---
title: "Asian and Emerging Equity Markets"
book: "Markets I: The Ecosystem and Exchange-Traded Markets"
subject: quant
language: en
chapter: 12
exercises: 8
source: https://one-course.com/books/quant/1/en/chapter/12-asian-and-emerging-equity-markets
---

# Chapter 12 — Asian and Emerging Equity Markets

In Shanghai a share that has risen ten percent since yesterday’s close cannot rise further today, and whoever bought it this morning cannot sell it until tomorrow. In Hong Kong buyer and seller each hand a tenth of a percent of every trade to the government. In Tokyo the smallest price step of a share depends on which index it belongs to. In Mumbai the seller of an option pays a tax on the premium, a trade may settle the same afternoon, and a foreign fund may find that foreigners, collectively, already own as much of the company as the law allows. A strategy that works in New York does not “port” to these markets; it has to be re-derived under a different set of rules. This chapter is a field guide to the rules that differ, and a method for reading any new market.

## 12.1 What can differ

**Method 12.1 (Reading a new equity market).**

Before any data is loaded, fill in this table for the market.

1. **Access:** who may hold shares directly; licences, quotas, ownership limits; whether a foreign investor trades the same line of stock as a domestic one.
2. **Unit and tick:** the lot in which orders must be sized; the tick table.
3. **Limits and halts:** daily [price limits](#def-m1-asian-and-emerging-equity-markets-limit) , circuit breakers, their reference price.
4. **Selling:** whether shares bought today can be sold today; whether, and how, they can be sold short.
5. **Settlement and cash:** cycle, pre-funding, currency convertibility.
6. **Taxes and fees:** per-trade taxes by instrument and by side; dividend withholding; capital gains.
7. **Sessions:** auctions, lunch breaks, after-hours fixed-price sessions.

Each line changes which strategies can exist; several of them change the statistical properties of the data itself.

## 12.2 Price limits

**Definition 12.2 (Price limit).**

A daily *price limit* forbids orders and trades at prices further than a fixed percentage (or amount) from a reference price, usually the previous close. A share at its upper limit is *limit-up*: buy orders queue at the limit price and trade only if someone sells there.

**Proposition 12.3 (Days locked at the limit).**

News changes the fair value of a share by a factor $1+S$ with $S>0$. Under a daily limit $L$, the share spends

$$
n = \left\lceil \frac{\ln(1+S)}{\ln(1+L)} \right\rceil - 1
$$

full days locked at the upper limit before a day on which it can trade at its fair value. For a fall, replace $1+S$ and $1+L$ by $1-S$ and $1-L$.

**Proof.** After $k$ limit days the price is at most $(1+L)^k$ times the initial one. The fair value becomes reachable on the first day $k$ with $(1+L)^k \ge 1+S$; the $k-1$ preceding days are locked. ∎

**Example 12.4 (Falls take longer).**

With $L = 10\%$ a rise of 50% needs $\lceil 4.25\rceil = 5$ days, four of them locked. A fall of 50% needs $\lceil \ln 0.5/\ln 0.9\rceil = \lceil
6.58\rceil = 7$ days, six locked: for six days holders who want to sell cannot, at any price. A fund that promises its own investors daily liquidity and holds such shares has a problem that no risk model built on daily returns will have measured ([Figure 12.1](#fig-m1-asian-and-emerging-equity-markets-locked)).

![Full days spent at the limit before a revaluation can be traded, by . Data: computed by the chapter’s script.](https://one-course.com/images/onecourse/chapters/quant-1/m1-asian-and-emerging-equity-markets/fig-f04d95f727b6.svg)

***Figure 12.1.** Full days spent at the limit before a revaluation can be traded, by [Proposition 12.3](#prop-m1-asian-and-emerging-equity-markets-locked). Data: computed by the chapter’s script.*

**Proposition 12.5 (What limits do to the data).**

Let true daily returns be independent. Returns observed under a [price limit](#def-m1-asian-and-emerging-equity-markets-limit) (i) have a smaller variance than the true ones, (ii) are positively autocorrelated, and (iii) have point masses at $\pm L$.

