CAPM

Question 1

Relationship between risk and return

Answer 1

Positive relationship between risk and realized return: The more risky an asset (higher volatility (st. dev.)), the higher the realized returns.

Question 2

Individual stocks (risk and return)

Answer 2

Unlike the case for large portfolios, there is no precise relationship between volatility and average return for individual stocks. Individual stocks have higher volatility and lower average returns than the relationship shown for large portfolios. Hence, volatility does not explain returns of individual stocks.

Question 3

Return of equities

Answer 3

Equities were the best performing asset class everywhere. The long-term real equity return was typically at level of 3% to 6% per year.

Question 4

Relationship between risk premium and price

Answer 4

Inverse relationship between risk premium and price. Risky assets have relatively low price but a relatively higher expected return.

Question 5

Investors demand compensation for…

Answer 5

1. Abstaining from consuming today and waiting until tomorrow
2. Taking on risk - measured by the risk premium.

Question 6

Sources for Equity Risk Premium

Answer 6

1. Survey based premiums
2. Historical premiums
3. Implied premiums

Question 7

Skewness

Answer 7

A measure of symmetry, or more precisely, the lack of symmetry.
Positive - skewed right (right tail is heavier)
Negative - skewed left (left tail is heavier)

People like positive skew because it gives higher probability to end up in a positive area (investors are willing to pay premium for that).

Question 8

Kurtosis

Answer 8

A measure of whether the data are peaked or flat relative to a normal distribution.

High kurtosis - distinct peak near the mean, decline rather rapidly, and have heavy tails.
Low kurtosis - flat top near the mean rather than a sharp peak

Positive excess kurtosis - “peaked” distribution (leptokurtic -> K>3); return series characterized by jumps, daily returns.
Negative excess kurtosis - “flat” distribution (platykurtic -> K<3)

Question 9

Diversification

Answer 9

As long as asset returns are not perfectly correlated, the standard deviation (risk) of the portfolio is less than the weighted average of the assets standard deviations, diversification reduces variability of returns.

Question 10

Market risk

Answer 10

Economy-wide sources of risk that affect the overall stock market (reason why stocks have a tendency to move together - common factor affecting all stocks)
Systematic, non-diversifiable

Question 11

Unique risk

Answer 11

Risk factor affecting only that firm.

Non-systematic, idiosyncratic, diversifiable.

Question 12

DIversification

Answer 12

By forming portf. of more than one asset, some of the volatility (risk) of individual assets is diversified away. Sicne investors can diversify away some of the risk for free, they can rationally only demand compensation for the systematic risk they carry.

Question 13

Beta

Answer 13

The beta of individual security measures its sensitivity to market movements (marginal contribution to portfolio risk).

Beta-value for the risk free asset is zero since uncorrelated with the market portfolio.

Market portfolio perfectly correlated with itself.

The higher systematic risk - higher beta an asset has - the larger the expected return (positive relationship between systematic risk and expected return).

Investors are only compensated for the systematic risk as gauged by asset’s beta.

Question 14

DIstribution

Answer 14

Stock prices follow lognormal distribution.

Stock returns follow normal distribution.

Question 15

Efficient portfolio

Answer 15

Locus of all non-dominated portfolios in the mean-standard deviation space
By definition, no (“rational”) mean-variance investor would choose to hold a portfolio not located on the efficient frontier.

Question 16

Correlation and diversification benefits

Answer 16

Positive corr. - no diversification benefits

Negative corr. - a perfectly hedged position, no variance.

Question 17

Capital Market Line (CML)

Answer 17

The efficient frontier with risk-free asset. CML measures the trade-off between risk and return.
The tangency portfolio (T) is the optimal risky portfolio to mix with T-bills - steepest slope of CML.

Question 18

2-Fund Separability

Answer 18

1. Determination of the optimal risky portfolio (purely technical) - The CML.
2. Allocation between the optimal risky portfolio and T-bills (personal preferences).

Question 19

Security Market Line (SML)

Answer 19

A line drawn on a chart that serves as a graphical representation of CAPM. The x-axis represents risk in terms of beta. and the y-axis respresents expected return. Determines what is the fair return for any security.

Only marginal systematic risk as gauged by beta matters for risk premium.

Underpriced stocks - above the line.
Overpriced stocks - under the line.

Question 20

CAPM asusmptions

Answer 20

Investors:

1. Aim to maximize economic utilities (Asset quantities are given and fixed).
2. Are rational and risk-averse.
3. Are broadly diversified across a range of investments.
4. Are price takers, i.e., they cannot influence prices.
5. Can lend and borrow unlimited amounts under the risk free rate of interest.
6. Trade without transaction or taxation costs.
7. Deal with securities that are all highly divisible into small parcels (All assets are perfectly divisible and liquid).
8. Have homogeneous expectations.
9. Assume all information is available at the same time to all investors.

Question 21

Arbitrage Pricing Theory (APT)

Answer 21

If there is no arbitrage in the economy, then we can also price assets relative to one another based on their comovement with some factors. It is derived from a statistical model.

The total return on a security is equal to its expected return plus a “surprise” return component which is the reaction of the security to the unexpected changes in factors plus unique return.

Question 22

Evaluation of portfolio performance

Answer 22

The position of portfolio in ranking based on rate of return depends on

• risk level of portfolio
• performance of the market
• skill level of the portfolio manager

Question 23

Sharpe Ratio

Answer 23

Risk premium earned per unit of TOTAL risk.

Average return earned in excess of the risk free per unit of volatility. The greater the value of the Sharpe ratio. the more attractive the risk adjusted return.

STANDARD DEVIATION

Question 24

Treynor Index

Answer 24

Excess return to NON-DIVERSIFIABLE risk.

The higher the index, the greater the excess return being generated per unit of overall market risk.

Question 25

Modigliani & Modigliani Measure

Answer 25

We mix portfolio P with a position in T-bills so the complete or “adjusted” portfolio P* matches the volatility of market index.

Question 26

Jensen’s measure

Answer 26

The expected return of portfolio above its CAPM counterpart.

Question 27

Appraisal ratio (aka Info ratio)

Answer 27

Alpha divided by portfolio’s non-systematic risk.

Used to measure the quality of a fund manager’s investment picking ability. The ratio shows how many units of active return the manager is producing per unit of non-syst. risk.

Question 28

Treynor-Black Model

Answer 28

CAPM does not hold. Find the optimal active portfolio among limited number of securities.

Question 29

R2

Answer 29

The proportion if firm risk that can be attributed to market risk. Proportion of total firm risk explained by the market risk.