TABLE 17-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
$\begin{array}{llcc}
\text {States } &\text { A1 }&\text { A2 }&\text {A3 }\
\hline1&12&-2&8\
2&4&10&5
\end{array}$

$\text {where:}$$\quad $$\quad $ $\text {S1 is state of nature 1 }$$\quad $$\text {A1 is action alternative 1}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\text {S2 is state of nature 2}$$\quad $$\text { A2is action alternative 2}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$ \text {A3 is action alternative3 } $
-Referring to Table 17-1, if the probability of S1 is 0.5, what is the return to risk ratio for A3?
A) 2
B) 1.5
C) 4.333
D) 0.667

Question

TABLE 17-1
The following payoff table shows profits associated with a set of 3 alternatives under 2 possible states of nature.
 $\begin{array}{llcc}
  \text {States  } &\text { A1 }&\text { A2 }&\text {A3  }\
\hline1&12&-2&8\
2&4&10&5
\end{array}$

$\text {where:}$$\quad $$\quad $ $\text {S1 is state of nature  1 }$$\quad $$\text {A1  is action alternative 1}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\text {S2 is state of nature 2}$$\quad $$\text { A2is action alternative 2}$
$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$ \text {A3 is action alternative3 } $
-Referring to Table 17-1, if the probability of S1 is 0.5, what is the return to risk ratio for A3?
A) 2
B) 1.5
C) 4.333
D) 0.667

Quizplus · Accepted Answer

The return to risk ratio is calculated by dividing the expected return by the standard deviation of the return. The expected return is the sum of the products of the probabilities and the returns for each state of nature. The standard deviation is the square root of the variance, which is the sum of the squared deviations from the mean.For A3, the expected return is (0.5 * 8) + (0.5 * 5) = 6.5. The variance is (0.5 * (8 - 6.5)^2) + (0.5 * (5 - 6.5)^2) = 2.25. The standard deviation is the square root of 2.25, which is 1.5.Therefore, the return to risk ratio for A3 is 6.5 / 1.5 = 4.333.

TABLE 17-1 the Following Payoff Table Shows Profits Associated with a Set

TABLE 17-1
the Following Payoff Table Shows Profits Associated with a Set