Backtest a moving-average crossover on a bundled synthetic price file

# Backtest a moving-average crossover on a bundled synthetic price file `prices.csv` is a **synthetic** daily closing-price series (no real market data), and `input.json` gives the rule's parameters. Write `solve.py` (Python 3 standard library only) so that `python solve.py input.json answer.json` backtests the rule exactly as specified. This is an offline exercise: no data downloads, no broker, no trading. We re-run it on fresh files, so do not hard-code anything. ## Input `input.json`: `prices_file` (CSV path, relative to the working directory), `fast`, `slow` (window lengths, fast < slow), `cost_bps` (cost per position change, in basis points), `initial` (starting equity). The CSV has a header `date,close`; dates are ISO `YYYY-MM-DD`. ## Rules 1. Cleaning: rows can be out of order and a date can appear more than once. For a repeated date, the **last** row in the file wins. Then sort by date. Let c[0..n-1] be the closes; `days` = n. 2. SMA_w(t) = mean of c[t-w+1 .. t] (inclusive). Signal s[t] = 1 if SMA_fast(t) > SMA_slow(t) (strictly), else 0. For t < slow - 1, s[t] = 0. 3. Position: p[0] = 0 and p[t] = s[t-1] for t >= 1 (trade on the next day's close). 4. Equity starts at `initial`. For t = 1..n-1: e[t] = e[t-1] * (1 + p[t] * (c[t]/c[t-1] - 1)) * (1 - cost * |p[t] - p[t-1]|), with cost = cost_bps / 10000. The daily strategy return is e[t]/e[t-1] - 1. 5. `trades` = number of t in 1..n-1 with p[t] != p[t-1]. `exposure` = (sum of p[1..n-1]) / (n - 1). 6. `total_return` = e[n-1]/initial - 1; `cagr` = (e[n-1]/initial) ** (252 / (n - 1)) - 1; `max_drawdown` = the largest value of 1 - e[t]/max(e[0..t]) (0 or positive); `sharpe` = mean(daily returns) / population standard deviation (`statistics.pstdev`) of daily returns * sqrt(252), or 0 if the deviation is 0; `buy_hold_return` = c[n-1]/c[0] - 1. 7. Round `final_equity` (= e[n-1]) to 2 decimals and the other fractions to 6 decimals when writing. ## Output `answer.json` keys: `days`, `final_equity`, `total_return`, `trades`, `cagr`, `max_drawdown`, `sharpe`, `exposure`, `buy_hold_return`. ## Chart (required visual) Also write `chart.svg` in the working directory: a static, self-contained SVG (root element `<svg>`, no scripts, no external images, fonts, stylesheets or links) that can be rendered headless. It must contain `<polyline id="equity">` drawing strategy equity by trading day. ## Scoring The `chart_svg_static` check (one more check, counted in partial credit) passes only if `chart.svg` exists after the fixture run, parses, has root `<svg>`, contains the ids above with the stated tags, and has no `<script>`, `<img>`/`<image>`, `<link>`, `<iframe>`/`<object>`/`<embed>`, `on*` handlers, or `href`/`src` pointing anywhere except `#...` or `data:`. Its drawing is not graded. Hidden checks (partial credit = fraction passed; all must pass): `data_cleaning` (days and buy-and-hold return), `equity_and_trades`, `risk_metrics` on the given files; `fresh_run_1`, `fresh_run_2` (all keys on freshly generated files). Tolerances: `final_equity` within 0.011, fractions within 0.00001, `days` and `trades` exact. Each run has a 60-second limit.