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 Maria's portfolio is ________. (Hint: For best results, retain at least four decimal places for any intermediate calculations.)

Answer 1

0.0784

Explanation:

From the information given:

The weight invested in stock A
`w_x = (7 * 70)/(7 * 70 + 4 * 100 )`

`w_x = (490)/(490+ 400 )`

`w_x = (490)/(890 )`

`w_x = 0.55056`

The weight invested in stock B
`w_y = (4 * 100)/(7 * 70 + 4 * 100)`

`w_y = (400)/(890)`

`w_y =0.44944`

Thus, expected rate of return

=
`w_x * (E) (x) + w_y * E(Y)`

= 0.55056(0.02) + 0.44944(0.15)

= 0.0110112 + 0.067416

= 0.0784272

`\simeq` 0.0784