Question

Suppose that the risk-free rate is 6 percent and the expected return on the market portfolio is 15
percent. An investor with $1.5 million to invest wants to achieve a 25 percent return on a
portfolio combining the risk-free asset and the market portfolio. Calculate how much this
investor would need to borrow at the risk-free rate in order to establish this target expected
return. Provide your final answers up to two decimal points.

Answer 1

Let weight of the risk asset be x
Then weight of risk free asset = 1-x
Now,
25 = 15*x+6*(1-x)
25 = 15*x+6-6*x
19 = 9*x
x = 19/9 =	2.11
Weight of the risk free asset = 1-19/9 =	-1.11
Borrowings at risk free rate = 1.5*10/9 =	$1.67	million
VERIFICATION:
Return from the risky asset = 3.17*15% =	$0.4755
Less: Borrowing cost = 1.67*6% =	$0.1002
Net dollar return	$0.3753
% return on investment = 0.3755/1.5 =	25.02%
ANSWER:
Amount to be borrowed at risk free rate =	$1.67	million