CFA Study Guide

Quantitative Methods: Statistical Concepts

Measuring the risk of error in any set of values incorporates basic statistical equations to find the variance. The variance, in terms of financial analysis, measures how wide or narrow your margin of risk will be from the normally expected values. The larger that variance, the larger the risk, which means investors will expect a significant opportunity for gains with such a risky venture.

The two equations for measuring risk in portfolios are the Coefficient of Variation, and the Sharpe Ratio. Both of these formulas include the component of risk , standard deviation (√variance), compared to the expected return. It should be noted that investors will always want risk to be as low as possible and return to be as high as possible. The important fact to realize is where (numerator or denominator) those factors are placed.

Coefficient of Variation (CV): Risk is found in the numerator; when you want the numerator smaller than the denominator, this means you want the answer of your equation to be as low as possible


Sharpe Ratio: Risk is found in the denominator; when you want the denominator as small as possible, this means you want the answer of your equation to be as large as possible.



Key Point:
CV: Smaller numerator: Smaller Answer is better
Sharpe: Smaller denominator: Larger answer is better