Question

Use the following table of states of the economy and stock returns to calculate the percentage standard deviation of a portfolio of a portfolio of 40 percent Roll and the rest in Ross.

		Security if State	Returns Occurs
	Prob of State of Economy	Roll	Ross
Bust	0.1	-17%	27%
Boom	?	39	9

Answer 1

Solution:
	Standard deviation of the portfolio	3.48%
Working Notes:
Notes:	Since there is only two state of economy , and probability of one state is given 0.10 for BUST then For Probability of BOOM = 1 - probability of bust = 1 - 0.10 = 0.90   as total probability is 1
	Hence, Prob of State of Economy
	BOOM   = 0.90
	40 percent invested in ROLL and the balance in ROSS
	Total Portfolio investment from both security will be 100%
	Invested in ROSS 100% -invested in ROLL
	Invested in ROSS= 100% -40%
	Invested in ROSS= 60% = 0.60
	Invested in ROLL= 40% = 0.40
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 0.40 x (-17%) + 0.60 x (27%)
	=9.40%
Return at Bust   (r Bust)	Return at Bust   (r Bust)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 0.40 x (39%) + 0.60 x (9%)
	=21.00%
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=0.10 x 9.40% + 0.90 x 21%
	=19.84%
The variance of this portfolio = Sum of [(Prob. Of each state) x ( (Return of the portfolio at each state - Expected return of the portfolio))^2 ]
=(0.10 x (9.40% - 19.84%)^2 ) + (0.90 x (21% - 19.84%)^2 )
=0.001211040
	The standard deviation of Portfolio = Square root of the variance of portfolio
	The standard deviation of Portfolio = (0.001211040)^(1/2)
	The standard deviation of Portfolio = 0.034800
	The standard deviation of Portfolio	3.48%
Please feel free to ask if anything about above solution in comment section of the question.