diff --git a/book/marimo/notebooks/cla.py b/book/marimo/notebooks/cla.py
index 4bf5c48d..80465004 100644
--- a/book/marimo/notebooks/cla.py
+++ b/book/marimo/notebooks/cla.py
@@ -4,6 +4,8 @@
 #     "marimo==0.14.13",
 #     "numpy==2.3.0",
 #     "plotly==6.7.0",
+#     "polars==1.44.1",
+#     "jquantstats==0.11.0",
 #     "cvx-linalg>=0.9.3",
 #     "cvxcla"
 # ]
@@ -22,9 +24,15 @@
 with app.setup:
     import marimo as mo
     import numpy as np
+    import polars as pl
+    from jquantstats import Data
 
     from cvxcla import CLA
 
+    # Trading days in a year, and the length of the simulated history.
+    PERIODS = 260
+    HISTORY = 4 * PERIODS
+
 
 @app.cell
 def _():
@@ -33,6 +41,13 @@ def _():
     # The Critical Line Algorithm
     We compute an efficient frontier using the critical line algorithm (cla).
     The method was introduced by Harry M Markowitz in 1956.
+
+    Rather than invent a mean vector and a covariance matrix out of thin air, we
+    simulate a return history, estimate both from it, and trace the frontier of
+    the estimated problem. That way every portfolio on the frontier has a
+    *realised* return series too, which we hand to
+    [jQuantStats](https://github.com/jebel-quant/jquantstats) at the bottom of
+    this notebook.
     """
     )
     return
@@ -47,40 +62,149 @@ def _():
 
 
 @app.function(hide_code=True)
-def cla(n):
+def business_dates(periods):
+    """Build a Monday-to-Friday date index of the given length."""
+    calendar = pl.date_range(pl.date(2015, 1, 1), pl.date(2035, 1, 1), interval="1d", eager=True)
+    return calendar.filter(calendar.dt.weekday() <= 5).head(periods)
+
+
+@app.function(hide_code=True)
+def simulate(n, seed=42):
+    """Simulate a daily return history for n assets.
+
+    The assets differ in their true drift and load on a handful of common
+    factors, so the estimated problem below has a genuinely tilted frontier
+    instead of one driven purely by estimation noise.
+
+    Args:
+        n (int): Number of assets.
+        seed (int): Seed for the random generator, so the notebook is reproducible.
+
+    Returns:
+        polars.DataFrame: A frame with a ``date`` column and one return column
+            per asset, with ``HISTORY`` rows.
+    """
+    rng = np.random.default_rng(seed)
+
+    # True annual drifts spread across the assets, expressed per day.
+    drift = np.linspace(0.02, 0.20, n) / PERIODS
+    # A low-rank common factor structure plus idiosyncratic noise.
+    k = max(2, n // 10)
+    exposures = rng.standard_normal((n, k)) * 0.4
+    factors = rng.standard_normal((HISTORY, k)) * 0.01
+    idiosyncratic = rng.standard_normal((HISTORY, n)) * 0.01
+
+    returns = drift + factors @ exposures.T + idiosyncratic
+    columns = [f"asset_{i:03d}" for i in range(n)]
+    return pl.DataFrame({"date": business_dates(HISTORY), **dict(zip(columns, returns.T, strict=True))})
+
+
+@app.function(hide_code=True)
+def cla(returns):
     """Compute using the Critical Line Algorithm (CLA) an efficient frontier.
 
+    The mean vector and the covariance matrix are the sample estimates taken
+    from the simulated return history. The portfolios are long-only, capped at
+    100% per name, and fully invested.
+
     Args:
-        n (int): The dimension size of the mean vector, lower and upper bounds
-            arrays, and covariance matrix used in the computation.
+        returns (polars.DataFrame): Return history with a leading ``date`` column.
 
