Markowitz Model

Markowitz Assumption 1

Investors consider investment alternatives with respect to probability distributions of expected returns

Markowitz assumption 2

Investors maximize one period utility and have a diminishing marginal utility of wealth

Markowitz assumption 3

Variability of returns is used to estimate hisk

Markowitz assumption 4

Investors base decisions on expected returns and risk

Markowitz assumption 5

Investors desire more returns and less risk

What are the two implicit assumptions

Only Risky assets and no leverage/borrowing

What does Markowitz introduce?

He introduces the idea of co-movement - how the assets move together

Correlation

takes covariance and measures its degree

Risk can totally be eliminated if correlation is?

-1

What do Markowitz differently when looking at risk?

He looked at investments together rather than alone and look at their co-movement

Correlation = 1

Investments move perfectly with each other

p = 0

Investments have no correlation

p = -1

investments move perfectly opposite of each other

correlation formula

COVijj/(oi)(oj)

What is the Markowitz efficient frontier

ITs a curve that gives you the highest possible return for a given level of risk

Why will investors chase the upper curve?

Because it gives more return for the same level of risk

How the actual graphs changed?

by changing the correlation the graphs change. At -1 they move opposite of each other, At 1 its a linear line, at 0 its a curve

What does the envelope curve show?

It shows every possible attainable set

What does the positive slope portion of the envelope curve?

It represents tha Markowitz efficient frontier → best/risk return portfolios

Where do the utility curve and the Markowitz efficiency curve connect?

They connect at the tangent point which is the optimal portfolio.

What is the optimal portfolio?

ITs the combo of the best portfolio(efficient frontier) and investors preferences(indifference curve)