most often.
Standard deviation and variance are extremely important concepts in investments. They are used to measure the volatility in price or returns and so imply the risk in an investment. The formula can be tough for math newbies so hang in there and you’ll get it. Just remember that standard deviation is the variability around the average. If you know the average (return) and you know by how much the actual (return) might differ from the average, then you can make a better investment decision.
The normal distribution is one of the cool ways that math relates to life and other areas of science. It just happens (ok there’s probably a more complicated reason than, “it just happens”) that events in nature fall around a ‘bell-shaped’ curve. There is the average, where events tend to occur by definition, and everything else falls around the average in a nice pattern. This pattern can be skewed left or right or can be a little fatter or thinner, but it is generally pretty much the same.
Correlation is another big one for investments and really just means the tendency for two (assets, variables, etc.) to move in the same or opposite directions. The measurement ranges from -1 to +1. For example, if the share price of Apple always goes up when the share price of Intel goes up, then they would be perfectly correlated (+1). If shares of Apple always went down when shares of Intel went up, then they would be perfectly negatively correlated (-1). If there really didn’t appear to be a pattern between the two share prices, then they would not be correlated (0). Few things have correlations of +1 or -1 but instead are somewhere in between.
The importance of correlation is that you can put stocks in a portfolio and the portfolio will have less risk than the two individual stocks. This is because when not all stocks will be increasing or decreasing at the same time so you’re overall return will be smoother.
The limited material in the chapter really isn’t so tough. Even if you have always avoided math and statistics, you are probably familiar with the concepts. Again, try to embrace the material as a new challenge and a road to being a strong asset to any employer.
‘til next time, happy studyin’
Joseph Hogue, CFA

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