Consider the Following Discrete Probability Distributions of Payoffs for 3

question 52

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 payoff,the 99% value at risk (VAR) and the expected shortfall (ES) of security Gamma (in millions) ?

• A)+$248;-$2,000;-$2000
• B)-$248;-$20;-$2,000
• C)-$2.150;-$2,150;-$2,150
• D)+$248;-$21.50;-$20.00

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Definitions:

Independent Variable

The variable in an experimental or observational study that is manipulated or categorized to observe its effect on the dependent variable.

Covariance Value

A measure indicating the extent to which two random variables change together, where a positive value implies direct correlation, and a negative value an inverse correlation.

Least Squares Regression

A statistical method used to determine the line of best fit by minimizing the sum of squares of the differences between observed values and the values predicted by the model.

Correlation Coefficient

A numerical measure that quantifies the degree of correlation or linear relationship between two variables, ranging from -1 to 1.