# Price impact of trades: five-day exploratory analysis

The calculation is complete for the fixed sample of HINDOILEXP, MMTC, BAJFINANCE and RELIANCE on 4-8 May 2020. It uses reconstructed quotes that passed internal checks. An independent bid/ask file was not available.

## Method

For each individual continuous-market execution, direction comes from the source-order aggressor identity. Relative size is trade shares divided by average daily shares over the previous 20 sessions; trade value divided by previous average turnover is a sensitivity check. Both endpoints use the latest one-second reconstructed quote sample at or before the target (strictly before the execution for the initial quote). Each sample must be clock-certain, positive and uncrossed, and the order-only and execution-informed books must agree on bid and ask. Signed impact is direction x (later midpoint - pre-trade midpoint) / pre-trade midpoint x 10,000. Negative responses are retained.

Primary horizons are 1, 5, 30 and 60 seconds; 10 seconds and 5 minutes are also saved. The primary execution window is 09:20-15:29. A horizon must end before 15:30. Endpoint quote-sample age is at most one second. Invalid samples are not filled with older quotes. The sampled endpoints can precede their targets by up to one second; the event-level clock-ambiguity diagnostics are retained separately. Each stock-day/horizon requires at least 95% valid pre-quote and post-quote coverage, at most 1% crossed pre-quotes, and the replay gates.

The conditional curves first average within each stock-day and fixed logarithmic size bin, then give stock-days equal weight. Curves use bins with at least 5 stock-days and 30 observations. Power curves are fitted on the original signed scale, with positive amplitude and beta between 0 and 1.5. Square-root and linear alternatives are reported. Intervals use 200 trading-date block bootstrap draws and are exploratory with only five dates.

## Coverage

Accepted primary stock-day/horizon combinations: 80 / 80.

| Group | Horizon | Equal stock-day mean response (bps) | Stock-days | Observations |
|---|---:|---:|---:|---:|
| illiquid | 1s | 8.4723 | 10 | 14,504 |
| illiquid | 5s | 8.6995 | 10 | 14,480 |
| illiquid | 30s | 9.0144 | 10 | 14,485 |
| illiquid | 60s | 9.1728 | 10 | 14,491 |
| liquid | 1s | 1.5451 | 10 | 4,266,692 |
| liquid | 5s | 1.8479 | 10 | 4,296,990 |
| liquid | 30s | 1.6072 | 10 | 4,295,674 |
| liquid | 60s | 1.4290 | 10 | 4,294,743 |

These unconditional means also reflect different trade-size distributions. Use liquidity_comparison.csv for comparisons within common relative-size bins.

## Interpretation and limits

- Only four fixed stocks over 4-8 May 2020; results do not cover the full 2019-2022 period.
- Order execution identities and quantities help reconstruct the book; exact execution agreement is not independent quote validation. Actual trade prices are held out of matching.
- Quotes are sampled once per second; endpoint timestamps precede execution/horizon targets by up to one second. Ambiguous, crossed/one-sided, disagreeing or stale samples are excluded without filling invalid intervals.
- Individual executions from the same aggressor order are dependent; date blocks preserve within-day dependence but 5 dates and 2 stocks per group give weak generalization.
- Liquidity classifications are provisional and based on prior turnover; daily normalization uses 20 preceding sessions.
- Responses include concurrent market moves and order flow; this is descriptive, not an isolated causal treatment effect.
- Fitted exponents, including a value near 0.5, do not establish a universal square-root law.
- Liquidity-group differences can also reflect price level, relative tick size, spread and volatility; this four-stock comparison does not isolate liquidity causally.
- Quote disagreement and clock exclusions may be related to trade size or volatility; the coverage tables make those exclusions visible.

## Files

impact_bins.csv: conditional curves and support counts. liquidity_comparison.csv: same-size-bin liquid/illiquid differences. power_fits.csv: free, square-root and linear fits. coverage.csv: all inclusion decisions. trade_panel.parquet under each stock-day retains both size normalizations, pre/post sampled midpoints, spreads, six horizons, exact-event diagnostics and quality flags. Failed earlier reconstruction variants and their logs remain on the VPS.

All computation and files are on the VPS. Raw source retention is bounded by the storage policy; inputs are verified before being marked complete.

## Findings in this sample

- At 1 seconds, the illiquid-group conditional mean response exceeds the liquid group in 8 of 8 common relative-size bins. Differences range from 3.14 to 7.09 basis points.
- At 5 seconds, the illiquid-group conditional mean response exceeds the liquid group in 8 of 8 common relative-size bins. Differences range from 3.08 to 5.92 basis points.
- At 30 seconds, the illiquid-group conditional mean response exceeds the liquid group in 8 of 8 common relative-size bins. Differences range from 2.92 to 6.81 basis points.
- At 60 seconds, the illiquid-group conditional mean response exceeds the liquid group in 8 of 8 common relative-size bins. Differences range from 3.56 to 7.75 basis points.
- One-second individual-execution power-fit exponents: illiquid 0.135, liquid 0.100. These are descriptive fits to individual executions; they cannot establish or refute a square-root law for unidentified parent orders.

Bin comparisons are approximate because relative size can still differ within a bin. The results are specific to these four stocks and five dates; price levels, ticks, spreads, volatility and excluded quote intervals can affect the comparison.


## Data and matching-rule reference

The trade/order sample is from the library-authorized NSE Capital Market data. Thirty official full-market daily summaries are also retained on the VPS for liquidity denominators and later stock selection. The primary calculations use the frozen 20-session prior reference data.

[NSE/CMTR/54851, 16 December 2022](https://archives.nseindia.com/content/circulars/CMTR54851.pdf), section A, describes the existing handling of DAY market-order remainders. Only that passivation mechanism was used; the proposed new market-price-protection rules in section B were not applied to the May 2020 data. The reconstruction changes were checked against the actual 2020 execution identities, quantities and held-out prices. The original parser source, project corrections, licence and source hashes are retained in the review bundle.