BKM 6-8: Portfolio Theory

Question 1

Risk premium

Answer 1

Expected return in excess of the risk-free rate

Question 2

Utility function

Answer 2

Question 3

Risk-averse

Answer 3

A > 0

Question 4

Risk-neutral

Answer 4

A = 0

Question 5

Risk-seeking

Answer 5

A < 0

Question 6

Mean-Variance Criterion

Answer 6

Portfolio A is preferred to portfolio B if the expected return of A >= expected return of B and risk of A <= risk B

Question 7

Certainty-equivalent rate

Answer 7

Rate of return that would cause the investor to be indifferent between risky and risk-free investment

Question 8

Indifference curve

Answer 8

X: standard deviation, Y: expected return

Question 9

Expected return of complete portfolio (1 risky, 1 risk free)

Answer 9

Question 10

Standard deviation of complete portfolio (1 risky, 1 risk free)

Answer 10

Question 11

Capital allocation line (CAL)

Answer 11

Combinations of risk (x-axis) and expected return (y-axis) for complete portfolio: y-intercept: SD = 0 other point: y = 1

Question 12

Sharpe ratio

Answer 12

Slope of the CAL Also called reward-to-risk ratio

Question 13

Weight on risky portfolio, based on risk tolerance, in complete portfolio (1 risky, 1 risk free)

Answer 13

Question 14

Capital Market Line

Answer 14

If risky asset is based on a broad index of common stocks (i.e. S&P 500) within a complete portfolio

Question 15

Passive strategies (Indexing)

Answer 15

Choosing a risky portfolio to be large, well-diversified (i.e. S&P 500)

Question 16

Why passive strategies make sense

Answer 16

Minimizes cost of information acquisition

Takes advantage of everyone else’s efforts to do so

Question 17

Criticisms of passive strategies

Answer 17

Undiversified Top Heavy Chasing Performance You can do better (few active fund managers beat indices)

Question 18

Portfolio variance with two risky assets

Answer 18

Question 19

Risk and return, correlation = 1

Answer 19

Straight line

Question 20

Risk and return, correlation = -1

Answer 20

Kinked line (sideways V) Will intercept y-axis

Question 21

Minimum variance portfolio

Answer 21

Portfolio with the lowest variance that can be constructed from assets with a certain level of correlation

Question 22

Optimal risky portfolio

Answer 22

Risky portfolio that produces the line tangent to the portfolio opportunity set

Question 23

Hedge Asset

Answer 23

Has negative correlation with other assets in the portfolio

Question 24

Minimum variance portfolio weight on A

Answer 24

Question 25

When correlation between assets = -1

Answer 25

Perfectly hedged position can be obtained by setting weighted SDs equal to each other

Question 26

Minimum variance portfolio SD

Answer 26

Must be smaller than that of either of the individual component assets

Question 27

Diversification and correlation of assets

Answer 27

Lower correlation, diversification is more effective and portfolio risk is lower

Question 28

Weights of optimal risky portfolio

Answer 28

Question 29

Steps to arrive at complete portfolio

Answer 29

1. Specify returns, variances, covariances 2. Calculate optimal risky portfolio weights 3. Allocate weights to optimal risky portfolio 4. Calculate y\* 5. Distribute y\* to weights of risky portfolio, (1 - y\*) to risk-free

Question 30

Minimum-variance frontier

Answer 30

Lowest possible variance that can be attained for a given portfolio expected return

Question 31

Graph of: CAL Indifference curve Optimal risky portfolio Complete portfolio Portfolio opportunity set

Answer 31

Question 32

Socially responsible investing

Answer 32

Cost of lower Sharpe ratio justifiably viewed as a contribution to underlying cause

Question 33

Separation property

Answer 33

Two tasks: 1. Determine optimal risky portfolio (technical) 2. Capital allocation based on risk preference

Question 34

Market vs. Firm-specific risk (graph)

Answer 34

Question 35

Equally weighted portfolio variance

Answer 35

First term can be diversified away (firm-specfic risk) Second term depends on covariances between returns (market risk)

Question 36

Risk pooling

Answer 36

Merging uncorrelated, risky projects as a means to reduce risk

Question 37

Results of pooling uncorrelated risks

Answer 37

Question 38

Issues with risk pooling

Answer 38

Probability of loss declines, but overall standard deviation increases; does not allow shedding of risk

Question 39

Risk sharing

Answer 39

Act of selling shares in an attractive risky portfolio to limit risk and maintain Sharpe ratio of resulting position

Question 40

Risk sharing results, two uncorrelated assets

Answer 40

Pool tow assets and sell off half of combined portfolio

Question 41

Two factors dampening process of risk sharing in insurance

Answer 41

Managing very large firms comes at a risk Misestimating correlations can cause failure

Question 42

Extending investment horizons for risk

Answer 42

Investing completely in risky asset for both periods analagous to risk pooling; investing half in risky asset for each period analogous to risk sharing

Question 43

Issues with Markowitz model

Answer 43

Requires (n² +3n)/2 total estimates Errors in estimation of correlations can lead to nonsensical results

Question 44

Decomposing rate of return

Answer 44

Question 45

Single-factor model

Answer 45

Question 46

Total risk of a security

Answer 46

Question 47

Single-factor model, systematic risk of a security

Answer 47

Question 48

Covariance between any pair of securities

Answer 48

Question 49

Regression equation of single-index model

Answer 49

Question 50

Single-index model

Answer 50

Uses market index to proxy for the common factor

Question 51

Number of single index model estimates

Answer 51

n estimates of alpha n estimates of beta n estimates of firm-specific variances 1 estimate for market risk premium 1 estimate for variance of common factor

Question 52

Security characteristic model

Answer 52

Straight line with intercept alpha and slope beta for a given security

Question 53

Alpha

Answer 53

Nonmarket premium

Question 54

Issues with relying on alpha

Answer 54

Past does not readily fortell the future; no correlation between estimates of one sample period to the next

Question 55

Hierarchy of preparation of input list for single-index

Answer 55

1. Macroeconomic analysis (risk premium) 2. Statistical analyses (betas, residual variances) 3.

Question 56

Initial weight in active portfolio, single-index model

Answer 56

Question 57

Final weight in active portfolio, single-index model

Answer 57

Question 58

Information ratio

Answer 58

The contribution of the active portfolio to the Sharpe ratio of the overall risky portfolio

Question 59

Sharpe ratio of an optiamally constructed risky portfolio

Answer 59

Question 60

Adjusted beta

Answer 60

2/3\*sample beta + 1/3 As firm becomes more conventional, it will tend toward 1

Question 61

Variables that help predict betas

Answer 61

Variance of earnings Variance of cash flow Growth in earnings per share Firm size Dividend yield Debt-to-Asset ratio

Question 62

Tracking portfolio

Answer 62

Designed to match the systematic component of a portfolio; must have same beta on index portfolio as P and as little firm risk as possible Also called beta capture

Question 63

Alpha transport

Answer 63

Separating search for alpha from the choice of market exposure

Question 64

σ²(e_P), formula

Answer 64

Σw_i²σ²(e_i)