Michele Vettorazzo’s research while affiliated with Harvard University and other places

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Publications (2)


Relation between bid-ask spread, impact and volatility in order-driven markets
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February 2008

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781 Reads

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157 Citations

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Michele Vettorazzo

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility per trade, with R2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatility comes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the NYSE, a liquid market with specialists, where monopoly rents appear to be present.

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Figure 1: Average over 68 pse stocks of the impact function R(ℓ) as a function of ℓ (plain line). The average is performed by rescaling the individual R(ℓ) such that R(ℓ = 1) ≡ 1, and by rescaling ℓ by the average daily number of trades and multiplying by 100. Dotted line: prediction of the mrr model with ρ = 3/7, such that λ ∞ = 1.75. The discrepancy with empirical data shows the importance of correctly accounting for long-range correlations in order flow.  
Figure 2: General " phase diagram " in the plane x = vR 1 (v)/v, y = vS/v,  
Figure 3: France Telecom in 2002. Each point corresponds to a pair (y = vS/v, x = vR 1 /v), computed by averaging over 10000 non overlapping trades (∼ two trading days). Both quantities are expressed in basis points. We also show the different bounds, Eqs. (18,19,26), and a linear fit that gives a slope of 2.14. The correlation is R 2 = 0.93.  
Figure 4: 68 stocks of the Paris Stock Exchange in 2002. Each point corresponds to a pair (y = vS/v, x = vR 1 /v), computed by averaging over the year. Both quantities are expressed in basis points. We also show the different bounds, Eqs. (18,19,26), and a linear fit that gives a slope of 2.86, while 2/(1 − C 1 ) ≈ 2.64. The correlation is R 2 = 0.90.
Figure 5: Small tick Index Futures in 2005: cac, dax, ftse, ibex, mib, smi, hangseng. Each black square corresponds to a pair (y = vS/v, x = R 1 v/v), computed by averaging over the year, while small crosses are computed by averaging over 1000 non overlapping trades on the hangseng futures. Both quantities are expressed in basis points. We also show the bounds, Eqs. (26,18), with 1/(1 − C 1 ) ≈ 1 (dotted blue line), corresponding to the hangseng, and 1/(1 − C 1 ) ≈ 1.72 (full blue line), corresponding to the average over all other futures.

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Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets

April 2006

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3,957 Reads

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39 Citations

We argue that on electronic markets, limit and market orders should have equal effective costs on average. This symmetry implies a linear relation between the bid-ask spread and the average impact of market orders. Our empirical observations on different markets are consistent with this hypothesis. We then use this relation to justify a simple, and hitherto unnoticed, proportionality relation between the spread and the volatility_per trade_. We provide convincing empirical evidence for this relation. This suggests that the main determinant of the bid-ask spread is adverse selection, if one considers that the volatility per trade is a measure of the amount of `information' included in prices at each transaction. Symmetry between market and limit orders stems from the self-organization of liquidity in electronic markets. Our results appear to hold approximately on liquid specialist markets as well, although the spread is significantly larger.

Citations (2)


... Constantinides (1986) shows that effects of spreads (as the measures of transactions costs) may be confounded with risk effect, because the higher volatility, the more frequent trading is. Additionally, liquidity and volatility share common features: both are unobservable and estimated through various methods; both are not stable but vary over time (Wyart et al., 2006). As Cohen et al. (1976) show, volatility reflects liquidityin a cross-section the deep markets are usually less volatile than the thin ones. ...

Reference:

The dynamics of low-frequency liquidity measures: The developed versus the emerging market
Relation between Bid-Ask Spread, Impact and Volatility in Double Auction Markets