Security and investment problem

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GRADE: 59%

Sector

Portfolio Weight

S&P Weighting

Differences in Weighting

Portfolio Return

S&P Return

Sector over-or under Performance

Sector Allocation Contributions

Telecommunications Services

3.10%

5.90%

-2.80%

2.50%

3.10%

.60%

-1.68%

Utilities

7.50%

3.80%

3.70%

3.10%

1.90%

1.20%

4.44%

Information Technology

14.30%

17.90%

-3.60%

4.90%

3.20%

1.70%

-6.12%

Materials

6.30%

3.70%

2.60%

4.80%

5.10%

-0.30%

-0.78%

Financials

13.40%

17.10%

-3.70%

6.20%

4.80%

1.40%

-5.18%

Consumer Discretionary

12.70%

13.50%

-0.80%

2.10%

4.00%

-1.90%

1.52%

Industrials

14.10%

11.90%

2.20%

4.90%

3.10%

1.80%

3.96%

Energy

8.40%

8.00%

0.40%

3.70%

8.60%

-4.90%

-1.96%

Healthcare

15.30%

11.70%

3.60%

9.80%

5.70%

4.10%

14.76%

Consumer Staples

4.90%

6.50%

-1.60%

1.50%

13.20%

-11.70%

18.72%

-2pts

a.

-2.80%

k.

.60%

u.

-1.68%

b.

3.70%

l.

1.20%

v.

4.44%

c.

-3.60%

m.

1.70%

w.

-6.12%

d.

2.60%

n.

-0.30%

x.

-0.78%

e.

-3.70%

o.

1.40%

y.

-5.18%

f.

-0.80%

p.

-1.90%

z.

1.52%

g.

2.20%

q.

1.80%

aa.

3.96%

h.

0.40%

r.

-4.90%

bb.

-1.96%

i.

3.60%

s.

4.10%

cc.

14.76%

j.

-1.60%

t.

-11.70%

dd.

18.72%

1. The manager underperformed -2pts. Below is the workings

Sector

Portfolio Return

S&P Return

Sector over-or under Performance

Telecommunications Services

2.50%

3.10%

.60%

Utilities

3.10%

1.90%

1.20%

Information Technology

4.90%

3.20%

1.70%

Materials

4.80%

5.10%

-0.30%

Financials

6.20%

4.80%

1.40%

Consumer Discretionary

2.10%

4.00%

-1.90%

Industrials

4.90%

3.10%

1.80%

Energy

3.70%

8.60%

-4.90%

Healthcare

9.80%

5.70%

4.10%

Consumer Staples

1.50%

13.20%

-11.70%

Idea is better than before, but calculation idea is still incorrect. Half credit, -4pts

2. Which sector turned in the greatest positive contribution to the portfolio’s performance? Explain why this investment made the greatest positive contribution based on the differences in weighting and the sector over- or under- performance.

Max positive contribution is from healthcare.-5pts

The portfolio was overweight on Healthcare by 3.6% and outperformed the index performance by 4.10%, resulting in 14.76% to the outperformance

3. Which sector made the greatest negative contribution to the portfolio’s perfor-mance? Explain why this investment made the greatest negative contribution based on the differences in weighting and the sector over- or under- performance

Sector

Portfolio Weight

S&P Weighting

Differences in Weighting

Portfolio Return

S&P Return

Sector over-or under Performance

Sector Allocation Contributions

1

2

3

4

5

6

7

8= 4*7

Telecommunications Services

3.10%

5.90%

-2.80%

2.50%

3.10%

-0.60%

1.68%

Utilities

7.50%

3.80%

3.70%

3.10%

1.90%

1.20%

4.44%

Information Technology

14.30%

17.90%

-3.60%

4.90%

3.20%

1.70%

-6.12%

Materials

6.30%

3.70%

2.60%

4.80%

5.10%

-0.30%

-0.78%

Financials

13.40%

17.10%

-3.70%

6.20%

4.80%

1.40%

-5.18%

Consumer Discretionary

12.70%

13.50%

-0.80%

2.10%

4.00%

-1.90%

1.52%

Industrials

14.10%

11.90%

2.20%

4.90%

3.10%

1.80%

3.96%

Energy

8.40%

8.00%

0.40%

3.70%

8.60%

-4.90%

-1.96%

Healthcare

15.30%

11.70%

3.60%

9.80%

5.70%

4.10%

14.76%

Consumer Staples

4.90%

6.50%

-1.60%

1.50%

13.20%

-11.70%

18.72%

Total

100.00%

100.00%

0.00%

Information technology sector made the greatest negative contribution (-6.12%) to the portfolio's performance.

