CFA Level 1 - Chapter 2 - Probability

PROBABILITY Conditional Probabilities The vertical line denotes the phrase “given”, so P(A|B) reads “the probability of A given B”…

The Rule of Addition At the end of the formula we must remove the ‘section of overlap’ in the Venn diagram of probabilities because any overlap in the two probabilities would be included twice otherwise due to the previous two terms.

Covariance Measures the extent to which two random variables tend to be above and below their respective means.

Correlation The Correlation is a standardised measure of association between two random variables.

Note that the sigma, σ, is shorthand for standard deviation and the range of the output value; -1 < Correlation < 1.

Expected Value and Variance The formulae for i terms are as follows…

So for a two asset portfolio the expected return and variance are given as…

Bayes Formula The following two formulae link together the addition rule and conditional probabilities…

1.

2.

Factorial The factorial of an integer is simply the product of that integer with all of those below it down to, and including 1. Note, by definition, although it’s largely irrelevant here, mathematicians define 0! = 1.

Combinations and Permutations - Combinations

…chooses r from n (and the order is irrelevant).

- Permutations

…chooses r from n (and the order matters).

The Effects of a Constant on x̄ and σ Multiplication - The mean, x̄, is multiplied by the same constant.

- The standard deviation, σ, is multiplied by the same constant.

Addition - The constant is added to the mean, x̄.

- The standard deviation remains unchanged; the constant has no effect!