Consider the following:
				Returns
Scenario		Probability		Auto	Gold		Portfolio (75% auto, 25% gold)
Recession		1/3		-8	+20		.75(-8) + .25 (20) = -1.0%
Normal		1/3		+5	+3		.75(5) + .25 (3) = +4.5%
Boom		1/3		+18	-20		.75(18) + .25 (-20) = +8.5%
Expected Return
Auto		(-8+5+18)/3 = 5%
Gold		(+20+3-20)/3 = 1%
Portfolio		(-1+4.5+8.5)/3 = 4%
Variance
Auto		(169+0+169)/3 = 112.7 (std. 10.6%)
Gold		(361+4+441)/3 = 268.7 (std. 16.4%)
Portfolio		(25+.25 +20.25)/3 = 15.2 (std 3.9%)
1) Show expected return & variance of a 90% auto, 10% gold portfolio
2) Show expected return & variance of a 25% auto 75% gold portfolio