Question

Suppose that an FI holds a $15 million trading position in stocks that reflect the Canadian stock market index (e.g., the S&P TSX). Over the last year, the ?m of the daily returns on the stock market index was 156 bp. Calculate the one-day VaR for this portfolio of stocks using a 99 percent confidence limit.

Answer 1

To calculate the one-day VaR for a $15 million position in stocks that reflect the Canadian stock market index with 156 bp average daily return, at a 99 percent confidence limit, the result is $544,680. This means there's a 1% chance of the portfolio losing more than this amount in one day.

Step-by-step explanation:

To calculate the one-day VaR (Value at Risk) for a portfolio using a 99 percent confidence limit, we first need to understand that VaR is a statistical measure used to assess the risk of loss on a portfolio. For a $15 million position in stocks reflecting the Canadian stock market index with an average daily return (μ) of 156 basis points (bp) or 1.56%, we can use the Z-score associated with the 99% confidence level.

To find the VaR at a 99% confidence level, one typically uses a Z-score of approximately 2.33 (for a one-tailed test from Z-tables). This Z-score is multiplied by the standard deviation of the portfolio returns to estimate the loss that will not be exceeded 99% of the time.

The VaR calculation would then be:

One-day VaR = Portfolio Value × Z-score × (Standard Deviation of daily returns / 100)

One-day VaR = $15,000,000 × 2.33 × (1.56% / 100) = $15,000,000 × 2.33 × 0.0156 = $544,680

Therefore, the one-day VaR at a 99% confidence level for the portfolio is $544,680, meaning there's a 1% chance that the portfolio could lose more than that amount in one day.