Lecture 3

Question 1

What is the market portfolio?

Answer 1

The market portfolio (M) is obtained if we aggregate all the identical risky portfolios. M contains all securities in the market in proportions equal to their market values

Question 2

How does the CAL become the CML?

Answer 2

Because the optimal risky portfolio simply is a small share of the market portfolio, if we take all opt. risky portfolios and aggregate them we move from the CAL to CML

Question 3

What is the CML formula?

Answer 3

σc is σ of the complete portfolio (partly risk-free, partly market portfolio)

Question 4

Why is it efficient to invest in a market index fund and a risk-free asset?

Answer 4

1. Because the market portfolio already reflects all the relevant information - M is based on the aggregation of all investors’ input lists and captures the risk-return characteristics of the entire market. This means that all publicly available information is already incorporated into M. Therefore, investors do not need to conduct individual security analysis.

Question 5

What are the key assumptions under the mutual fund theorem?

Answer 5

Investors are rational, mean-variance optimizers and have homogeneous
expectations (i.e. the same input lists).

All stocks are publicly available, short positions are allowed, borrowing
and lending are allowed.

All information is publicly available, there are no taxes and transaction costs.

Question 6

CAPM formula - portfolio

Answer 6

Question 7

What is the security market line?

Answer 7

Security Market Line (SML) is the linear expected return-beta relationship.
Stock’s beta measures its contribution to the variance of the market portfolio. CAPM implies that the required risk premium for the security is proportional to both the beta and the risk premium of the market portfolio.

Question 8

Please distinguish between the SML and CML

Answer 8

CML – plots risk premiums of efficient portfolios (P + F) as a function of standard deviation. SD is a valid measure of risk since P is a well-diversified portfolio.

SML – plots individual asset risk premiums as a function of asset risk (beta). Individual asset risk is its contribution to portfolio variance, measured by beta.

Question 9

How does the SML indicate whether securities are over- or undervalued?

Answer 9

The SML displays the level of systemic (market) risk commensurate with return. Individual stocks can be plotted. Stocks on this line are ‘fairly priced’.

Shares that are not on this line are either undervalued or overvalued, represented by their alpha

Question 10

According to CAPM, please state the following:
Expected return
Total risk
cov(Ri,Rj)
cov(Ri,Rm)

Answer 10

Question 11

What does each element represent?

Answer 11

1/n∑αi:The average alpha, representing the abnormal (non-market) returns of the stocks in the portfolio

Beta: The contribution of the market return, weighted by the average beta of the portfolio.

Error term: The average of the firm-specific shocks (random errors or idiosyncratic returns).

Question 12

What is the formula for total risk under CAPM?

Answer 12

Question 13

Covariance between two assets

Answer 13

Question 14

Covariance between single asset and the market

Answer 14

Question 15

Correlation between two assets

Answer 15

Question 16

What happens to firm-specific variance as we approach zero?

Answer 16

It tends to 0 as N–> infinity

Question 17

Please explain and provide the formula for the information ratio

Answer 17

It measures the extra return an
investor can get from security analysis per unit of firm-specific risk incurred
when securities are under- or overweighted relative to the passive portfolio. Maximizing this ratio means maximizing the overall Sharpe ratio.

Question 18

What are the three key assumptions of the multi-factor APT?

Answer 18

1. Returns exhibit a factor structure (asset returns are influenced by multiple systemic factors)
2. Markets are well-functioning, any investor can take a sufficiently large position to move prices back to “non-arbitrage condition” irrespective of risk aversion
3. Well-diversified portfolios are available (Investors can form portfolios that diversify away idiosyncratic (firm-specific) risk, leaving only exposure to systematic risks.)