Zipfolio Tearsheet: Portfolio, Execution & Cost Analysis

Annual return is compounded (CAGR); volatility, Sharpe and Sortino count 252 sessions a year. The Sharpe ratio over the risk-free rate uses the one-month T-bill, 4.60% a year on average over the backtest -- the rate the factor analysis uses. QuantStats, beside this report, uses 0%; both are shown.

Interest on idle cash is not credited: the backtest earns nothing on cash. Had it earned the rate, the strategy's idle cash would have added about 0.15% a year, and its Sharpe ratio over the rate would be 1.26.

Buy & hold, 10 names buys the traded names in equal amounts on the first session and holds them to the end, on prices alone -- dividends are in neither it nor the strategy. The names were picked by the strategy, so this measures its timing, not its choice of names.

Every profit on this page is one of these. Realized is what the closed trades made -- each sale with the shares it closed, first in, first out; unrealized, what the shares still held are worth at the last price over what they cost. Both are before commission, and slippage is inside both, because it is inside the fill prices: Trading Costs reconstructs it and nothing takes it off again. The net profit is the change in the book, cash plus positions, and is checked against the start value compounded by the daily returns, which the engine records apart.

The interval and the probabilistic Sharpe ratio (PSR) allow for the skew and fat tails of the daily returns. Every version of a strategy that was backtested is a try: among N strategies with no edge at all, the best one shows a Sharpe ratio of about the second column by chance alone, and the third is the chance this one beats it -- the deflated Sharpe ratio. Tries are taken as independent. 95% is the usual bar.

The backtest cut in two at its middle session. A rule whose parameters were tuned on the whole period often works in one half only.

The same backtest with its best sessions spent in cash -- the 5, 10, 20 days with the highest returns, out of 752. A strategy whose edge is spread over time loses some return; one that rests on a few days loses all of it.

Trades are counted as in Closed Trades: each sale with the shares it closed, PnL before commission.

The luck test takes the 76 trades and draws 76 of them again at random -- some twice, some not at all -- and adds them up; 5,000 times, from a fixed seed so the same backtest gets the same answer. If many of those totals are losses, the result depended on which trades happened to come up, not on an edge most of them share. It treats trades as independent and keeps their sizes.

The trade-by-trade curve climbs through the winners and falls through the losers to 100%. The higher its peak, the more the losers took back from a few large wins.

Net PnL is each instrument's mark-to-market result: the change in the value of its position, less what was paid for it, less its commission. Slippage is inside it, as it is in the fill prices. Contribution adds up its daily PnL over the portfolio's value at the start of each day, so the contributions add up to the strategy's return before compounding. Avg. weight is over the days the position was held.

The two can disagree, even in sign. A dollar earned when the portfolio was small is a larger share of it than a dollar earned after it grew: a name that made money early and gave back a similar amount later shows a positive contribution and a small or negative PnL, and the reverse.

The trade columns count closed trades, as in Closed Trades -- each sale with the shares it closed -- and a trade's return is its PnL over what those shares cost.

Each tile is a name, inside its sector. Its size is the capital it took -- its share of the portfolio averaged over the whole backtest -- and its colour what it added to the return: red a loss, green a gain, darkest at ±15.8% and beyond. Hover a tile for its numbers.

The attribution adds up the arithmetic mean return over the sessions the factors cover -- not the compounded annual return of Key Performance Metrics, and not past the last month the library has published.

The strategy's daily return over the risk-free rate, regressed on the fama-French 5 factors + momentum from Kenneth French's data library. Mkt-RF -- the US stock market over the risk-free rate. SMB -- size: small companies minus big ones. HML -- value: high book-to-market (cheap) minus low (expensive). RMW -- profitability: robust operating profitability minus weak. CMA -- investment: companies that invest conservatively minus aggressively. MOM -- momentum: the past year's winners minus its losers.

A beta is how much of a factor the strategy carries: 1.0 on Mkt-RF moves with the market, a positive HML leans to value. Alpha is the return the factors do not explain; it is worth something only with a t-stat beyond about 2 (p < 0.05). Standard errors are Newey-West, robust to the autocorrelation of daily returns. The attribution splits the average annual return into what each factor paid at its average beta, and the alpha.

The style box places the strategy by how its returns moved: with small against big companies (SMB) and cheap against expensive ones (HML). The lines are at SMB 0.15 and 0.55 and HML ±0.15; the S&P 500 sits near SMB -0.15, the Russell 2000 near 0.8. The path is the 126-session betas a month apart, darker as they get recent.

