A book is $200m long a basket with beta 1.0 and $150m short a basket with beta 1.2. Stress it for a 20% market fall together with a 10% adverse move on $50m of net style exposure. What is the loss, and what does a value at risk model miss here?

A book is $200m long a basket with beta 1.0 and $150m short a basket with beta 1.2. Stress it for a 20% market fall together with a 10% adverse move on $50m of net style exposure. What is the loss, and what does a value at risk model miss here?

Approach: Convert both legs into beta dollars before applying the market shock, then add the style shock on the stated net exposure.

-$9m. Net beta exposure is 200*1.0 - 150*1.2 = $20m of beta dollars, so a 20% market fall costs 0.20*20 = $4m, and 10% on $50m of net style exposure costs a further $5m, giving $9m. The book is market neutral on notional and carries $20m of beta exposure, which is where the first four million comes from. A value at risk model fitted to the last two years would size the equity shock off a realised volatility that never contained a 20% month and would treat the two shocks as close to independent, so it understates both the size and the joint move. Stress testing fixes the scenario rather than estimating it, which is why it survives a correlation regime the sample period never held.

Follow-up: How would you choose the size of the style shock so the scenario is severe and still plausible?

Key concepts: stress testing, beta exposure, market neutral, value at risk.