高级财管考点总结

高级财管考点总结

计算题（50分）

10.1 a. Expected Return = (0.1)(-0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207)

= 0.1057

= 10.57%

The expected return on Q-mart’s stock is 10.57%.

b. Variance (σ2) = (0.1)(-0.045 – 0.1057)2 + (0.2)(0.044 – 0.1057)2 + (0.5)(0.12 – 0.1057)2 +

(0.2)(0.207 – 0.1057)2

= 0.005187

Standard Deviation (σ) = (0.005187)1/2

= 0.0720

= 7.20%

The standard deviation of Q-mart’s returns is 7.20%.

10.2 a. Expected Return A = (1/3)(0.063) + (1/3)(0.105) + (1/3)(0.156)

= 0.1080

= 10.80%

The expected return on Stock A is 10.80%.

Expected Return B = (1/3)(-0.037) + (1/3)(0.064) + (1/3)(0.253)

= 0.933

= 9.33%

The expected return on Stock B is 9.33%.

b. Variance A (σA2) = (1/3)(0.063 – 0.108)2 + (1/3)(0.105 – 0.108)2 + (1/3)(0.156 – 0.108)2

= 0.001446

Standard Deviation A (σA) = (0.001446)1/2

= 0.0380

= 3.80%

The standard deviation of Stock A’s returns is 3.80%.

Variance B (σB2) = (1/3)(-0.037 – 0.0933)2 + (1/3)(0.064 – 0.0933)2 + (1/3)(0.253 – 0.0933)2

= 0.014447

Standard Deviation B (σB) = (0.014447)1/2

= 0.1202

= 12.02%

The standard deviation of Stock B’s returns is 12.02%.

C .Covariance(R A, R B) = (1/3)(0.063 – 0.108)(-0.037 – 0.0933) + (1/3)(0.105 – 0.108)(0.064 –

0.933) + (1/3)(0.156 – 0.108)(0.253 – 0.0933)

= 0.004539

The covariance between the returns of Stock A and Stock B is 0.004539.

Correlation(R A,R B) = Covariance(R A, R B) / (σA * σB)

= 0.004539 / (0.0380 * 0.1202)

= 0.9937

The correlation between the returns on Stock A and Stock B is 0.9937.

10.3 a. Expected Return HB = (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154)

= 0.0733

= 7.33%

The expected return on Highbull’s stock is 7.33%.

Expected Return SB = (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074)

= 0.0608

= 6.08%

The expected return on Slowbear’s stock is 6.08%.

b. Variance A (σHB2) = (0.25)(-0.02 – 0.0733)2 + (0.60)(0.092 – 0.0733)2 + (0.15)(0.154 –

0.0733)2

= 0.003363

Standard Deviation A (σHB) = (0.003363)1/2

= 0.0580

= 5.80%

The standard deviation of Highbear’s stock returns is 5.80%.

Variance B (σSB2) = (0.25)(0.05 – 0.0608)2 + (0.60)(0.062 – 0.0608)2 + (0.15)(0.074 –

0.0608)2

= 0.000056

Standard Deviation B (σB) = (0.000056)1/2

= 0.0075

= 0.75%

The standard deviation of Slowbear’s stock returns is 0.75%.

c. Covariance(R HB, R SB) = (0.25)(-0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 –

0.0733)(0.062 – (0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608)

= 0.000425

The covariance between the returns on Highbull’s stock and Slowbear’s stock is

0.000425.

Correlation(R A,R B) = Covariance(R A, R B) / (σA * σB)

= 0.000425 / (0.0580 * 0.0075)

= 0.9770

The correlation between the returns on Highbull’s stock and Slowbear’s stock is

0.9770.

10.4Value of Atlas stock in the portfolio = (120 shares)($50 per share)

= $6,000

Value of Babcock stock in the portfolio= (150 shares)($20 per share)

= $3,000

Total Value in the portfolio= $6,000 + $3000

= $9,000

Weight of Atlas stock = $6,000 / $9,000

= 2/3

The weight of Atlas stock in the portfolio is 2/3.

Weight of Babcock stock = $3,000 / $9,000

= 1/3

The weight of Babcock stock in the portfolio is 1/3.

11.1 Real GNP was higher than anticipated. Since returns are positively related to the level

of GNP, returns should rise based on this factor.

Inflation was exactly the amount anticipated. Since there was no surprise in this announcement, it will not affect Lewis-Striden returns.

Interest Rates are lower than anticipated. Since returns are negatively related to

interest rates, the lower than expected rate is good news. Returns should rise due to interest rates.

