Question

An investor is deciding which stocks to purchase among Stocks A, B, and C. All three stocks pay quarterly dividends with a known mean of $10/share and standard deviation of $2/share. All three stocks have the same price per share. Assume dividends paid by Stocks A, B, and C are independent.

a) What is the total expected value and variance of dividends over the course of one year, for an investment of 30 shares in Stock A?

b) What is the total expected value and variance of dividends over the course of one year, for an investment of 10 shares each in Stocks A, B, and C?

c) What advice would you give the investor on which investment to make, based on what you calculated in parts a) and b)?

Answer 1

a) Expected Value of dividends = 30*$10 = $300

Variance = (30^2)*(2^2) = $3600.This is because correlation is 1 as all same stocks A.

b) Expected Value of dividends = 30*$10 = $300

Variance = (10^2+10^2+10^2)*(2^2) = $1200.This is because correlation is 0 among the three types of stocks as they are independently distributed

c) Invest in Option b as Expected return is same with lesser risk i.e. variance.