Question

You have $390,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $230,000. Consider the summary measures in the following table:

Investment	Expected Return		Standard Deviation
Old portfolio	5	%	13	%
House	15	%	18	%

The correlation coefficient between your portfolio and the house is 0.43.

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 $230,000 to buy risk-free T-bills that promise a 10% 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

Expected Return of a portfolio is given by,

  

Where

Here is the weight of the i^th asset

And r_i is the return (expected) from the i^th asset

Assets	Investment ($)	Weight (Wi)	Expected Return(%) (ri)	Standard Deviation(%) (si)
Old Portfolio	390000	0.629032258	5	13
House	230000	0.370967742	15	18
Total	620000	1

So, expected return is= 0.629032258*5 + 0.370967742*15

                                         =8.709677419

                                         ≈ 8.71%

Standard Deviation =

Where r is the correlation coefficient between the 2 assets.

Here, S.D = 12.58640563 (Calculated using Excel with the help of the above formula)

Expected Return (%)	8.709677419
Standard deviation(%)	12.58640563

2.    

He sold the house and bought a Risk-free-T bills with 10% return so, the portfolio becomes:

Assets	Investment ($)	Weight(W)	Expected Return(%)	Standard Deviation(%)
Old Portfolio	390000	0.629032258	5	13
Risk-free-T bills	230000	0.370967742	10	18
Total	620000	1

So, expected return for the new portfolio is =6.85%

(since the Correlation coefficient is 0, So the formula for S.D becomes as follows:

Standard Deviation = ( since, r=0)

Standard deviation = 10.56 %

Expected Return (%)	6.85483871
Standard deviation(%)	10.55737262