Portfolio Construction

01 — Dollars vs. Risk

A balanced portfolio that isn't

The classic 60/40 puts 60% of the money in equities. Because equities are roughly three times as volatile as bonds, and volatility enters risk quadratically, that same portfolio puts about 90% of the in equities. It is a stock portfolio with a bond-shaped rounding error, and almost nobody who owns one knows that.

² = Σᵢ Σⱼ wᵢwⱼσᵢσⱼ = wᵢ·(∂σ_p/∂wᵢ) / σ_p

Equity weight 60%

Equity vol 16%

Bond vol 6%

Correlation 0.10

Equity share of money

60%

Equity share of

90%

the number that matters

Portfolio vol

10.2%

diversification saved 1.4%

Equity weight for 50/50 risk

27%

where risk actually balances

Where the money is, and where the risk is

Why the gap is so wide. Risk contributions come from squared volatilities and covariances, so a 3:1 vol ratio becomes roughly a 9:1 risk ratio before correlation is even considered. Halving your equity weight doesn't halve your risk — it barely dents it, because the remaining equity still dominates the variance. Any portfolio conversation conducted in percentages of capital is, quietly, not about risk at all.

Try this

DoLeave the weights alone and drag correlation from 0.10 to 0.90.

WatchPortfolio vol jumps, and the diversification benefit collapses toward nothing — without a single weight changing.

WhyDiversification is entirely a correlation phenomenon. This is also the mechanism behind every "our models failed" post-mortem: correlations estimated in calm markets go into the optimiser, the crisis introduces a common factor, and a portfolio built for ρ = 0.1 turns out to have been built for ρ = 0.9 all along. Same positions, twice the risk.

02 — Risk Parity

Give every bet the same say

If you don't believe you can forecast returns well — and the backtest evidence suggests humility — then don't build a portfolio that depends on forecasting them. ignores expected returns entirely and solves for the weights where every asset contributes an equal share of risk. Compare it against equal weights and against the that thinks it knows the future.

find w such that = RC₂ = … = RCₙ = 1/n

Three assets — a stock index, a bond, and a whose quiet volatility hides a fat tail:

Equity vol 16%

Bond vol 6%

Short-vol vol 7%

Equity·short-vol ρ 0.60

Dollar weight (pale) vs. risk contribution (solid)

Risk parity's own blind spot. It equalises measured volatility, and measured volatility is exactly what a short-convexity strategy hides. Give the short-vol sleeve a quiet 7% vol and risk parity hands it a huge weight — precisely the leverage you'd least want when its real risk shows up. The method is a genuine improvement on counting dollars, and it inherits the same flaw as everything else on this page: it can only see the risk that appeared in the sample.

Try this

DoSwitch between Risk parity, Equal weight and Optimiser and watch the risk-contribution bars.

WatchEqual weight gives equal dollars and wildly unequal risk. Risk parity levels the risk bars exactly. The optimiser concentrates into whichever asset has the best return-to-risk ratio.

WhyEach scheme encodes a different confidence about what you know. Equal weight says "I know nothing, not even the volatilities." Risk parity says "I trust the covariances but not the returns." The optimiser says "I trust both" — and because it inverts the covariance matrix, small errors in its inputs become large, confident, wrong positions. That fragility is why risk parity exists at all.

03 — Volatility Targeting

Constant risk, moving leverage

Once risk is the unit you think in, the next step follows: pick a risk level and hold it steady. scales leverage inversely with recent volatility — lever up when markets are calm, cut when they're wild. It genuinely improves risk-adjusted returns in most backtests. It also means that when volatility spikes, every fund running it sells at the same time.

leverage = / σ_recent capped at L_max

Target vol 10%

Leverage cap 3.0×

Vol look-back 60d

Crisis severity 3.0×

Realised vol, targeted

10.3%

target 10%

Realised vol, unlevered

14.8%

buy and hold

Worst

−18%

unlevered: −31%

Selling into the crash

−58%

of the position, forced

Leverage (gold) against realised volatility (blue) through a crisis

Value of $1 · gold = vol-targeted, blue = unlevered

The crowded exit. Vol targeting is a good idea that becomes a systemic risk when everyone runs it. Volatility spikes are common to all portfolios, so every targeted fund receives the same sell signal on the same morning, in the same assets. The selling raises volatility, which lowers the target leverage further, which forces more selling. February 2018 and March 2020 both had this mechanism inside them. Your individual risk control is fine; its correlation with everyone else's is the problem — the same correlated-tail logic, one level up.