**Partial proof.** (iii) is the definition. For (i) and (ii): on a limit day the observed return is $L$ and the unexpressed part of the move is carried to the next day, where it adds to that day’s independent return. The carried part has the sign of today’s return, so consecutive observed returns covary positively; and since a large move is split over several days, the sum of squared daily returns is smaller than the square of the move. A full computation needs the return distribution and is left to the tutorial’s simulation. ∎

![Heavy-tailed returns with and without a 10% daily limit. The observed series has no tail beyond the limit and a spike at it; its standard deviation is 3.03% against 3.45%, and its first autocorrelation +0.09 against zero. Data: the tutorial’s simulation.](https://one-course.com/images/onecourse/chapters/quant-1/m1-asian-and-emerging-equity-markets/fig-1da73fad23f9.svg)

***Figure 12.2.** Heavy-tailed returns with and without a 10% daily limit. The observed series has no tail beyond the limit and a spike at it; its standard deviation is 3.03% against 3.45%, and its first autocorrelation $+0.09$ against zero. Data: the tutorial’s simulation.*

A volatility estimated from limit-constrained closes is too low; a momentum signal fitted on them finds a “continuation” that cannot be traded, because on the days it predicts nobody can buy. Both are among the commonest errors in cross-market research.

## 12.3 Mainland China and the Connect

**Definition 12.6 (T+0 restriction).**

A *T+0 restriction* (in mainland China, the “T+1 trading rule”) forbids selling shares on the day they were bought. It is a rule about trading, distinct from the [settlement cycle](https://one-course.com/books/quant/1/en/chapter/5-clearing-and-settlement#def-m1-clearing-and-settlement-cycle).

**Definition 12.7 (Qualified foreign investor and Stock Connect).**

A *qualified foreign investor* is a foreign institution licensed by the mainland regulator to invest directly in onshore securities. *Stock Connect* is the link between the Hong Kong exchange and the Shanghai and Shenzhen exchanges that lets investors on each side trade eligible shares on the other through their home brokers and clearing houses, within a daily quota, without a licence.

**As of September 2026 — Mainland A-share trading rules.**

Main-board shares in Shanghai and Shenzhen may move 10% a day; shares on the STAR Market and ChiNext 20%, with no limit during a STAR listing’s first five days. Revised trading rules of the Shanghai, Shenzhen and Beijing exchanges took effect on 6 July 2026: the limit for main-board shares under special treatment was widened to 10%, and the after-hours fixed-price session (15:05 to 15:30) was extended to all A-shares and exchange-traded funds. Shares bought cannot be sold the same day. The northbound [Stock Connect](#def-m1-asian-and-emerging-equity-markets-connect) quota is RMB 52 billion a day for each of the Shanghai and Shenzhen links.

![A northbound Stock Connect order. The investor faces only its Hong Kong broker; the Hong Kong exchange’s subsidiary is the member of the mainland exchange, and the two clearing houses are each other’s counterparties. Mainland rules — limits, lots, the ban on same-day selling — apply to the order in full.](https://one-course.com/images/onecourse/chapters/quant-1/m1-asian-and-emerging-equity-markets/fig-7406fdaf85c7.svg)

***Figure 12.3.** A northbound [Stock Connect](#def-m1-asian-and-emerging-equity-markets-connect) order. The investor faces only its Hong Kong broker; the Hong Kong exchange’s subsidiary is the member of the mainland exchange, and the two clearing houses are each other’s counterparties. Mainland rules — limits, lots, the ban on same-day selling — apply to the order in full.*

**Remark 12.8 (The same company at two prices).**

Many mainland companies are listed both as A-shares onshore and as H-shares in Hong Kong. The two lines carry the same dividends and votes and are *not* convertible into each other; they routinely trade at different prices, because the populations allowed to hold each are different and no arbitrageur can deliver one against the other. A price difference that cannot be closed by delivery is a fact about access, not a free lunch ([Chapter 17](https://one-course.com/books/quant/1/en/chapter/17-delta-one-instruments#ch-m1-delta-one-instruments)).

