---
title: "Options-Implied Signals for Stocks"
book: "Strategies I: Equities and Futures"
subject: quant
language: en
chapter: 15
exercises: 8
source: https://one-course.com/books/quant/8/en/chapter/15-options-implied-signals-for-stocks
---

# Chapter 15 — Options-Implied Signals for Stocks

When a stock’s out-of-the-money puts become expensive relative to its at-the-money options, someone is paying up for protection, and the stock tends to fall. Xing, Zhang and Zhao found that stocks with the steepest volatility smirks underperformed those with the flattest by 10.9% a year, risk-adjusted, and had the worst earnings surprises the following quarter: informed traders with bad news prefer puts. The option market is where leverage is cheap and shorting is unnecessary, so it is where some information shows first. This chapter adds an options layer to the synthetic market, with informed traders who buy options ahead of planted earnings news, and measures what skew, the call–put volatility spread and option volume predict, how fast it decays, and why it is best traded around events. The build is `firm.optsignal`.

## 15.1 Skew as a signal

**Definition 15.1 (Informed options trading).**

*Informed options trading* is trading in a stock’s options by investors with private information about the stock, who choose options over the stock for their leverage and, for bad news, to avoid the costs and constraints of short selling; their demand moves the prices and volumes of the options they buy before the information reaches the stock.

The volatility skew (Book 1, chapter 25) is the extra implied volatility of out-of-the-money puts over at-the-money options. It is there on every stock (a premium for crash protection), and it moves when buyers of puts outnumber sellers. In the synthetic options layer every stock has an at-the-money implied volatility equal to its realised volatility plus a two-point premium, a put skew of three points, and daily noise of one point in each; informed traders, in the ten days before each earnings announcement (chapter 7’s calendar), buy puts ahead of bad surprises and calls ahead of good ones, and each standard deviation of surprise moves the implied volatility of the options they buy by 0.3 points. Bad news is weighted 1.5 times good news, for the reason Johnson and So give below. The skew’s sign as a signal is negative: a steep skew predicts a fall.

## 15.2 Implied minus realised volatility

**Definition 15.2 (Implied volatility spread).**

A stock’s *implied volatility spread* is the difference between the implied volatilities of its calls and its puts at matched strikes and maturities; under put–call parity it is zero, and a positive spread means calls are relatively expensive.

Cremers and Weinbaum measured deviations from put–call parity this way and found that stocks with relatively expensive calls outperformed those with relatively expensive puts by 50 basis points a week, not explained by short-sale constraints, stronger where options were liquid and stocks were not, and declining over their sample. Bali and Hovakimian separated two spreads: the call–put spread (positively related to future returns, a proxy for jump risk and informed trading) and the implied–realised spread (negatively related to returns through realised minus implied, a proxy for volatility risk); levels of volatility predicted nothing. In the synthetic layer the implied–realised spread carries no planted information, and its IC is zero at every horizon: a useful control.

| mean daily rank IC, years 3 to 10 | 1 day | 5 days | 20 days | 60 days |
| --- | --- | --- | --- | --- |
| skew (minus), all stocks | 0.004 | 0.014 | 0.018 | 0.012 |
| call–put volatility spread, all stocks | 0.005 | 0.017 | 0.022 | 0.015 |
| option-to-stock volume (minus), all stocks | 0.002 | 0.008 | 0.010 | 0.007 |
| implied minus realised volatility, all stocks | 0.000 | 0.001 | 0.000 | $-0.000$ |
| skew (minus), announcing within ten days | 0.026 | 0.085 | 0.111 | 0.082 |
| call–put volatility spread, announcing within ten days | 0.030 | 0.101 | 0.129 | 0.094 |
| option-to-stock volume (minus), announcing within ten days | 0.015 | 0.047 | 0.061 | 0.045 |

## 15.3 Option volume and the put–call ratio

**Definition 15.3 (Put–call ratio, option-to-stock volume ratio).**

A stock’s *put–call ratio* is its put option volume divided by its call option volume over a period, ideally counting only volume that opens new long positions. Its *option-to-stock volume ratio* is its total option volume (in shares of the underlying) divided by its stock volume.

