System and method for evaluating trade execution
A method and system for evaluating the execution of a trade of n shares from among a total of N shares of a security traded in a selected time period. According to one embodiment, a trader determines a single share price variance of the N shares, determines a correction coefficient for adjusting the single share price variance to represent a multi-share price variance, determines an adjusted variance by multiplying the single share price variance by the correction coefficient, and evaluates trade execution performance based on the adjusted variance.
1 . A method for evaluating execution of a trade of n t shares from among a total of N shares of a security traded in a selected time period T, comprising:
determining a single share price variance of the N shares;
determining a correction coefficient for adjusting the single share price variance to represent a multi-share price variance;
determining an adjusted variance by multiplying the single share price variance by the correction coefficient; and
evaluating trade execution performance based on the adjusted variance.
2 . The method of claim 1 , wherein evaluating trade execution performance comprises:
determining an efficiency score based on the adjusted variance.
3 . The method of claim 1 , wherein the single share price variance represents a variance of a distribution of prices corresponding to each of the N traded shares.
4 . The method of claim 3 , wherein the adjusted variance represents a variance of a distribution of average prices corresponding to each possible subset of n t traded shares from among the N traded shares.
5 . The method of claim 1 , wherein the correction coefficient is determined according to the formula:
N
-
n
t
n
t
(
N
-
1
)
6 . The method of claim 1 , wherein the correction coefficient is determined according to the formula:
1
α
-
1
N
-
1
where α corresponds to n t /N.
7 . The method of claim 1 , wherein the correction coefficient is determined according to the formula:
V
-
n
t
n
t
(
V
-
1
)
where V corresponds to an average daily volume or median daily volume of traded shares.
8 . The method of claim 7 , wherein V is scaled to fit the selected time period.
9 . The method of claim 3 , wherein the single share price variance represents an actual variance.
10 . The method of claim 9 , wherein the actual variance is determined according to the formula:
∑
n
t
N
(
P
t
-
∑
n
t
P
t
N
)
2
where n t corresponds to the shares traded at price P t , and N=Σn t .
11 . The method of claim 3 , wherein the single share price variance represents an estimated variance.
12 . The method of claim 11 , wherein the estimated variance accounts for historical volatility.
13 . The method of claim 12 , wherein the estimated variance is determined according to the formula:
σ
hist
2
·
T
·
P
0
2
6
where σ hist corresponds to a normalized historical volatility over a specified time period, T corresponds to a time period measured in years, and P 0 corresponds to a starting price associated with time period T.
14 . The method of claim 13 , wherein the specified time period of the normalized historical volatility includes a number of days.
15 . The method of claim 14 , wherein the number of days includes one of the group consisting of: 30 days, 60 days, and 90 days.
16 . The method of claim 12 , wherein the estimated variance is determined according to the formula:
σ
hist
2
·
T
·
P
0
2
6
where σ hist corresponds to a normalized historical volatility over a specified time period, T corresponds to a time period measured in years, and P 0 corresponds to a starting price associated with a future time period.
17 . The method of claim 11 , wherein the estimated variance is derived from an assumption of a Geometric Brownian Motion process.
18 . The method of claim 17 , wherein the estimated variance is determined according to the formula:
π
8
(
Ln
(
High
Low
)
)
2
·
P
0
2
6
where High corresponds to a highest price observed in the selected time period T, Low corresponds to a lowest price observed in the selected time period T, and P 0 corresponds to a starting price in the time period T.
19 . The method of claim 17 , wherein the estimated variance is determined according to the formula:
π
8
(
Ln
(
High
Low
)
)
2
·
P
0
2
6
where High corresponds to a highest price observed in the selected time period T, Low corresponds to a lowest price observed in the selected time period T, and P 0 corresponds to a starting price associated with a future time period.
20 . The method of claim 2 , wherein the efficiency score is determined by a function of an actual weighted average price, a benchmark price, and a standard deviation based on the adjusted variance.
21 . The method of claim 20 , wherein the benchmark price includes a VWAP of the security for the selected time period.
22 . The method of claim 20 , wherein the benchmark price includes a starting price of the security for the selected time period.
23 . The method of claim 20 , wherein the benchmark price includes an adjusted VWAP of the security for the selected time period, the adjusted VWAP being a function of a VWAP for the selected time period and a market movement factor for the selected time period.
24 . The method of claim 20 , wherein the benchmark price includes an adjusted starting price of the security for the selected time period, the adjusted starting price being a function of a starting price for the selected time period and a market movement factor for the selected time period.
25 . The method of claim 23 , wherein the market movement factor includes a percentage gain or loss of the market as a whole for the selected time period.
26 . The method of claim 24 , wherein the market movement factor includes a percentage gain or loss of the market as a whole for the selected time period.
27 . The method of claim 20 , wherein the efficiency score includes a z-score determined according to the formula:
Actual
Price
-
Benchmark
Price
σ
where σ corresponds to the standard deviation, and the standard deviation corresponds to the square root of the adjusted variance.
28 . The method of claim 2 , wherein evaluating trade execution performance further comprises:
determining a ranking score based on the efficiency score based on the adjusted variance in combination with one or more other efficiency scores associated with other trades.
29 . The method of claim 27 , wherein the ranking score is an unweighted average of the plurality of efficiency scores.
30 . The method of claim 27 , wherein the ranking score is a weighted average of the plurality of efficiency scores.