The firm has estimated the three different returns under different states of economy. The probabilities of economy reaching a particular state and the returns are provided in the table below. What is the standard deviation of the firm's returns?
$$\begin{array} { | l | l | l | l | }
\hline \text { State of Economy } & \text { Recession } & \text { Normal } & \text { Boom } \
\hline \text { Probability } & 0.4 & 0.5 & 0.1 \
\hline \text { Return } & - 100 & 200 & 500 \
\hline
\end{array}$$
A) 161.55
B) 192.09
C) 26100
D) 36900

Question

The firm has estimated the three different returns under different states of economy. The probabilities of economy reaching a particular state and the returns are provided in the table below. What is the standard deviation of the firm's returns?
$$\begin{array} { | l | l | l | l | } 
\hline \text { State of Economy } & \text { Recession } & \text { Normal } & \text { Boom } \
\hline \text { Probability } & 0.4 & 0.5 & 0.1 \
\hline \text { Return } & - 100 & 200 & 500 \
\hline
\end{array}$$
A) 161.55
B) 192.09
C) 26100
D) 36900

Quizplus · Accepted Answer

To calculate the standard deviation of the firm's returns, we first need to find the expected return and then use it to calculate the variance before taking the square root to get the standard deviation. The expected return (E(R)) is calculated as follows:$$E(R) = (0.4 \times -100) + (0.5 \times 200) + (0.1 \times 500) = -40 + 100 + 50 = 110$$Next, we calculate the variance ($\sigma^2$):$$\sigma^2 = (0.4 \times (-100 - 110)^2) + (0.5 \times (200 - 110)^2) + (0.1 \times (500 - 110)^2)$$$$= (0.4 \times 44100) + (0.5 \times 8100) + (0.1 \times 152100)$$$$= 17640 + 4050 + 15210 = 36900$$The standard deviation ($\sigma$) is the square root of the variance:$$\sigma = \sqrt{36900} = 192.09$$Therefore, the correct answer is B) 192.09.

The Firm Has Estimated the Three Different Returns Under Different