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Assignment 1. Plot in...

Assignment

1. Plot in Excel the risky asset opportunity set for Portfolios A & B. Hint: create the

following table in excel assuming weights of portfolio A & B in 10 percentage

point increments. Then calculate expected return and standard deviation for

each allocation to A & B.

Weight Port A

Weight Port B

Return

Standard

Deviation

Sharpe Ratio

0%

100%

10

90

20

80

30

70

40

60

50

50

60

40

70

30

80

20

90

10

100

0

Determine the optimal allocation of A & B and draw in the Capital Allocation Line

(CAL). You can arrive at an approximate optimal allocation using a table similar to

the one shown above OR you can obtain a more precise optimal allocation using the

formula shown in Chapter 7 (equation 7.13). When drawing the CAL on the efficient

frontier graph plotted in Excel, you can manually draw a line starting at the risk free

rate to the tangent point.

2. Find the optimal complete portfolio based on your client’s indifference curve.

Hint: Plot an indifference curve on the same graph you just created using the

utility function formula from Chapter 6. Use the range of expected return and

standard deviations shown in the table below. Assume U = 9% and a risk

aversion coefficient (A) of 10 to complete the table below.

Expected Return

Standard Deviation

5%

7.5

10

12.5

15

17.5

20

22.5

25

3. Use the capital asset pricing model (CAPM) to determine the beta and alpha of

Portfolio A & Portfolio B. Show the CAPM relationship graphically for BOTH

Portfolio A and Portfolio B (separate graphs). The market portfolio is represented

by the S&P 500 and the risk free rate is represented by 90 day Treasury Bill.

Determine the beta for portfolio A & B using: i) the slope function in Excel; and ii)

the formula for beta – the co-variance between the asset and the market dividedby the variance of the market. This is explained in the Modules 6& 7 notes and

pages 296 & 297 in the text. Recall the covariance between two assets is the

volatility of asset 1 times the volatility of asset 2 times the correlation between

them.

Calculate the expected alpha for each portfolio A & B using the intercept function

in Excel and the index model of CAPM formula (equation 9.9 on page 302 – note

that the terms are in excess return form). Ignore the error term and you have all

the information to solve for alpha based on the monthly returns. Compare the

betas and y-intercepts using the two different methods.

1. Plot in Excel the risky asset opportunity set for Portfolios A & B. Hint: create the

following table in excel assuming weights of portfolio A & B in 10 percentage

point increments. Then calculate expected return and standard deviation for

each allocation to A & B.

Weight Port A

Weight Port B

Return

Standard

Deviation

Sharpe Ratio

0%

100%

10

90

20

80

30

70

40

60

50

50

60

40

70

30

80

20

90

10

100

0

Determine the optimal allocation of A & B and draw in the Capital Allocation Line

(CAL). You can arrive at an approximate optimal allocation using a table similar to

the one shown above OR you can obtain a more precise optimal allocation using the

formula shown in Chapter 7 (equation 7.13). When drawing the CAL on the efficient

frontier graph plotted in Excel, you can manually draw a line starting at the risk free

rate to the tangent point.

2. Find the optimal complete portfolio based on your client’s indifference curve.

Hint: Plot an indifference curve on the same graph you just created using the

utility function formula from Chapter 6. Use the range of expected return and

standard deviations shown in the table below. Assume U = 9% and a risk

aversion coefficient (A) of 10 to complete the table below.

Expected Return

Standard Deviation

5%

7.5

10

12.5

15

17.5

20

22.5

25

3. Use the capital asset pricing model (CAPM) to determine the beta and alpha of

Portfolio A & Portfolio B. Show the CAPM relationship graphically for BOTH

Portfolio A and Portfolio B (separate graphs). The market portfolio is represented

by the S&P 500 and the risk free rate is represented by 90 day Treasury Bill.

Determine the beta for portfolio A & B using: i) the slope function in Excel; and ii)

the formula for beta – the co-variance between the asset and the market dividedby the variance of the market. This is explained in the Modules 6& 7 notes and

pages 296 & 297 in the text. Recall the covariance between two assets is the

volatility of asset 1 times the volatility of asset 2 times the correlation between

them.

Calculate the expected alpha for each portfolio A & B using the intercept function

in Excel and the index model of CAPM formula (equation 9.9 on page 302 – note

that the terms are in excess return form). Ignore the error term and you have all

the information to solve for alpha based on the monthly returns. Compare the

betas and y-intercepts using the two different methods.

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