Financial Risk Manager Part 1
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The average salary for an employee at Capital Asset Managers is $50,000 per year, with a variance of 6,000,000. This year, the management has decided to award bonuses to every employee:
- A Christmas bonus of
$1,000 - An incentive bonus equal to 15% of the employee's salary
Calculate the standard deviation of employee bonuses.
Other
Community
NNikitesh
A
$8,500
B
$250
C
$367
D
$10,500
Explanation:
To compute the bonus, we apply the following linear transformation to each employee's salary:
Y = α + βx
Y = 1,000 + 0.15x
where Y is the transformed variable (bonus), X is the original variable (salary), β is the scale constant, and α is the shift constant.
The variance of Y, i.e., variance of bonuses, is given by:
Var(Y) = Var(α + βx) = β²Var(X) = β²σ²
The variance of salary [Var(X) = σ], is 6,000,000. Thus,
Var(Y) = 0.15² × 6,000,000 = 135,000
Standard deviation is equal to the square root of the variance, and therefore the standard deviation of employee bonuses is equal to the square root of 135,000 or $367.42
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