Try this

DoSet the look-back to 10 days, then to 250 days.

WatchA short look-back tracks the target tightly but whipsaws leverage around constantly. A long one is stable and slow — it's still de-levering weeks after the crash has passed.

WhyYou are choosing between responsiveness and turnover, and there's no free version. Fast estimates react to noise and trade constantly, which costs money and, in a crisis, sells at the bottom. Slow estimates miss the regime change entirely. Every risk system in the industry sits somewhere on this dial, and where it sits is a genuine decision, not a technical detail.

04 — Factor Models

Was that alpha, or just beta wearing a suit?

A manager beats the market by 6% a year. Skill, or exposure? A regresses their returns on a set of known, cheaply-purchasable risk premia — the market, small caps, value, momentum — and asks what's left. Whatever survives is . Very often, almost nothing survives.

r_t = + ·MKT + β_smb· + β_hml· + β_mom· +

Build a manager. Give them some true skill and some factor tilts, simulate five years of monthly returns, then run the regression and see what an allocator would conclude.

True skill 1.0%/yr

Market β 0.60

Size β 0.40

Value β 0.30

Momentum β 0.20

Track record 5 years

Raw excess return

+6.4%

what the pitch deck says

Alpha after factors

+1.2%

t-stat 0.4 — indistinguishable from luck

Explained by factors

81%

R² of the regression

Verdict

no evidence

of skill beyond exposure

Where the return came from

The t-stat is the whole argument. A regression will always produce some alpha number; the question is whether it's distinguishable from zero. With five years of monthly data and a volatile residual, the standard error on alpha is so wide that even genuine skill can't be proven — and neither can its absence. Drag the track record out to twenty years and watch the t-stat finally separate the two cases. This is why allocators care about tenure, why "three good years" means very little, and why the honest answer to "is this manager skilled?" is usually we cannot yet tell.

Try this

DoSet true skill to 0% and leave the factor tilts on. Then press New sample a few times.

WatchThe raw return is impressively positive in most samples — while measured alpha bounces either side of zero and almost never reaches significance. Occasionally the raw return is negative, from a manager with identical skill and identical tilts: the factors themselves had a bad five years.

ThenSet true skill to 4% and stretch the record to 25 years. Only now does the t-stat reliably clear 2.

WhyFactor exposures produce real, persistent returns without any skill at all — and you can buy them in an ETF. That's the manager's problem: their return was real, their alpha was a loading on value and size. It's also the allocator's problem, since separating the two takes more history than most funds live to accumulate.

05 — What The Course Adds Up To

Five modules, one argument

The material across these pages looks like separate topics — option pricing, spread trading, portfolio maths. It isn't. It is one argument told from five angles, and it comes out the same way each time.

Page	Its version of the argument
The Desk	Growth is capped by Sharpe², and leverage past the optimum reduces return while adding risk. The winning fund is the surviving one.
The Greeks	Every exposure can be measured as a derivative. What you can measure, you can hedge — and what you hedge away tells you what bet you actually hold.
The Derivation	The most successful model in finance is built on assumptions that are all false. It survives because it's wrong in a legible, quotable way.
The Arbitrage Book	Most strategies are insurance sales. The premium is real; so is the claim, and it arrives when everything else is already going wrong.
Portfolio Construction	Risk isn't money, measured risk isn't real risk, and most alpha is beta that hasn't been named yet.
All five	Every number in finance is an estimate from a sample. The risks that matter are the ones your sample didn't contain.

The single sentence. Finance has no shortage of exact mathematics; what it lacks is exact inputs. Black–Scholes is exactly right about a world with no jumps. Kelly is exactly right if you know your edge. Mean–variance is exactly right given the true covariance matrix. Every formula on this course is a correct answer to a question about a world we can only estimate — so the skill being tested is never the algebra. It's knowing which assumption is doing the load-bearing work today, and what happens the morning it stops.

Finished?

ReviewThe Course lists every module in order with what each one is meant to prove — useful for a second pass, or for checking you didn't skip the ones that matter.

PlayRun the fund puts the whole thing together: pick your skill and leverage, then survive twenty quarters of random markets, crises, fees and redemptions.

CheckReality Check points the model at live market data and asks whether the simulated cone actually brackets what happened.