## 12.4 Hong Kong

**Definition 12.9 (Board lot).**

A *board lot* is the number of shares in which orders on an exchange’s main order book must be multiples. Where the issuer chooses it, the board lot differs from stock to stock.

**Definition 12.10 (Stamp duty).**

A *stamp duty* on share transfers is a tax charged as a percentage of the value of each transaction, on the buyer, the seller or both, whatever the profit or loss.

**As of September 2026 — Hong Kong: duty and lots.**

[Stamp duty](#def-m1-asian-and-emerging-equity-markets-stamp) on Hong Kong stock transfers is 0.1% of the value for the buyer and 0.1% for the seller, since 17 November 2023 (previously 0.13%). [Board lots](#def-m1-asian-and-emerging-equity-markets-lot) were chosen freely by issuers, in more than forty different sizes; a reform implemented from July 2026 restricts them to eight standard sizes (1, 50, 100, 500, 1 000, 2 000, 5 000 and 10 000 shares), with a lower minimum and a new maximum value per lot.

**Example 12.11 (Twenty basis points).**

A round trip in a Hong Kong share costs 20 basis points in duty before any spread, commission or impact. A market-making strategy that captures one or two basis points per round trip ([Box 1.2](https://one-course.com/books/quant/1/en/chapter/1-what-a-trading-firm-does#dat-m1-what-a-trading-firm-does-listed)) cannot exist under that tax; strategies with holding periods of days, earning fifty basis points per position, can. Transaction taxes do not shave every strategy equally: they delete the short-horizon end of the spectrum, and with it the participants who would have provided intraday liquidity.

## 12.5 Japan, Korea and the uptick rule

The Tokyo exchange trades shares in units of 100 and publishes several tick tables: the constituents of its large-capitalisation indices use a finer table than other shares, down to a fraction of a yen for the most liquid. A share that enters or leaves the index changes table, which moves its spread, its queue lengths and the economics of making a market in it, with no change in the company.

**Definition 12.12 (Uptick rule).**

An *uptick rule* restricts the prices at which a [short sale](https://one-course.com/books/quant/1/en/chapter/6-financing-repo-securities-lending-and-prime-brokerage#def-m1-financing-short) may be entered: typically not below the last traded price, or not below it once the share has fallen by a given amount during the day.

**Example 12.13 (Seventeen months without short selling).**

In November 2023 the Korean authorities banned short selling of all listed shares, citing naked [short sales](https://one-course.com/books/quant/1/en/chapter/6-financing-repo-securities-lending-and-prime-brokerage#def-m1-financing-short) by global banks. The ban ended on 31 March 2025, when short selling resumed for every listed share together with a new electronic system for detecting naked [short sales](https://one-course.com/books/quant/1/en/chapter/6-financing-repo-securities-lending-and-prime-brokerage#def-m1-financing-short). For seventeen months no long–short equity strategy could be run onshore in one of the world’s larger markets; index arbitrage, convertible-bond hedging and market making in single-stock derivatives were all impaired at once. Regulatory risk of this kind is a parameter of the market, like volatility.

## 12.6 India

**Definition 12.14 (Securities transaction tax and foreign ownership limit).**

A *securities transaction tax* (STT) is a tax on exchange transactions whose rate and payer depend on the instrument: shares, futures or options. A *foreign ownership limit* caps the fraction of a company that non-residents may hold in aggregate; when it is reached, foreigners can buy only from other foreigners.

**As of September 2026 — India: tax and settlement.**

STT on shares bought or sold for delivery is 0.1% of the value on each side. From 1 April 2026 the rate on futures is 0.05% of the value, paid by the seller (previously 0.02%), and on options 0.15% of the premium, paid by the seller (previously 0.10%). Shares settle at $T{+}1$; an optional same-day ($T{+}0$) cycle is available in the 500 largest shares.

