Understand before you act.

A share is a residual claim: shareholders are paid AFTER suppliers, employees, lenders and the tax authority. Being last in line is what explains both the higher expected return and the higher risk — you only receive what is left. In a liquidation the same ranking applies, and there is usually nothing left. This is why a company's debt structure changes the risk borne by its shareholders radically, for an identical business.

Market cap ignores debt. To compare two companies where one borrows heavily, enterprise value is used instead: market cap plus net debt. Buying an indebted company also means taking on its debt — the real acquisition price. This is why multiples such as EV/EBITDA are preferred to the P/E in leveraged sectors: they compare what is actually paid, not just the shareholders' portion.

The payout ratio compares the dividend to earnings: above 80%, a company distributes nearly everything it earns and has no room left if profits soften. An abnormally high dividend yield is most often the symptom of a price that has collapsed rather than of any particular generosity — a yield being a ratio, it climbs when its denominator falls. Checking coverage against free cash flow rather than accounting earnings avoids most of the unpleasant surprises.

Growth is exponential, so duration weighs more than the rate. Moving from 6% to 7% over thirty years improves the outcome by about a third; adding ten years at the same rate nearly doubles it. It is also why annual fees cost far more than their percentage suggests: 1% in fees over thirty years does not remove 1% of the result but close to a quarter, since it withdraws each year a slice of capital that would have compounded.

Specific risk, which belongs to one company, is distinguished from market risk, which strikes everyone together. Only the first can be diversified away; the second remains no matter how many lines you hold. This is why theory does NOT reward specific risk: since it can be removed for free by adding holdings, nobody pays you to bear it. Most of the benefit is reached around twenty to thirty uncorrelated holdings; beyond that, you mostly add complexity.

The order book stacks intentions by price level. A market order consumes successive levels until it is filled: on an illiquid stock, a large order walks up the book and degrades its own average price — that is slippage. The gap between the best bid and the best offer is an implicit cost paid on every round trip, often larger than the commission itself on lightly traded names.

Inflation hits assets unevenly. A fixed-rate bond is structurally vulnerable: its payments are nominal and melt in real terms. A company able to raise prices without losing customers passes inflation on to its customers and protects its margins — a direct expression of pricing power. Long-duration assets suffer more, because a rise in rates cuts the present value of distant cash flows harder.

The P/E only means something in comparison: to the stock's own history, to its peers, to its own growth rate. It has three structural weaknesses. It is blind to debt, since it ignores the balance sheet. It rests on accounting earnings, which depreciation and non-recurring items can shape. And it becomes absurd near zero: an almost nil profit sends the ratio into the hundreds without that meaning anything. On property companies, depreciation crushes earnings to the point of making the P/E misleading — price to funds from operations replaces it.

The comparison that matters sets ROIC against the cost of capital. Above it, growth creates value; below it, growth destroys value, and growing makes the problem worse. It is the most direct test of a durable competitive advantage: in theory competition should erode any superior return, so a high ROIC sustained for years signals that something is preventing it. Watch the denominator: heavy buybacks shrink equity and inflate return on equity artificially — ROIC, which also carries debt in its denominator, resists that better.

A lasting gap between earnings and cash deserves an explanation. It often comes from working capital: a fast-growing company funds its inventory and receivables before collecting, so it can post profits while burning cash. Depreciation produces the opposite effect — an accounting charge with no money leaving. The distinction between maintenance and growth capital expenditure is decisive and rarely disclosed: that is the point where analysis calls for judgement rather than a formula.

Volatility is not risk — it is a convenient approximation because it can be computed. It treats rises and falls symmetrically, when no investor experiences them that way. It is also unstable: it clusters in periods, so a past measure says little about the next one. Beta adds a limitation of its own — it is estimated over a historical window, and a company that changes its business or its debt structure no longer has the beta that window measured.

Recovery is asymmetric, and brutally so: a 50% loss requires a 100% gain to return to the starting point; a 20% loss requires only 25%. A strategy's average return therefore says nothing about the path taken to get it. Two strategies with the same annualised return can be radically different to hold — and the one abandoned at the worst moment never delivers its average return.

Rebalancing is first a risk-control tool, not a return tool. It imposes counter-cyclical discipline, but it costs: transaction fees, and tax on realised gains outside registered accounts. Hence two settings — by calendar, or by drift threshold, the latter generally more efficient because it acts only when the gap justifies it. In a long trend it mechanically removes performance: that is the price of controlling risk, and it should be accepted knowingly.

An option's price breaks down into intrinsic value — what it would be worth exercised right now — and time value, which pays for the chance of moving favourably before expiry. That time value decays, and faster and faster as expiry approaches. The sensitivities have names: delta for the reaction to the underlying price, theta for time decay, vega for sensitivity to implied volatility. An option can lose value even while the underlying moves in the hoped-for direction, if implied volatility contracts or time passes faster than the move.

The families differ by what they bound. A vertical spread — buying one option and selling another of the same expiry at a different strike — caps the gain AND the loss, while reducing the entry cost. A straddle, buying a call and a put at the same strike, bets on the size of the move without choosing its direction; it loses if nothing moves enough to cover both premiums. Butterflies and condors combine four legs to form a narrow gain zone at the centre, very profitable if the underlying finishes in that window and worthless otherwise. A calendar spread plays two expiries, exploiting the fact that time value decays faster on the nearer one. Three realities the payoff diagrams hide. First, every extra leg adds a bid-ask spread to cross: a four-leg structure pays that implicit cost four times, on the way in and on the way out, which is enough to cancel the theoretical edge on an illiquid underlying. Second, a short position in American options can be assigned before expiry, in particular just before an ex-dividend date, which turns a bounded structure into a directional position in the stock without warning. Third, the risk is no longer only directional: the same position can lose because implied volatility contracted, even as the underlying behaved exactly as expected.

Leverage introduces a sequence risk absent from an unfunded position. Without leverage, a 60% fall followed by a recovery leaves the investor whole. With leverage, the same path can liquidate the position at the trough and put the recovery out of reach — the final outcome then depends on the ORDER of the moves, not only on their sum. Add to that the carrying cost, which runs whatever happens, and a margin call whose trigger depends on a mark-to-market value at one moment in time, often the least favourable.

Liquidity is procyclical: it contracts precisely when it is needed, because market makers widen their spreads as uncertainty rises. A portfolio can therefore look liquid in normal conditions and prove impossible to unwind cleanly under stress. The effect hits exchange-traded funds holding illiquid underlyings especially hard: the fund's units keep trading, but their price can drift meaningfully from the value of its assets, and the arbitrage mechanism that normally corrects that gap works poorly exactly when you are counting on it.

Correlation measured on historical data is an average across different regimes, which makes it misleading at the decisive moment. Under stress, positions are liquidated to raise cash regardless of their individual merit, and assets with no economic link fall together. The protection you thought you held therefore disappears at the exact moment it was meant to serve. There is also a limitation in the coefficient itself: it captures only linear relationships, and misses dependencies that appear only in the extremes.