LiquidityRiskChapter 21RiskManagementandFinanciallnstitutions3e,Chapter21,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 Liquidity Risk Chapter 21 1
RiskTypes ofLiquidityLiquidity trading riskLiquidity funding risk2RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull2012
Types of Liquidity Risk ⚫ Liquidity trading risk ⚫ Liquidity funding risk Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 2
Liquidity Trading Risk Price received for an asset depends onThe mid market priceHow much is to be soldHow quickly it is to be soldThe economic environmentAlso we found in August 2007transparency is factor that affects liquidity3RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull2012
Liquidity Trading Risk ⚫ Price received for an asset depends on ⚫ The mid market price ⚫ How much is to be sold ⚫ How quickly it is to be sold ⚫ The economic environment ⚫ Also we found in August 2007 transparency is factor that affects liquidity Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 3
Bid-Offer Spread As a Function ofQuantity (Figure 21.1, page 448)OfferPriceBid PriceQuantityRiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull20124
Bid-Offer Spread As a Function of Quantity (Figure 21.1, page 448) Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 Offer Price Bid Price Quantity 4
Bid-Offer Spread (page 450)Dollar bid -offer spread, p= Offer price -Bid priceOffer price -Bid priceProportional Bid -offer spread, s =Mid - market priceCost of liquidatio n in normal markets2wheren isthenumber of positions, α,is thepositionin the ith instrument , and s, is the proportion albid -offer spread fortheith instrument5RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull2012
Bid-Offer Spread (page 450) Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 bid - offer spread for the th instrument . in the th instrument , and is the proportion al where is the number of positions, is the position 2 1 Cost of liquidatio n in normal markets Mid -market price Offer price Bid price Proportion al Bid - offer spread, Dollar bid - offer spread, Offer price Bid price 1 i i s n s α s p i i n i i i − = = − = 5
Cost of Liquidation in StressedMarketsX-(μ, +,)αi=lwhere μ, and o, are the mean and standarddeviation of the spreadand αgives the requiredconfidence levelRiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull20126
Cost of Liquidation in Stressed Markets Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 confidence level deviation of the spread and gives the required where and are the mean and standard + = i i i i i n i ( ) 2 1 1 6
Liquidity-AdjustedVaR(page452)>Liquidity-adjusted VaR=VaR+s,aLiquidity-adjusted stressedVaR=VaR+(u; +入o,)α;i=lRiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull20127
Liquidity-Adjusted VaR (page 452) Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 = = = + + = + n i i i i n i i i s 1 1 ( ) 2 1 2 1 Liquidity -adjusted stressed VaR VaR Liquidity -adjusted VaR VaR 7
Unwinding aPosition Optimally(page452-454)Supposedollarbid-offer spread asafunctionofunits traded is p(q)Suppose standard deviation of mid-market pricechanges per day is oSuppose that g, is amount traded on day i and x, isamount held on day i (x, = xi-1-qi)Trader's objective might be to choose the q; tominimize0x +qip(q.)RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull20128
Unwinding a Position Optimally (page 452-454) ⚫ Suppose dollar bid-offer spread as a function of units traded is p(q) ⚫ Suppose standard deviation of mid-market price changes per day is ⚫ Suppose that qi is amount traded on day i and xi is amount held on day i (xi = xi-1−qi ) ⚫ Trader’s objective might be to choose the qi to minimize Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 = = + n i i i n i xi q p q 1 1 2 2 ( ) 2 1 8
Example 21.3 (page 453) A trader wishes to unwind a position in100 million units over 5 days p(q) = a+becq with a= 0.1, b = 0.05, and c =0.03g= 0.1With 95% confidence level the amountsthat should be traded on successive daysis 48.9. 30.0. 14.1, 5.1. and 1.9RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull20129
Example 21.3 (page 453) ⚫ A trader wishes to unwind a position in 100 million units over 5 days ⚫ p(q) = a+becq with a = 0.1, b = 0.05, and c = 0.03 ⚫ = 0.1 ⚫ With 95% confidence level the amounts that should be traded on successive days is 48.9, 30.0, 14.1, 5.1, and 1.9 Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 9
LiquidityFundingRisk Sources of liquidity Liquid assetsAbility to liquidate trading positionsWholesale and retail deposits Lines of credit and the ability to borrow atshort noticeSecuritization Central bank borrowing10RiskManagementandFinancialInstitutions3e,Chapter21,CopyrightJohnC.Hull2012
Liquidity Funding Risk ⚫ Sources of liquidity ⚫ Liquid assets ⚫ Ability to liquidate trading positions ⚫ Wholesale and retail deposits ⚫ Lines of credit and the ability to borrow at short notice ⚫ Securitization ⚫ Central bank borrowing Risk Management and Financial Institutions 3e, Chapter 21, Copyright © John C. Hull 2012 10