     Returns:
-        numpy.ndarray: The efficient frontier generated by the CLA based on the
-            provided parameters.
+        cvxcla.types.Frontier: The efficient frontier of the estimated problem.
     """
-    mean = np.random.randn(n)
-    lower_bounds = np.zeros(n)
-    upper_bounds = np.ones(n)
-
-    factor = np.random.randn(n, n)
-    covariance = factor @ factor.T
-
-    f1 = CLA(
-        mean=mean,
-        covariance=covariance,
-        lower_bounds=lower_bounds,
-        upper_bounds=upper_bounds,
-        a=np.ones((1, len(mean))),
+    matrix = returns.drop("date").to_numpy()
+    n = matrix.shape[1]
+
+    return CLA(
+        mean=matrix.mean(axis=0),
+        covariance=np.cov(matrix, rowvar=False),
+        lower_bounds=np.zeros(n),
+        upper_bounds=np.ones(n),
+        a=np.ones((1, n)),
         b=np.ones(1),
     ).frontier
-    return f1
 
 
 @app.cell
 def _(slider):
-    frontier = cla(slider.value)
-    frontier.interpolate(2).plot(volatility=True, markers=True)
-    frontier.plot()
+    returns = simulate(slider.value)
+    frontier = cla(returns)
+    mo.md(f"The frontier of the estimated problem has **{len(frontier)}** turning points.")
+    return frontier, returns
+
+
+@app.cell
+def _(frontier):
+    frontier.plot(volatility=True, markers=True)
+    return
+
+
+@app.cell
+def _():
+    mo.md(
+        r"""
+    ## From weights to a track record
+
+    The frontier is a set of weight vectors. Applied to the return history they
+    generated, each one becomes a return series, and a return series is what
+    jQuantStats analyses. We look at three portfolios: the maximum-Sharpe point
+    on the frontier, the minimum-variance point, and equal weight as a
+    reference.
+
+    These are *in-sample* numbers -- the same history produced the estimates the
+    optimiser used -- so read the table as a description of the frontier, not as
+    a backtest. `experiments/frontier_stats.py` runs the out-of-sample version
+    on real S&P 500 data.
+    """
+    )
+    return
+
+
+@app.function(hide_code=True)
+def track_records(frontier, returns):
+    """Turn frontier portfolios into a jQuantStats `Data` object.
+
+    Args:
+        frontier (cvxcla.types.Frontier): The traced efficient frontier.
+        returns (polars.DataFrame): The return history the frontier was estimated on.
+
+    Returns:
+        jquantstats.Data: The realised return series of the maximum-Sharpe, the
+            minimum-variance and the equal-weight portfolio.
+    """
+    matrix = returns.drop("date").to_numpy()
+    n = matrix.shape[1]
+
+    _, max_sharpe = frontier.max_sharpe
+    # Frontier order runs from maximum return towards minimum variance, but read
+    # the minimiser off the variance vector rather than relying on that order.
+    min_variance = frontier.weights[int(np.argmin(frontier.variance))]
+
+    portfolios = {
+        "max_sharpe": max_sharpe,
+        "min_variance": min_variance,
+        "equal_weight": np.full(n, 1.0 / n),
+    }
+    series = {name: matrix @ weights for name, weights in portfolios.items()}
+    return Data.from_returns(pl.DataFrame({"date": returns["date"], **series}))
+
+
+@app.cell
+def _(frontier, returns):
+    data = track_records(frontier, returns)
+    return (data,)
+
+
+@app.cell
+def _(data):
+    mo.ui.table(data.stats.summary(), selection=None)
+    return
+
+
+@app.cell
+def _(data):
+    data.plots.returns(title="Cumulative return of three frontier portfolios")
     return
 