![Per-trade taxes on a purchase followed by a sale. A market with no such tax would show zero. Data: the rates of .](https://one-course.com/images/onecourse/chapters/quant-1/m1-asian-and-emerging-equity-markets/fig-93bb8dfa688f.svg)

***Figure 12.4.** Per-trade taxes on a purchase followed by a sale. A market with no such tax would show zero. Data: the rates of Boxes [12.2](#dat-m1-asian-and-emerging-equity-markets-hk) and [12.3](#dat-m1-asian-and-emerging-equity-markets-india).*

## 12.7 What changes for a trading firm

**Proposition 12.15 (The tax floor on turnover).**

A strategy earns a gross edge of $e$ per round trip and pays a round-trip transaction tax $\tau$ and other costs $\kappa$, all as fractions of value. It is viable only if $e > \tau + \kappa$; and if its edge per unit of holding time is roughly constant, $e \approx \alpha h$ for a holding period $h$, the shortest viable holding period is $h^\star = (\tau+\kappa)/\alpha$.

**Proof.** Net profit per round trip is $e - \tau - \kappa$; substitute $e = \alpha h$. ∎

With $\alpha$ of 5 basis points a day and $\kappa$ of 5 basis points, a market without tax admits holding periods from one day; a market with 20 basis points of duty only from five days. The same signal that is traded intraday in one market must be slowed down, or dropped, in another.

## 12.8 Tutorial: what a price limit does to returns

**Goal.** Pass a series of true returns through a 10% limit and measure what it does to volatility and autocorrelation. **End state:** [Figure 12.2](#fig-m1-asian-and-emerging-equity-markets-hist) and its three statistics.

1. **The limit with carry-over.** The observed price cannot move more than $L$ a day; the rest of the move waits. `def truncate (true_returns: np.ndarray, limit: float ) -> np.ndarray: """Observed daily returns when the price cannot move more than `limit` a day and the untraded remainder carries over to the following days.""" obs = np.empty_like(true_returns) gap = 0.0 # log distance between fair and observed price for t, r in enumerate (true_returns): want = gap + math.log1p(r) capped = min (max (want, math.log(1.0 - limit)), math.log(1.0 + limit)) obs[t] = math.expm1(capped) gap = want - capped return obs` **Listing 12.1.** Truncation with carry-over, in log space so that the total move is conserved. code/markets-1/12-asian-and-emerging-equity-markets/python/asia_rules.py
2. **Check conservation.** A single $+35\%$ revaluation becomes $+10\%$ , $+10\%$ , $+10\%$ and a remainder; the product of the observed gross returns is 1.35.
3. **Measure.** With heavy-tailed returns of 3.45% daily standard deviation, 2% of days end at a limit; the observed standard deviation is 3.03% and the first autocorrelation $+0.088$ .
4. **Days locked.** `def locked_days (shock: float , limit: float ) -> int : """Full limit-days needed before a price can reach a shock of relative size `shock` (same sign as the shock) when each day's move is capped at `limit`.""" if shock == 0 : return 0 n = math.log(1.0 + abs (shock)) / math.log(1.0 + limit) if shock > 0 else \ math.log(1.0 - abs (shock)) / math.log(1.0 - limit) return max (0 , math.ceil(n - 1e-12 ) - 1 )` **Listing 12.2.** The proposition as a function, with the asymmetry between rises and falls. code/markets-1/12-asian-and-emerging-equity-markets/python/asia_rules.py

**What to change next.** Fit a one-day momentum rule to the observed series and compute its “profit”; then forbid trading on limit days and recompute. Then widen the limit to 20% and see how much of the distortion remains.

## 12.9 Build: the market-rules table

**Purpose.** Every order the miniature firm creates is validated, before it leaves, against the rules of the market it goes to; every backtest asks the same table what was allowed on that date.

**Interface.** `MarketRules(market, valid_from, lot, tick_table, limit_up, limit_down, same_day_sell, short_selling, settlement_days, tax_buy, tax_sell)`; `RuleBook.load(csv)`; `rules(market, date)`; `validate(order, reference_price, bought_today)` returning a list of violations; `tax(side, value)`.

**Rules.** Rules are versioned by date: a query for a past date returns the rules then in force, never today’s. Quantities must be multiples of the lot; prices multiples of the tick applicable at that price and inside the limit band around the reference price; a sale exceeding the position held at the start of the day is rejected where same-day selling is forbidden.

