Question

A portfolio consists of the following two funds.

	Fund A			Fund B
Expected Return		?			9	%
Standard deviation		21	%		11	%
Portfolio market value	$	27,000		$	33,000
Correlation (RA,RB)		0.21
Risk-free rate		2.5	%
Portfolio Sharpe ratio		0.7771104

What is the expected return on fund A?

Multiple Choice

• 13.7 percent

• 13.3 percent

• 15.7 percent

• 14.5 percent

• 12.0 percent

Answer 1

Total Portfolio value = Value of Fund A + Value of Fund B

=27000+33000

60000

Weight of Fund A = Value of Fund A/Total Portfolio Value

= 27000/60000

=0.45

Weight of Fund B = Value of Fund B/Total Portfolio Value

= 33000/60000

=0.55

std dev=( w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*Cor(R_A, R_B)*σ(R_A)*σ(R_B))^0.5

=(0.45^2*21^2+0.55^2*11^2+2*0.45*0.55*0.21*21*11)^(1/2)

=12.244%

sharpe ratio = (portfolio return-riskfree rate)/std dev

0.7771104=(portfolio return-2.5)/12.244

portfolio return=12%