Tutorial 8: Portfolio Allocation II:CAPM

Question 1

What’s the difference between an Efficient frontier than considers risk-free assets versus one that doesn’t?

Answer 1

See slides 4 & 5

In case of one risk-free and one risky asset, the efficient frontier is a straight upward sloping line. (CAPITAL ALLOCATION LINE; CAL)

Question 2

CAPM

Central question: What happens if we have many investors and bring them together in a capital market?

Answer 2

CAPM introduces the idea of equilibrium –>

telling us which asset prices will result if the market participants invest in efficient Markowitz portfolios

According to the CAPM, the market portfolio = the tangency portfolio in equilibrium

Question 3

Assumptions of the CAPM: what are the four of them?

Answer 3

Investors have:
- mean variance preferences
- same beliefs about the distribution from which returns are drawn
- common investment horizon
&& no costs to trading in financial markets; easy to go short; all investors can borrow and lend at the risk-free rate

Question 4

The CML - Capital Market Line

Write down the equations for the CML and the Sharpe ratio.

Answer 4

CML: risk is defined as total risk and measured by standard deviation (see slide 9 for graph)

For all efficient portfolios, the normalised risk premium is the same in equilibrium.

E[Rp] = risk-free + (E[Rm] - riskfree) * SR

SR :::
(E[Rportfolio] - risk free) / std(portfolio) = E[Rmarket] - riskfree/std (mkt)

Question 5

The SML - Security Market Line

Define it. Write its equation.

Answer 5

SML: Risk is defined as systematic risk and measured by beta
The beta of asset D with respect to the market portfolio: INSERT FORMULA

Ri = Rf + ß (Rm-Rf)

Shows the linear relationship between asset risk and its expected return

Question 6

Systematic risk of beta ß

ß = (std D/ std mkt) * correlation btw m & D

How could those terms be interpreted?

Answer 6

std D/ std mkt = How much riskier is D relative to the mkt portfolio?

correlation btw m & D = how much of the risk of D is relevant in the market portfolio

Question 7

The risk of a stock can be separated inti a systematic and a non-systematic component.

Answer 7

• write in the formula sheet*
  slide 11
  Systematic risk is linear in beta
  Idiosyncratic risk depends negatively on the correlation coefficient of stock returns with market returns

Question 8

Relationship between CML & SML

Answer 8

• write in the formula sheet*

The risk premium per unit risk for a single asset is equal to the market’s portfolio risk premium per unit risk (SR) * coefficient of correlation

ie Sharpe ratio D = Sharpe Ratio M * Corr. M&D