The decomposition and the attribution by year use the full-period betas, and add daily returns up rather than compounding them, so the parts sum exactly to the strategy's return over the risk-free rate (the black line and diamonds).

Each drawdown -- from the close of its peak to the close of its valley -- split across the names that made it. A name's share is its mark-to-market PnL over those days, after commission, over the portfolio's value at the peak, so the shares are points of the drawdown and add up to its depth. What remains, mostly dividends paid into cash, is shown on its own.

The same split by sector: whether a drawdown was one bet held several times, or losses spread across the book.

Up capture is how much of S&P 500 Equivalent's rise the strategy took in the months S&P 500 Equivalent rose -- 120% is a fifth more than the market, 60% a bit over half -- and down capture how much of its fall it took when it fell; under 100% is protection. A ratio above 1 is the asymmetry a strategy wants. The two betas are the same question day by day: a strategy that falls with the market but lags it up has a down beta above its up beta.

A month is rising or falling by S&P 500 Equivalent's return, and volatile when S&P 500 Equivalent's daily volatility in it is above the median month's.

On the last chart, shaded months are volatile ones: red when the market fell, green when it rose.

VaR 95% is the daily loss exceeded on one day in twenty, read from the backtest's own days rather than from a normal curve -- which fat tails would make too mild; CVaR is the average loss on those days. EVaR (entropic VaR) is an upper bound on both, derived from the whole distribution rather than its tail alone, so it reacts more to fat tails. Drawdown at risk, CDaR and EDaR are the same three ideas applied to drawdowns: the depth exceeded on the 5% of days furthest below a peak, the average depth on those days, and its entropic bound. The Ulcer index is the root mean square of all drawdowns, so it grows with both depth and duration. The Gini mean difference is the average gap between any two daily returns -- a dispersion measure that, unlike volatility, is not dominated by a few extreme days.

Each holding's share of the portfolio's volatility and of its CVaR, for the average weights held over the backtest. A name whose risk share is well above its weight is where the risk is concentrated.

Daily-return correlations of the 10 most-held names, average pair 0.19. Clustering puts names that move together side by side: a block of high correlation is one bet held several times.

Each rule is fitted on the previous 252 sessions and held for the next 21, over the names this strategy traded, from 14 Oct, 2024, without trading costs. The names themselves come from the strategy, so this compares its timing and sizing with simple rules -- not its choice of stocks. Where no name is expected to beat cash, max Sharpe holds them equally.

The capital asset pricing model (CAPM) holds that the market pays for one risk only: the part that moves with the market, measured by beta. Risk a portfolio could have diversified away earns nothing. The security market line is the return the model asks for each beta -- the risk-free rate at 0, the benchmark's return at 1. A point above the line made more than its beta asks for; the gap is Jensen's alpha.

The capital market line runs from the risk-free rate through the benchmark: every mix of the market and cash sits on it. Above it is a better Sharpe ratio than the market's. M² is the strategy's return scaled to the benchmark's volatility, so the two compare in percent; the Treynor ratio is excess return per unit of beta rather than of volatility. Specific volatility is the risk the market does not explain, the part CAPM says goes unpaid.

The efficient frontier is the highest return any fixed mix of the traded names offered at each volatility -- long only, fully invested -- and the line from the risk-free rate that touches it marks the mix with the best Sharpe ratio. It is measured with the returns the names went on to make, so it is hindsight: no one could have held it, and it is a ceiling, not a target. A strategy that changes its holdings can still land above it -- that is what timing is for. One well inside the equal-weight point did worse than the simplest fixed mix of its own names.

Returns here are means of daily returns times 252, and volatility the daily one times √252, as mean-variance theory has them -- not the compounded returns of Key Performance Metrics, whose alpha is at a 0% rate, as QuantStats has it. The risk-free rate is the one-month T-bill, 4.60% a year on average.

Predicted is the volatility the book carried each morning: that day's weights times the covariance of its names over the previous 63 sessions. Realized is the strategy's volatility over the next 21 sessions it held positions -- days in cash are left out, as the prediction is the risk of the positions. A bias near 1 and a high correlation mean the strategy's risk was what its positions said it was. Well above 1, risk arrived that the positions did not show -- crowded names, regime changes, gaps. Well below 1, the positions were calmer than their history: the strategy tends to hold them after a volatile stretch, as a breakout entry does.

