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051

Case 051Volatility tradingHard

A covered call overlay that added 2.1% a year in a ten-year backtest lost about 1.5% in its first live year. The backtest filled at mid, the live market was 2 vol points wide, volatility halved and one month rallied 8%. Where did the gap come from?

Jump TradingChicago · 2018

1The situation

Kalavantin Asset Management runs a large-cap fund tracking the Satpura 50. Its quant team backtested an overlay: at the start of every month, sell one-month calls on the index struck 5% above spot against the whole holding, and let them expire. Over ten years of history, filling every trade at the mid price, the overlay added 2.1% a year to the fund's return.

The overlay went live. In its first year it cost the fund 1.5% against the index. Three things were different from the history: the live bid-offer in those calls was 2 volatility points wide and the desk sold at the bid; implied volatility averaged 12% in the live year against 18% across the backtest decade; and in one month the index rallied 8%, so the calls finished 3% in the money.

2Your task

Attribute the 3.6-point gap between the backtest and the live year to its causes, and say what the backtest should have been built to show.

Quick check

Before working it: which of the three differences is the biggest single cause?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The gap is mostly the volatility regime, then the fills, then the rally. At 12 vol the monthly premium drops from about 0.61% to 0.18% of the holding, which cuts the overlay's expected net from +2.1 to roughly +0.6 a year. Selling 1 vol point under mid each month costs another 0.7 points. The 8% month paid out 3%, about 1.4 points more than the backtest's average payout. Together they land at -1.5%.

Step 1What does the overlay actually earn, and what sets it?

Think of a shopkeeper who sells insurance against his own stock rising in price. His income is the premium; his cost is the months when the stock does rise and he hands over the gain above the strike. The premium on a 5% out-of-the-money one-month call is set almost entirely by implied volatility, so the overlay's income is a bet on the volatility regime, not on the index. Priced with Black-Scholes at a 7% rate and no dividends, the call is worth about 0.61% of spot at 18 vol and 0.18% at 12 vol. Twelve months of selling at 18 vol collects about 7.3% a year; at 12 vol it collects about 2.2%.

Now read the backtest through that lens. Collecting 7.3% and netting 2.1% means the calls paid out about 5.2% a year in rally months, roughly 71% of the premium. That ratio is the market's price for the upside the fund gave away. If the same ratio holds at 12 vol, the overlay collects 2.2%, pays back 1.6% and nets only about 0.6%, before costs. The premium level bar in the waterfall is that fall from 2.1 to 0.6, about -1.5 points.

From the backtest to the live year, percent of the holding per year0+2%+1%-1%+2.1Backtest-1.5Premium level18 to 12 vol-0.7Fills at the bidnot the mid-1.4The 8% rally month-1.5Live yearEach bar changes one thing from the backtest; together they explain the whole gap
The backtest's 2.1% a year falls by about 1.5 points when volatility drops from 18% to 12%, by 0.7 points when every call is sold 1 vol point below mid, and by 1.4 points because the 8% month paid out 3% against an expected 1.6%, reaching the live -1.5%.
Step 2How much do fills cost when the market is 2 vol points wide?

A market quoted 11 bid at 13 offered in volatility terms means the desk sells 1 vol point below the mid every month. The cost per month is the option's vega, about 0.055% of spot per vol point for this call at 12 vol, so the year's fills cost about 0.7% of the holding. The backtest assumed that cost away by filling at mid. For a strategy whose entire gross income is 2.2% a year, a 0.7% execution cost is not a rounding error; it is a third of the income.

Step 3Was the rally month bad luck or part of the design?

The index rose 8%, the calls were struck 5% up, so the fund handed over 3% of the holding in that one month. Payouts of 1.6% were already expected at 12 vol; the 8% month added about 1.4 points of loss above that expectation. Months like it were inside the backtest decade too, which is why the backtest showed only 2.1% net and not 7.3%. The honest reading is that the rally is the smallest of the three causes and the one most likely to reverse.

Same overlay, two worldsBacktest decadeVolatility18%Monthly premium at mid0.61% of holdingFillat the midPayouts on callsabout 71% of premiumNet per year+2.1%Live yearVolatility12%Monthly premium at mid0.18% of holdingFill1 vol point under midPayouts on callsone 8% month paid 3%Net per year-1.5%
The backtest decade and the live year differ on every input: 18 vol against 12, mid fills against 1 vol point under mid, and an average payout against a single 8% month that paid 3%, which turns +2.1% a year into -1.5%.
Step 4What should the backtest have been built to show?

Three things, each of which was available before going live. Fill every sale at the bid, or at mid less half the historical spread, and show the result net of that. Split the decade by volatility regime and report the overlay's net in the low-vol years on their own, because a strategy that only pays in high-vol years is a different product from one that pays every year. And show the distribution of monthly outcomes, not the average, so the committee sees that the overlay earns small amounts most months and gives back large amounts in a few. A backtest that fills at mid and trains on a higher-volatility decade overstates what a premium-selling overlay can earn, and the overstatement is largest exactly when volatility is low. Say the limitation out loud: the attribution here holds the backtest's payout ratio fixed, and that ratio is itself an estimate from ten years of data.

Where candidates lose it

Candidates blame the one dramatic event, the 8% rally, because it is the easiest story to tell. The interviewer wants to see you size the three causes and find that the quiet one, the volatility regime, did most of the damage before the rally happened.

The second miss is treating execution as a detail. On a strategy with a gross income of a few percent, selling 1 vol point under mid is a third of the income, and a backtest that ignores it is not a backtest of the strategy that was traded.

What the interviewer asks next

  • How would you decide whether the live year is a draw from the backtest's distribution or evidence the backtest was wrong?
  • If the overlay sold 10% out-of-the-money calls instead, how would each of the three causes change?
  • What would make you keep the overlay running after a losing year, and what would make you stop it?

Asked at Jump Trading, Quantitative Research, Chicago, 2018 (Wall Street Oasis): Suppose you backtested a trading strategy, it did very well. But in live trading, you keep losing money, what would you do?

← Case 050Saramati Cement trades at Rs 800 and its three-month futures at Rs 820, lot size 500. The rate is 7% continuous and no dividend is due. What is fair value, are the futures rich or cheap, and what does the cash-and-carry lock in per lot?Case 052 →You are short Rs 5 lakh of one-month vega and can only hedge with three-month options. Size the hedge, then show what happens when one-month vol rises 4 points and three-month vol rises 2.

Company names and figures are illustrative.

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