Flashcards in BKM Chapter 7 Deck (25)

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1

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

(BKM - 7)

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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

2

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Main sources of uncertainty (2) - description & examples

(BKM - 7)

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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

3

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Insurance principle

(BKM - 7)

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

4

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Efficient portfolios

(BKM - 7)

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

5

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Expected return for the complete portfolio

(BKM - 7)

### weighted sum of expected returns

6

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Variance of the complete portfolio

(BKM - 7)

### = sum from i to n sum from j to n of w(i) * w(j) * Cov(r(i), r(j))

7

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Diversification benefit

(BKM - 7)

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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

8

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

(BKM - 7)

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

9

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Hedge asset

(BKM - 7)

### asset that has a negative correlation with other portfolio assets

10

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Diversification benefit with perfect correlation (rho = 1)

(BKM - 7)

### no diversification benefit, all risk is systematic risk

11

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Perfect hedge

(BKM - 7)

### perfect negative correlation (rho = -1)

12

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Optimal weights for 2 risky assets in the optimal risky portfolio

(BKM - 7)

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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

13

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Separation property (2)

(BKM - 7)

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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)

14

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Risk pooling (aka insurance principle)

(BKM - 7)

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

15

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Risk-sharing

(BKM - 7)

### allowing other investors to share the risk for a portfolio

16

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Risk-pooling, risk-sharing, and risk reduction

(BKM - 7)

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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)

17

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

(BKM - 7)

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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

18

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Optimization considerations (3)

(BKM - 7)

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1. whether shorting is permitted

2. minimum dividend yield

3. exclude ethically or politically controversial investments

19

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Minimum variance risky portfolio weights

(BKM - 7)

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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)

20

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Goal of the optimal risky portfolio vs. minimum variance portfolio

(BKM - 7)

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optimal risky portfolio: maximize the Sharpe ratio

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

21

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Time diversification myth

(BKM - 7)

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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

22

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

(BKM - 7)

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

n = # of securities

23

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Systematic risk for an equally weighted portfolio of n securities

(BKM - 7)

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systematic risk = rho * sigma^2

*does not depend on n

24

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

(BKM - 7)

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firm-specific risk = total risk - systematic risk

"risk" = variance

25