1.3 Portfolio expected return and variance formula Flashcards
the Modern portfolio theory is based on what?
on the principle that investment opportunities should be evaluated in the context of how they impact the tradeoff between a portfolio’s expected return and the level of portfolio risk, as measured by variance
portfolio variance
typically used to quantify the riskiness of a portfolio’s returns
in order to calculate a portfolio’s expected variance, what do we need?
we need to use information about individual asset returns and their covariance with each other
covariance
measures the tendency for two variables to move in sync
covariance formula
Cov(Ri, Rj) = E[(Ri − E[Ri])(Rj − E[Rj])]
when is covariance positive?
when one asset is generating above-average returns, the other asset is as well
Both assets will also tend to generate returns below their respective averages in the same periods.
when is covariance negative?
if one asset is generating above-average returns while the other’s returns are below its average (or vice versa)
The covariance of an asset’s returns with itself (own covariance) is equal to what?
its own covariance
variance for a portfolio with two securities formula
σ2(Rp) = w^2A + σ^2A + w^2B + σ^2B + 2 * wA * wB * Cov[RA, RB]
becomes increasingly complex as you add more securities
The correlation between two sets of returns, Ri
and Rj, is calculated how?
ρ(Ri, Rj) = pij = Cov(Ri, Rj) / (σ(Ri) * σ(Rj))
formula #2 for covariance between two securities
Cov(Ri, Rj) = ρij * σ(Ri) * σ(Rj)
explain how we can plot relationships between two securities using the scatter plot
Positive correlations indicate a positive linear relationship
–> A perfectly positive relationship will have a correlation of 1 and will be depicted on a scatter plot as a straight upward sloping line.
Negative correlations indicate a negative linear relationship. A correlation of -1 indicates a perfectly inverse relationship.
a joint probability function
used to estimate covariance or correlation measures
We can calculate the covariance and correlation between assets based on their probability-weighted returns under different market conditions
Which of the following is most likely one of the parameters required to completely describe a multivariate normal distribution?
A
Kurtosis
B
Skewness
C
Correlation