Pan and Poteshman built [put–call ratios](#def-s1-options-implied-signals-for-stocks-volume) from buyer-initiated volume that opened new positions, a data set most researchers do not have, and found that stocks with low ratios beat those with high ratios by more than 40 basis points the next day and more than 1% over the next week, from nonpublic information held by option traders. Johnson and So showed why unsigned volume is informative too: short-sale costs make informed traders use options more for bad news than for good, so a high [option-to-stock volume ratio](#def-s1-options-implied-signals-for-stocks-volume) signals bad news; the lowest decile beat the highest by 0.34% a week. In the synthetic layer option volume rises with the size of the informed demand whatever its direction, weighted toward bad news, so its IC is about half that of the price signals: volume says someone knows something, and the asymmetry says what.

## 15.4 Where informed traders trade

The table’s lower half is the chapter’s lesson. Across all stocks the signals’ ICs are small (0.02 for the volatility spread at twenty days), because most stocks on most days have no informed traders in their options and the signals are noise. Among stocks announcing within ten days (11.7% of stock-days) the same signals have ICs about six times larger: the information is concentrated where the events are. The ICs rise to twenty days and then decay, since the announcement’s jump, which the informed traders anticipated, falls inside the twenty-day window and the planted post-announcement drift carries part of it further.

![Rank IC of the options signals against the market-adjusted return over the next 1 to 60 days on the synthetic market with informed options traders: among stocks announcing within ten days (solid) and all stocks (dashed). Data: s1_options.ic.](https://one-course.com/images/onecourse/chapters/quant-8/s1-options-implied-signals-for-stocks/fig-d619ce6327f3.svg)

***Figure 15.1.** Rank IC of the options signals against the market-adjusted return over the next 1 to 60 days on the synthetic market with informed options traders: among stocks announcing within ten days (solid) and all stocks (dashed). Data: `s1_options.ic`.*

The books follow. A weekly decile book on the volatility spread across all stocks earns 8.5% a year before costs (Sharpe ratio 3.67) and loses 0.9% after ten basis points per unit traded: the implied volatilities’ daily noise churns the ranking. Restricted to stocks announcing within ten days (quintiles of that smaller set), it earns 31.9% a year after costs at a Sharpe ratio of 6.12, the skew book 23.0% and the volume book 9.1%. Those synthetic numbers are far above anything in the literature, and the reason is the model: its informed traders know the whole surprise and their demand is a clean function of it. Real informed flow is a small, unsigned part of option volume, shared with hedgers and speculators; what carries over is the structure: trade the signals where the events are, and rebalance only as fast as the information changes.

## 15.5 Strategy files

**Strategy file 15.1 — Skew signal.**

**Who pays you, and why.** Informed traders who reveal bad news by buying puts, and the stock market’s slowness to follow.

**Instruments and venues.** Stocks with liquid options; the signal from the options, the trade in the stock.

**Signal.** Out-of-the-money put implied volatility minus at-the-money, against the stock’s own history.

**Sizing and execution.** Short steep skews, long flat ones; concentrate around scheduled events.

**Costs.** Stock trading; the signal’s noise drives turnover.

**How it dies.** Crowding; skew driven by hedging demand rather than information.

**Horizon, capacity, infrastructure.** Weeks to months; option surfaces by stock (Book 5).

**Backtest honestly.** Implied volatilities from closing quotes before the stock trade, with their bid–ask; the event calendar known in advance.

