Volatility and MicrostructureSome thoughts and a review of the literature

Introduction

Microstructure aspects can be safely ignored at longer horizons They are however first symptoms of market asymmetries First port of call for Private information ( as soon as the order is entered) The research topic has hardly been explored in the Indian markets

despite the financial markets being deep and widely traded Volatility in Prices seen as carrier of Information ( Filtration set) as

information is carried in Prices esp during Price Discovery and in Volumes traded (Information about demand)

Global research in the areas of volatility and microstructure in financial markets a salient area since the 80s

Microstructure as Volatility

The structure of markets ( Continuous Double Auction Markets in BSE and NSE) lead to typical effects in the microstructure.

However once the latent effects of non synchronous trading are detected and taken care of in the data (spurious correlations) from Non Synchronous trading (high frequency noise) U shaped serial correlation in price volatility

Volatility emerges as a key effect of the Price discovery and Order execution processes: The price effect of volatility The volume effect of volatility

The study of Price trends and Efficient Markets All forms of Market Efficiency rely on Price reflecting public and private

information in prices As a construct, the Efficient Market Hypothesis continues to be a

bulwark of Financial Markets research The existence of Price and Volume based trends and the existence of

trading around a denomination of Fundamental Value drive trading algorithms and informed Human traders to the market for every trade in Financial markets (Electronic exchanges, OTC markets and trading floors) in Currencies, Equities, Derivatives, Fixed Income or Credit and complex derivative combinations of these to satisfy the need to price and exchange risks and with the underlying motivation of a (fair) profit

Model of Asynchronous trading

Lo and Mackinlay, created one of the first micro models for focusing on the return generating process of N securities

In the absence of trading frictions or institutional rigidities , we can assign a virtual return rit (CCR)reflecting company specific information and economy wide effects for each security i

These virtual returns, intuitively differ from observed returns because of trading frictions.

Lo and Mackinlay assume a non trading probability it in each period t, assumed a s a IID sequence of coin tosses independent of the returns rit

rito , the Observed return of the security can be set to 0 if there is no transaction as rit

o = ln (pt/pt-1), thus if we consider 5 periods consecutively in which the security trades only in 1,2,5, the security reflects the same virtual return till period 2 and then observed return is 0 for 3 and 4 to get the 5th period return accumulating that of 3 4 and 5

Lo and Mackinlay

One factor linear model for returns: ri = I + ifi + it

f is a 0 mean common factor and is idiosyncratic noise, both independent of all leads and lags and f(t) Is independent of (it-k)

We use non trading probabilities to designate two new RVs The first one is 1 while it does not trade while X is switched to 1 only

when the security trades

The duration of non trading k can then be expressed as a Product of all the delta consecutively, and observed returns a re a function of X

This duration can be expressed as E(k) = pi/(1-pi), Var(k) = pi/(1-pi)^2 The variance of observed returns and other moments are thus:

With a security with non zero expected returns, variances are dilated and negative serial correlation induced decays geometrically

The minimum autocorrelation as pi varies from 0 to 1 is achieved at Min Corr(rit

o, rit+1o)=-(CV/1+1.414*|CV|)^2

At Pi= 1/1+sqrt(2)|CV| This spurious autocorrelation can be generalized and erased from a

portfolio of securities to reflect common news reflected in illiquid securities with jumps

Bid-Ask Spread

Roll (1984) If P*(t) be the fundamental value in a frictionless economy and s be the spread,P(t) = P*(t) + I*s/2Where I is IID in +1 for buyer initiated trades with p=0.5

and -1 for seller initiated trades with p = 0.5Thus Change in Price = P = I(t) – I(t-1)*s/2Here, the second moments of the process areVar(P) = s2/2 , Cov(one period) = - s2/4, Cov k period k>1 = 0Corr( one period) = -1/2 This intuition can be used to price the spread a s new information is produced for

the security

Ordered Probit Model

Lo and Mackinlay (1992) go on to present an ordered probit model which allows volatility to be modeled in generally conditionally heteroscedastic models and maps discrete time to continuous time assumed for price functions

