E(R_A) = 0.4 * 0.3 + 0.6 * (-0.10) = 0.06

E(R_B) = 0.4 * (-0.05) + 0.6 * 0.25 = 0.13

Expected Returns for a Portfolio with 50% of your money invested in A and 50% invested in B:

If there is a Boom, we have: R_P = 0.5 * 0.30 + 0.5 * (-0.05) = 0.125

If there is a Recession we have: R_P = 0.5 * (-0.10) + 0.5 * 0.25 = 0.075

hence,

E(R_P) = 0.4 * 0.125 + 0.6 * 0.075 = 0.095

Variance and S.D. of the Returns for Stock A and Stock B:

VAR(R_A) = 0.4 * (0.30 - 0.06)² + 0.6 * (-0.10 - 0.06)² = 0.0384
 

VAR(R_B) =  0.4 * (-0.05 - 0.13)² + 0.6 * (0.25 - 0.13)² = 0.0216

SD(R_A) = (0.0384)^0.5 = 0.1960

SD(R_B)  = (0.0216)^0.5 = 0.1470

Covariance  and Correlation Coefficient for Stock A and Stock B:

COV(R_AR_B) = 0.4 * (0.3 - 0.06) * (-0.05 - 0.13) + 0.6 * (-0.10 - 0.06) * (0.25 - 0.13) = -0.0288

CORR(R_AR_B) = -0.0288 / (0.1960 * 0.1470) = -0.99
 

Variance and S.D. of the Portfolio (2 ways):

Using the formula for the variance of a portfolio:

VAR(R_P) = (0.5)² * 0.0384 + (0.5)² * 0.0216 + 2 * 0.5 * 0.5 * -0.0288 = 0.0006

SD(R_P) = (0.0006)^0.5 = 0.0245

Or, using the portfolio returns and expected returns directly:

VAR(R_P) = 0.4 * (0.125 - 0.095)² + 0.6 * (0.075 - 0.095)² = 0.0006

SD(R_P) = (0.0006)^0.5 = 0.0245

Result:

Because of the high negative correlation (-0.99 and -1.00 is the lowest), we have a strong diversification effect.
The movements of the two stock cancel each other almost out, when one does well, the other does poorly, and
vice versa. You can see that the individual risks of the two stocks [SD(R_A) and SD(R_B)] are much higher than when
combined in equal proportions into a portfolio.

Exercise:

See what happens when you put 75% of your money in stock A and 25% in stock B. Is there still a diversification effect?