 
diff --git a/book/marimo/notebooks/factor.py b/book/marimo/notebooks/factor.py
index 0fd8fec1..5fb70f29 100644
--- a/book/marimo/notebooks/factor.py
+++ b/book/marimo/notebooks/factor.py
@@ -4,6 +4,8 @@
 #     "marimo==0.14.13",
 #     "numpy==2.3.0",
 #     "plotly==6.7.0",
+#     "polars==1.44.1",
+#     "jquantstats==0.11.0",
 #     "cvx-linalg>=0.9.3",
 #     "cvxcla"
 # ]
@@ -22,6 +24,8 @@
 with app.setup:
     import marimo as mo
     import numpy as np
+    import polars as pl
+    from jquantstats import Data
 
     from cvxcla import CLA, FactorCovariance
 
@@ -42,6 +46,9 @@ def _():
        which is exactly what `FactorCovariance` solves via the Woodbury
        identity in $O(nk)$ memory.
     4. Hand it to `CLA` and plot the frontier.
+    5. Check the operator against the data: the volatility the Woodbury
+       quadratic form predicts for a frontier portfolio has to equal the
+       volatility its realised return series actually shows.
     """
     )
     return
@@ -94,7 +101,7 @@ def _(n_slider):
     returns = simulate_returns(rng, t=2 * n, n=n)
     covariance = clip_covariance(returns)
     mo.md(f"Kept **{covariance.k}** factors out of {n} sample eigenvalues.")
-    return covariance, n, rng
+    return covariance, n, returns, rng
 
