The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Market impact

Market impact: effect of trades on prices

Trades move the price against the buyer or seller due to two effects:

• trades convey information=⇒ a permanent impact affects the fair price

• instantaneous liquidity in the market is finite=⇒ a temporary impact affects the transaction price

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Market impact of buy trades

• Unperturbed price: assumed to follow a Brownian motion• Fair price: moved upward by each buy trade with a permanent effect• Transaction prices: higher than fair prices with temporary effect

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Trading P&L

Trading P&L in [tstart , tend)

Π̂h(·),tstart→tend = ht−end

(Ptend − Ptstart )︸ ︷︷ ︸“no-trade” P&L

+∑k̄−1

k=0(Ptstart − P̂tk )∆hchildtk︸ ︷︷ ︸

implementation shortfall

(10.6)

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Trading P&L

Trading P&L in [tstart , tend)

Π̂h(·),tstart→tend = ht−end

(Ptend − Ptstart )︸ ︷︷ ︸“no-trade” P&L

+∑k̄−1

k=0(Ptstart − P̂tk )∆hchildtk︸ ︷︷ ︸

implementation shortfall

(10.6)

• Execution interval split into k̄ (= number of trades) subintervals such that

tstart = t0 < · · · < tk < · · · < tk̄−1 < tk̄ = tend

∆hchildt0 · · · ∆hchild

tk · · · ∆hchildtk̄−1

• Total trading P&L (10.6) obtained as Π̂h(·),tstart→tend =∑k̄−1

k=0 Π̂h(·),tk→tk+1

trades times and amounts

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Trading P&L

Trading P&L in [tstart , tend)

Π̂h(·),tstart→tend = ht−end

(Ptend − Ptstart )︸ ︷︷ ︸“no-trade” P&L

+∑k̄−1

k=0(Ptstart − P̂tk )∆hchildtk︸ ︷︷ ︸

implementation shortfall

(10.6)

∑k̄−1k=0(Ptstart − P̂tk )∆hchild

tk︸ ︷︷ ︸implementation shortfall

=∑k̄−1

k=1(Ptstart − Ptk )∆hchildtk︸ ︷︷ ︸

timing P&L

+∑k̄−1

k=0(Ptk − P̂tk )∆hchildtk︸ ︷︷ ︸

slippage P&L

(10.7)

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Trading P&L

Trading P&L in [tstart , tend)

Π̂h(·),tstart→tend = ht−end

(Ptend − Ptstart )︸ ︷︷ ︸“no-trade” P&L

+∑k̄−1

k=0(Ptstart − P̂tk )∆hchildtk︸ ︷︷ ︸

implementation shortfall

(10.6)

∑k̄−1k=0(Ptstart − P̂tk )∆hchild

tk︸ ︷︷ ︸implementation shortfall

=∑k̄−1

k=1(Ptstart − Ptk )∆hchildtk︸ ︷︷ ︸

timing P&L

+∑k̄−1

k=0(Ptk − P̂tk )∆hchildtk︸ ︷︷ ︸

slippage P&L

(10.7)

< 0 (permanent effect) < 0 (temporary effect)

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveMarket impact

Trading P&L

Trading P&L in [tstart , tend)

Π̂h(·),tstart→tend = ht−end

(Ptend − Ptstart )︸ ︷︷ ︸“no-trade” P&L

+∑k̄−1

k=0(Ptstart − P̂tk )∆hchildtk︸ ︷︷ ︸

implementation shortfall

(10.6)

∑k̄−1k=0(Ptstart − P̂tk )∆hchild

tk︸ ︷︷ ︸implementation shortfall

=∑k̄−1

k=1(Ptstart − Ptk )∆hchildtk︸ ︷︷ ︸

timing P&L

+∑k̄−1

k=0(Ptk − P̂tk )∆hchildtk︸ ︷︷ ︸

slippage P&L

(10.7)

< 0 (permanent effect) < 0 (temporary effect)< 0 ⇐=

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

Bid-ask spread

Simple indicator of the liquidity in the market:

bid-ask spread: St ≡ P askt − P bid

t (10.7)

• integer multiple of the tick size γ (see Section 1.8.1)• small when the respective financial instrument is liquid

Deeper analysis of the limit order book (1.91) =⇒ liquidity curve

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

Bid-ask spread

Simple indicator of the liquidity in the market:

bid-ask spread: St ≡ P askt − P bid

t (10.7)

• integer multiple of the tick size γ (see Section 1.8.1)• small when the respective financial instrument is liquid

Deeper analysis of the limit order book (1.91) =⇒ liquidity curve

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market buy" liquidity curve

Consider the following function:

p→ ∆Hmbt (p) ≡

∑pj∈[P ask

t ,p]Haskj,t (10.8)

↓

best askP askt

↓

target pricep > P ask

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market buy" liquidity curve

Consider the following function:

p→ ∆Hmbt (p) ≡

∑pj∈[P ask

t ,p]Haskj,t (10.8)

↓

best askP askt

↓

target pricep > P ask

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market buy" liquidity curve

Consider the following function:

p→ ∆Hmbt (p) ≡

∑pj∈[P ask

t ,p]Haskj,t (10.8)

∆Hmbt (p) is non-decreasing and piecewise constant in p

The "market buy" liquidity curve is the "inverse" of (10.8) defined as

∆h > 0→ Pmbt (∆h) = min{p such that ∆Hmb

t (p) ≥ ∆h} (10.9)

• Hypothetical order ∆Hmbt = ∆h =⇒ best ask = Pmb

t (∆h)

• Pmbt (∆h): liquidity consumption, or market impact, of ∆Hmb

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market sell" liquidity curve

Consider the following function:

p→ ∆Hmst (p) ≡ −

∑pj∈[p,P bid

t ]Hbidj,t (10.10)

↓

best bidP bidt

↓

target pricep < P bid

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market sell" liquidity curve

Consider the following function:

p→ ∆Hmst (p) ≡ −

∑pj∈[p,P bid

t ]Hbidj,t (10.10)

↓

best bidP bidt

↓

target pricep < P bid

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

"Market sell" liquidity curve

Consider the following function:

p→ ∆Hmst (p) ≡ −

∑pj∈[p,P bid

t ]Hbidj,t (10.10)

∆Hmbt (p) is non-decreasing and piecewise constant in p

The "market sell" liquidity curve is the "inverse" of (10.10) defined as

∆h < 0→ Pmst (∆h) = max{p such that ∆Hms

t (p) ≤ ∆h} (10.11)

• Hypothetical order ∆Hmst = ∆h =⇒ best bid = Pms

t (∆h)

• Pmst (∆h): liquidity consumption, or market impact, of ∆Hms

t

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The “Checklist’’ > Execution> 10.1 Market impact and liquidity curveLiquidity curve

Construction of the liquidity curve

• The liquidity curve is obtained by joining the "market buy"liquidity curve (10.9) and the "market sell" liquidity curve (10.11)

• Interpretation of the curves as market impact of market orders tobuy/sell

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