Question

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%)
Homework:
1) Show expected return & variance of a 90% auto, 10% gold portfolio
2) Show expected return & variance of a 25% auto 75% gold portfolio

Answer 1

1)  

				Returns
Scenario		Probability		Auto	Gold		Portfolio (90% auto, 10% gold)
Recession		0.33		-8	20		.9(-8) + .1 (20) = -5.2%
Normal		0.33		5	3		.9(5) + .1 (3) = +4.8%
Boom		0.33		18	-20		.9(18) + .1 (-20) = +14.2%
Expected Return
Auto		(-8+5+18)/3 = 5%
Gold		(+20+3-20)/3 = 1%
Portfolio		(-5.2+4.8+14.2)/3 = 4.6%
Variance
Auto		(169+0+169)/3 = 112.7 (std. 10.6%)
Gold		(361+4+441)/3 = 268.7 (std. 16.4%)
Portfolio		(96.04+.04 +92.16)/3 = 62.74 (std 7.92%)

2)

				Returns
Scenario		Probability		Auto	Gold		Portfolio (25% auto, 75% gold)
Recession		0.33		-8	20		.25(-8) + .75 (20) = +13%
Normal		0.33		5	3		.25(5) + .75(3) = +3.5%
Boom		0.33		18	-20		.25(18) + .75 (-20) = -10.5%
Expected Return
Auto		(-8+5+18)/3 = 5%
Gold		(+20+3-20)/3 = 1%
Portfolio		(13+3.5-10.5)/3 = 2%
Variance
Auto		(169+0+169)/3 = 112.7 (std. 10.6%)
Gold		(361+4+441)/3 = 268.7 (std. 16.4%)
Portfolio		(121+2.25+156.25)/3 = 93.17 (std 9.65%)

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