 # Portfolio standard deviation help

I am not quite sure I understand why my answer is wrong.

A portfolio manager creates the following portfolio:
1- Weight 0.3, Standard dev. 20%
2- Weight 0.7, Standard dev. 12%

If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to:

A. −1.0.
B. 0.0.
C. 1.0.

The correct answer is C. The example doesn’t really tell you they are perfectly correlated, so what I tried doing was calculating it through the long formula, the following way:

14.4% = (0.3^2*0.2^2 + 0.7^2 * 0.12^2 + 0.3 * 0.7 * X * 0.2 * 0.12)^0.5

I don’t arrive to 1.0, and in fact, if then I try plugging the 1 directly in the X and seeing if I get to 14.4%, I end up getting 12.52%?

Any advise?

You forgot class vi algebra. (a+b)^2

14,14%=(0.30.2)^2+(0.70.12)^2+ 20.30.20.70.12*correlation

To the right of the equal sign you have a formula for the variance of returns for the portfolio; to the left you have the standard deviation of the portfolio’s returns.

Ooops…you are right.

you are missing the 2 in the formula is must be (.3^2*.2^2+.7^2*.12^2+2*.7*.3*.2*.12*1)^.5