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Marat540 [252]
3 years ago
11

Suppose that there are many stocks in the security market and that the characteristics of stocks A and B are given as follows: S

tock Expected Return Standard Deviation A 12 % 3 % B 19 9 Correlation = –1 Suppose that it is possible to borrow at the risk-free rate, rf. What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) (Do not round intermediate calculations. Round your answer to 3 decimal places.)
Business
1 answer:
Tomtit [17]3 years ago
4 0

Answer:

0.135 or 13.5%

Explanation:

Given in the question are the following:

ERA = Expected return of Stock A = 12% = 0.12

ERB = Expected return of Stock B = 19% = 0.19

SDA = Standard deviation of Stock A = 3% = 0.03

SDB = Standard deviation of Stock B = 9% = 0.09

CAB = Correlation between A and B = -1

The correlation of -1 between Stock A and Stock B indicates that there a perfect negative correlation between the two stocks. Therefore, we can create a risk-free portfolio which its rate of return will be the risk-free rate in equilibrium.  

If we let wA denotes the proportion of investment in Stock A, and let wB denotes the proportion of investment in Stock B, the proportion of this portfolio can be obtained by setting its standard deviation equal to zero. Since there is a perfect negative correlation, the standard deviation of this portfolio (SDP) can be given as follows:

Absolute value [(wA × SDA) – (wB × SDB)] = SDP …………………………………….. (1)

Note that wB = (1 – wA) since the sum of the weight must be equal to 1.

Substituting all the relevant values into equation and set SDP = 0, we have  

[(0.03 × wA) − (0.11 × (1 - wA))] = 0

0.03wA – 0.11 + 0.11wA = 0

0.03wA + 0.11wA = 0.11

0.14wA = 0.11

wA = 0.11 ÷ 0.14 = 0.785714285714286

Since wB = 1 –wA, therefore:

wB = 1 - 0.785714285714286 = 0.214285714285714

The expected rate of return of the portfolio (ERP) can be estimated as follows:

ERP = (wA × ERA) + (wB × ERB)  ................................. (2)

Substituting all the relevant values into equation (2), we have:

ERP = (0.785714285714286 × 0.12) + (0.214285714285714 × 0.19)  

       = 0.0942857142857143 + 0.0407142857142857

ERP = 0.135 or 13.5%

Therefore, the value of the risk-free rate must be 13.5%.

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Answer:

a. The number sentence that is the topic sentence is sentence (1).

b. Sentence (6) does not contribute to the paragraph's unity.  It can be eliminated, without changing the meaning that can be obtained from the paragraph.  It does not support the topic.

c. The writer, in sentences 3 through 7, provides an example and further details to help the reader to understand her point.

d. The example in a sentence makes the idea clearer to the reader.  Without the example, which provides further details, the reader may not clearly appreciate the topic under discussion.

Explanation:

The purpose of the topic sentence is to introduce the theme of the paragraph or the point of view of the writer.  It captures the essence of the story.  As it bears the central idea, it focuses the paragraph to achieve unity.

5 0
2 years ago
Rachel sells 100 shares short at $43. The sale requires a margin deposit equal to 60 percent of the proceeds of the sale. If the
andrew11 [14]

Answer:

23.25%; 62.01%

Explanation:

(a) Amount received:

= No. of shares × selling price

= 100 × $43

= $4,300

Sales deposit = 60% of Amount received

                        = 0.6 × $4,300

                        = $2,580

Amount paid = No. of shares × Purchase price

                      = 100 × $49

                      = $4,900

Therefore, Loss = $4,900 - $4,300

                           = $600

(b) If buys at $27, then

Amount paid = $27 × 100

                     = $2,700

Profit = $4,300 - $2,700

         = $1,600

Loss on investment:

= ($600 ÷ $2,580) × 100

= 23.25%

Profit on investment:

= ($1,600 ÷ $2,580) × 100

= 62.01%

7 0
2 years ago
Suppose that widgets are produced by a monopolistically competitive industry. If each firm in this market has the same cost stru
natulia [17]

Answer:

The equilibrium number of firms is 20.

Explanation:

Q = SH × b

   = 2,400 × (1/20)

   = 2,400 × 0.05

   = 120

Also given, Q = S / n

                120 = 2,400 / n

                  n = 20

3 0
3 years ago
Cedric has been following a detailed review schedule in preparation for his test. He feels confident that he knows the material,
rewona [7]

Answer: Noting down of ideas

Explanation: Cedric could note down the ideas and points he remembers on the back of his test booklet. He should first read the question and  make short notes of every point he remembers regarding that question.

This strategy will help Cedric to answer the questions while doing the final writing in answer sheet. By doing this he can also improve his speed with accuracy while answering.

5 0
3 years ago
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melomori [17]

The option that makes the most sense for the party by Mr and Mrs Atoll is one case of 24 sodas at $18.50.

<h3>Why this option is the cheapest</h3>

The reason for this is that given the guests they are entertaining, this option is the most cheapest and effective.

How to calculate for the way that the drink would go round

a. Each bottle is $1.5. Two bottles for 1 = 1.5x2 = 3 dollars

b. six packs at 5$. One= $0.88

c. A case of 24 sodas at $18.5. one soda is going to be  18.5/24 = $0.77

d. Two cases of 24 soda at 18.5 = $1.54

Given the calculations that have been done above, option c at $0.77 is the cheapest. It would require them to send the less money in getting sodas that would go round twice for 10 people.

Read more on the economy here: brainly.com/question/1106682

5 0
1 year ago
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