Question

Please solve and show the calculation

Question 16 8 pts Given the following information, what is the standard deviation for this stock? (Hint: you'll need to find the expected return first) Probabilities: Recession: 0.3 Normal: 0.4 Boom: 0.3 Returns: Recession: -9% Normal: 7.5% Boom: 16% 09.88% 09.18% O 8.42% 11.35% 7.38%

Answer 1

From the given data, we can calculate the standard deviation as follow:

p(x)	x	(x^2)*P(x)	x*p(x)
0.3	-9%	0.00243	-0.027
0.4	7.50%	0.00225	0.03
0.3	16%	0.00768	0.048

So, standard deviation is $\sqrt{\sum x^{2}p(x) - u^{2}}$

where u =$\sum xp(x)$

=> u = -0.027 + 0.03 + 0.048 = 0.051

So, standard deviation = $\sqrt{0.00243+0.00225+0.00768 - 0.051^{2}}$ = 0.0988 or 9.88%