**Sources.** Xing, Zhang and Zhao (2010): 10.9% a year risk-adjusted between extreme smirk portfolios.

**Strategy file 15.2 — Implied-volatility spread signal.**

**Who pays you, and why.** As for skew, from both sides: expensive calls signal good news, expensive puts bad.

**Instruments and venues.** Stocks with liquid options at matched strikes.

**Signal.** Call minus put implied volatility, open-interest weighted across strikes.

**Sizing and execution.** Long high spreads, short low; weekly or around events.

**Costs.** As for skew.

**How it dies.** It weakened over Cremers and Weinbaum’s sample.

**Horizon, capacity, infrastructure.** Days to weeks.

**Backtest honestly.** Early-exercise premia removed from American options before computing the spread.

**Sources.** Cremers and Weinbaum (2010): 50 basis points a week; Bali and Hovakimian (2009).

**Strategy file 15.3 — Option volume signal.**

**Who pays you, and why.** Informed traders whose option volume rises before news, more so for bad news.

**Instruments and venues.** Stocks with option volume data.

**Signal.** The [option-to-stock volume ratio](#def-s1-options-implied-signals-for-stocks-volume) (unsigned) or a [put–call ratio](#def-s1-options-implied-signals-for-stocks-volume) of opening buys (signed).

**Sizing and execution.** Short high ratios; with signed data, long low [put–call ratios](#def-s1-options-implied-signals-for-stocks-volume).

**Costs.** As above.

**How it dies.** Volume from hedging and structured products that swamps informed flow.

**Horizon, capacity, infrastructure.** Days to a week; volume by option series.

**Backtest honestly.** Volume as reported that day, not revised; signed volume only where the data really is signed.

**Sources.** Pan and Poteshman (2006): more than 1% a week; Johnson and So (2012): 0.34% a week between extreme deciles.

**Strategy file 15.4 — Implied-minus-realised volatility signal.**

**Who pays you, and why.** Investors paying for volatility insurance, and the risk premium that insurance carries.

**Instruments and venues.** Stocks and their options.

**Signal.** Realised minus implied volatility (Bali and Hovakimian’s sign).

**Sizing and execution.** Cross-sectional sorts, monthly.

**Costs.** Low turnover.

**How it dies.** As a risk premium, in volatility spikes.

**Horizon, capacity, infrastructure.** Months; volatility surfaces.

**Backtest honestly.** Realised volatility from data before the implied quote.

**Sources.** Bali and Hovakimian (2009); this chapter’s control (IC zero where nothing is planted).

## 15.6 Tutorial: someone is buying protection

**Goal.** Add an options layer with informed traders to the synthetic market, compute the options signals, and measure them by horizon and around events. **End state:** the table and [Figure 15.1](#fig-s1-options-implied-signals-for-stocks-ic).

1. **The layer**: implied volatilities and volume, moved by informed demand before announcements. `def simulate_options (flag, surprise, listed, rv, cfg: OptionConfig | None = None , rng=None ): cfg = cfg or OptionConfig() rng = rng or np.random.default_rng(cfg.seed) flag, listed = np.asarray(flag, bool ), np.asarray(listed, bool ) s = np.where(flag, np.nan_to_num(np.asarray(surprise, float )), 0.0 ) T, N = s.shape demand = np.zeros((T, N)) # informed demand on day t: the surprise of an event within the window for k in range (1 , cfg.window + 1 ): demand[:-k] += s[k:] weight = np.where(demand < 0 , cfg.bad_news, 1.0 ) d = demand * weight atm = rv + cfg.premium + cfg.noise * rng.standard_normal((T, N)) put = atm + cfg.skew + cfg.noise * rng.standard_normal((T, N)) + cfg.impact * np.maximum(-d, 0.0 ) call = atm + cfg.noise * rng.standard_normal((T, N)) + cfg.impact * np.maximum(d, 0.0 ) os_ = cfg.os_base * np.exp(cfg.os_noise * rng.standard_normal((T, N)) + cfg.os_impact * np.abs(d)) mask = lambda x: np.where(listed, x, np.nan) # noqa: E731 return {" atm " : mask(atm), " put " : mask(put), " call " : mask(call), " os " : mask(os_)} def signals (opt, rv): return {" skew " : opt[" put " ] - opt[" atm " ], " spread " : opt[" call " ] - opt[" put " ], " os " : np.log(opt[" os " ]), " ivrv " : opt[" atm " ] - rv}` **Listing 15.1.** Informed options demand and the signals it leaves. code/firm/optsignal/firm_optsignal.py
2. **Run** `ic(name, h)` and `ic(name, h, True)` for the four signals and four horizons, `book(name)` and `book(name, True)` , and `fig_options.py` .

