q: Explain the relationship among covariance, standard deviation, and correlation.
Thecovariance is a more general representation of the same concept as the variance. The variance measures how a random variable moves with itself. The covariance measures how one random variable moves with another random variable.
The covariance of RAwith itself is equal to the variance of RA
The covariance can be zero and even negative. For example, the returns of a stock and of a put option on the stock would have a negative covariance.
The covariance is difficult to interpret by itself. For this reason, we usually divide the covariance by the standard deviations of the two random variables to get the correlation between the two random variables. The correlationis a measure of the strength of the linear relationship between two random variables.
r: Calculate the expected return and the variance for return on a portfolio.
An analyst can determine the expected value and variance of a portfolio of assets using the corresponding properties of the assets in the portfolio. To do this, we must first introduce the concept of portfolio weights:
wi= market value of investment in asset i / market value of the portfolio
For the exam, memorizethe formula for the two-stock portfolio:
Var(Rp) = wA2* Var(RA) + wB2* Var(RB) + 2 * wA* wB* Cov(RA,RB)
s: Calculate covariance given a joint probability function.
Example:A covariance matrix contains both the covariances and the variances (recall that the covariance of an asset with itself is the variance - the terms along the diagonal in the table below are the variances). This is the simplest case because the most tedious calculations have already been performed. To make this example more interesting, let's assume that we have a portfolio that consists of a stock "S" and a put option on the stock "O." We are given wS= 0.90, wO= 0.10, and the covariance table below.
Covariances
RS
RO
RS
0.0011
-0.0036
RO
-0.0036
0.016