**Acceptance tests.** `code/firm/marketrules/tests/`: lot and tick rounding; limit bands; the same-day-sell rejection; a rate change on a given date applied only from that date.

**Stretch.** Load the rule history of one real market from its exchange’s circulars and reproduce the dated boxes of this chapter as queries.

Sources and further reading

- KPMG, *Hong Kong: Reduced stamp duty rate on stock transfers effective 17 November 2023* ; HKEX, consultation and conclusions on the board lot framework, 2025–2026.
- HKEX, *Stock Connect: Information Booklet and FAQ* , 2024.
- Shanghai, Shenzhen and Beijing stock exchanges, revised trading rules effective 6 July 2026 (as reported in the financial press).
- Financial Services Commission of Korea, *Stock Short Selling to be Fully Reinstated from March 31* , press release, 2025.
- ClearTax, *Securities Transaction Tax: latest updates* , and ICICI Direct, *STT changes in Budget 2026* (rates from 1 April 2026); Securities and Exchange Board of India, circulars on the optional $T{+}0$ settlement cycle.
- Japan Exchange Group, *Trading Rules of Domestic Stocks: Tick Size* .
- K. Kim and S. Rhee, “Price limit performance: evidence from the Tokyo Stock Exchange”, *Journal of Finance* 52 (1997).

## 12.10 Exercises

**Exercise 12.1 ★.**

A share closed at 24.00 with a 10% limit and a tick of 0.01. Give today’s upper and lower limit prices. A broker’s system computes the upper limit as 26.40 exactly; under what rounding convention could the exchange’s be different?

**Solution of Exercise 12.1.**

Upper limit 26.40, lower limit 21.60. The two agree here because $24.00\times1.1$ falls on a tick. In general $P\times1.1$ does not, and exchanges differ in rounding it to the nearest tick, inward or by a rule of their own: a system that rounds differently sends orders one tick outside the band, which are rejected exactly on the days that matter.

**Exercise 12.2 ★.**

An investor wants HKD 250 000 of a share trading at HKD 61.30 with a [board lot](#def-m1-asian-and-emerging-equity-markets-lot) of 500. How many shares can it buy, for what value, and what [stamp duty](#def-m1-asian-and-emerging-equity-markets-stamp) does it pay on the purchase?

**Solution of Exercise 12.2.**

$250\,000/61.30 = 4\,078$ shares, that is 8 full lots: 4 000 shares, HKD 245 200; duty $0.1\% =$ HKD 245.20 (and as much again on the eventual sale). HKD 4 800 stays uninvested: lot sizes matter for small accounts and for precise hedges.

**Exercise 12.3 ★.**

Using [Box 12.3](#dat-m1-asian-and-emerging-equity-markets-india), compute the tax on (a) buying and later selling INR 5 million of shares for delivery; (b) selling index futures with a contract value of INR 20 million; (c) selling options for a premium of INR 400 000.

**Solution of Exercise 12.3.**

(a) $0.1\%$ on each side: INR 5 000 $+$ 5 000 $=$ 10 000. (b) $0.05\%
\times 20$ million $=$ INR 10 000, on the sale only. (c) $0.15\% \times
400\,000 =$ INR 600.

**Exercise 12.4 ★★.**

Bad news cuts a share’s fair value by 35%. How many days is it locked limit-down under a 10% limit? Under 20%? Under 5%?

**Solution of Exercise 12.4.**

$\ln0.65/\ln0.9 = 4.09$: five days, four locked. At 20%: $1.93$, two days, one locked. At 5%: $8.40$, nine days, eight locked.

**Exercise 12.5 ★★.**

A signal earns 4 basis points of gross edge per day held; costs other than tax are 6 basis points per round trip. Give the shortest viable holding period with no transaction tax, with a 20-basis-point round-trip duty, and the net profit per round trip at a holding period of ten days in each case.

**Solution of Exercise 12.5.**

No tax: $h^\star = 6/4 = 1.5$ days. With duty: $26/4 = 6.5$ days. At ten days the gross edge is 40 basis points: net 34 without the duty, 14 with it — the tax takes 59% of the profit of a strategy it does not forbid.

