Estimating Liquidity Risk

from High Frequency tick Data Bruce Uponi in...FINANCE What is Liquidity ? Simply Put! Liquidity is

the availability

of Cash But, Liquidity is the degree to which an Asset can be bought or sold in a Market without affecting the price of the Asset. In a more

Economical sense ... Liquidity Risk

is ... ... the risk of buying or selling an Asset above or below the actual Market price of the Asset at any given time. We have about 3 ways in which Liquidity risk could manifest. This is just one of them, referred to as

"Market Liquidity Risk". We shall now try to quantify or estimate the Liquidity Risk in a typical Market. A system for collecting the orders placed by Buyers and Sellers in a market place such as the

London Stock Exchange (LSE) The Order Book Buyers - Bid

Sellers - Ask "Best Ask" is the lowest Ask price. "Best Bid" is the highest Bid price. "Bid-Ask Spread is difference between

Bid and Ask prices. Bid-Ask Spread = $55.00 Typical Liquidity Risk Issue 1st Best "Offer" Order = 671 Qty @ 2215 Offer Side - Sellers 2nd Best "Offer" Order = 10000 Qty @ 2238 Bid Side - Buyers 1st Best "Bid" Order @ 1874 Qty. Cost of Liquidity 671 * 2215 = 1486265 (1874 -671) * 2238 = 2692314 1874 * 2215 = 4150910 4178579 = 27669 2215 + 2238 = 4453 4453 / 2 = 2226.5 2226.5 should be minimum sale price for the Buyer if he should sell. ...and the Effect increases with more Quantities to buy. Making the issue of Liquidity less trivial to overlook. Spread

Depth But How Did the Order Book come about ? Because we need to base our analysis on real data, we need stock market data. But these market events occured in some time past, how do we really know what the Order Book was like at each moment a new order entered and caused a change in the Order Book. We resort to "Reconstructing the Order Book"... back to it's former state This was the first thing I had to do given the raw market data from the London Stock Exchange...let's briefly see how that was accomplished. Order Book Reconstruction Process 3 Core tasks were carried out in this Liquidity Risk Estimation process. Order Book Reconstruction Marginal Supply and Demand Curve (MSDC) derivation. Liquidation Cost Calculation. TASK CHECKLIST Order Book Reconstruction. Marginal Supply and Demand Curve (MSDC) derivation. Liquidation Cost Estimation. Using the Order Book, the MSDC shows the trade off between Bid and Ask prices in relation to their volume The MSDC Ask prices must be higher than Bid prices economically. To derive the MSDC, we need the Order Book, at least a snap shot. We take a snap shot of Astrazeneca (AZN) stock from the LSE @ 8:30 02/06/2008 Order Book MSDC Bid-Ask Spread Market Depth Bid-Ask Spread Market Depth This can be considered as the cost it would take to liquidate a market position (i.e. sell an asset) or the cost it takes to secure a position (i.e. buy an asset) The Liquidation Cost TASK CHECKLIST Order Book Reconstruction Marginal Supply and Demand Curve derivation. Liquidation Cost Estimation The term "Mark-to-Market" MtM. The new Liquidity Risk Formalism by Carlo Acerbi and Giacomo. Scandolo in their paper titled - Liquidity risk and Coherent Risk Measures, 2008. Liquidation MtM L(p) Upper Liquidation MtM U(p) Cost of Liquidity C(p) L(p) - is valuing the worth of a portfolio or an asset with the prevalent (obtainable) price for that asset. In this context, we use the order book. MtM - is a portfolio idea of valuing the worth of a portfolio or an asset with prevalent market price (value). U(p) - is valuing the worth of a portfolio or an asset with only the best, prevalent (obtainable) price for that asset. Using the order book in context too. C(p) - is the difference between L(p) and U(p) which we refer to as the Liquidation Cost. Acerbi and Scandolo were able to deduce properties for L(p) , U(p) and C(p) in a vector space of portfolio - literally a collection of portfolios. Properties of L(p), U(p) and C(p) These properties are:

L(p) is concave in a vector space of portfolios.

U(p) is also concave just as L(p).

C(p) is convex in a vector space of portfolios. Using our Order Book, Estimating L(p), U(p) and C(p) we can calculate L(p), U(p) and C(p) for a simple portfolio (p). p = [10000, 3000, -1000] -- (4,000 Stock of AZN) Cash Long Short L(p) = 10000 + (2192.400+2192.1000+2191.1600) − (2203.400+2203.400+2203.200) Long Cash Short L(p) = 4,381,400 U(p) = 10000 + (2192.3000) – (2203.1000) U(p) = 4,383,00 Cash Long Short C(p) = U(p) - L(p) = 1,600 Using real stock market data we estimate the value of C(p) for a portfolio of 2 different stocks. MSDCs for both stocks reveal some liquidity properties 2 Stock from the LSE on 02/06/2008 AZN - Astrazeneca

BATS - British American Tobacco With 10 different portfolios of AZN and BATS, AZN = [1000 2000 3000 4000 5000 10000 20000 30000 40000 50000] BATS = [500 1000 1500 2000 2500 5000 10000 15000 20000 25000] Cash = 50,000 We estimate the L(p), U(p) and C(p) for 2 Scenarios. Long AZN and Short BATS – 10 possible quantities of each at 12:30 and 16:30. Long AZN and Short BATS – 10 x 10 possible quantities of each at 12:30 and 16:30. Long AZN and Short BATS – 10 possible quantities of each at 12:30 and 16:30 Long AZN and Short BATS – 10 x 10 possible quantities of each at 12:30 and 16:30 Results & Observations In Conclusion The results for L(p), U(p) and C(p) are consistent with the properties given by Acerbi and Scandolo's formalism. There is higher Liquidation Cost (higher Liquidity Risk) in liquidating large positions. i.e. Liquidity Risk increases as the volume of stock or asset to liquidate increases. The tighter, closer or smaller the Bid-Ask Spread, the less the Liquidation Cost for an asset or a portfolio. 2. Loose or wide bid-ask spread characterizes illiquid markets with impact on liquidation cost. Two facts stylized by the MSDC which are exemplified in the corresponding results obtained from C(p) are: 1. Liquidation costs increases with the volume of stock to be liquidated. Liquidation Cost Estimation TASK CHECKLIST Order Book Reconstruction Marginal Supply and Demand Curve (MSDC) derivation Task Completed. THANKS FOR LISTENING Buying - Above Selling - Below http://prezi.com/qatqsvdrubgq/estimating-liquidity-risk-from-high-frequency-financial-data/ http://prezi.com/qatqsvdrubgq/estimating-liquidity-risk-from-high-frequency-financial-data/

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# Estimating Liquidity Risk from High Frequency Financial Data.

A presentation on Estimating Liquidity Risk using High Frequency financial data.

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