**What to change next.** Let most option volume be hedging and noise, with informed flow a small share; smooth the signals to cut turnover; add a cost of shorting and let informed traders choose between the stock and the options.

## 15.7 Build: the options layer

**Purpose.** A synthetic option market attached to the stock panel, and the option-implied signals built from it.

**Interface.** `OptionConfig`, `simulate_options(flag, surprise, listed, rv, cfg, rng)`, `signals(opt, rv)`.

**Rules.** Informed demand only before events and in the direction of their surprise; everything else noise; signals from the day’s closing values.

**Acceptance tests.** `code/firm/optsignal/tests/`: the right options move, by the right amount, only in the window before the event; volume rises more for bad news; implied minus realised equals the premium without noise.

**Stretch.** A full volatility surface per stock (Book 5); hedging and structured-product flow; signed volume.

Sources and further reading

- Y. Xing, X. Zhang and R. Zhao, “What does the individual option volatility smirk tell us about future equity returns?”, *Journal of Financial and Quantitative Analysis* 45(3), 2010.
- M. Cremers and D. Weinbaum, “Deviations from put-call parity and stock return predictability”, *Journal of Financial and Quantitative Analysis* 45(2), 2010.
- J. Pan and A. M. Poteshman, “The information in option volume for future stock prices”, *Review of Financial Studies* 19(3), 2006.
- T. L. Johnson and E. C. So, “The option to stock volume ratio and future returns”, *Journal of Financial Economics* 106(2), 2012.
- T. G. Bali and A. Hovakimian, “Volatility spreads and expected stock returns”, *Management Science* 55(11), 2009.

## 15.8 Exercises

**Exercise 15.1 ★.**

In the synthetic layer, how much does a surprise of $-2$ standard deviations raise the put implied volatility in the days before the announcement? And a surprise of $+2$ the call implied volatility?

**Solution of Exercise 15.1.**

Bad news is weighted 1.5: $0.003 \times 1.5 \times 2 = 0.009$, 0.9 volatility points on the puts; good news $0.003 \times 2 = 0.006$, 0.6 points on the calls. Both are below the daily noise of one point, which is why single days are uninformative and the signal must be read against its history.

**Exercise 15.2 ★.**

Johnson and So’s spread of 0.34% a week is how much a year, without compounding? And Cremers and Weinbaum’s 50 basis points a week?

**Solution of Exercise 15.2.**

$0.34\% \times 52 = 17.7\%$ a year and $0.5\% \times 52 = 26\%$ a year, before costs and without compounding.

**Exercise 15.3 ★.**

Why is the skew’s sign as a signal negative and the call–put spread’s positive?

**Solution of Exercise 15.3.**

A steep skew means puts are bid up, as they are when informed traders expect a fall: the stock is more likely to fall, so the skew enters with a minus. A high call–put spread means calls are bid up relative to puts, as they are when good news is expected: it enters with a plus.

**Exercise 15.4 ★★.**

Why might informed traders prefer options for bad news more than for good news?

**Solution of Exercise 15.4.**

Shorting the stock costs a borrow fee, needs a locate, and may be impossible or recalled; buying a put has none of these costs and adds leverage. For good news, buying the stock is cheap and easy, so options offer only leverage.

**Exercise 15.5 ★★.**

The ICs are about six times larger among stocks announcing within ten days. Why, and what does it suggest for the book?

**Solution of Exercise 15.5.**

The informed traders act only before events, so the signals contain information only there; elsewhere they are noise that dilutes the IC. The book should trade the signals in stocks with an event ahead and stay out of the rest.

