Question

You have 10 shares of stock R1 and 15 shares of stock R2 such that your annual return is 10R1 + 15 R2.

The returns are uncertain and can be negative.

I am using equation for total variance = var(x) + var(y) + 2 sigma(xy) with the coefficients in front of the term per linear function (100 var r1 + 225 var r2 + 300 sigma r1r2).

But cannot solve this question:

Under what conditions will the variance of the return on your portfolio be less than the variance of returns on either of the individual stocks?

Answer 1

Given that the variance of return on the portfolio is:

sigma(p) = (100 var r1 + 225 var r2 + 300 sigma r1r2).

TThe sum of th evariance of individial returns is

variance of return on stock 1 is sigmar1

variance of return on stock 1 is sigmar2

So the required condition is:

variance of retern on portfolio should less than varaince of return on stock 1

Let us consider that one has 10 stocks of stock 1

Then we need

100sigmar1 > 100sigmar1 + 225sigmar2 + 300 sigma r1r2

-300sigmar1r2 > 225sigmar2

Similarly the second condition is:

-300sigmar1r2 > 100sigmar1

(This is how I could interpret the question. Let me know if the approch is correct.)