 
 @app.cell
@@ -117,5 +124,88 @@ def _(frontier):
     return
 
 
+@app.cell
+def _():
+    mo.md(
+        r"""
+    ## Does the operator agree with the data?
+
+    `FactorCovariance` never forms the $n \times n$ matrix, so the volatilities
+    plotted above come out of the Woodbury identity rather than a dense
+    quadratic form. That is worth checking against the returns themselves.
+
+    Below, each frontier portfolio is applied to the simulated history to give a
+    realised return series, which
+    [jQuantStats](https://github.com/jebel-quant/jquantstats) measures. The
+    predicted column is $\sqrt{w^\top \Sigma w}$ from the operator; the
+    realised column is the sample standard deviation of the series, and their
+    ratio sits within a few percent of 1 across the whole slider range. Not
+    exactly 1: clipping deliberately discards the part of the sample spectrum
+    it calls noise, so the cleaned $\Sigma$ is *not* the sample covariance of
+    this history. A few percent is that discarded noise. An order-of-magnitude
+    gap, or one that widened with $n$, would instead point at the low-rank
+    solve.
+
+    Risk is all we ask of this table. The means fed to the CLA are a synthetic
+    forecast unrelated to the simulation, and `simulate_returns` draws from a
+    standard normal rather than at a realistic return magnitude, so the
+    return-, Sharpe- and drawdown-based metrics jQuantStats also offers would
+    be measuring the simulation's conventions rather than the frontier.
+    `experiments/frontier_stats.py` reads those metrics off real S&P 500 data
+    instead.
+    """
+    )
+    return
+
+
+@app.function(hide_code=True)
+def score(frontier, returns):
+    """Compare each portfolio's predicted volatility with its realised one.
+
+    Args:
+        frontier (cvxcla.types.Frontier): The traced efficient frontier.
+        returns (numpy.ndarray): The t x n simulated return history.
+
+    Returns:
+        polars.DataFrame: One row per portfolio with the volatility the
+            covariance operator predicts, the volatility jQuantStats measures on
+            the realised series, and their ratio.
+    """
+    t, n = returns.shape
+    # Frontier order runs from maximum return towards minimum variance, but read
+    # the minimiser off the variance vector rather than relying on that order.
+    min_variance = frontier.weights[int(np.argmin(frontier.variance))]
+    portfolios = {
+        "max_sharpe": frontier.max_sharpe[1],
+        "min_variance": min_variance,
+        "equal_weight": np.full(n, 1.0 / n),
+    }
+
+    calendar = pl.date_range(pl.date(2015, 1, 1), pl.date(2045, 1, 1), interval="1d", eager=True)
+    dates = calendar.filter(calendar.dt.weekday() <= 5).head(t)
+    series = {name: returns @ weights for name, weights in portfolios.items()}
+    data = Data.from_returns(pl.DataFrame({"date": dates, **series}))
+
+    # Per-observation volatility, so it is comparable with the frontier's own:
+    # the simulation carries no annualisation convention.
+    realised = data.stats.volatility(annualize=False)
+    # The Woodbury operator's own quadratic form -- no dense matrix is formed.
+    predicted = {name: float(np.sqrt(w @ frontier.covariance.matvec(w))) for name, w in portfolios.items()}
+    return pl.DataFrame(
+        {
+            "portfolio": list(portfolios),
+            "predicted volatility": [predicted[name] for name in portfolios],
+            "realised volatility": [realised[name] for name in portfolios],
+            "ratio": [realised[name] / predicted[name] for name in portfolios],
+        }
+    )
+
+
+@app.cell
+def _(frontier, returns):
+    mo.ui.table(score(frontier, returns), selection=None)
+    return
+
+
 if __name__ == "__main__":
     app.run()
diff --git a/experiments/frontier_stats.py b/experiments/frontier_stats.py
new file mode 100644
index 00000000..cbafab67
--- /dev/null
+++ b/experiments/frontier_stats.py
@@ -0,0 +1,119 @@
+"""Score CLA frontier portfolios out-of-sample with jQuantStats.
+
+The CLA reports what a portfolio is *expected* to do: `Frontier` exposes the
+expected return, volatility and Sharpe ratio implied by the mean/covariance it
+was handed. This experiment closes the loop and asks what those portfolios
+actually *did*, on data the optimiser never saw.
+
+  1. Split the committed S&P 500 return snapshot in half by time.
+  2. Estimate the mean and the sample covariance on the first half only.
+  3. Trace the long-only, fully-invested frontier with the CLA.
+  4. Pick two portfolios off it -- the maximum-Sharpe one (exact, via
+     ``Frontier.max_sharpe``) and the minimum-variance turning point -- and
+     hold both fixed through the second half.
+  5. Hand the three realised daily return series (the two frontier portfolios
+     plus an equal-weight benchmark) to ``jquantstats`` and print its report.
+
+The point is the contrast between the two blocks of output: the expected
+figures come from ``cvxcla``, the realised ones from ``jquantstats``, and the