**Exercise 12.6 ★★.**

A trader in a market with a ban on same-day selling buys 10 000 shares at the open; at noon the share is up 6% and she wants to lock in the gain. The share has a liquid futures contract and no single-stock options. What can she do, and what risk remains?

**Solution of Exercise 12.6.**

She cannot sell the shares. She can sell futures on the index, or on the share if a single-stock future exists, for the same notional: that removes the market part of the risk and leaves the share’s specific move until tomorrow’s open, plus the basis of the hedge. If she already held the same share from a previous day she could sell *those* shares today: the ban applies to the day’s purchases, which is why local funds keep a standing inventory in the names they trade intraday.

**Exercise 12.7 ★★★.**

*Coding.* With `truncate`, generate 60 000 heavy-tailed returns as in the tutorial (seed 12) and compute the observed standard deviation and first autocorrelation for limits of 5%, 10% and 20%. Explain the pattern.

**Solution of Exercise 12.7.**

Standard deviation and autocorrelation: 2.60% and $+0.195$ at 5%; 3.03% and $+0.088$ at 10%; 3.26% and $+0.033$ at 20%, against a true 3.45% and zero. The tighter the limit, the more of the distribution is cut and carried forward: volatility is understated and spurious momentum grows roughly in proportion to the share of days that end at a limit.

**Exercise 12.8 ★★★.**

*Find the flaw.* A researcher reports: “A-shares that close [limit-up](#def-m1-asian-and-emerging-equity-markets-limit) gain a further 3.1% on average the next day; buying at the [limit-up](#def-m1-asian-and-emerging-equity-markets-limit) close earns 3.1% a day.” Identify the two reasons the profit is not available, and the statistic that should have been reported.

**Solution of Exercise 12.8.**

First, the close on a [limit-up](#def-m1-asian-and-emerging-equity-markets-limit) day is not a price at which one can buy: the order book shows a queue of buyers and almost no sellers, and the expected fill of a new order is close to zero — and is largest precisely in the cases where the next day is bad (when holders were willing to sell at the limit). Second, the purchase could not be sold on the day it is made, so the “next-day” exit itself may be locked if the share gaps down. The statistic to report is the return conditional on an order *actually filled* at the limit, weighted by filled quantity: a fill-weighted, not an equal-weighted, average.

## 12.11 Problem: Limit-Up

**Problem 12.1.**

Weekend problem — a takeover in a market with limits

A share closes at 20.00 on Monday in a market with a 10% daily [price limit](#def-m1-asian-and-emerging-equity-markets-limit) (limit prices are rounded down to the cent), a [board lot](#def-m1-asian-and-emerging-equity-markets-lot) of 100 shares, a ban on selling shares bought the same day, and a duty of 0.1% on each side. After the close an acquirer announces a cash offer at 29.00, which the market considers certain to complete in three months. The interest rate is 4% a year.

**Part I — The path.**

1. What is the share worth on Tuesday morning, discounting the offer at the interest rate for three months?
2. Give the upper limit price on Tuesday, Wednesday, Thursday and Friday, each computed from the previous close.
3. On which day can the share first trade at its fair value? How many days is it locked?
4. Check against [Proposition 12.3](#prop-m1-asian-and-emerging-equity-markets-locked) .

**Part II — The queue.** On Tuesday buy orders for 40 million shares queue at the limit price; 300 000 shares are sold there during the day, allocated in time priority. You entered an order for 50 000 shares 0.2 seconds after the open, behind 9 million shares already queued.

5. How many shares do you receive?
6. What is a share bought at Tuesday’s limit worth relative to its price, in percent?
7. Someone at the very front of the queue buys 100 000 shares. What is the expected gain in currency, before costs?
8. What determines who is at the front, and what would a firm pay for that?
9. If you do buy on Tuesday, when can you first sell, and at what limit price at best?

