Question

1. You currently have $100,000 invested in a portfolio that has an expected return of 12% and a volatility of 8%. Suppose the risk-free rate is 5%, and there is another portfolio that has an expected return of 20% and a volatility of 12%.

1. How do you construct a new portfolio that has a higher expected return than your current portfolio but with the same volatility?   
2. How do you construct a new portfolio that has a lower volatility than your current portfolio but with the same expected return?                     

To get the full marks of this question, you need to specify the dollar amount that you invest in the new portfolios in (i) and (ii)

Answer 1

Answer : (i) To construct a new potfolio that has higher expected return we need to calculate the weights to be invested in Other stocks and risk free rate.

Let Weight to be invested in other stock = x

Weight to be invested in risk free asset = (1 - x)

Given that expected return will be higher but volatility will be same :

Therefore (Weight * Volatility of portfolio having higher expected return) = Volatility of existing Portfolio

(x * 12%) = 8%

x = 8% / 12%

= 0.6666666667 or 66.666667%

Therefore Amount to be invested in other stocks = 1000000 * 0.666666667 = 66,666.67

Amount to be invested in risk free asset = 100000 * (1 - 0.6666666667) = 33333.33

(ii.) Portfolio that has a lower volatility than your current portfolio but with the same expected return

Expected retun of current portfolio = Risk free rate + Weight * (Expected return of new portfolio - Risk free rate)

Let Weight to be invested in other stock = x

Weight to be invested in risk free asset = (1 - x)

12% = 5% + x * (20% - 5%)

7% = 15% * x

==> x = 7% / 15%

= 0.466667 or 46.6667%

Therefore Amount to be invested in other stocks = 1000000 * 0.46666667 = 46,666.67

Amount to be invested in risk free asset = 100000 * (1 - 0.46666667) =53,333.33