The President’s death is bad news. Although the president was expected to retire, his

retirement would not be effective for six months. During that period he would still contribute to the firm. His untimely

death mean that those contributions would not be made. Since he was generally considered an asset to the firm, his death will cause returns to fall.

The poor research results are also bad news. Since Lewis-Striden must continue to

test the drug, it will not go into production as early as expected. The delay will affect expected future earnings, and thus it will dampen returns now.

The research breakthrough is positive news for Lewis Striden. Since it was

unexpected, it will cause returns to rise.

The competitor’s announcement is also unexpected, but it is not a welcome surprise.

This announcement will lower the returns on Lewis-Striden.

Systematic risk is risk that cannot be diversified away through formation of a portfolio. Generally, systematic risk factors are those factors that affect a large number of firms in the market, however, those factors will not necessarily affect all firms equally. The systematic factors in the list are real GNP, inflation and interest rates.

Unsystematic risk is the type of risk that can be diversified away through portfolio formation. Unsystematic risk factors are specific to the firm or industry. Surprises in these factors will affect the returns of the firm in which you are interested, but they will have no effect on the returns of firms in a different industry and perhaps little effect on other firms in the same industry. For Lewis-Striden, the unsystematic risk factors are the president’s ability to contribute to the firm, the research results and the competitor.

11.2 a. Let m = systematic risk portion of return:

()()()112233

0.0424,480-4,416 1.4 4.3%-3.1%-0.6711.8%-9.5%0.53%

m F F F βββ=?+?+?=-=

b. Let ε= the unsystematic portion of risk, since the news was only about this firm:

2.6%

ε=-

c. Total Return = Expected return, plus 2 the components of unexpected return: the

systematic risk portion of return and the unsystematic portion:

9.5%.53% 2.6%6.37%

R R m ε

=++=--=

11.3 a. Let m = systematic risk portion of return:

()()2.04 4.8% 3.5% 1.415.2%14.0%0.372%

m =---=

b. Let ε= the unsystematic portion of risk:

()0.36%27231.44%

ε=-=

c. Total Return:

10.0%0.37% 1.44%11.81%

R R m ε

=++=++=

11.4 a. The market model is specified by :

()m m R R R R β

ε

=+-+

so applying that to each Stock:

Stock A:

()()10.5% 1.214.2%A A A m m A

m A

R R R R R βεε=+-+=+-+

Stock B:

()()13.0%0.9814.2%B B m m B

m B

R R R R R βεε=+-+=+-+

Stock C:

()15.7% 1.37(14.2%)C C C m m C

m C

R R R R R βεε=+-+=+-+

b. Since we don't have the actual market return or unsystematic risk, we will get a

formula with those values as unknowns:

()()()()()()()()(){}()0.300.450.250.3010.5% 1.214.2%0.4513.0%0.9814.2%0.2515.7% 1.3714.2%0.3010.5%0.4513%0.2515.7%0.30 1.20.450.980.251.3714.2%0.300.450.2512.9P A B C

m A m B m c m A B c

R R R R R R R R εεεεεε=++??=+-+????++-+????++-+??=+++++-+++=()25% 1.143514.2%0.300.450.25m A B C

R εεε+-+++

c. Now, continuing with the Market Model (as in part a), when m R =15%, and all i ε=

0 :

i.returns of individual stocks:

()10.5% 1.2(15%14.2%)

11.46%

13%0.98(15%14.2%)

13.78%

15.7% 1.3715%14.2%16.8%

A B C R R R =+-==+-==+-=

ii. return of the portfolio:

12.925% 1.1435(15%14.2%)

13.84%

p R =+-=

Alternate Solution for return on portfolio, where i X is the weight in the

portfolio of stock i :

()()().311.46.4513.78.2516.813.84

p a a b b c c

R X R X R X R =++=++= 12.1

The discount rate for the project is equal to the expected return for the security, R S , since the project has the same risk as the firm as a whole. Apply the CAPM to express the firm’s required return, R S , in terms of the firm’s beta, β, the risk-free rate, R F , and the expected market return, R M .

R S = R F + β ? (R M – R F ) = 0.05 + 0.95 (0.09) = 0.1355

Subtract the initial investment at year 0. To calculate the PV of the cash inflows, apply the annuity formula, discounted at 0.1355.

NPV = C 0 + C 1 A T r

= -$1,200,000 + $340,000 A 50.1355

= -$20,016.52

Do not undertake the project since the NPV is negative.

