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

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

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=(7* 70)/(7* 70+4* 100)`

`\Rightarrow W_x=(490)/(490+400)\\\Rightarrow W_x=(490)/(890)\\\Rightarrow W_x=(49)/(89)\\\Rightarrow W_x=0.5505`

Weight invested in stock B is
`W_y=(4* 100)/(7* 70+4* 100)`

`\Rightarrow W_y=(400)/(490+400) \\\Rightarrow W_y=(400)/(890) \\\Rightarrow W_y=(40)/(89) \\\Rightarrow W_y=0.4494`

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

`=0.5505*0.02+0.4494*0.15`

`=0.01101+0.06741`

`=0.17751`