Question

You have $500,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $150,000. Consider the summary measures in the following table:

Investment	Expected Return		Standard Deviation
Old portfolio	7	%	10	%
House	19	%	21	%

The correlation coefficient between your portfolio and the house is 0.34.

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 $150,000 to buy risk-free T-bills that promise a 15% 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	%

Answer 1

Given that

Investment	Expected Return		Standard Deviation
Old portfolio	7%		10%
House	19%		21%

a)

Expected return = 0.07 * (50/65) + 0.19 (15/65) = 0.0977 =9.77%

Standard deviation = sqrt((10*50/65)²+(21*15/65)²+2*10*21*0.34*(50/65)*(15/65)) = 10.39%

b)

15% rate of rate of return

Expected return = 0.07 * (50/65) + 0.15 (15/65) = 0.0885 = 8.85 %

The correlation coefficient between any asset and the risk-free T-bills is zero

Standard deviation = sqrt((10*50/65)²+(15*15/65)²+2*10*15*0*(50/65)*(15/65))

=sqrt((10*50/65)²+(15*15/65)²

= 8.43 %