Consider the Following Discrete Probability Distributions of Payoffs for 3

question 69

Multiple Choice

Consider the following discrete probability distributions of payoffs for 3 securities that are held in a DI's trading portfolio (payoff amounts shown are in $millions) : $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Alpha } & 0.50 & 355 \\\hline & 0.49 & 150 \\\hline & 0.01 & - 300 \\\hline\end{array}$$ $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Beta } & 0.50 & 400 \\\hline & 0.49 & 150 \\\hline & 0.0025 & - 300 \\\hline & 0.0075 & - 3,300 \\\hline\end{array}$$ $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Gamma } & 0.49 & 400 \\\hline & 0.49 & 150 \\\hline & 0.01 & - 150 \\\hline & 0.01 & - 2,000 \\\hline\end{array}$$
-Based on your answers to the previous three question, which of the following is true?

• A)Security Alpha represents the riskier of the two assets in the trading portfolio because there is a one-percent probability of loss the following day.
• B)Both securities have the same expected payoff; therefore, it makes no difference which is in the trading portfolio.
• C)Security Beta is the better asset to have in the trading portfolio since there is a 50 percent probability of a $400 payoff versus only $355 with security Alpha.
• D)Both securities have the same expected payoff and value at risk (VAR), therefore it makes no difference which is in the trading portfolio.
• E)According to the expected shortfall measure, if tomorrow is a bad trading day, losses will exceed $25 million.

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Definitions:

Stepping-stone Method

A linear programming method used to find the most efficient way to move products from sources to destinations such that the total transportation cost is minimized.

Northwest-corner

A method used in solving transportation or allocation problems in operations research by starting with the northwest corner of a cost matrix and moving through the matrix to optimize costs or resources.

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