Consider the Following Discrete Probability Distributions of Payoffs for 3

question 86

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) :

$\begin{array} { | l r r | } \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\text { Alpha } & 0.50 & 355 \\& 0.49 & 150 \\& 0.01 & - 300\end{array}$
$\begin{array} { lcc } \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\text {Beta } & 0.50 & 1500 \\& 0.49 & - 300 \\& 0.0025 & - 3,300\end{array}$
$\begin{array} { lcc } \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\text {Gamma } & 0.49 &400 \\&0.49&150 \\&0.01 &-150 \\&0.01&-2,000\end{array}$
What is the expected shortfall (ES) of securities Alpha and Beta at the 99 percent confidence level,respectively (in millions) ?

• A)-$300 and -$3,300
• B)-$3 and -$24.75
• C)-$3 and -$25.50
• D)-$300 and -$300

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Definitions:

Logistic Equation

A mathematical model used to describe the growth of populations under limiting conditions, showing a sigmoid curve.

Aggregated Distribution

A pattern of population distribution where individuals are clustered together in groups.

Random Dispersion

The spatial distribution pattern of a population in which the presence of one individual has no effect on the distribution of other individuals. Compare with clumped dispersion and uniform dispersion.

Clumped Dispersion

A pattern of population distribution in which individuals are aggregated in patches, often due to environmental factors or social interactions, enhancing survival.