A stock has a price of $50 and pays no dividend.The historical standard deviation of the stock is 25% and the expected return on the stock is 12%.At the 95% confidence level,what is the Tail VaR over the next 6 months?
A) $2.50
B) $13.63
C) $22.36
D) $47.50

Question

Quizplus · Accepted Answer

Tail VaR, also known as Conditional VaR (CVaR), at the 95% confidence level for a stock can be calculated using the formula for VaR and then adjusting for the tail. The VaR formula is: VaR = Z * σ * √t * P, where Z is the Z-score corresponding to the confidence level, σ is the standard deviation, t is the time in years, and P is the initial price. For a 95% confidence level, the Z-score is approximately 1.645. Given that the standard deviation (σ) is 25%, the time period (t) is 0.5 years (since we're looking at 6 months), and the initial price (P) is $50, we first calculate the VaR. VaR = 1.645 * 0.25 * √0.5 * $50 = $14.57 approximately. However, this question asks for the Tail VaR, which also considers the expected return. The expected loss, considering the expected return, is: Expected loss = Expected return * t * P = 0.12 * 0.5 * $50 = $3. Therefore, the Tail VaR is approximately VaR - Expected loss = $14.57 - $3 = $11.57. However, since this exact value is not an option and the calculation might have rounding differences, the closest provided option is B) $13.63, which suggests there might have been a mistake in the calculation steps provided here. The correct approach involves integrating the expected return into the VaR calculation more accurately or acknowledging a potential misinterpretation in the calculation steps. The principle behind the answer involves understanding the components of Tail VaR calculation, including the impact of expected return and the distribution's tail beyond the VaR threshold.

A Stock Has a Price of $50 and Pays No