This is solved using MLE and conditional volatility coefficients are squared to ensure non negative volatility

Others: Barrier Models by Cho and Freres and Marsh and Rosenfeld model transactions as

achievement of new discrete Price barriers, mapping the tau interval of trading Rounding models (Gottleib and Kalay 1985) Glosten and Harris (1988) – A permanent adverse selection component is present in

the data on bid ask spreads 43% adverse selection, 10% inventory holding costs and 47% transaction processing

Kyle Measures and Order Flow

Current literature on Microstructure still uses first principles. Intuitively measures of Order flow (Bid Volume – Ask Volume) are the

most appealing The latest measure by Easley and O Hara in PIN or VPIN measuring

Probability of Informed trading and Toxicity of the Order flow. These measures initially helped explain a lot in High Frequency traded

markets in High Frequency Data PIN measures are updated daily with methodological variants likely to

ensue in the future and also likely to be used by us in our work in this term

Volatility Spillovers and Cross Market movements Global integration of markets marked by a literature spanning the last decade

measuring commonality in movements between global indices The literature shows obvious relations for dependent economies with the Dow

index . Some literature also assumes a strengthening commonality of market moves a sign

of progress Spillovers more interesting in Cross asset moves and hard to measure by

cointegration . Currency markets to non traded financial asset markets most affected by equity and

derivatives markets trends Without spillovers, yield curves can measure and predict foreing exchange

premiums (Ang and Chen, 2010) These predictions exhibit low skewness and low correlation with carry returns

News Impact Curve and GARCH models Engel’s original study of volatility and its econometric measures guided

by and impactful is assessing the News impact of volatility of markets while they assimilate information

A current study of news transmission and efficient price transmission in markets may be handled by a microstructure approach

However microstructure approach effects of discrete markets already available to discount from price and trading data

Arrival of news studied thru event studies a distinct class of analysis that show the literature’s play with news arrival and assimilation at a larger level

Market Orders vs Limit Orders

A buy order is at a higher price than the mid rate, a sell order is at a lower price than the mid rate

The early literature has assumed Market Orders signal informed trading as the orders typically demand instant liquidity as if they have an expectation of price (gains)

However this is changing as most mature markets in the trading zone convert into Limit orders even if Market orders signal arrival of new information.

Thus Limit orders are not only suppliers of liquidity but also arbitraging off the availability of fundamental value and can be classified

The measures of illiquidity

It is generally known that if you take the effects of both price component of liquidity and volume effects of liquidity you can mirror the intuition of less traded stocks/assets also identifying significant Private information available in the security vis a vis a general non interest in the stock/asset

Amihud and Mendelson and Hasbrouck and Gideon Saar set early benchmark measures to determine the illiquidity premium

Asset pricing and the bid-ask spread

Amihud and Mendelsen 1986 The bid ask spread reflects the cost of execution and is found to be

negatively related to trading volume and the stock price continuity First to reflect the increasing bid ask spread as the return premia

observed in the returns Clientele effect implies here that longer horizon investors choose

securities with a higher spread Slope of the return spread relationship decreases with the spread Amihud (2002) time average absolute return with Dollar Volume of

Trading

Assymetric information measures

Early measures quoted by Hasbrouck relate the Asymmetric component with the plight of an uninformed dealer having to make market order trades including the work of Kyle (1985) and Glosten and Milgrom(1984) as well as the earliest work of Easley and O Hara (1987) and Glosten and Harris (1988)

The effect of inventory is available on specialized trading platforms aka the NYSE with a contemporaneous and subsequent price impact

The Glosten and Harris measure ignores inventory The quote revisions are treated as serially correlated with the quote revision

attributed to the assumption of trade event belonging to an informed trader, assuming an Inventory state as white noise I=- t

q(t)-q(t-1)= v(t) – v(t-1) – Beta(I(t)-I(t-1)) Demand is then modeled as a moving average of the white noise terms