**Part III — The data.**

10. Write the series of daily close-to-close returns from Monday to the first day at fair value, assuming the share then closes at fair value.
11. Give the sum of squared daily returns, and the square of the total return; compare.
12. A risk system estimates this share’s volatility from the last 20 daily returns, the other 16 being zero. What daily volatility does it report, and what would it report had the move occurred in one day?
13. Compute the first autocorrelation of your series of question 10 (without subtracting the mean). What would a momentum signal conclude?

**Part IV — The trade that exists.**

14. After the share reaches fair value it trades at 28.60 with the offer at 29.00 three months away. Give the gross return of buying and tendering, annualised.
15. Subtract the duty on the purchase (tendering is a sale) and the financing at 4%. Is the trade worth doing?
16. Your [board lot](#def-m1-asian-and-emerging-equity-markets-lot) is 100 shares and you want to invest 2 million. How many shares?
17. The same company has a line listed in another market with no [price limit](#def-m1-asian-and-emerging-equity-markets-limit) , not convertible into this one. What would you expect that line to have done on Tuesday, and what does the gap between the two lines measure?
18. Name the one risk that the certain-completion assumption removed, and say how it would change question 14.
19. State the *named result* : the number of days the share is locked at the limit.
20. In one sentence, what does a [price limit](#def-m1-asian-and-emerging-equity-markets-limit) protect, and what does it cost?

**Solution of Problem 12.1.**

**1.** $29.00/(1 + 0.04\times0.25) = 28.71$. **2.** 22.00; 24.20; 26.62; 29.28. **3.** Friday: 29.28 is the first limit above 28.71. Locked Tuesday, Wednesday and Thursday: three days. **4.** $\ln(1.4356)/\ln(1.1) = 3.79$; $\lceil3.79\rceil - 1 = 3$. **5.** None: 9 million shares are ahead of you and 300 000 trade. **6.** $28.71/22.00 - 1 = 30.5\%$. **7.** $100\,000 \times (28.71 - 22.00) = 671\,000$. **8.** Time priority at the opening: the orders entered in the first microseconds after order entry opens, or queued in the pre-open by the brokers with the fastest lines. A firm would pay up to the expected gain times its probability of being filled — which is why [limit-up](#def-m1-asian-and-emerging-equity-markets-limit) queues are a latency race in markets with [price limits](#def-m1-asian-and-emerging-equity-markets-limit). **9.** Wednesday at the earliest, at Wednesday’s limit of 24.20 at best — and only if someone buys there, which everyone will. **10.** Closes 20.00, 22.00, 24.20, 26.62, 28.71: returns $+10\%$, $+10\%$, $+10\%$, $+7.9\%$. **11.** $\sum r^2 = 0.0362$ against $(0.4356)^2 = 0.1898$: five times less. **12.** $\sqrt{0.0362/20} = 4.3\%$ a day, against $\sqrt{0.1898/20} =
9.7\%$ for the same move made in one day. **13.** $(0.01 + 0.01 + 0.0079)/0.0362 = 0.77$: a momentum signal sees the strongest trend in its sample, in a share nobody could buy. **14.** $29.00/28.60 - 1 = 1.40\%$ in three months, 5.6% a year. **15.** Less 0.10% of duty and 1.00% of financing: 0.30% in three months, 1.2% a year above the interest rate. With completion certain, that is a pure liquidity premium; whether it is worth the balance sheet depends on the firm’s hurdle. **16.** $2\,000\,000/28.60 = 69\,930$: 699 lots, 69 900 shares. **17.** It would have opened near 28.7 (in its own currency) on Tuesday. During the three locked days the gap between the two lines measures the move the limited market has not yet been allowed to make, not an arbitrage: the lines cannot be delivered against each other. **18.** Deal-break risk. With a probability $p$ of failure and a fall to about 20 in that case, the 1.40% gross return must pay for an expected loss of $p \times 30\%$: at $p = 5\%$ the trade already loses money. **19.** **Three days.** **20.** It protects participants from trading at prices formed in panic or error within a day, at the cost of suspending everyone’s ability to trade at the right price for as many days as the news is large.