+gap between them is estimation error, not a defect in either library.
+
+The return matrix is the frozen snapshot at
+``experiments/data/sp500_pct_returns.parquet``, so this reproduces offline;
+``experiments/fetch_sp500.py`` is only for refreshing that snapshot.
+
+Usage:
+    uv run python experiments/frontier_stats.py [--assets 100]
+"""
+
+from __future__ import annotations
+
+import argparse
+from pathlib import Path
+
+import numpy as np
+import polars as pl
+from jquantstats import Data
+
+from cvxcla import CLA
+
+DATA = Path(__file__).parent / "data" / "sp500_pct_returns.parquet"
+DATE_COL = "Date"
+TRADING_DAYS = 260
+
+
+def load(assets: int) -> pl.DataFrame:
+    """Read the snapshot and keep the date column plus the first ``assets`` names."""
+    frame = pl.read_parquet(DATA)
+    names = [c for c in frame.columns if c != DATE_COL][:assets]
+    return frame.select([DATE_COL, *names]).sort(DATE_COL)
+
+
+def frontier_portfolios(train: pl.DataFrame) -> dict[str, np.ndarray]:
+    """Trace the frontier on the training window and pick portfolios off it.
+
+    Returns the maximum-Sharpe and minimum-variance weight vectors, plus an
+    equal-weight benchmark, keyed by the column name they get in the report.
+    """
+    matrix = train.drop(DATE_COL).to_numpy()
+    mean = matrix.mean(axis=0)
+    covariance = np.cov(matrix, rowvar=False)
+    n = mean.size
+
+    frontier = CLA.problem(mean=mean, covariance=covariance).long_only().budget().trace().frontier
+    print(f"assets                  : {n}")
+    print(f"turning points          : {len(frontier)}")
+
+    _, w_sharpe = frontier.max_sharpe
+    # Frontier order runs from maximum return towards minimum variance, but read
+    # the minimiser off the variance vector rather than relying on that order.
+    w_minvar = frontier.weights[int(np.argmin(frontier.variance))]
+
+    portfolios = {"max_sharpe": w_sharpe, "min_variance": w_minvar, "equal_weight": np.full(n, 1.0 / n)}
+    for name, weights in portfolios.items():
+        # Annualise the daily estimates so they are comparable with the
+        # annualised figures jquantstats reports for the test window.
+        expected = float(mean @ weights) * TRADING_DAYS
+        volatility = float(np.sqrt(weights @ covariance @ weights)) * np.sqrt(TRADING_DAYS)
+        print(
+            f"{name:<24}: return {expected:7.2%}  volatility {volatility:6.2%}  "
+            f"Sharpe {expected / volatility:5.2f}  names held {int(np.sum(weights > 1e-8)):3d}"
+        )
+    return portfolios
+
+
+def realised(test: pl.DataFrame, portfolios: dict[str, np.ndarray]) -> Data:
+    """Build the jQuantStats view of the buy-and-hold return series.
+
+    Each portfolio is held fixed over the test window, so its realised return
+    on a given day is the weighted average of that day's asset returns.
+    """
+    matrix = test.drop(DATE_COL).to_numpy()
+    frame = pl.DataFrame({DATE_COL: test[DATE_COL], **{name: matrix @ w for name, w in portfolios.items()}})
+    return Data.from_returns(frame, date_col=DATE_COL)
+
+
+def main() -> None:
+    """Fit on the first half of the snapshot, report the second half."""
+    parser = argparse.ArgumentParser(description="Score CLA frontier portfolios with jQuantStats.")
+    parser.add_argument("--assets", type=int, default=100, help="number of S&P 500 names to use (default: 100)")
+    args = parser.parse_args()
+
+    returns = load(args.assets)
+    split = len(returns) // 2
+    train, test = returns.head(split), returns.tail(len(returns) - split)
+    for label, window in (("train", train), ("test", test)):
+        first, last = window[DATE_COL][0].date(), window[DATE_COL][-1].date()
+        print(f"{label + ' window':<24}: {first} -> {last} ({len(window)} days)")
+
+    print("\n--- expected, in-sample (cvxcla) ---")
+    portfolios = frontier_portfolios(train)
+
+    print("\n--- realised, out-of-sample (jquantstats) ---")
+    data = realised(test, portfolios)
+    with pl.Config(tbl_rows=-1, tbl_width_chars=100, float_precision=4):
+        print(data.stats.summary())
+
+
+if __name__ == "__main__":
+    main()
diff --git a/pyproject.toml b/pyproject.toml
index a08e6a88..a4f426be 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -38,6 +38,14 @@ dev = [
     "mosek==11.2.3",
     "marimo==0.24.0",
     "pandas==3.0.5",
+    # Portfolio analytics for the notebooks/experiments: turns a frontier
+    # portfolio's realised return series into stats and plots. Never imported
+    # from src/, hence dev-only.
+    "jquantstats==0.11.0",
+    # jquantstats is polars-native, and polars reads the committed S&P 500
+    # parquet snapshot without pulling in a pyarrow engine. Declared because
+    # experiments/frontier_stats.py imports it directly, not just transitively.
+    "polars==1.44.1",
 ]
 test = [
     "pytest>=7.0",
@@ -140,6 +148,8 @@ loguru = "loguru"
 mosek = "mosek"
 marimo = "marimo"
 pandas = "pandas"
+jquantstats = "jquantstats"
+polars = "polars"
 
