Question

Jack is looking to try his luck in the stock market and is trying to decide if Ace INC is a good investment or not. He is looking to invest for 1 month only. After examining the past history he has determined that there is a 0.2 probability Ace INC will decline by 5%, 0.5 probability that it will increase by 2%, and a 0.3 probability that the value will increase by 9%.

1. The Expected Return on Ace INC is:

2. The Standard Deviation of the Return on Ace INC. is:

3. The Coefficient of Variation is:

4. If Jack invests $100 in Ace INC, what is the Expected Value of his return?

5. If Jack decided to invest $100 this month and $200 next month, the Expected Value of return is:

6. If Jack decided to invest $100 this month and $200 next month, the variance of his return is:

Answer 1

Mean for probability distribution = μ = Σx * p

Variance = Var(X) = Σ x² * p − μ²

So see this table

Column 1 - X%= % change in Stock

P - Prob of X

X%	P	X*P	X2*P
-5	0.2	-1	5
2	0.3	0.6	1.2
9	0.5	4.5	40.5
Total	1	4.1	46.7

1 . So from table  μ = Σx * p = 4.1

The Expected Return on Ace INC is 4.1%

2. Var(X) = Σ x² * p − μ² = 46.7 - 4.1² = 29.89

Std Dev. = Var^0.5 = 29.89^0.5 = 5.47 %

3. Coefficient of variance = .   

C_v = 5.47/4.1 = 1.33

4 The Expected Return on Ace INC is 4.1%

So for 4.1 * 100 / 100 = 4.1 $

5 The Expected Return will be 4.1 * 100 / 100 + 4.1 * 200 / 100 = 12.3/2 = 6.15 $

6.Similarly variance = 5.47*3/2 = 8.205$

If any doubt please feel free to ask through the comments section. Thank You