Finanzas ii

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Chapter 10: Return and Risk: The Capital-Asset-Pricing Model (CAPM)

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 (2) = (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
= 0.005187Standard Deviation () = (0.005187)1/2
= 0.0720
= 7.20%

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

10.2 a. Expected ReturnA = (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 ReturnB = (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. VarianceA (A2) = (1/3)(0.063 – 0.108)2 + (1/3)(0.105 – 0.108)2 + (1/3)(0.156 – 0.108)2
= 0.001446

Standard DeviationA (A) = (0.001446)1/2
= 0.0380
= 3.80%

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

VarianceB (B2) = (1/3)(-0.037 – 0.0933)2 + (1/3)(0.064 – 0.0933)2 +(1/3)(0.253 – 0.0933)2
= 0.014447

Standard DeviationB (B) = (0.014447)1/2
= 0.1202
= 12.02%

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

c. Covariance(RA, RB) = (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 betweenthe returns of Stock A and Stock B is 0.004539.


Correlation(RA,RB) = Covariance(RA, RB) / (A * B)
= 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 ReturnHB = (0.25)(-0.02) + (0.60)(0.092) + (0.15)(0.154)
= 0.0733
= 7.33%

The expected returnon Highbull’s stock is 7.33%.

Expected ReturnSB = (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. VarianceA (HB2) = (0.25)(-0.02 – 0.0733)2 + (0.60)(0.092 – 0.0733)2 + (0.15)(0.154 – 0.0733)2
= 0.003363

Standard DeviationA (HB) = (0.003363)1/2
= 0.0580= 5.80%

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

VarianceB (SB2) = (0.25)(0.05 – 0.0608)2 + (0.60)(0.062 – 0.0608)2 + (0.15)(0.074 – 0.0608)2
= 0.000056

Standard DeviationB (B) = (0.000056)1/2
= 0.0075
= 0.75%

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

c. Covariance(RHB, RSB) = (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(RA,RB) = Covariance(RA, RB) / (A * B)
= 0.000425 / (0.0580 * 0.0075)
= 0.9770

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

10.4
Value 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.

10.5 a. The expected return on the portfolio equals:

E(RP) = (WF)[E(RF)] + (WG)[E(RG)]

where...
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