The capital Asset pricing model

Question 1

What is realised return and what is the problem of it?

Answer 1

the return you have made after actually selling your stocks. You can only compute realised return after you know this year and next year returns.

Question 2

What is the formula for market risk premium (The market risk premium reflects the overall level of risk in the market and is determined by the supply and demand for capital. I) and expected excess return?

Answer 2

Question 3

How can we calculate the expected return of an asset over a long period of time when we don’t know the the probabilities

Answer 3

If we take a large number of observations then the average will converge to the expected return. This is called law of large numbers.

Question 4

What is the expected return of portfolio ( 2 asset case)?

Answer 4

Question 5

Remind us what short sale is and what is portfolio return?

Answer 5

f

Question 6

What is variance?

Answer 6

c

Question 7

What is the formula for covariance and correlation?

Answer 7

Question 8

Lets say a and b are constants, then what are the expected returns

Answer 8

Question 9

Lets say a and b are constants, then do the same thing for variances

Answer 9

Question 10

What is the variance of a portfolio 2 stock case?

Answer 10

similar to the last rule from last slide
covariance can also be written as correlation multiplied by the individual standard deviations.

Question 11

a Quick recap to portfolio theory, what are efficient portfolios?

Answer 11

The Efficient Frontier is a curve that represents the set of optimal portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given level of expected return. These portfolios are considered “efficient” because they provide the best risk-return trade-offs.

Question 12

What does this show?

Answer 12

essentially, when you add more and more assets, two your portfolio with negative correlation, the risk( SD) keeps going down and down, until a point where adding more assets doesn’t reduce your standard deviation that much, there is a certain amount of risk that cannot be diversified and this is systematic risk.

Question 13

What is the covariance between a risk free asset and an asset?

Answer 13

it is 0.(because the risk-free rate represents a safe investment with stable returns, while the asset’s returns fluctuate due to various risks)

Question 14

How comes the CML coincides with the efficient frontier? ( The CML does not coincide with the Efficient Frontier, but it is tangent to it at the Market Portfolio ( or only touches the tangency portfolio.)

Answer 14

it only works when the assumption of CAPM is true (

Question 15

What is the equation for the CML ( relationship between risk and return for a portfolio of investments that includes both risk-free assets and risky assets.) ?

Answer 15

Question 16

What is beta and why is it in CAPM investors demand a risk premium?

Answer 16

risk is measured by the beta coefficient,Beta is a measure of the systematic risk of an individual security or portfolio relative to the overall market A security with a higher beta is more volatile and therefore carries a higher level of systematic or market risk. As such, investors demand a higher return to compensate for the additional risk.

Question 17

Do investors care about variance of assets?

Answer 17

it contains idioscratic risk which can be diversified away when you construct portfolios, so investors care about the exposure to market risk which is beta!!

Question 18

So here if CAPM is true where should all stocks be?
Finish off this sentence If investors can borrow and lend then…

Answer 18

All stocks should be on the SML

Question 19

What is the formula for Beta of portfolio?

Answer 19

beta is a measure of systematic risk that indicates the volatility of an asset’s returns relative to the market as a whole. rb = rm.

Question 20

What is the method of ordinary least squares and what can it be used to calculate?

Answer 20

we can calculate Beta and alpha
The objective of OLS is to find the best-fitting line that minimizes the sum of the squared differences between the observed data points and the predicted values based on the linear model.

Question 21

So we use the method of ordinary least squares to calculate the coefficient Beta and alpha, so we want to now test these. how?

Answer 21

We test the hypothesis that alpha is = 0, for CAPM

Question 22

When you are asked to workout out volatility what do you work out?

Answer 22

the standard deviation.

Question 23

In CAPM what does the Market portfolio consist of ( assuming frictionless domestic market )?
In CAPM the market portfolio = what?

Answer 23

In the CAPM, the market portfolio is a hypothetical, well-diversified collection of all investable assets, weighted by their market value, representing optimal portfolio of all risky assets, offering the highest risk-adjusted return.

In CAPM the market portfolio = tangency portfolio

Question 24

What is the definition of CML AND SML what is their gradients?

Answer 24

The Capital Market Line (CML) is a line that represents the relationship between the expected return and the total risk (standard deviation) of a portfolio consisting of a risk-free asset and a market portfolio of risky assets. Gradient = Sharpe ratio

The Security Market Line (SML) is a line that represents the relationship between the expected return and the systematic risk (beta) of individual securities or portfolios in relation to the market portfolio within the context of the Capital Asset Pricing Model (CAPM). Gradient = beta ( in cape beta = 1)(Expected Return = Risk-Free Rate + β * (Market Return - Risk-Free Rate))

Question 25

What is the formula for variance when the risk of the asset is split into firm specific and idioscraytic risk? and answer this question? notice that if it asks about variance/sd of portfolio and gives you weights, don’t use this.

Answer 25

Question 26

What is the formula for the Standard deviation of Epsom? of a stock? ( rearrange the previous formula?

Answer 26