Liquidity Risk

Acharya and Pedersen(2005) Liquidity is risky and is modeled for individual stocks with a common market

component A Liquidity CAPM is drawn up using the ILLIQ premium C/P for C in transaction costs

and P the current price, return r = (D-C’+P)/P(t-1) Here Dividend is modeled as D-C Similar measures of illiquidity and return are aggregated for the market component The market return & stock return increases with the covariance of market and stock

liquidity, Covariance between market liquidity and stock return negatively impacts the

idiosyncratic return (Pastor and Stambaugh, 2003) Thirdly, investors accept a lower return on the liquid securities

Paper goes on to realise a differing role for the persistence of liquidity Return also decreases with previous year’s volume and increases with spread Bekaert (2003) implies illiquidity directly predicts returns in

emerging markets This may or may not be a temporary condition The original volatility feedback effect is rarely documented in this

literature . As Expected returns increase the increase in required returns depresses the current state of Price functions for the security

Michael Brennan

Brennan goes on in a series of studies linking volatilities in debt to a higher peg than in emerging market and foreign equities

In Brennan Huh and Subrahmanyam (2013) authors build on the earlier validation of the Amihud (2002) measure

They also build on their study of the symmetric Kyle measure in Brennan et al (2010) where they find only seller initiated trades reflect a relationship ( trade at bid prices) (relation between return and changes in illiq)

Thus they decompose the Amihud measure for down markets and up markets

Half Amihud measure is strongly priced in the cross section of returns on down days

Liquidity and Asset Prices Amihud, Mendelson and Pedersen(2005) Measures in the impact of the volatility feedback effect with higher expected

returns depressing prices on reduction of liquidity It can be assumed in general that hard to trade securities are trading at hard

positive discounts to their fair value This series of literature thru 2013 reflects a desire to patch up Asset pricing

anomalies(Small Firm effect and others) using the liquidity risk priced in the microstructure including Brunnermeier, Acharya , Pedersen, Subrahmanyam and Brennan

The Paper merges different sources of (il)liquidity Transaction costs ( exogenous), Demand Pressure ( hitherto inventory risk, not in CDA markets) Private Information Order flow and search frictions

Price Formation

Joel Hasbrouck(2003) studies ETF and index futures trades Volumes positively impacted on a large scale by presence of Index

ETFs , Futures and exchange traded sector funds Traded on Open Electronic Limit Order Books (available outside the

‘floor’) A natural offshoot of trading for liquidity traders interested in

diversification Pennacchhi(1993) and Admati and Pfeiderrer(1988) Brennan and Xia study Macroeconomic effects aas real interest rates on

different categories of stocks demarcated by Sharpe Ratio measuring the impact on Pricing thru Discounted Cash flows

Probability of Informed Trading

Easley, Hvidkjaer and O Hara Tools are also readily available in R for this measure Initial validation paper with Engle and Wu in 2002(2008) Bivariate Autoregressive intensity process

Arrival rates of informed and uninformed trades Market Liquidity , Order Depth and Order Flow Daily conditional rates construct forecasts of the PIN measure PCA of PIN reflects a dominating impact of the systemic liquidity factor

Order Arrival used in a GARCH like process fitting to liquidty based returns

PIN

Measures components of order imbalance Order flow information

Impact on market Depth Liquidity

Price impact of transaction used as barrier to measure number of buy trades required to reduce Price impact below barrier(HDFC Bank never exceeds 0.6%)

These PINS may be high before earnings announcement on expectations and lower in post announcement trading as Private information converts into public information

PINs work in a smaller time window in event studies (+/- 7 days) Bad News with probability delta and Good news with probability 1-delta

(analogous to the Lo and Mackinlay measures)

PIN

Reflect the same concern with a delineation of only two types of traders,uninformed = liquidity traders