4. Based on beta, which portfolio has the highest level of systematic risk? Show your work.

Portfolio 1

Security

Amount Invested

Weight

Beta

Beta*Weight

Security A

$4,000

13.79%

0.8

0.11

Security B

$5,000

17.24%

1.15

0.20

Security C

$12,000

41.38%

0.95

0.39

Security D

$8,000

27.59%

1.23

0.34

Total

$29,000

100.00%

1.04

Portfolio 2

Beta*Weight

Security A

$3,000

10%

1.22

0.13

Security B

$11,000

38%

1.54

0.58

Security C

$9,000

31%

0.87

0.27

Security D

$6,000

21%

0.81

0.17

Total

$29,000

100%

1.15

Portfolio 3

Security A

$15,000

46.88%

1.72

0.81

Security B

$12,000

37.50%

0.81

0.30

Security C

$3,000

9.38%

0.72

0.07

Security D

$2,000

6.25%

1.54

0.10

Total

$32,000

100.00%

1.27

Portfolio 3 has the highest beta of 1.27

5. If the risk-free rate is 5.5 percent, which of these portfolios has the highest reward-to-risk ratio? Show your work

Security

Investment

Returns

Beta

Security A

$4,000

9%

0.8

Security B

$5,000

12%

1.15

Security C

$12,000

14%

0.95

Security D

$8,000

15%

1.23

Portfolio 1

13.24%

1.04

Security

Investment

Returns

Beta

Security A

$3,000

16%

1.22

Security B

$11,000

13%

1.54

Security C

$9,000

8%

0.87

Security D

$6,000

11%

0.81

Portfolio 2

11.34%

1.15

Security

Investment

Returns

Beta

Security A

$15,000

10%

1.72

Security B

$12,000

9%

0.81

Security C

$3,000

12%

0.72

Security D

$2,000

15%

1.54

Portfolio 3

10.13%

1.27

Portfolio's Expected Returns = Sum of Investment x Returns / Sum of Investment

Portfolio's Beta = Sum of Investment x Beta / Sum of investment

Beta is a measure of risk.

Portfolio 1 has the lowest beta and higher expected returns. thus, select Portfolio 1.

Need to calculate reward-to-risk ratio. Beta is different. -10pts

6. Suppose that the risk-free rate is 5.5 percent, the return over a three-year period for each portfolio matches its expected return, and the portfolios have 3-year annual return standard deviations as follows:

Portfolio 1

22%

Portfolio 2

26%

Portfolio 3

18%

If you were restricted to selecting one of the three portfolios to invest all your money in, which should you choose based on that portfolio having the best ratio of excess return per unit of total risk as measured by its Sharpe ratio?

Formula

https://d2vlcm61l7u1fs.cloudfront.net/media%2F936%2F936a6698-6672-4453-893d-f06c2b308bbe%2FphpJTx4VG.png

https://d2vlcm61l7u1fs.cloudfront.net/media%2F646%2F6464865c-4e6b-497d-864b-90df95a5fbcd%2FphpOcq3yc.png

Formula

https://d2vlcm61l7u1fs.cloudfront.net/media%2F0ab%2F0ab1f810-bca8-4229-98b6-7960725c0d64%2FphplKIMI1.png

https://d2vlcm61l7u1fs.cloudfront.net/media%2F225%2F225a5a76-dbaf-4797-9b07-503cad3b04f8%2FphprWw9xz.png

Formula

https://d2vlcm61l7u1fs.cloudfront.net/media%2Fbf4%2Fbf473ca9-1fd3-4bfc-ad72-303a42c9f610%2Fphp81X6aH.png

https://d2vlcm61l7u1fs.cloudfront.net/media%2Fb35%2Fb35bbe51-6ae3-4ea6-a098-72ec0caeafd6%2Fphppysasg.png

Portfolio 2 sharpe ratio incorrect -3pts

The sharp ratio is the best method to measure the efficiency of the portfolio.

