show how the portfolio SD is 3.9

Table 11.6 Rate of return assumptions for two stocks

		Rate of Return (%)
Scenario	Probability	Auto Stock	Gold Stock
Recession	1/3	8	+20
Normal	1/3	+5	+3
Boom	1/3	+18	20
		Rate of Return (%)
Scenario	Probability	Auto Stock	Gold Stock	Portfolio Return (%)*
Recession	1/3	8	+20	1.0
Normal	1/3	+5	+3	+4.5
Boom	1/3	+18	20	+8.5
Expected return		5	1	4
Variance		112.7	268.7	15.2
Standard deviation		10.6	16.4	3.9??????

Show why standard deviation of portfolio is 3.9.

Hint: After calculate Covariance, use SDp p = (Wa2 SDa a 2 + Wb2 SDb b 2 + 2 * Wa * Wb Cova,b) a,b)