Portfolio Theories and Models

Question 1

Modern Portfolio Theory (MPT)

Answer 1

Theory based on research by Harry Markowitz and others. Created a model for investment.

seeks to create efficient portfolios by maximizing portfolio returns for a given or acceptable level of risk. The benefits of (low and negative) correlations between investments in the portfolio led to key characteristic of MPT being diversification. Efficiently constructed portfolios

You may maximize returns for a given level of risk or you may minimize risk for a target amount of return.

Question 2

Assumptions of MPT

Answer 2

Normal return distributions
Fixed asset correlations
Investors are rational
Investors are risk averse
Risk is known and constant
All information is public
No taxes or transactions costs

Question 3

Market Risk Premium

Answer 3

The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor: E(Rm)-Rf = A(SDm)^2

where (SDm)^2 is the variance of the market portolio and A is the average degree of risk aversion across investors

Question 4

The risk premium on individual securities

Answer 4

is a function of the individual security’s contribution to the risk of the market portfolio.

Question 5

Mean Variance Optimization

Answer 5

developed by Harry Markowitz and considered a core tenant of MPT, MVO is a quantitative model designed to select securities for inclusion in an “optimal” portfolio that maximizes return for a stated level of risk

Technically speaking, “Portfolios on the mean variance efficient frontier are found by searching for the portfolio with the least variance given some minimum return.”

Question 6

MVO inputs

Answer 6

• Inputs necessary:
Security’s expected returns
Expected risk (e.g., standard deviations)
Expected cross security correlations

Question 7

The Efficient Frontier

Answer 7

a set of optimal portfolios with the highest expected return for a set (or defined) amount or risk as measured by standard deviation

• theoretically demonstrates the best use of investment capital “IF” optimizing for risk adjusted return is the objective
• optimal portfolios that lie on the efficient frontier demonstrate more effective diversification

Question 8

Capital Allocation Line (CAL)

sometimes called the Capital Asset Line

Answer 8

• Defined: this line represents all possible combinations of risk free and risky assets; represents possible returns by taking on different levels of risk

CML (capital market line) is a special case of the capital allocation line (CAL) where the risk portfolio is the market portfolio.

Question 9

Criticisms of MPT

Answer 9

• Investment returns are not normally distributed
• Asset correlations are not fixed
• Investors are not rational
• behavioral economics
• technical analysis
• Investors are not exclusively risk averse
• Risk is not known and constant
• All information is not publicly known
• Taxes and transactions costs are real

Question 10

The slope of the CAL

Answer 10

If you choose the CAL with the highest slope, that is the Sharpe ratio of the portfolio

Question 11

A “kinked” CAL

Answer 11

indicates that:

a. leverage is being used, and
b. the rate to borrow exceeds the lending rate

Question 12

Markowitz Portfolio Selection Model - which portfolios to take on the efficient frontier?

Answer 12

All portfolios that lie on the minimum variance frontier from the global minimum variance portfolio and upward provide the best risk return combinations (don’t select portfolios on the lower portion of the parabola… duh)

Question 13

Markowitz Portfolio Selection Model

Answer 13

Everyone invests in P, regardless of their degree of risk aversion.
–More risk averse investors put more in the risk free asset.
–Less risk averse investors put more in P.

P is the Optimal Risky Portfolio

Question 14

Brinson Beebower & Hood (study)

Answer 14

1986 study of 91 of the largest pension funds
Conclusion: regarding the determinants of portfolio performance
–Asset allocation is the primary determinant of a portfolio’s return variability
–Security selection and market timing played only a minor role in portfolio performance

Question 15

The Black Litterman Model

Answer 15

• Created by Fischer Black and Robert Litterman
• Combines CAPM, MPT, and MVO
• Creates return forecasts that allows one to employ tactical asset allocation.
• Overcomes return sensitivity issues with prior models.
• Allows the user flexibility to change data (e.g., risk and return assumptions) and add more data points (e.g., asset classes, invest styles, etc.).
• Is subject to input error and faulty assumptions made by the user.

Question 16

Challenges to semi-strong efficient markets hypothesis

Answer 16

• P/E Effect
• Small Firm Effect (January Effect)
• Neglected Firm Effect and Liquidity Effects
• Book to Market Ratios
• Post Earnings Announcement Price Drift

Question 17

Capital asset pricing model (CAPM)

Answer 17

• a theoretical model that attempts to explain the relationship between risk and expected return
• the model holds that investors should be compensated for both the time value of money and risk taken
• It is the equilibrium model that underlies all modern financial theory
• Derived using principles of diversification with simplified assumptions
• Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

Question 18

Security Market Line (SML)

Answer 18

• the SML is a graphical expression of the CAPM
• the slope of the SML represents the market risk premium

Stocks plotted above the SML are undervalued; those under are overvalued

Question 19

Arbitrage Pricing Theory (APT)

Answer 19

• seeks to explain security returns beyond the usual metrics by introducing risk factors such as expected return, sector and systematic factors
• while far more expansive than CAPM given the flexibility of the model, it is limited in accuracy because it cannot measure unanticipated changes in the variables

Question 20

Arbitrage Pricing Theory Assumptions

Answer 20

• Does not require an expected market return.
• Uses the asset’s expected return and the risk premium of a number of macro economic factors.
• Arbitrageurs use APT to buy underpriced assets and short those that are overvalued.

Question 21

More on APT

Answer 21

• Equilibrium means no arbitrage opportunities.
• APT equilibrium is quickly restored even if only a few investors recognize an arbitrage opportunity.
• Predicts asset returns through a linear combination of many different independent macro economic variables

Question 22

Fama French Type Factor Models

Answer 22

• Market (aka: equity) premium
• Size and book to market ratios explain returns on securities.
• High book to market firms experience higher returns (value style)
• Smaller firms experience higher returns.
Momentum is a fourth factor

Question 23

The Minimum Variance Portfolio

Answer 23

• The minimum variance portfolio is the portfolio composed of the risky assets that has the smallest standard deviation, the portfolio with least risk.
• When correlation is less than +1, the portfolio standard deviation may be smaller than that of either of the individual component assets.
• When correlation is -1, the standard deviation of the minimum variance portfolio is zero. Given Corr -1 you can find the portfolio weightings WeightA = SD(B)/(SD(A) + SD(B))

Question 24

Value at Risk (VaR)

Answer 24

VaR is a measure of risk that quantifies potential loss (e.g., $1 million), the probability of the potential loss (e.g., 3%), and the time frame for potential loss (e.g., three months)
• Assumes market to market pricing, no trading, and normal market conditions.
• A measure of loss most frequently associated with extreme negative returns

Question 25

Expected Shortfall (ES)

Answer 25

• Also called conditional tail expectation (CTE)
• More conservative measure of downside risk than VaR
–VaR takes the highest return from the worst cases
–ES takes an average return of the worst cases