According to the sharp ratio, the portfolio 1, 2, and 3 show 35.19%, 33.78%, and 24.86% respectively. It indicates the rate of return the portfolio can give with the given level of risk. The best portfolio is portfolio 1 which shows sharp ratio 35.19%.

7. Suppose that the risk-free rate is 5.5 percent, the return over a three-year period for each portfolio matches its expected return, and the portfolios have 3-year annual return standard deviations as follows:

Portfolio 1

22%

Portfolio 2

26%

Portfolio 3

18%

Security

Amount Invested

Weights

Expected Return

Beta

Security A

$4,000

13.79%

9%

0.8

Security B

$5,000

17.24%

12%

1.15

Security C

$12,000

41.38%

14%

0.95

Security D

$8,000

27.59%

15%

1.23

Portfolio 1

$29,000

13.24%

1.04

Security A

$3,000

10.34%

16%

1.22

Security B

$11,000

37.93%

13%

1.54

Security C

$9,000

31.03%

8%

0.87

Security D

$6,000

20.69%

11%

0.81

Portfolio 2

$29,000

11.34%

1.15

Security A

$15,000

46.88%

10%

1.72

Security B

$12,000

37.50%

9%

0.81

Security C

$3,000

9.38%

12%

0.72

Security D

$2,000

6.25%

15%

1.54

Portfolio 3

$32,000

10.13%

1.27

For portfolio 1, beta1 = 13.79% x 0.8 + 17.24% x 1.15 + 41.38% x 0.95 + 27.59% x 1.23 = 1.04

Similarly, beta2 = 1.15

beta3 = 1.27

Jensen alpha = Rp - [Rf + beta x (Rm - Rf)

Here, Rf = 5.5%, Rm = 8%

For Portfolio 1,

Jensen alpha = 11.3% - [5.5% + 1.04 x (8% - 5.5%)] = 3.20%

For Portfolio 2,

Jensen alpha = 12.5% - [5.5% + 1.15 x (8% - 5.5%)] = 4.13%

For Portfolio 3,

Jensen alpha = 9.4% - [5.5% + 1.27 x (8% - 5.5%)] = 0.72%

Therefore, Portfolio 2 has the highest Jensen alpha

Treynor Ratio = (Rp - Rf) / Beta

For Portfolio 1,

Treynor Ratio = (11.3% - 5.5%) / 1.04 = 0.0557

For Portfolio 2,

Treynor Ratio = (12.5% - 5.5%) / 1.15 = 0.0610

For Portfolio 3,

Treynor Ratio = (9.4% - 5.5%) / 1.27 = 0.0306

Thus, Portfolio 2 has the highest Treynor Ratio has well.

8. In your role as a financial advisor, you’re advising a client, Sally, a 30-year old com-puter programmer who makes an above-average salary. She’s investing money in her 401(k) that she doesn’t plan to use until retirement. In your opinion, which of the two portfolios above would be most appropriate for these funds? In your answer, explain why you believe the portfolio you’ve chosen is appropriate and explain why the portfolio you didn’t choose is not appropriate.

Sally should choose portfolio one. In this portfolio, most of his money will be invested in government and corporate bonds. These are appropriate for her since they are more of long-term investments. Since she has an above average salary she may not need this money soon. Portfolio 2 is best for Sally – this was correct in your initial exam. -8pts

9. In your role as a financial advisor, you’re advising a client, Bob, who has just retired and rolled over his 401(k) into a self-directed IRA account. Bob intends to use these funds to provide income to live on in his retirement. In your opinion, which of the two portfolios above would be most appropriate for these funds? In your answer, explain why you believe the portfolio you’ve chosen is appropriate and explain why the port-folio you didn’t choose is not appropriate.

Portfolio 2 is the best option for Bob. This portfolio has larger portions of investment distributed to short-term assets. Since bob isn’t earning a salary, he may need constant short-term finances for upkeep. Portfolio 2 will be most suited for him.Portfolio 1 is best for Bob. This was correct in the initial exam. -7pts