Probability of news measured as alpha Both traders modeled as Poisson processes with mu and epsilon arrival

rate parameters Expected(Total Trades)

Order Imbalance

PIN results

High turnover stocks exhibiting continuing returns continue to show returns unaffected by earnings events if they have high PINs ( liquidity)

They may have low PINS in this case they are subject to return reversals High PIN stocks thus consistent with High Private information passing to

uninformed dealers keeping up returns Uncertainty in Zhang (2006) also shown to work with PIN

Information uncertainty (Zhang 2006) Blume, Ohara and Easley Stock price continuations studied in market literature A sequence of stock prices reflect information and a single price does not reflect

underlying information Information is revealed slowly because of higher information uncertainty In high Uncertaainty , as expected from the volatility feedback effect , the required

positive returns on good news increase but the negative impact of bad news is minimized

Volumes can however not contribute to dissemination of information. Can be shown that volume correlated the quality of information being supplied to

changes in expected prices/returns One period model of trader demand ( needs explanation) Zhang uses Firm age and Coverage as parameters in uncertainty model woth analyst

dispersion and SIGMA(volatility) as well as cash flow volatility

Trading Price jump clusters

Novotny , Petrov and Urga (2014) Cluster of Price Jumps in Yen and Euro around tapering news and

Abenomics/ECB releases of liquidity Assessment of trading oppoirtunities represented by price clusters Show that Bid ask spreads eat into the returns The market makers mark-up the short-term (overnight) implied volatility at

the foreign exchange markets as the uncertainty increases and the impact of the announcements may increase the realized volatility Verdelhan(2010) risk aversion rises around news announcements ( News

Impact relation with higher volatility) Liquidity shocks timed with market news except for temporal inefficiencies

provided by central banks

News and Sentiment

Paul Tetlock study of the WSJ broadcast ‘Heard on the Street’ column Negative sentiment as posited by author or Spreads

Stop Loss Rules

Kaminsky and Lo Can substantially reduce volatility Can substantially increase expected returns

Impossible Frontiers

Market portfolios do not all end up with positive weights At least ten per cent combinations include short sales positions Is that a microstructure component?

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Using High – Lows and Variance

Corwin and Schultz (2012) Bid-ask spreads can be estimated from Daily highs and lows The Daily high is almost always a buy The Daily low is almost always a sell The difference is an indicator of the daily variance Variance is proportional to the return interval(chosen) Spread estimates can be developed from these high-low differences Comparable with Roll(1984) spread estimators Hasbrouck’s(2009) Gibbs estimator computer intensive

ARCH like estimator

Different costs on the Bid and Ask side of the Market

Earning from the Bid Ask spread

Menkveld 2013 HFT can trade assets cross markets and earn spreads as passive traders Akin to liquidity making trades as quasi market maker In Continuous Double Auction markets, traders need not be market

makers Yet Bid Ask spread can earn them a steady income without crossing the

spread and in volume trades that can be sustained by new information IN US and Europe share of dominant stock exchanges down to 20%

Two scale realized Volatility

Recent research by Zhang, Mykland and Ait Sahalia(2002) Using squared returns as volatility indicator Non parametric estimation Breaks down realized volatility and allows reconciliation to implied volatility Y(it) = X(it) + e Sum of squared returns then switches to

Use overlapping sub grids from t(k-1) with different time intervals(scales) The presence of ht as endogenous to realized volatility

Ait Sahalia et al

To estimate the leverage effect in volatility and differentiate/integrate the leverage and the volatility feedback effect

Related to high frequency estimation of volatility

Future Directions

Berger and Yang estimate Frontier Markets diversification benefits, showing idiosyncratic variance more than ½ of the total variance in Variance decomposition analysis

Marshall, Nguyen and Nuttawat(Advance) Frontier markets have high transaction costs ( Illiquid spread)

Bandi et al _ Realised Volatility vs Implied Volatility Traders use different Volatility estimates

