Question

Suppose a bank holds a $2 million trading position in stocks that has a beta 2.0. Suppose that the daily changes in returns for the portfolio have a mean 0 and standard deviation 1%. Determine the bank's DEAR for this equity position using a 99 percent confidence level.

Answer 1

Here, Trading Position of the bank = $ 2 Million, Beta = 2.0

Daily Standard Deviation of Portfolio = 1%, Mean = 0.

Calculation of VAR of this equity position using a 99% confidence level:

VAR means Value at Risk. It calculates the maximum loss expected (or worst case scenario) on an investment, over a given period of time and at given a specific degree of confidence.

Here we have been given daily standard deviation of the portfolio so we are required to calculate daily VAR.

Further, we are required to calculate VAR at 99% Confidence Level i.e. 1% VAR.

Formula to Calculate VAR:

VAR = z-score * Standard Deviation of Portfolio * Portfolio Value

What is z-score?

z-score represents the probability at a given confidence level which helps us to calculate the mum expected loss.

Now, Z-score for 99% Confidence Level is 2.33 (derived from a z-score table).

So, VAR = 2.33 *  (Beta of Stock * Daily Standard Deviation) * $ 2,000,000.

VAR = 2.33 * 2% * * $ 2,000,000.

VAR = $ 93,200.

The VAR (1%) i.e. at a confidence level of 99%, of $ 93,200 indicates that there is a 1% chance on any given day the portfolio will experience a loss of $ 93,200 or more. Also, there is a 99% chance that on any given day the portfolio will experience gain or loss less than $ 93,200.