Flashcards in BKM Chapter 8 Deck (33)

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1

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Drawbacks to the Markowitz Optimization Model (3)

(BKM - 8)

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1. model requires a large number of estimates for the input list

2. requires accurate correlations for covariance calculations - poor estimates could lead to nonsensical results

3. Does not provide guidance for forecasting security risk premiums to construct the efficient frontier of risky assets

2

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Total number of estimates needed for the Markowitz Optimization Model input list

(BKM - 8)

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n estimates of expected return

+ n estimates of variances

+ (n^2 - n) / 2 estimates of covariances

n = # of securities in the portfolio

3

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Single-factor model return (r(i))

(BKM - 8)

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r(i) = E[r(i)] + beta(i) * M + e(i)

beta(i) = firm-sensitivity to market index

M = uncertainty about the economy (systematic uncertainty)

e(i) = firm-specific (non-systematic) uncertainty

4

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Relationship between market uncertainty (M) and firm-specific uncertainty (e(i)) in a single-factor model

(BKM - 8)

### M and e(i) are assumed to be uncorrelated and E[M] = E[e(i)] = 0

5

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Variance of the single-factor model and single-index model (sigma^2(i))

(BKM - 8)

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sigma^2(i) = beta(i)^2 * sigma^2(M) + sigma^2(e(i))

where beta(i)^2 * sigma^2(M) = systematic risk and

sigma^2(e(i)) = firm-specific risk

firm-specific risk goes to 0 with diversification

6

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Cov(r(i), r(j)) in a single-factor model and single index model

(BKM - 8)

### Cov(r(i), r(j)) = beta(i) * beta(j) * sigma^2(M)

7

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Difference between the single-factor model and the single-index model

(BKM - 8)

### the single-index model uses the rate of return on a broad market index as a proxy for the systematic factor (M)

8

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Single-index model (R-i(t))

(BKM - 8)

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R-i(t) = alpha-i + beta-i * R-M(t) + e-i(t)

R-i(t) = firm's excess returns

t = month of return

9

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Independence assumption of the single-index model

(BKM - 8)

### assumes securities are independent

10

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Security characteristic line (SCL)

(BKM - 8)

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regression line that plots excess monthly returns for the security on the y-axis and excess monthly returns for the market index on the x-axis

the line has slope = beta-i and intercept = alpha-i

11

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Interpretation of alpha

(BKM - 8)

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security's expected excess return when the market return = 0 (e.g. non-market risk premium)

alpha > 0 means the security is underpriced

positive alpha values are more attractive

negative alpha values should be shorted (if allowed)

12

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Interpretation of beta

(BKM - 8)

### amount security return changes for every 1% increase in return on the index (e.g. sensitivity to the market index)

13

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Interpretation of the firm-specific surprise (e(i))

(BKM - 8)

### firm-specific unexpected variation in security return (aka residual)

14

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Beta values

(BKM - 8)

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beta > 1 = cyclical/aggressive stocks (high sensitivity to macroeconomy)

beta < 1 = defensive stocks (low sensitivity to macroeconomy)

avg beta of all stocks = beta of market index = 1

15

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Expected excess return for the single-index model (E[R(i)])

(BKM - 8)

### E[R(i)] = alpha(i) + beta(i) * E[R(M)]

16

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Number of estimates needed for the single-index model input list

(BKM - 8)

###
n estimates of alpha values

+ n estimates of beta values

+ n estimates of firm-specific variances (sigma^2(e(i)))

+ 1 estimate of market risk premium (E[R(M)])

+ 1 estimate of the variance for the common macroeconomic factor (sigma^2(M))

= 3n + 2 total estimates

17

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Interpretation of R^2 in regression output and formula

(BKM - 8)

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% of variation in excess returns that is explained by market factors

R^2 = systematic variance / total variance

18

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Adjusted R^2

(BKM - 8)

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R^2(A) = 1 - (1 - R^2) * (n - 1) / (n - k - 1)

k = # of independent variables

corrects for bias from estimated slope (beta) and intercept (alpha) parameters

19

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Meaning of standard error for the regression and parameter estimates of regression output

(BKM - 8)

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regression: high standard error means firm-specific events have a larger impact (aka residual std. dev)

parameter estimates: a measure of imprecision/estimation error

20

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T-statistic formula and meaning of regression output

(BKM - 8)

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t-stat = (estimated value - hypothesized value) / standard error

used to test null that beta = 1

reveals the # of standard errors by which the estimate exceeds 0

21

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Interpretation of the p-value in regression output

(BKM - 8)

### level of significance = probability of an estimate as large as the given coefficient if the true parameter = 0

22

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Reasons beta tends to 1 over time (2)

(BKM - 8)

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1. new firms are unconventional but eventually resemble the rest of the economy

2. average beta over all securities = 1

23

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Adjusted beta

(BKM - 8)

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Adjusted beta = (2/3) * estimated beta + (1/3) * 1

(kind of like a credibility weighted beta with 1/3 weight to the average beta for the market

24

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Most predictive variables for betas (6)

(BKM - 8)

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1. variance of earnings

2. variance of cash flow

3. growth in earnings per share

4. market capitalization (firm size)

5. dividend yield

6. debt-to-asset ratio

25

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Components of the optimal risky portfolio (2)

(BKM - 8)

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1. active portfolio (A) - made up of n analyzed securities

2. passive portfolio (M) - market-index portfolio - used to aid in diversification

26

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Relationship between Sharpe ratio of an optimally constructed risky portfolio (S(P)) and the Sharpe ratio of the index portfolio (S(M))

(BKM - 8)

### S(P)^2 = S(M)^2 + (information ratio(A))^2

27

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Information ratio

(BKM - 8)

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information ratio = alpha(i) / sigma(e(i))

the contribution of each security is the square of its own information ratio (e.g. information ratio(A)^2 = sum of information ratio(security)^2)

28

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Advantages of the single-index model over the Markowitz Optimization Model (2)

(BKM - 8)

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1. saves time b/c fewer estimates are required

2. allows for specialization in security analysis (without calculating the covariance b/w industries)

29

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Disadvantages of the single-index model over the Markowitz Optimization Model (2)

(BKM - 8)

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1. oversimplifies uncertainty by splitting it into broad categories of micro or macro risk (vs. full covariance matrix with covariances b/w all securities)

2. can produce an inferior optimal portfolio if correlated stocks make up a large part of the portfolio (because of independence assumption)

30