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statuscvo [17]
3 years ago
11

A fund manager is considering three mutual funds. The 1st is a stock fund, the 2nd is a long-term government and corporate bond

fund (investment grade), and the third is a T-bill money market fund that yields a sure rate of 3.00%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 12.00% 41.00% Bond fund (B) 5.00% 30.00% The correlation between the fund returns is 0.0667. What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds
Business
1 answer:
Vinil7 [7]3 years ago
8 0

Answer:

Expected return is: 7.37% and the Standard deviation is: 24.96%

Explanation:

Correlation between fund S&B=0,0667

Standard Deviation of Fund S=41%

Standard Deviation of Fund(B)=30%

E(R) of Stock Fund S=12%

E(R) of Stock Fund B=5%

Covariance between the funds = Standard Deviation of Fund(B) × Standard Deviation of Fund S × correlation between these funds

Cov = 0.41 × 0.30 × 0.0667 = 0.008204

Now minimum variance portfolio is found by applying:

W min(S)=(SDB)^2-Cov(B,S) / ((SDS)^2+(SDB)^2-2Cov(B,S)

W min(S) = 0.338431

W min(B) = 1-0.338431=0.661569

1) E(r)min= 0.338431 × 12% + 0.661569 × 5% = 7.37%

2) Standard Deviation:

SD Min = (Ws^2XSDs^2+Wb^2XSDb^2+2XWsWb*Cov(s,B)^1/2

SDmin=(0.338431^2 × 0.41^2 + 0.661569^2 ×   0.3^2   + 2 × 0.338431 × 0.661569 × 0.008204)^1/2

SDmin=24.96%

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a) Data and Calculations:

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Budgeted unit sales     8,400   10,000    12,000       13,000

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40% month of sale      3,360     4,000      4,800        5,200

60% month following                5,040      6,000        7,200

Total cash collections 3,360     9,040    10,800       12,400

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Ending Inventory        2,000     2,400     2,600

Cost of goods sold     8,400   10,000    12,000       13,000

Goods available        10,400   12,400    14,600

Beginning Inventory   1,680    2,000      2,400         2,600

Production costs        8,720   10,400    12,200

Unit cost of materials $10         $10          $10   ($2 * 5)

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Accounts receivable balance at July end:

June credit sales      $8,400

June cash collection  3,360

July 1 Beginning bal.  5,040

July credit sales       10,000

Cash collections       9,040

Ending balance        6,000

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