**Exercise 15.6 ★★.**

Why does the all-stock weekly book lose after costs when its gross Sharpe ratio is above 3?

**Solution of Exercise 15.6.**

The implied volatilities carry daily noise of a point, so the weekly ranking changes a lot from week to week: the book trades heavily for a small, diffuse signal, and ten basis points per unit traded costs more than the 8.5% a year it earns gross.

**Exercise 15.7 ★★★.**

*Coding.* Run `book(’os’, True)` and compare it with the price-based books. Why is volume the weakest signal here?

**Solution of Exercise 15.7.**

The volume book around events earns 9.1% a year after costs (Sharpe ratio 1.75) against 23.0% and 31.9% for skew and spread. Volume rises with the size of the informed demand whatever its direction; only the extra weight on bad news gives it a sign, so its IC is about half that of the price signals.

**Exercise 15.8 ★★★.**

*Find the flaw.* “The volatility-spread book earns 32% a year after costs on the synthetic market; we should expect a large part of that in practice.”

**Solution of Exercise 15.8.**

The number comes from a model in which the informed traders know the whole surprise and their demand is a clean function of it. Real informed flow is small, unsigned in most data, mixed with hedging, and competed for; the published effects are tens of basis points a week before costs. Expect a small fraction, and test on real option data with costs.

## 15.9 Problem: Someone Is Buying Protection

**Problem 15.1.**

Weekend problem — information in the options market

The chapter’s options layer and the public record.

**Part I — The signals.**

1. Define [informed options trading](#def-s1-options-implied-signals-for-stocks-informed) , the [implied volatility spread](#def-s1-options-implied-signals-for-stocks-spread) , the [put–call ratio](#def-s1-options-implied-signals-for-stocks-volume) and the [option-to-stock volume ratio](#def-s1-options-implied-signals-for-stocks-volume) .
2. What did Xing, Zhang and Zhao find about the smirk?
3. What did Cremers and Weinbaum, and Bali and Hovakimian, find about spreads?
4. What did Pan and Poteshman, and Johnson and So, find about volume?

**Part II — The layer.**

5. Describe the synthetic options layer and its informed traders.
6. Why is bad news weighted more?
7. Why is implied minus realised a control here?
8. How is the event calendar used?

**Part III — The measurements.**

9. Give the ICs by horizon for all stocks.
10. Give them for stocks announcing within ten days.
11. Why do the ICs peak at twenty days?
12. Give the books’ results, all stocks and around events.

**Part IV — The verdict.**

13. State the *named result* : the IC of the skew and volatility-spread signals and their decay with horizon.
14. Why are the synthetic returns far above the literature’s?
15. What would you change to make the layer realistic?
16. How would you cut the all-stock book’s turnover?
17. What data would you need to trade these strategies?
18. Which signal decayed in the published record?
19. How do these signals relate to chapter 7’s earnings strategies?
20. In one sentence: why look at options to trade stocks?

