Applying the CAPM to Performance Measurement
[vsw id=”dg8GZluFxDI” source=”youtube” width=”611″ height=”344″ autoplay=”no”] After completing this reading, you should be able to: Calculate, compare, and evaluate the Treynor measure, the Sharpe measure, and Jensen’s alpha. Compute and interpret tracking error, the information ratio, and the Sortino ratio….
Exam P Syllabus – Learning Outcomes
General Probability 1.a – Define set functions, Venn diagrams, sample space, and events. Define probability as a set function on a collection of events and state the basic axioms of probability. 1.b – Calculate probabilities using addition and multiplication rules. 1.c – Define…
State and apply the Central Limit Theorem
For this learning objective, a certain knowledge of the normal distribution and knowing how to use the Z-table is assumed. The central limit theorem is of the most important results in the probability theory. It states that the sum of…
Calculate probabilities for linear combinations of independent normal random variables
Definition: Let \(X_1, X_2,\ldots,X_n\) be random variables and let \(c_1, c_2,\ldots, c_n\) be constants. Then, $$ Y=c_1X_1+c_2X_2+\ldots+c_nX_n $$ is a linear combination of \(X_1, X_2,\ldots, X_n\). In this reading, however, we will only base our discussion on the linear combinations…
Determine the distribution of a transformation of jointly distributed random variables
Transformation for Bivariate Discrete Random Variables Let \(X_1\) and \(X_2\) be a discrete random variables with joint probability mass function \(f_{X_1,X_2}(x_1,x_2)\) defined on a two dimensional set \(A\). Define the following functions: $$ y_1 =g_1 (x_1, x_2)$$ and $$y_2 =g_2(x_1,x_2)$$…
Calculate joint moments, such as the covariance and the correlation coefficient
Let \(X\) and \(Y\) be two discrete random variables, with a joint probability mass function, \(f\left(x, y\right)\). Then, the random variables \(X\) and \(Y\) are said to be independent if and only if, $$ f\left(x,\ y\right)=f\left(x\right)\times f\left(y\right),\ \ \ \…
Calculate variance, standard deviation for conditional and marginal probability distributions
Variance and Standard Deviation for Conditional Discrete Distributions In the previous readings, we introduced the concept of conditional distribution functions for random variable \(X\) given \(Y=y\) and the conditional distribution of \(Y\) given \(X=x\). We defined the conditional distribution function…
Explain and apply joint moment generating functions
We can derive moments of most distributions by evaluating probability functions by integrating or summing values as necessary. However, moment generating functions present a relatively simpler approach to obtaining moments. Univariate Random Variables In the univariate case, the moment generating…
Calculate moments for joint, conditional, and marginal random variables
Moments of a Probability Mass function The n-th moment about the origin of a random variable is the expected value of its n-th power. Moments about the origin are \(E(X),E({ X }^{ 2 }),E({ X }^{ 3 }),E({ X }^{ 4 }),….\quad\) For…
Determine conditional and marginal probability functions for discrete random variables only
Marginal Probability Distribution In the previous reading, we looked at joint discrete distribution functions. In this reading, we will determine conditional and marginal probability functions from joint discrete probability functions. Suppose that we know the joint probability distribution of two…
