Question

You find a certain stock that had returns of 9 percent, −16 percent, 18 percent, and 14 percent for four of the last five years. If the average return of the stock over this period was 10.3 percent, what was the stock’s return for the missing year? What is the standard deviation of the stock’s return?

Answer 1

26.5, 14.344

Explanation:

given that you find a certain stock that had returns of 9 percent, −16 percent, 18 percent, and 14 percent for four of the last five years. The average return of the stock over this period was 10.3 percent,

Let the missing return in the 5 years be x

Then we get total of all five years

=
`9-16+18+14+x\\=x+25`

This will also be equal to the given average multiplied by 5

=
`5(10.3)\\=51.5`

Equate both to get an equation in X as

`x+25 =51.5\\x=26.5`

Missing year return =26.5

Variance = sum of (x-10.3)^2

=
`1.3^2+26.3^2+7.7^2+3.7^2+16.2^2\\=205.76`

Std dev= 14.344