**Solution of Problem 15.1.**

1. Option trading by the privately informed; call minus put implied volatility at matched strikes; put volume over call volume; option volume over stock volume.
2. Steepest smirks underperform flattest by 10.9% a year risk-adjusted, for at least six months, with worse earnings shocks next quarter.
3. Expensive calls beat expensive puts by 50 basis points a week, declining over time; the call–put spread predicts positively, realised minus implied negatively.
4. Low [put–call ratios](#def-s1-options-implied-signals-for-stocks-volume) beat high by 40 basis points a day and over 1% a week; low option-to-stock volume beats high by 0.34% a week.
5. At-the-money volatility equal to realised plus two points, a three-point put skew, a point of daily noise; informed traders buying puts or calls in the ten days before announcements, 0.3 points per standard deviation of surprise.
6. Short-sale costs make options more attractive for bad news.
7. It carries no planted information, so its IC should be zero, and is.
8. To mark the ten days before each announcement, when the informed traders act.
9. Skew 0.004, 0.014, 0.018, 0.012; spread 0.005, 0.017, 0.022, 0.015; volume 0.002, 0.008, 0.010, 0.007; implied minus realised zero.
10. Skew 0.026, 0.085, 0.111, 0.082; spread 0.030, 0.101, 0.129, 0.094; volume 0.015, 0.047, 0.061, 0.045.
11. The announcement’s jump falls within twenty days of the informed buying; beyond, the window adds noise.
12. All stocks: gross Sharpe ratios of 3.17–3.67, negative after costs; around events: 23.0%, 31.9% and 9.1% a year after costs for skew, spread and volume.
13. **Named result.** The volatility spread’s IC is 0.005, 0.017, 0.022 and 0.015 at 1, 5, 20 and 60 days across all stocks and 0.030, 0.101, 0.129 and 0.094 among stocks announcing within ten days; the skew’s 0.004, 0.014, 0.018, 0.012 and 0.026, 0.085, 0.111, 0.082.
14. The model’s informed traders know the surprise exactly and are the only source of informed demand.
15. Make informed flow a small share of option volume, add hedging and structured flow, and let informed traders choose the stock when it is cheaper.
16. Smooth the signals, trade them only where events are near, and rebalance less often.
17. Implied volatility surfaces by stock, option volume (signed if possible), an event calendar, and borrow costs.
18. The call–put spread (Cremers and Weinbaum).
19. They trade the same events: the options signals anticipate the surprise that chapter 7’s drift book trades after it.
20. Because informed traders often trade options first.

## 15.10 Interview questions

**Interview question 15.1 ★ researcher, trader.**

Why might option prices predict stock returns?

**Solution of Interview question 15.1.**

Informed traders use options for leverage and to avoid short-sale costs; their demand moves option prices and volumes before the stock moves, and the stock market is slow to follow.

**Interview question 15.2 ★★ researcher.**

How would you compute a stock’s volatility skew for a cross-sectional signal?

**Solution of Interview question 15.2.**

From a fitted surface at a fixed maturity (for example 30 days): the implied volatility at a fixed out-of-the-money moneyness (a delta of $-0.2$ or a strike at 90%) minus the at-the-money implied volatility, from closing quotes, compared with the stock’s own history and the market’s skew.

**Interview question 15.3 ★★ researcher.**

What is the difference between the call–put [implied volatility spread](#def-s1-options-implied-signals-for-stocks-spread) and implied minus realised volatility as signals?

**Solution of Interview question 15.3.**

The call–put spread compares two options on the same stock and measures relative demand for upside against downside, an information signal; implied minus realised compares options with the stock’s own history and measures the volatility risk premium, a risk signal.

**Interview question 15.4 ★★ trader.**

A stock’s put volume triples ahead of earnings. What do you do?

**Solution of Interview question 15.4.**

Check whether it is buyer-initiated and opening, compare it with the usual pre-earnings volume, the skew and the stock’s short interest; if it looks like informed buying of protection, reduce or hedge longs, and consider the stock underweight into the event.

**Interview question 15.5 ★★ risk.**

What are the pitfalls of backtesting option-implied signals?

**Solution of Interview question 15.5.**

Stale or non-synchronous quotes between options and stock; bid–ask bounce in implied volatilities; early-exercise premia; survivorship in option data; and costs of trading the stock on noisy signals.

**Interview question 15.6 ★★★ researcher.**

In a model where informed traders choose between shorting the stock at a cost $c$ and buying puts with leverage $L$, derive when they prefer the puts, and what that implies for the information in put volume.

**Solution of Interview question 15.6.**

With private information of a fall of size $x$, shorting earns $x - c$ per unit; a put with leverage $L$ earns roughly $Lx$ minus its premium’s time value. The informed prefer puts when $Lx$ net of premium exceeds $x - c$, which is more likely the higher $c$: when shorting is costly, bad news moves into puts, so put volume (and the [option-to-stock volume ratio](#def-s1-options-implied-signals-for-stocks-volume)) carries more negative information than call volume carries positive.