Question

1. The following returns have been estimated for Security T and Security S:

   Scenario	Security T	Security S
   1	20%	10%
   2	13%	-6%
   3	15%	20%

   Each scenario is equally likely to occur, and you plan to invest 70% in Security T and 30% in Security S. What is the standard deviation of the rate of return of the portfolio? Round your answer to the nearest tenth of a percent.

   		A) 0.0%
   		B) 4.5%
   		C) 19.9%
   		D) 59.7%

Answer 1

Solution:
	Answer is B) 4.5%
Working Notes:
	Each scenario is equally likely to occur
	Means each Scenario probability (1/3) as there are three scenario
Hence
	Weight in the portfolio	70%	30%
Probability	Scenario	Security T	Security S
(1/3)	1	20%	10%
(1/3)	2	13%	-6%
(1/3)	3	15%	20%
	First of all we calculate Return of portfolio at each scenario
Return of portfolio at 1    (r1)	Return of portfolio at 1 (r1)= Weighted average return of individual stock
	= 0.70 x (20%) + 0.30 x (10%)
	=0.17
	=17%
Return at 2 (r2)	Return at 2 (r2)= Weighted average return of individual stock
	= 0.70 x (13%) + 0.30 x (-6%)
	=0.073
	=7.30%
Return at 3 (r3)	Return of portfolio at 3 (r3)= Weighted average return of individual stock
	= 0.70 x (15%) + 0.30 x (20%)
	=0.1650
	=16.50%
	Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=17% x (1/3)+ 7.30% x (1/3)+ 16.50% x (1/3)
	=0.136
	=13.60 %
	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 ]
	=(1/3) x(17% -13.60%)^2 + (1/3) x(7.30% -13.60%)^2 +(1/3) x(16.50% -13.60%)^2
	=0.001988667
	The standard deviation of this portfolio = Square root of the variance of this portfolio
		=(0.001988667)^(1/2)
		=0.044594473
		=0.0446
		=0.0450	nearest tenth of a percent
		=4.5%
Please feel free to ask if anything about above solution in comment section of the question.