Question

Select Stock Portfolio has 5 stocks in it (each with the same amount of initial investment), which you have selected randomly from the S&P 500 list.
Broad Stock Portfolio has 100 stocks in it (each with the same amount of initial investment), which you have selected randomly from the S&P 500 list.

Which portfolio would have a greater expected average return or would it be the same? Explain.

Answer 1

Assuming the average return of all stocks in S&P 500 list is same and is equal to

Let X1, X2,..., X5 be the return of 5 stocks of Select Stock Portfolio

Average return of Select Stock Portfolio = E[(X1 + X2 + X3 + X4 + X5)/5]

= [E(X1) + E(X2) + E(X3) + E(X4) + E(X5)]/5

= ( + + + + ) / 5

= 5 / 5

=

Let Y₁, Y₂,..., Y₉₉, Y₁₀₀ be the return of 100 stocks of Broad Stock Portfolio

Average return of Select Stock Portfolio = E[(Y₁ + Y₂ +... + Y₉₉ + Y₁₀₀)/100]

= [E(Y₁) + E(Y₂) + .. + E(Y₉₉) + E(Y₁₀₀)]/100

= ( + + ... + + ) / 100

= 100 / 100

=

Thus, the expected average return for both portfolio are same.