Shares of risk are marginal contributions to the predicted volatility, averaged over each month; a hedge, whose share is negative, is drawn as zero.

The effective number of names is 1 / Σ w² over the gross book: ten equal positions count as ten, one 90% position and nine small ones as barely more than one. Below the names held, the book is concentrated in a few of them.

Turnover is the value traded, buys and sells together, over the portfolio's value: buying the whole portfolio and selling it again is 2×. One-way counts only the smaller of the two sides -- how many times the portfolio was replaced.

What Counts as a Trade

A trade is shares bought and later sold -- or sold short and later bought back -- and what they earned in between. Every sale closes the shares bought earliest first, and every sale is a trade of its own:

• buy 100, later sell 100: one trade;
• buy 100; sell 30 at the next rebalance and the other 70 a month later: two trades, of 30 and of 70 shares, each held from the purchase to its own sale;
• buy 100, buy 50 more, sell all 150: one trade, at the average of the two purchases.

So a strategy that trims its holdings at every rebalance shows many more trades than positions. Fills on the same side within 8 hours count as one. What is still held at the end is not a trade -- it was never sold -- and its paper profit is counted apart, as unrealized PnL (Profit Reconciliation, in Performance). A trade's PnL is before commission; its return is its PnL over what its shares cost.

Signs: a move in bps is positive when the next open was worse for the fill -- higher for a buy, lower for a sell. The effect on PnL is positive when waiting would have paid more, negative when it would have cost.

This backtest fills each order on the bar whose data produced it, at that bar's close. A real order sent on that data reaches the market on the bar after. Here every fill is priced again at the open of the instrument's next bar in the data -- the next session for daily bars -- with the same quantity and the same slippage. From that open on the two books hold the same shares, so the difference is exactly the price paid, booked on the day of the next bar and kept in cash rather than reinvested.

A strategy that buys what has just risen and sells what has just fallen tends to pay for the wait; one whose edge is real survives it. The trades themselves are not re-decided: the same shares, a bar later.

How the Backtest Fills Orders

A market order fills on the bar it is placed in, at that bar's close, moved 5 bps against the strategy for slippage. A single bar fills at most 10% of its volume; the rest of the order waits for the next bars, at their prices.

A limit order fills only on a bar that trades through its limit, and never at a worse price; a stop becomes a market order once a bar trades through the stop. Orders stay open until filled or cancelled.

Not simulated: the bid-ask spread (other than inside the fixed basis points), the order book and queue position, partial liquidity inside a bar, and the price impact of the strategy's own size -- which is why the checks below compare every fill with its bar.

Cost vs bar typical price compares each fill with its bar's (high + low + close) / 3, a stand-in for the bar's average trade (VWAP); positive is worse. Fills at the close far above it mean the strategy trades after a strong move inside the bar -- buying near the top of a rising day. An order worked through the day would have paid that difference; Next-Bar Fills shows the same question a bar later.

How Costs Are Modeled

Commission is 0.0354% of the value of each fill (ziplime's PerDollar model). It is charged to the order as it fills and comes out of cash; it is not part of the fill price.

Slippage: every fill is priced 5 bps worse than the bar's close -- a buy at close × 1.0005, a sell at close × 0.9995 (ziplime's FixedBasisPointsSlippage). It stands in for the bid-ask spread and market impact. It is in the fill price, so the backtest never records it as a cost; the report reconstructs it from the fills.

Volume limit: a fill takes at most 10% of the bar's volume. The rest of the order waits for later bars, so a large order can fill over several bars, at several prices, and pay commission on each fill.

Execution: an order fills on the bar it was placed in, at that bar's close.

Both costs are already inside every return, metric and chart in this report. Not modeled by these settings: borrowing costs of short positions, financing of leverage, taxes, and market impact beyond the fixed basis points.

The last two charts charge every dollar traded an extra 3 to 50 bps on top of the costs above -- how much worse execution the strategy can take before its edge is gone. The cost summary has the point where it is: the extra cost that would erase the profit.

The strategy sizes its orders from its capital, so more capital means larger fills. Up to 1% of a day's volume a fill barely moves the price; 10% is the most the engine lets a fill take of a bar. The checks below sell every position at $2.4m, taking at most 10% of a day's volume, with the trailing 5-day mean as that volume.