12.2 a.

Calculate the average return for Douglas stock and the market.

R D = (Sum of Yearly Returns) / (Number of Years) = (-0.05 + 0.05 + 0.08 + 0.15 + 0.10) / (5)

= 0.066

R M = (-0.12 + 0.01 + 0.06 + 0.10 + 0.05) / (5) = 0.020

To calculate the beta of Douglas stock, calculate the variance of the market, (R M - R

M )2

, and the covariance of Douglas stock’s return with the market’s return, (R D - R D ) ? (R M - R M ). The beta of Douglas stock is equal to the covariance of Douglas stock’s return and the market’s return divided by the variance of the market. Remember to divide both the covariance of Douglas stock’s return and the market’s return and the variance of the market by 4. Because the data are historical, the appropriate denominator in the calculation of the variance is 4 (=T – 1).

R D - R D R M - R M (R M - R M )2 (R D - R D ) (R M - R M )

-0.116 -0.14 0.0196 0.01624

-0.016

-0.01

0.0001

0.00016

0.014 0.04 0.0016 0.00056

0.084 0.08 0.0064 0.00672

0.034 0.03 0.0009 0.00102

0.0286 0.02470

βD= [Cov (R D, R M) / (T-1)] / [Var (R M) / (T-1)]

= (0.02470 / 4) / (0.0286 / 4)

= 0.864

The beta of Douglas stock is 0.864.

12.3 Calculate the square root of the stock’s variance and the market’s variance to find the standard

deviation, σ, of each.

σC= (σ2C)1/2

= (0.004225)1/2

= 0.065

σM= (σ2M)1/2

= (0.001467)1/2

= 0.0383

Use the formula for beta:

βC= [Corr (R C, R M) ?σC] / σM

= [(0.675) (0.065)] / (0.0383)

= 1.146

The beta of Ceramics Crafts man is 1.146.

12.4 a. To compute the beta of Mercantile’s stock, divide the covariance of the stock’s

return

with the market’s return by the market variance. Since those two values are

provided in the problem, the 13 quarte rly returns of Mercantile’s stock and the

market are not needed for the calculation.

βD= Cov (R D, R M) / σ2M

= (0.038711) / (0.038588)

= 1.0032

The beta of Mercantile Banking Corporation is 1.0032.

b.The beta of the average stock is one. Since Mercantile’s beta is close to one, its

stock has approximately the same risk as the overall market.

Correlation(R A,R B) = Covariance(R A, R B) / (σA * σB)

= 0.004539 / (0.0380 * 0.1202)

= 0.9937

The correlation between the returns on Stock A and Stock B is 0.9937.

10.3 a. Expected Return HB= (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154)

= 0.0733

= 7.33%

The expected return on Highbull’s stock is 7.33%.

Expected Return SB= (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074)

= 0.0608

= 6.08%

The expected return on Slowbear’s stock is 6.08%.

b. Variance A (σHB2) = (0.25)(-0.02 – 0.0733)2 + (0.60)(0.092 – 0.0733)2 + (0.15)(0.154

– 0.0733)2

= 0.003363

Standard Deviation A (σHB) = (0.003363)1/2

= 0.0580

= 5.80%

The standard deviation of Highbear’s stock returns is 5.80%.

Variance B (σSB2) = (0.25)(0.05 – 0.0608)2 + (0.60)(0.062 – 0.0608)2 + (0.15)(0.074 –

0.0608)2

= 0.000056

Standard Deviation B (σB) = (0.000056)1/2

= 0.0075

= 0.75%

The standard deviation of Slowbear’s stock returns is 0.75%.

c. Covariance(R HB, R SB) = (0.25)(-0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 –

0.0733)(0.062 –

(0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608)

= 0.000425

The covariance between the returns on Highbull’s stock and Slowbear’s stock is

0.000425.

Correlation(R A,R B) = Covariance(R A, R B) / (σA * σB)

= 0.000425 / (0.0580 * 0.0075)

= 0.9770

The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770.

10.5Value of Atlas stock in the portfolio = (120 shares)($50 per share)

= $6,000

Value of Babcock stock in the portfolio= (150 shares)($20 per share)

= $3,000

Total Value in the portfolio= $6,000 + $3000

= $9,000

Weight of Atlas stock = $6,000 / $9,000

= 2/3

The weight of Atlas stock in the portfolio is 2/3.

Weight of Babcock stock = $3,000 / $9,000

= 1/3

The weight of Babcock stock in the portfolio is 1/3.