lecture 4 - mean variance framework Flashcards
what is the state preference theory?
general framework for asset pricing, cannot be tested empircally: payoffs in different states of nature must be known for all assets, complete capital market required
what is the mean varience framework?
simplified theory of choice and pricing using the normality assumptions of asset returns:
less information needed (mean and variance of the asset only)
empircally testable with historical data
what is the mean
weighted average of all values
what is the variance?
measure of dispersion or spread of a random variable around its mean
what is the standard deviation?
the square root of the variance, same unit of measurement as the mean
what is the covariance?
measures the comovement between two asset returns
E[(R_x - u_x)(R_y - u_y)]
what is the correlation coefficent?
the standardised measure of comovement
r_xy = cov(R_x,R_y)/(σ_xσ_y)=σ_xy/(σ_xσ_y)
what does the magnitude of the correlation vary between?
it varies between negative and postive 1
if the two return series are perfectly correlated than what is the correlation?
the correlation is 1 if the two return series are perfectly correlated
if the two return series are perfectly negatively correlated than what is the value of the correlation?
the value is negative 1
if the two return series are independent than what is the correlation coefficient?
the correlation coefficient is equal to 0
what contains more information, two seperate individual probability distributions or a joint probability distribution?
a joint probability distribution contains more information, it shows how the the assets comove
what is the normal distrubution?
it is a continuous distribution which is completely described by the mean and variance, if asset return (R) follows N(μ, σ^2), its PDF is:
f(R)= 1/(σ√2π) * e^(-0.5[(R-u)/σ]^2)
what are the assumptions for the mean variance framework and portfolio selection?
1) an investor maximises their expected utiltity based on portfolio returns given risk
2) future portfolios returns follow a normal distribution completely specified by mean and variance of returns
the investors expected utility depends only on the mean and variance of the portfolio returns
what is the fraction a in a two asset portfolio indicate?
the fraction a of an individuals wealth tat is invested in asset X
what is the expected return of the portfolio?
it is equal to the weighted average of the portfolios assets
R_p= aR_x + (1-a)R_y
what is the variance of portfolio return?
var(R_p) = E[R_p - E(R_p)]^2
= E[aR_x +(1-a)R_y - E(aR_X +(1-a)R_y)]^2
=a^2 *var(R_x) + (1-a)^2 *var(R_y) + 2a(1-a)cov(R_x,R_y)
what type of function is the expected return in relation to a]
the expected return is a linear function of a
what type of function is the portfolio variance in relation to a?
portfolio variance is a non linear parabolic function of a
how do you find the minimum point of variance of a portfolio in terms of a?
you differentiate the variance with respect to a and equal that to zero then make a the subject of the equation to find variance minimising a
what is the efficient set?
highest mean return for a given variance of two risky assest
what is two fund seperation?
each investor will have a utility maximising portfolio that is a combination of the risk free asset and a portfolio of risky assets determined by the capital market line
what does the capital market line descibe?
the CML describes the linear relationship between the risk and return of efficient portfolios
what is the slope of the capital market line equal to ?
the slope of the CML is the market price of risk
what is the slope of the CML equal to for every investor?
the slope of the capital market line is the same and equal to the optimal marginal rate of substitution between the risk and return
