Question

Maria has a portfolio consisting of 7 shares of stock A (purchased for $70 per share) and 4 shares of stock B (purchased for $100 per share). She assumes the expected rates of returns after 1 year will be 0.02 for stock A and 0.15 for stock B, with variances of 0.04 and 0.18, respectively. The expected rate of return after 1 year for Mary's portfolio is________

Answer 1

Answer:

Hence, the expected rate of return after 1 year for Mary's portfolio is $0.17751$

Step-by-step explanation:

We have,

Purchase 7 shares of stock A  for $70 per share and 4 shares of stock B for $100 per share then The expected rate of return after 1 year for Mary's portfolio.

Weight invested in stock A is $W_x=\frac{7\times 70}{7\times 70+4\times 100}$

                                               $\Rightarrow W_x=\frac{490}{490+400}\\\Rightarrow W_x=\frac{490}{890}\\\Rightarrow W_x=\frac{49}{89}\\\Rightarrow W_x=0.5505$

Weight invested in stock B is$W_y=\frac{4\times 100}{7\times 70+4\times 100}$

                                             $\Rightarrow W_y=\frac{400}{490+400} \\\Rightarrow W_y=\frac{400}{890} \\\Rightarrow W_y=\frac{40}{89} \\\Rightarrow W_y=0.4494$

The expected value of the rate of return$=W_x\times\;\text{expected rates of stock A}+W_y\times\;\text{expected rates of stock B}$

$=0.5505\times0.02+0.4494\times0.15$

$=0.01101+0.06741$

$=0.17751$