Question

Suppose an FI has a $1 mil market value position in 0-cpn bonds of 7 years to maturity with a FV of $1,631,483. The yield today is 7.243% per year. If the standard deviation is 10 bp and you have a multiplier of 2.33. What is the One-day VaR?

Answer 1

The one-day Value at Risk (VaR) is calculated by multiplying the market value of the bond position by the daily standard deviation and the VaR multiplier. The standard deviation is adjusted to daily volatility and the VaR represents the potential loss with a specified confidence level.

Step-by-step explanation:

The student is asking about calculating the one-day Value at Risk (VaR) for a zero-coupon bond portfolio using the given market value, standard deviation of yield changes (also known as basis points or bp), and a VaR multiplier. The VaR represents the potential loss in value of a risk position due to market movements over a certain time horizon, with a specified confidence level.

To calculate the one-day VaR, we first need to convert the given standard deviation of 10 basis points (which is 0.10%) to a daily volatility by dividing by the square root of the number of days in a year (assuming 250 trading days, for simplification, it would be the square root of 250). Then, we multiply the daily volatility by the given VaR multiplier of 2.33. Finally, we multiply the result by the market value of the position to estimate the potential one-day loss at the given confidence level.

Here's the formula for one-day VaR: One-day VaR = Market Value × (Standard Deviation / √250) × Multiplier. Applying the numbers from the question: One-day VaR = $1,000,000 × (0.10% / √250) × 2.33.