Question

1. 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)

Answer 1

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.