As a portfolio manager for Bank of America Merrill Lynch, you are managing a portfolio of $48.50 million. You would like to estimate how much your portfolio might be losing over the next 9 trading days. Suppose the portfolio has a daily volatility of 2.5%.
a. What is 9 day volatility?
(sample answer: 15.50% or 0.1550)
b. What is the VaR (in dollars) over a 9 day time period at a 95% confidence level?
(Sample answer: $2.5 million; or $2,500,000.0)
a. What is 9 day volatility?
Volatility over 9 days period = Daily volatility *√9
= 2.5% *√9 = 2.5% * 3 = 7.5%
b. What is the VaR (in dollars) over a 9 day time period at a 95% confidence level?
Formula to calculate value at risk over a 9 day time period at the 95% confidence level
VaR over a 9 day time period = V0 * (z *σ)
Where,
V0 is the value of investment = $48.50 million
Z-score at 95% confidence interval = 1.96
Volatility over 9 days period of asset σ = 7.5%
Therefore
VaR over 9 days’ time period = $48,500,000* 1.96 *7.5%
= $7,129,500
Therefore 95% of the time, you will not lose more than $7,129,500 of your investments in 9 days’ time period.
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