BKM Chapter 7

Question 1

Reasons investors distinguish between asset allocation & security selection (3)

(BKM - 7)

Answer 1

1. demand for investment mgmt has increased over time
2. financial markets have become too sophisticated for amateur investors
3. economies of scale in investment analysis

Question 2

Main sources of uncertainty (2) - description & examples

BKM - 7

Answer 2

1. systematic - risks common to all stocks, including: inflation, interest, and foreign exchange rates (aka non-diversifiable)
2. non-systematic - risks from firm-specific influences such as firm sucess in R&D and personnel changes

Question 3

Insurance principle

BKM - 7

Answer 3

risk reduction from spreading exposures across many independent risk sources (eliminates firm-specific risk)

Question 4

Efficient portfolios

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Answer 4

risky portfolios with the maximum expected return for a given level of risk

Question 5

Expected return for the complete portfolio

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Answer 5

weighted sum of expected returns

Question 6

Variance of the risky portfolio

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Answer 6

= double sum of w(i) * w(j) * Cov(r(i), r(j))

Question 7

Diversification benefit

BKM - 7

Answer 7

as long as correlation (rho) <> 0, then the standard deviation of the total portfolio is < the weighted average standard deviations of the individual assets

there is no diversification benefit if rho = 1

Question 8

Cov(r(i), r(j))

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Answer 8

Cov(r(i), r(j)) = rho(i,j) * sigma(i) * sigma(j)

Question 9

Hedge asset

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Answer 9

asset that has a negative correlation with other portfolio assets

Question 10

Diversification benefit with perfect correlation (rho = 1)

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Answer 10

no diversification benefit, all risk is systematic risk

Question 11

Perfect hedge

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Answer 11

perfect negative correlation (rho = -1)

Question 12

Optimal weights for 2 risky assets in the optimal risky portfolio

(BKM - 7)

Answer 12

w(D) = {E[R(D)] * sigma^2(E) - E[R(E)] * Cov (R(D), R(E))} / {[E[R(D)] * sigma^2(E) + E[R(E)] * sigma^2(D) - (E[R(D)] + E[R(E))] * Cov(R(D), R(E))}

w(E) = 1 - w(D)

D = debt (bonds) 
E = equity (stocks) 
R = excess return

apply w(D) and w(E) to y* (% in risky portfolio) to get weights for individual assets relative to the total portfolio

Question 13

Separation property (2)

BKM - 7

Answer 13

portfolio choice comes down to:

1. determining the optimal risky portfolio (objective - same portfolio for every investor)
2. determining the proper capital allocation (amount allocated to risk-free vs. risky portfolio) based on investor’s risk aversion (subjective - different portfolio for every investor)

Question 14

Risk pooling (aka insurance principle)

BKM - 7

Answer 14

adding uncorrelated risky projects to a portfolio (spreading exposures across uncorrelated projects)

Question 15

Risk-sharing

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Answer 15

allowing other investors to share the risk for a portfolio

Question 16

Risk-pooling, risk-sharing, and risk reduction

BKM - 7

Answer 16

risk-pooling by itself does not reduce risk, but does improve the Sharpe ratio

combining risk-pooling and risk-sharing reduces risk (b/c the total size of the portfolio is unchanged vs. adding risks and increasing the investment)

Question 17

Markowitz portfolio optimization model (3 + 2 sub-steps)

BKM - 7

Answer 17

1. determine available risk-return opportunities
   a. create input list of expected returns, variances, and covariance estimates
   b. optimization model finds the efficient frontier
2. find the CAL that maximizes the Sharpe ratio
3. identify the optimal mix b/w the optimal risky portfolio & risk-free asset

Question 18

Optimization considerations (3)

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Answer 18

1. whether shorting is permitted
2. minimum dividend yield
3. exclude ethically or politically controversial investments

Question 19

Minimum variance risky portfolio weights

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Answer 19

w(D) = [sigma^2(E) - Cov(r(D), r(E))] / [sigma^2(E) + sigma^2(D) - 2 * Cov(r(D), r(E))]

w(E) = 1 - w(D)

Question 20

Goal of the optimal risky portfolio vs. minimum variance portfolio

(BKM - 7)

Answer 20

optimal risky portfolio: maximize the Sharpe ratio

minimum variance risky portfolio: minimize overall variance (may produce a lower, less attractive Sharpe ratio)

Question 21

Time diversification myth

BKM - 7

Answer 21

risk is not reduced by spreading investments across time

instead, it is preferable to invest in an efficient portfolio over many periods, reducing the amount in the risky asset in each period

Question 22

Total variance for an equally weighted portfolio where all securities share the same sigma & correlation

(BKM - 7)

Answer 22

sigma^2(p) = (1 / n) * sigma^2 + ((n - 1) / n) * rho * sigma^2

n = # of securities

Question 23

Systematic risk for an equally weighted portfolio of n securities

(BKM - 7)

Answer 23

systematic risk = rho * sigma^2

*does not depend on n

Question 24

Firm-specific risk for an equally weighted portfolio of n securities

(BKM - 7)

Answer 24

firm-specific risk = total risk - systematic risk

“risk” = variance

Question 25

Correlation and risk as the number of securities increases

BKM - 7

Answer 25

when rho > 0, as n increases, portfolio risk approaches systematic risk (firm-specific risk is diversified away)

when rho = 0, as n increases, portfolio risk approaches 0 (there is no systematic risk & all firm-specific risk is diversified away)