Cornell and Green (!991) Spread to Price Performance of High yield Bonds

Signal or Noise

Banerjee and Green develop a model to recognize whether traders are informed ( rather than just liquidity makers and takers)

They relate the phenomenon back to volatility clustering Stein(2013)talks of traders inability to recognize other traders’ motive

as creating two externalities- One is the spread moving away from fundamentals and the second is a fire sale effect

Private Information

M U and J shaped patterns in FX spot markets Patterns in bid ask, trading volume and return volatility outside noise Strong relationship between Cumulative order flow and exchange rates (Easley) Unanticipated deviations from intraday trading volumes Bilateral relationships between volatility and volume, volatility and bid ask

spreads McGroarty et al study the introduction of the Euro and relate anticipated

and unanticipated order flow and volume and all three with bid ask spread Best bid and ask orders per second with trade data Log prices and log squares (volatility) Total Volume from Bid and Ask trades added

Measures of Private Information

Order Flow

Volume

• Expected Volume not linked to market making , yet a basic ‘inventory’ available in all traded assets

Relative liquidity as a future information measure Valenzuela et al(advance) Quoted depth distribution in the Order book at different times Indicator of consensus on traded price ( can be extended to other measures of

price /valuation stability) Higher liq provision away from the book

Disagreement on current price High volatility (intuition) Exploration/spurious orders from a high volume investor/trader

PCA used to identify the important quotes in the book Use Ait Sahalia, Mykland and Zhang TSRV Goettler Parlour and Rajan, Frequency of quotes waiting at the traded price

Volatility thresholds

Kasch and Caporin 2013 Correlations increase during high volatility periods reducing

diversification effects Dynamic behavior of cross correlations during switching of regimes Volatility threshold using both Conditional volatility h^1/2 and

covariance matrix The threshold Xt above which the variance becomes instrumental in

cross correlations, Not like increased cross correlations are not contagion

Idiosyncratic Volatility

Stock specific/Name specific volatility Can be an indicator of acquisition premium and higher market premiums

in Information poor economies

Volatility and Market Depth

Ahn Bae and Chan, Transitory volatility rises and then declines on increase in market depth

Depth increases due to increase in Limit Orders The TV affects mix between limit and market orders These limit orders arise without market making yet provide liquidity Earlier studies on superdot orders helped Hasbrouck identify migration of buyers to

limit orders and the phenomena of fleeting orders Potential loss from trading with informed trader(“market orders”) Foucault game theoretic model of a limit order market Glosten(1994) Patient traders: Limit Orders, Urgent traders ( Market orders) Limit Orders have to be wider spread to avoid market traders/informed traders in high

volatility markets

Order Book Slope and Price Volatility

Duong and Kalev (2008) Negative relation between future volatility and variations in the liquidity

provision in the order book Order book slope of the buy side more informative Institutional orders more informative Requirement of anonymous markets proved in ASX Indian markets proved to be anonymous Frontrunning minimized in anonymity yet information available in the

order book transforming private information to public information

Trade Autocorrelation

Chung and Li Using PIN measure Price impact of trade Positive correlation in direction of trade Both measure positively related to trading frequency Quote revisions earlier studies also because of liquidity, inventory and

non information reasons PIN better measure than use of small firms and liquidity proxies Kyle study initially on trade size and pace of information assimilation Institutional trading may contribute more to clustering during high

volatility before a news break

Volatility of Liquidity

Volatility Feedback Puzzle (Bollerslev) resolved microstructure: Zhang and Perreira 2010

Liquidity influences returns beyond trading costs Liquidity modeled as stochastic price impact Liquidity Premium = Additional return necessary (Adverse Price impact

of trading) Not required for patient investors waiting on Limit Orders Zhang and Perreira go on to use a CRRA risk aversion model Granger causality from Price impact to trading activity

Volatility discovery across the LOB Wang(2014) Using trading in both stock and options markets A new picking off risk in limit orders different from adverse selection because of