## 12.12 Interview questions

**Interview question 12.1 ★ trader, researcher.**

What is a daily [price limit](#def-m1-asian-and-emerging-equity-markets-limit), and what happens to a share when its fair value moves by more than the limit?

**Solution of Interview question 12.1.**

A band around the previous close outside which no order is accepted. If fair value moves beyond it, the share goes [limit-up](#def-m1-asian-and-emerging-equity-markets-limit) or limit-down: one-sided queue, almost no trading, and the move is completed over several days, each day’s band being reset from the previous close.

*What the interviewer is looking for: the one-sided queue, and that the move still happens.*

**Interview question 12.2 ★ researcher, mle.**

You are given daily closes for a market with 10% [price limits](#def-m1-asian-and-emerging-equity-markets-limit). Name two statistics that will be biased if you treat them like US data.

**Solution of Interview question 12.2.**

Volatility (understated, since large moves are split across days) and autocorrelation (spuriously positive). Also tail estimates and value at risk, correlations with unconstrained markets on event days, and any backtest that assumes trading at a limit-day close.

*What the interviewer is looking for: the mechanism, carry-over, not just the list.*

**Interview question 12.3 ★★ trader, researcher.**

A market charges 10 basis points of tax on each side of a share trade. Which strategies disappear, and who ends up providing liquidity?

**Solution of Interview question 12.3.**

Anything whose edge per round trip is below the 20 basis points of tax: electronic market making, index and ETF arbitrage, intraday statistical strategies. Liquidity is then provided by longer-horizon investors and by brokers, spreads are wider, and price discovery migrates to instruments the tax does not reach — futures, swaps, depositary receipts or exempted [market makers](https://one-course.com/books/quant/1/en/chapter/1-what-a-trading-firm-does#def-m1-what-a-trading-firm-does-market-maker), where the law grants exemptions.

*What the interviewer is looking for: migration to untaxed instruments.*

**Interview question 12.4 ★★ researcher, trader.**

A company’s onshore and offshore shares trade 30% apart. Why is that not an arbitrage, and how might you still trade it?

**Solution of Interview question 12.4.**

The two lines are not fungible: one cannot be delivered against the other, and the investors allowed to hold each differ, as do their funding costs and short-selling constraints. So there is no convergence date. It can be traded as a statistical relative-value position — long the cheap line, short the dear one where shorting is possible — sized for the possibility that the gap widens for years, or as a view on access reforms that would narrow it.

*What the interviewer is looking for: no forced convergence, and sizing accordingly.*

**Interview question 12.5 ★★ developer.**

Your order-validation layer must support fifteen markets whose lot, tick and limit rules change several times a year. How do you design it?

**Solution of Interview question 12.5.**

Rules as data, not code: a table keyed by market, instrument class and validity date, holding lot, tick table, limit formula and its rounding, session times, selling constraints; one generic validator that reads it. Every change is a new dated row with its source circular; backtests query the table as of the simulated date. Test with the exchange’s own examples and replay recent production orders against a new rule version before its effective date. Rejections from the exchange are fed back as a monitoring signal that the table is stale.

*What the interviewer is looking for: versioning by date and a single generic validator.*

**Interview question 12.6 ★★★ researcher, trader.**

A regulator bans short selling overnight. List the strategies and market functions affected, in order of severity, and what you would do on the first morning if you ran a long–short book there.

**Solution of Interview question 12.6.**

Most severe: long–short equity (no new shorts, existing shorts possibly recalled), convertible-bond and warrant hedging, single-stock options market making (cannot hedge sold puts or bought calls by shorting). Then index arbitrage and ETF market making (the short-basket leg), and lending revenue for long holders. Futures typically trade at a discount to fair value because they become the only way to be short. First morning: check whether existing shorts may be kept; replace single-name shorts by index futures where correlation allows, accepting basis and specific risk; reduce [gross exposure](https://one-course.com/books/quant/1/en/chapter/7-p-l-and-the-accounting-of-a-position#def-m1-pnl-and-positions-exposure) to what the hedge can support; and price in that the ban has no announced end.

*What the interviewer is looking for: futures discount as a consequence, and concrete first actions.*