Question

PLEASE answer the question correctly and neatly so I'm able to see how you arrived at your answer. If you do not know how to round or answer the question correctly PLEASE do not answer.

You have $460,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $180,000. Consider the summary measures in the following table:

Investment	Expected Return		Standard Deviation
Old portfolio	8	%	12	%
House	19	%	23	%

The correlation coefficient between your portfolio and the house is 0.33.

a. What is the expected return and the standard deviation for your portfolio comprising your old portfolio and the house? (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

Expected return	%
Standard deviation	%

b. Suppose you decide to sell the house and use the proceeds of $180,000 to buy risk-free T-bills that promise a 14% rate of return. Calculate the expected return and the standard deviation for the resulting portfolio. [Hint: Note that the correlation coefficient between any asset and the risk-free T-bills is zero.] (Do not round intermediate calculations. Round your final answers to 2 decimal places.)

Expected return	%
Standard deviation	%

At a local community college, 43% of students who enter the college as freshmen go on to graduate. Seven freshmen are randomly selected.

a. What is the probability that none of them graduates from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.)

	Probability . What is the probability that at most six will graduate from the local community college? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability c. What is the expected number that will graduate? (Round your final answer to 2 decimal places.) Expected number

Answer 1

(a) Old Portfolio Value = $ 460000 and House Value = $ 180000

Total Resultant Portfolio Value = 460000 + 180000 = $ 640000 (Resultant Portfolio is created by combining existing old portfolio and the house)

Weight of Old Portfolio in Resultant Portfolio = 460000 / 640000 = 0.71875 and Weightage of House in Resultant Portfolio = 1-0.71875 = 0.28125

Expected Return on Old Portfolio = 8 % and Expected Return on House = 19 %

Expected Return of Total Resultant Portfolio = 0.71875 x 8 + 0.28125 x 19 = 11.09375 % or 11.09 % approximately.

Correlation Coefficient = 0.33

Standard Deviation of Old Portfolio = 12 % and Standard Deviation of House = 23 %

Standard Deviation of Resultant Total Portfolio = [(Weightage of Old Portfolio x Standard Deviation of Old Portfolio)^(2) + (Weightage of House x Standard Deviation of House)^(2) + (2 x Weightage of Old Portfolio x Weightage of House x Correlation Coefficient of House and Old Portfolio x Standard Deviation of Old Portfolio x Standard Deviation of House)]^(1/2)

= [(0.71875 x 12)^(2) + (0.28125 x 23)^(2) + 2 x 0.71875 x 0.28125 x 0.33 x 12 x 23]^(1/2) = 12.37 % approximately.

(b) Instead of keeping the house, the same is sold and $ 180000 worth of T-Bills are bought with the sale proceeds.

Resultant Portfolio is created by combining T-Bills with the Old Portfolio.

Weightage of T-Bills in the Resultant Portfolio = 0.28125 and Weightage of Old Portfolio in the Resultant Portfolio = 0.71875

Return on T-Bills = 14 %

Expected Return on Resultant Portfolio = 8 x 0.71875 + 14 x 0.28125 = 9.6875 % or 9.69 % approximately.

Standard Deviation of Resultant Portfolio

= [(Weightage of Old Portfolio x Standard Deviation of Old Portfolio)^(2) + (Weightage of T-Bills x Standard Deviation of T-Bills)^(2) + (2 x Weightage of Old Portfolio x Weightage of T-Bills x Correlation Coefficient of T-Bills and Old Portfolio x Standard Deviation of Old Portfolio x Standard Deviation of T-Bills)]^(1/2)

= [(0.71875 x 12)^(2) + (0.28125 x 0)^(2) + (2 x 0.71875 x 0.28125 x 0 x 12 x 0)]^(1/2) (Standard Deviation of T-Bills is zero as T-Bills are Risk-Free)

= 8.625 % or 8.63 % approximately.

NOTE: Please raise a separate query for the solution to the second unrelated question.