lecture 4 - mean variance framework

Question 1

what is the state preference theory?

Answer 1

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

Question 2

what is the mean varience framework?

Answer 2

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

Question 3

what is the mean

Answer 3

weighted average of all values

Question 4

what is the variance?

Answer 4

measure of dispersion or spread of a random variable around its mean

Question 5

what is the standard deviation?

Answer 5

the square root of the variance, same unit of measurement as the mean

Question 6

what is the covariance?

Answer 6

measures the comovement between two asset returns
E[(R_x - u_x)(R_y - u_y)]

Question 7

what is the correlation coefficent?

Answer 7

the standardised measure of comovement
r_xy = cov(R_x,R_y)/(σ_xσ_y)=σ_xy/(σ_xσ_y)

Question 8

what does the magnitude of the correlation vary between?

Answer 8

it varies between negative and postive 1

Question 9

if the two return series are perfectly correlated than what is the correlation?

Answer 9

the correlation is 1 if the two return series are perfectly correlated

Question 10

if the two return series are perfectly negatively correlated than what is the value of the correlation?

Answer 10

the value is negative 1

Question 11

if the two return series are independent than what is the correlation coefficient?

Answer 11

the correlation coefficient is equal to 0

Question 12

what contains more information, two seperate individual probability distributions or a joint probability distribution?

Answer 12

a joint probability distribution contains more information, it shows how the the assets comove

Question 13

what is the normal distrubution?

Answer 13

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)

Question 14

what are the assumptions for the mean variance framework and portfolio selection?

Answer 14

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

Question 15

what is the fraction a in a two asset portfolio indicate?

Answer 15

the fraction a of an individuals wealth tat is invested in asset X

Question 16

what is the expected return of the portfolio?

Answer 16

it is equal to the weighted average of the portfolios assets
R_p= aR_x + (1-a)R_y

Question 17

what is the variance of portfolio return?

Answer 17

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)

Question 18

what type of function is the expected return in relation to a]

Answer 18

the expected return is a linear function of a

Question 19

what type of function is the portfolio variance in relation to a?

Answer 19

portfolio variance is a non linear parabolic function of a

Question 20

how do you find the minimum point of variance of a portfolio in terms of a?

Answer 20

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

Question 21

what is the efficient set?

Answer 21

highest mean return for a given variance of two risky assest

Question 22

what is two fund seperation?

Answer 22

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

Question 23

what does the capital market line descibe?

Answer 23

the CML describes the linear relationship between the risk and return of efficient portfolios

Question 24

what is the slope of the capital market line equal to ?

Answer 24

the slope of the CML is the market price of risk

Question 25

what is the slope of the CML equal to for every investor?

Answer 25

the slope of the capital market line is the same and equal to the optimal marginal rate of substitution between the risk and return