Case 059Position sizing and bankrollWarm up
A Rs 100 crore book targets 10% annual volatility. The asset's volatility is 25% today against 15% last month. What gross exposure does the target imply now and then, and what happens if volatility spikes to 40%?
1The situation
Kovantra Capital runs a Rs 100 crore book in a single futures position on an equity index. The mandate sets a volatility target of 10% a year on capital: the book's exposure is resized every day so that its expected volatility stays at the target, using a trailing estimate of the index's volatility.
Last month the index's volatility was 15%. Today it is 25%. The risk committee asks what exposure each level implies, and what the rule would do if volatility spiked to 40%, as it does in a sharp sell-off.
2Your task
Compute the gross exposure at 15%, 25% and 40% volatility, say what the rule forces the book to trade in a spike, and name what the rule cannot protect against.
Quick check
Volatility rises from 25% to 40%. What does the volatility target make the book do?
Worked solution
Try it on paper, then open one step at a time.
30-second answerThe answer to give first
The target implies Rs 66.7 crore of exposure at 15% volatility, Rs 40 crore at 25% and Rs 25 crore at 40%. Exposure is capital times target over volatility, so it falls as risk rises. A spike from 25% to 40% forces the book to sell Rs 15 crore exactly when spreads are widest, and because the volatility estimate trails, the first days of a spike run at well above target before the cut arrives.
Step 1How does a volatility target turn into a position size?
Think of driving to keep a fixed safety margin rather than a fixed speed: on a dry road you drive at 80, in heavy rain at 50, and the risk stays about the same. A volatility target does this with money: exposure equals capital times the target divided by the asset's volatility, so the book's risk stays at 10% whatever the asset is doing. At 15% volatility that is 100 x 10/15 = Rs 66.7 crore; at 25%, Rs 40 crore; at 40%, Rs 25 crore. Each of these positions has the same expected annual swing: about Rs 10 crore on the Rs 100 crore of capital, or about Rs 63 lakh on a typical day.
Step 2What does the rule force the book to trade in a spike?
Going from 25% to 40% volatility cuts exposure from Rs 40 crore to Rs 25 crore. The book must sell Rs 15 crore into a falling, volatile market, the moment when trading is most expensive. If a normal day costs 10 bps to trade and a stressed day 30 bps, the cut costs about Rs 4.5 lakh, three times what the same trade would cost in calm conditions. Many volatility-targeted funds sell together in these moments, which deepens the fall they are reacting to. The rule does the reverse when calm returns, buying back as volatility falls, often after the market has recovered.
Step 3What can the rule not protect against?
The rule uses a trailing estimate, so it learns about a spike only after it has happened. On the first day volatility jumps from 25% to 40%, the book still holds Rs 40 crore, so its daily risk is about Rs 101 lakh against a target of 63 lakh, 1.6 times what the mandate intends. And a single gap, such as an overnight fall of 8%, is not reduced by any resizing: it costs 8% of whatever exposure was held when it happened, Rs 3.2 crore on Rs 40 crore. The second limit sits at the other end. When volatility is very low the formula asks for huge exposure, Rs 200 crore at 5%, which is why every real volatility target carries a leverage cap; here 1.5 times capital would stop it at Rs 150 crore.
| Asset volatility | Gross exposure, Rs crore | Exposure / capital | Typical daily move, Rs lakh |
|---|---|---|---|
| 5% | 150.0 (capped) | 1.50x | 47 |
| 15% | 66.7 | 0.67x | 63 |
| 25% | 40.0 | 0.40x | 63 |
| 40% | 25.0 | 0.25x | 63 |
Where candidates lose it
Candidates often compute the three exposures correctly and stop, as if the rule were free. The interviewer wants the second half: the rule sells into stress, pays stressed costs to do it, and moves with every other fund running the same rule.
The second miss is believing a volatility target caps losses. It caps expected volatility using yesterday's estimate; a gap or the first days of a spike land on the old, larger position.
What the interviewer asks next
- How would a shorter volatility lookback change the trade-off between lag and turnover?
- Why might a fund target volatility with a band rather than a point, say 9% to 11%?
- What happens to a volatility-targeted book's return if volatility and returns are negatively correlated?
Company names and figures are illustrative.