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Market Impact Estimation
Hard
·
23 min read
Market Microstructure
Market Impact
Kyle Model
Price Impact
Empirical Methods
1
Article
2
Notebook
3
Quiz
Quick Quiz
1.
In Kyle (1985),
λ
=
1
2
σ
u
Σ
0
\lambda=\frac{1}{2\sigma_u}\sqrt{\Sigma_0}
λ
=
2
σ
u
1
Σ
0
(
σ
u
\sigma_u
σ
u
= noise-trader volume,
Σ
0
\Sigma_0
Σ
0
= prior value variance). What happens to
λ
\lambda
λ
as
σ
u
→
∞
\sigma_u\to\infty
σ
u
→
∞
, and why?
λ
→
Σ
0
1
/
2
\lambda\to\Sigma_0^{1/2}
λ
→
Σ
0
1/2
: impact is set solely by fundamental uncertainty
λ
→
0
\lambda\to 0
λ
→
0
: the maker cannot separate informed from noise flow, so price reaction per unit flow vanishes
λ
→
∞
\lambda\to\infty
λ
→
∞
: noisier flow is more likely informed, so the maker moves price more
λ
\lambda
λ
stays constant: informed and noise trading exactly offset
2.
The square-root law is
I
m
p
a
c
t
(
Q
)
≈
Y
σ
Q
/
V
\mathrm{Impact}(Q)\approx Y\sigma\sqrt{Q/V}
Impact
(
Q
)
≈
Y
σ
Q
/
V
. For
Q
=
0.01
V
Q=0.01V
Q
=
0.01
V
,
Y
=
1
Y=1
Y
=
1
,
σ
=
1
%
\sigma=1\%
σ
=
1%
/day, the expected impact is:
100 bps: equal to one day's volatility
10 bps:
1
%
×
0.01
=
1
%
×
0.1
=
0.1
%
1\%\times\sqrt{0.01}=1\%\times0.1=0.1\%
1%
×
0.01
=
1%
×
0.1
=
0.1%
1 bp: the impact is linear in
Q
/
V
Q/V
Q
/
V
0.1 bp: the square root makes impact far smaller than linear
3.
Regressing mid-price changes on signed order flow (Lee-Ready signs) to estimate Kyle's lambda can be upward-biased. The primary source is:
Lee-Ready misclassifies about half of all trades, adding noise that biases
λ
\lambda
λ
toward zero
The informed trader hides trades, making signed flow uncorrelated with price
Discrete tick sizes round the mid-price, biasing the regression slope
Bid-ask bounce: alternating bid/ask trades inflate the apparent slope
4.
The permanent impact of a trade is the price move that persists after execution; a near-zero permanent impact implies the trade was uninformative and price reverts to its pre-trade level.
True
False
5.
Execution cost accumulates as
Cost
=
∫
0
T
v
(
t
)
h
(
v
(
t
)
)
d
t
\text{Cost}=\int_0^T v(t)\,h(v(t))\,dt
Cost
=
∫
0
T
v
(
t
)
h
(
v
(
t
))
d
t
with temporary impact
h
(
v
)
=
η
σ
v
/
V
h(v)=\eta\sigma\sqrt{v/V}
h
(
v
)
=
η
σ
v
/
V
(sub-linear per-share impact; ignore permanent impact). Comparing TWAP over a day (constant rate
v
0
=
Q
/
T
v_0=Q/T
v
0
=
Q
/
T
) with near-immediate execution, which holds?
Immediate is cheaper because per-share cost falls with size for concave
h
h
h
TWAP is cheaper: spreading lowers the rate, so total cost falls as
T
T
T
grows
Same cost:
∫
v
h
(
v
)
d
t
\int v\,h(v)\,dt
∫
v
h
(
v
)
d
t
is independent of the execution schedule
TWAP is always cheaper for any
h
h
h
, concave or convex
6.
What is a 'meta-order', and why does correctly identifying its boundaries matter for estimating the square-root law?
An order routed to several venues at once; boundaries prevent double-counting
An iceberg order; boundaries separate displayed from hidden size
An order spanning multiple assets; boundaries matter for measuring cross-impact
The sequence of child orders filling one parent; wrong boundaries mis-measure
Q
Q
Q
and distort impact-vs-size
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