Private information Informed traders use Limit orders established in the literature

Informative of future liquidity Directions of future stock price movements Future stock price volatility

Price aggressiveness of the Limit Order Book Winners Curse Aggressiveness of limit orders related to Options Price trading Infer volatility from Options prices and change the aggressiveness of the Limit order

book

Emerging Limit Order Market

Jain and Jiang(2014) Information content of the Limit Order Book on the Shanghai Stock

Exchange LOB consistently predicts future price volatility from the slope of the

order book Sell orders become more informative during extreme wide movement

days ( higher no. of extreme moves on the Shanghai stock exchange) Buy orders more informative during normal market and up move days Order submission strategies

Sentiment

Berger and Turtle(2015) Short term increases in sentiment precede positive returns Sustained increases in sentiment precede negative returns Especially true for market portfolios and Opaque portfolios with high

uncertainty and/or higher arbitrage for private information and greater frictions

Sophisticated investors /arbs contribute to mispricing Build up of short interest usually quieter than the behavioral bias in

buying Diminishing bubble growth rate

Indian trading/investing relations of liquidity Simultaneous price discovery in Banknifty options and futures markets Large price moves across a bid spread and Price impact spanning Bid –

Ask pf 300 to 500, Price impact of 25*200 per lot in a single move Actively traded with large volumes Selling Puts in a monotonically rising trend Risk induces trades on the other side, ensures high spreads and low

volume ( in no. of lots) trading Most of the float from Public sector banks

Continued Bayesian inference

Sequential deterministic modelling updated for new information LOB as an information store Information lost between the cup and the lip restored by Bayesian inference Information to trade conversion based on Matching engine and order flow Heavily traded securities can reveal the patchwork First in First out at best prices First few levels are broadcast, all levels are available readily ( except of some

exchanges) Adds, Modifies and Cancels Explicit vs Implied ( Hidden/iceberg) Off book trades / Bulk trades mechanisms

Price Discovery and Liquidity

Impact of information arrival Newswires on intra day movements Riordan et al(2013) Impact on liquidity and trading intensity Liquidity decreases around negative messages ( May increase on lower

prices) Negative messages induce stronger reactions

HFT data increased the study of such trading by HFT traders Hoffman, fast and slow traders

Latency

Hasbrouck and Saar (2011) Technology of trading Easy execution Flash crash potential from mistakes Reduction in transaction costs but increase in spreads

Microstructure related increase in concentration effects Highly concentrated industries with low competition feature more

abnormal returns factoring product market cash flows in financial markets

Competitve industries see far lower risk premiums and abnormal returns Industry concentration links to behavioral phenomena in the

microstructure

Frontier markets and idiosyncratic risk Berger and Yang(2013) As mentioned earlier far away illiquid markets good idiosyncratic risk

proxies Frontier funds more illiquid extensions of emerging markets 1/3 of fund risk idiosyncratic for Frontier funds and ½ of regional funds,

commonality decreasing The criticality of index proxies for Passive investors in Emerging Debt

trading Marshall, Nguyen et al fixate on transaction costs (Bid Ask spread) that

negate such diversification (Liquidity risk) Chunky Price moves

Returns in Private Equity ‘ Markets’

Ang et al 2014 Model Partner cash flows Unbalanced panel and Time varying PE premium ( Liquidity and chunky

transaction moves and related risk measures)

Limit Order Markets Parlour and Seppi (2007) LOMs : No Uniform clearing price Each order filled at limit Market orders changed to limit after partial fill (exchange

characteristic/manual in India) Iceberg orders in the interest of market disclosure ( during sells) In India cannot choose as exchange after large order arrives (market order)

at least technically Dynamic trading strategies ‘ also’ depend on monitoring changing market

conditions ( frequency of monitoring) in news and transaction volume terms Seen as fair in light of adverse selection frictions Asset valuations now a social activity in Economics because most economic

assets have trading proxies Coordination problems ruled over by ease of anonymity