Question

The Lubin’s Investment Team is considering investing in two securities, A and B, and the relevant information is given below:

State of the economy	Probability	Return on A(%)	Return on B(%)
Trough	0.05	-20%	2%
Recession	0.4	-5%	2%
Expansion	0.5	15%	2%
Peak	0.05	20%	2%

Calculate the expected return and standard deviation of two securities.

Answer 1

Expected or Average return =sum of (Prob.*Return)              
Variance formula = Sum of (Probability * (Actual return - Expected return)^2)              
Standard deviation formula = √ Variance              
              
Market condition   Prob.   Return A   Prob*Return   (Prob.*( return- Expected return)^2)
              
Trough   0.05   -20.00   -1.00   32.51
Recession   0.40   -5.00   -2.00   44.10
Expansion   0.50   15.00   7.50   45.13
Peak   0.05   20.00   1.00   10.51
              
              
Total           5.50   132.25
Expected Return=   5.50   %      
              
Variance of stock Investment is   132.25          
standard deviation = √(132.25)              
11.50   %          
              
So, Expected return of A is 5.5% and standard deviation is 11.50%              

Market condition   Prob.   Return B   Prob*Return   (Prob.*( return- Expected return)^2)  
                  
Trough   0.05   2.00   0.10   0.00  
Recession   0.40   2.00   0.80   0.00  
Expansion   0.50   2.00   1.00   0.00  
Peak   0.05   2.00   0.10   0.00  
                  
                  
Total           2.00   0.00  
Expected Return=   2.00   %          
                  
Variance of stock Investment is   0.00              
standard deviation = √(0)                  
0.00   %              
                  
So, Expected return of B is 2% and standard deviation is 0%