The short course
What we’ve learned
Every heading below is a claim, so reading the contents list is most of the course. The paragraph under each heading says what we measured and where it stops, and the link at the end of it goes to the page that owns the number. Words you have not met yet live in the glossary.
Lesson 1
“The market” is two different benchmarks, and they never add
Beating a cheap index fund and beating the portfolio you would otherwise have owned are different claims about different reference portfolios. Cost and tax discipline is worth about 109 bp a year against the second and about 5 bp against the first, and adding them would double-count the same work. This repository's own code raises an error rather than summing lines measured against different benchmarks, because it made that mistake in four places before it did.
Lesson 2
Extra return from extra risk is not skill
A portfolio that holds more equity, or that borrows to hold more of everything, should earn more on average. That is more beta, not alpha, and the honest comparison is against the same risk taken the simple way. Moving from 60/40 to 90/10 is worth about +127 bp a year, and it wanders 485 bp getting there: more than all the factor leans on this site put together, and still only 92% likely to be ahead after thirty years. Anyone can do it by changing one number, which is why it does not count as an edge.
Lesson 3
Tracking error, not the size of the edge, decides whether a lifetime is enough
How long you wait to find out grows with the square of how far the thing wanders, divided by how much it gains. Squaring is what makes it run away from you. The same 50 bp edge is 90% certain in about 24 days if it wanders 10 bp, and takes about 105 years if it wanders 400. It is why a 109 bp gain that comes out of contracts is settled inside a year, while the gain measured against an index cannot be shown at any horizon a person has. What decides it is the wander, not the size of the gain.
Lesson 4
A strategy with a positive expected return can lose for decades
If a factor lean earns 25 bp a year against 135 bp of dispersion, a run of ten bad years is ordinary rather than evidence of anything. Simulating the same model shows the route as well as the destination: with a small gain and a lot of wander, most paths spend years below their own previous best relative to the benchmark. Deciding in advance how long you will hold is the only defence, because deciding afterwards always looks like the strategy broke.
Lesson 6
A capital weight does not tell you what you are exposed to
A fund holding 30% of a portfolio can carry 32% of equity and 30% of managed futures at the same time, because the futures are financed rather than bought. Every portfolio on this site that uses one states that financed exposure separately from its capital weight, and a weight stated as a share of capital may never be compared with a weight stated as a share of exposure.
Lesson 7
Implementation cost routinely erases a paper premium
The largest gross factor premium measured here is momentum at +7.33 pp/yr. The academic construction turns over 27.5% to 91.5% of its book a month, which implies 3.3 to 18.7 pp/yr of trading cost. The one investable route audited files 105% annual turnover and loses 43% of its gross exposure to cost. The premium is real and it does not reach the shareholder.
Lesson 8
Two funds with the same label are not the same fund
Among audited US value products the exposure to HML ranges from +0.32 to +0.71 while the fee runs from 5 bp to 35 bp. A fund's cost is its fee less its securities-lending income, which reorders the shelf. IEMG costs less to own than VWO at a 50% higher fee. Buy the exposure and the cost, never the category.
Lesson 9
A long-only fund is not the academic factor
Published premiums are long-short spreads with no costs and no shorting constraint. What a shareholder receives is weight × (fund exposure − incumbent exposure) × premium, less the incremental cost. Three terms. Multiplying by a further “capture fraction” discounts the same exposure twice: 94% of the measured 0.520 capture is the 0.4891 exposure, an identity exact to 4.4 × 10⁻¹⁶, and doing it understated this repository's own value lean by about half.
Lesson 10
Trend following is a correlation claim before it is a return claim
Managed futures correlate near zero with equity unconditionally and about −0.59 inside crisis months, with a downside beta of −0.67. That part holds on three independent instruments. The mean return does not resolve on any of them: post-publication the trend holding measures +0.883 pp/yr with an interval containing zero. Size it for the drawdown it changes, not for the return it might add.
Lesson 11
An asset can be useful without being expected to beat equities
Gold's Sharpe ratio is 0.18 against equity's 0.59 since 1975, and its correlation to equity sits between −0.02 and +0.03. Held pro rata it costs about 0.40 pp/yr of growth; held instead as a position paid for by borrowing rather than by selling something else, it adds about 0.18. Its case is entirely about what it does beside other things, and on this repository's 0.30 pp/yr bar it still fails.
Lesson 12
Rebalancing is risk control, not a source of return
The rebalancing premium is real and tiny: γ* = ½(Σwᵢσᵢ² − σp²). Measured over 420 months the drift gap ran 35 times larger than the premium, and rebalancing lost 38.7 bp a year against buy-and-hold. What it bought was exposure control, with mean drift held to 0.6–3.1 points instead of 14.8 points, for 0.3 to 1.2 bp a year. Keep doing it. Do not budget a bonus for it.
Lesson 13
A portfolio that borrows has to be judged against a benchmark that borrows too, not against the index
Borrowing to hold more of everything raises the expected return and the drawdown together, so beating an index that does no borrowing proves nothing, because the borrowing did it. The honest control is the same base scaled to the same volatility. Held that way, a 25% trend position paid for by borrowing improved the Sharpe ratio by +0.050 over 426 months while the same base borrowed to the same degree improved it by +0.001: a real difference, and about a fiftieth the size the comparison against an index that does no borrowing would have implied.
Lesson 14
A drawdown, a rolling return and a wander figure answer three different questions
A drawdown says how far you fell from your own best and is measured on month ends, so it always understates what a holder actually saw. A rolling return says what a holder who started at an awkward moment earned, and consecutive windows share almost all their months, so a long run of them is one observation wearing many hats. A wander figure says how far you drift from the thing you are being judged against, and it alone decides whether a gain can ever be shown.
Lesson 15
Deciding whether underperformance is the strategy or a broken thesis
Write the answer down before you need it. A lean earning 25 bp against 135 bp of dispersion will trail for years as a matter of arithmetic, and that is not evidence. What would be evidence is the mechanism failing: the exposure you bought no longer showing up in what the fund actually holds, the cost rising until it eats the premium, or the correlation that justified a diversifier turning positive in exactly the months it was held for. Those are checkable. A run of bad years is not.
Lesson 16
Where a fund is held changes what you keep
Foreign withholding is paid and permanently lost inside an IRA, because §408(e)(1) exempts the account and §904's numerator becomes zero. The resulting ranking between developed and emerging markets inverts at a 21.51% qualified dividend rate, which sits between two live US brackets — so a rule of thumb is wrong for a large share of readers and the arithmetic has to be done for your own bracket.
Lesson 17
A backtest is evidence, and a weak kind
On this shelf 96 of 109 factor exposures survive multiple-comparison correction, and 5 of 327 alpha tests do, all five of them negative. The median alpha these windows could detect is about 5 pp/yr against roughly 1.25 pp/yr of true dispersion between funds, so most alpha findings are noise by construction. Exposure is measurable; skill is not.