Consider the Following Discrete Probability Distributions of Payoffs for 3

question 68

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) : $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Alpha } & 0.50 & 355 \\\hline & 0.49 & 150 \\\hline & 0.01 & - 300 \\\hline\end{array}$$ $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Beta } & 0.50 & 400 \\\hline & 0.49 & 150 \\\hline & 0.0025 & - 300 \\\hline & 0.0075 & - 3,300 \\\hline\end{array}$$ $$\begin{array} { | l | l | l | } \hline \text { SECURITY } & \text { PROBABILITY } & \text { PAYOFF } \\\hline \text { Gamma } & 0.49 & 400 \\\hline & 0.49 & 150 \\\hline & 0.01 & - 150 \\\hline & 0.01 & - 2,000 \\\hline\end{array}$$
-What is the one-day, 99% confidence level, value at risk (VAR) of securities Alpha and Beta, respectively (in millions) ?

• A)$3 and $25.50
• B)$3 and $0.75
• C)$248 and 248
• D)$300 and $300
• E)300 and 3,300

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Definitions:

Independent Variable

In an experiment, it is the variable that is manipulated or changed to observe its effects on the dependent variable.

Residual Analysis

The analysis of the residuals used to determine whether the assumptions made about the regression model appear to be valid. Residual analysis is also used to identify outliers and influential observations.

Regression Model

A statistical technique used to estimate the relationship between a dependent variable and one or more independent variables.

SST

A measure of the total variation in a dataset that is the sum of squares total, often used in the context of regression analysis.