Question

Stock C
		Rate of Return (r )	Probability ( p )
The Economic Status	Optimistic	12 %	30 % or 0.30
	Most Likely	9 %	50 % or 0.50
	Pessimistic	-8%	10 % or 0.10

1. Calculate the Expected Rate of Return E(r) for Stock C.

2. Calculate Variance and Standard Deviation for Stock C.
3. Calculate the Sharpe Ratio, assuming risk free rate is 4%.

It's ok tha t the probability is = 90

please make sure the answer is correct 100%

Answer 1

1) Expected rate of return on C

Economic Status	Rate of return	Probablity	Expected return
Optimistic	12%	0.30	3.60
Most Likely	9%	0.50	4.50
Pessimistic	-8%	0.10	-0.80
		Total	7.30%

2) Variance and Standard Deviation

Economic Status	Rate of return	Probablity	(Return - average)2	Probablity * (Return - average)2
Optimistic	12%	0.30	22.09	6.627
Most Likely	9%	0.50	2.89	1.445
Pessimistic	-8%	0.10	234.09	23.409
		Total		31.481

Variance = [ Sum of Probablity * (Return - average)² ]

              = 31.481 %²

Standard Deviation = [ Sum of Probablity * (Return - average)² ]^1/2

                            = [ 31.481 ]^1/2

                            = 5.61% Answer

3) Sharpe ratio = [ ( Expected retun on security - Risk free rate ) / Standard deviation ]

                      = [ ( 7.3 - 4 ) / 5.61 ]

                      = 0.5882 Answer