Question

Suppose you have $325,000 in cash, and you decide to borrow another $68,250 at a 2% interest rate to invest in the stock market. You invest the entire $393,250 in a portfolio J with a 16% expected return and a 30% volatility.

a. What is the expected return and volatility (standard deviation) of your investment?

The expected return of your investment is  (Round to two decimal places.)

The volatility (standard deviation) of your investment is  (Round to two decimal places.)

b. What is your realized return if J goes up 20% over the year?

Your realized return if I goes up 20% over the year is  (Round to two decimal places.)

c. What return do you realize if J falls by 40% over the year?

The return you realize if I falls by 40% over the year is  (Round to two decimal places.)

Answer 1

Solution:

a)Calculation of Beta

Beta=Total Investment in Portfolio/Cash Invesrment

=$393,250/ $325,000

=1.21

Calculation of Expected Return of investment as per CAPM

=Risk free rate+Beta(Return of Portfolio-Risk Free rate)

=2%+1.21(16%-2%)

=18.94%

Calculation of Volatility of Investment

Volatility=Beta*Standard deviation of portfoli

=1.21*30%

=36.30%

b)Calculation of realized return

Return=Value of portfoli(1+rate)

=$393,250(1+0.20)

=$471,900

Realised Return=Return-Cash investment-(Loan+Interest)

=471,900-$325,000-($68,250+$1365)

=$77,285

Realised Return(%)=($77,285/$325,000)*100

=23.78%

c)Calculation of Realised Return

Return=Value of Portfolio(1+rate)

=$393,250(1-0.40)

=$235,950

Realised Return=$235,950-$325,000-($68,250+$1365)

=-$158,665

Realised Return(%)=(-$158,665/$325,000)*100

=-48.82%