You have a portfolio of two mutual funds, A and B, with 75% invested in A.
E(RA) = 20%; E(RB) = 12%.
The values on the main diagonal are the variances and the other values are the covariances.
The expected return on the portfolio is:
E(Rp) = wA E(RA) + (1 - wA) E(RB) = 0.75 x 20% + 0.25 x 12% = 18%
The correlation matrix:
σ(RA) = (625)1/2 = 25, σ (RB) = (196)1/2 = 14
ρ(RA, RB) = Cov(RA, RB) / [σ(RA) x σ(RB)] = 120 / (25 x 14) = 0.342857, or 0.34
The variance of the portfolio is:
σ2(RP) = wA2σ2(RA) + wB2σ2(RB) + 2wAwBCov(RA, RB)
= (0.75)2(625) + (0.25)2(196) + 2(0.75)(0.25)(120) = 408.8125
The standard deviation is σ(RP) = (408.8125)1/2 = 20.22%.
It's also possible that you could be given a correlation matrix, which is simply a matrix that shows the correlation between any two assets in the portfolio. Consider the following correlation matrix for assets A, B and C.
Note that the matrix is symmetrical about its main diagonal (top left to bottom right). The entries on this diagonal are all 1, as the correlation between any variable and itself is obviously 1. Similarly, the correlation between RA and RB is 0.53, the correlation between RA and RC is 0.78, and the correlation between RB and RC is 0.6.
The steps that would now be involved would be:
Familiarize yourself with the two different types of matrices, as explained in this section, and know what each term represents in each covariance formula.