Use the following table: $$\begin{array} { | l | c | c | c | c | }
\hline \begin{array} { l }
\text { States of the } \
\text { Economy }
\end{array} & \begin{array} { c }
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c }
\text { 3-Month } \
\text { T-Bill }
\end{array} & \begin{array} { c }
\text { Large-Company } \
\text { Stock }
\end{array} & \begin{array} { c }
\text { Small-Company } \
\text { Stock }
\end{array} \
\hline \text { Boom } & 0.3 & 4 & 10 & 30 \
\hline \text { Steady } & 0.5 & 4 & 5 & 20 \
\hline \text { Recession } & 0.2 & 4 & 0 & 10 \
\hline
\end{array}$$ How large is the difference between the standard deviation of a small-company stock and a 3-month T-bill?
A)7.0%
B)5.5%
C)4.0%
D)3.5%

Question

Use the following table: $$\begin{array} { | l | c | c | c | c | } 
\hline \begin{array} { l } 
\text { States of the } \
\text { Economy }
\end{array} & \begin{array} { c } 
\text { Probability of the } \
\text { State }
\end{array} & \begin{array} { c } 
\text { 3-Month } \
\text { T-Bill }
\end{array} & \begin{array} { c } 
\text { Large-Company } \
\text { Stock }
\end{array} & \begin{array} { c } 
\text { Small-Company } \
\text { Stock }
\end{array} \
\hline \text { Boom } & 0.3 & 4 & 10 & 30 \
\hline \text { Steady } & 0.5 & 4 & 5 & 20 \
\hline \text { Recession } & 0.2 & 4 & 0 & 10 \
\hline
\end{array}$$ How large is the difference between the standard deviation of a small-company stock and a 3-month T-bill?
A)7.0%
B)5.5%
C)4.0%
D)3.5%

Quizplus · Accepted Answer

The standard deviation of the 3-month T-bill is 0% because its return does not change across different states of the economy, remaining constant at 4%. To find the standard deviation of the small-company stock, we first calculate its expected return:$$E(R) = (0.3 \times 30) + (0.5 \times 20) + (0.2 \times 10) = 9 + 10 + 2 = 21\%$$Then, we calculate the variance:$$Var(R) = (0.3 \times (30-21)^2) + (0.5 \times (20-21)^2) + (0.2 \times (10-21)^2)$$$$Var(R) = (0.3 \times 81) + (0.5 \times 1) + (0.2 \times 121)$$$$Var(R) = 24.3 + 0.5 + 24.2 = 49$$The standard deviation is the square root of the variance:$$\sigma = \sqrt{49} = 7\%$$Therefore, the difference in standard deviation between the small-company stock and the 3-month T-bill is 7% - 0% = 7%.

Use the Following Table How Large Is the Difference Between the Standard Deviation of |