 # bump-my-version only auto-discovers .bumpversion.toml, .bumpversion.cfg,
 # setup.cfg and pyproject.toml. Without a table here it falls back to
diff --git a/uv.lock b/uv.lock
index 390f225d..5889a67e 100644
--- a/uv.lock
+++ b/uv.lock
@@ -158,10 +158,12 @@ plot = [
 
 [package.dev-dependencies]
 dev = [
+    { name = "jquantstats" },
     { name = "loguru" },
     { name = "marimo" },
     { name = "mosek" },
     { name = "pandas" },
+    { name = "polars" },
 ]
 test = [
     { name = "hypothesis" },
@@ -181,10 +183,12 @@ provides-extras = ["plot"]
 
 [package.metadata.requires-dev]
 dev = [
+    { name = "jquantstats", specifier = "==0.11.0" },
     { name = "loguru", specifier = "==0.7.3" },
     { name = "marimo", specifier = "==0.24.0" },
     { name = "mosek", specifier = "==11.2.3" },
     { name = "pandas", specifier = "==3.0.5" },
+    { name = "polars", specifier = "==1.44.1" },
 ]
 test = [
     { name = "hypothesis", specifier = ">=6.100" },
@@ -333,6 +337,35 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/c0/5a/9cac0c82afec3d09ccd97c8b6502d48f165f9124db81b4bcb90b4af974ee/jedi-0.19.2-py2.py3-none-any.whl", hash = "sha256:a8ef22bde8490f57fe5c7681a3c83cb58874daf72b4784de3cce5b6ef6edb5b9", size = 1572278, upload-time = "2024-11-11T01:41:40.175Z" },
 ]
 
+[[package]]
+name = "jinja2"
+version = "3.1.6"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "markupsafe" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/df/bf/f7da0350254c0ed7c72f3e33cef02e048281fec7ecec5f032d4aac52226b/jinja2-3.1.6.tar.gz", hash = "sha256:0137fb05990d35f1275a587e9aee6d56da821fc83491a0fb838183be43f66d6d", size = 245115, upload-time = "2025-03-05T20:05:02.478Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/62/a1/3d680cbfd5f4b8f15abc1d571870c5fc3e594bb582bc3b64ea099db13e56/jinja2-3.1.6-py3-none-any.whl", hash = "sha256:85ece4451f492d0c13c5dd7c13a64681a86afae63a5f347908daf103ce6d2f67", size = 134899, upload-time = "2025-03-05T20:05:00.369Z" },
+]
+
+[[package]]
+name = "jquantstats"
+version = "0.11.0"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "jinja2" },
+    { name = "narwhals" },
+    { name = "numpy" },
+    { name = "plotly" },
+    { name = "polars" },
+    { name = "scipy" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/a5/cd/18a5becec5ac530cb963ebc317db9d3b1ec2e7d76e1fa3ec4e5ca57fd35f/jquantstats-0.11.0.tar.gz", hash = "sha256:806b80eb6913cb30dae689358d1e1c14ddfb8533b4139e145b30cd8370f79e99", size = 162893, upload-time = "2026-08-31T17:54:30.428Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/26/9d/631ca8a45a923482e937db788a69f0d45f59c0577e774e4f95974ffd0e3a/jquantstats-0.11.0-py3-none-any.whl", hash = "sha256:c340d390807610f95ae247d5290e9d947d4c107f9bf8f0cb82e1c225bf64a5e6", size = 200268, upload-time = "2026-08-31T17:54:28.849Z" },
+]
+
 [[package]]
 name = "kaleido"
 version = "1.3.0"
@@ -500,6 +533,80 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/de/1f/77fa3081e4f66ca3576c896ae5d31c3002ac6607f9747d2e3aa49227e464/markdown-3.10.2-py3-none-any.whl", hash = "sha256:e91464b71ae3ee7afd3017d9f358ef0baf158fd9a298db92f1d4761133824c36", size = 108180, upload-time = "2026-02-09T14:57:25.787Z" },
 ]
 
+[[package]]
+name = "markupsafe"
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