Knowledge
Knowledge for investors
Metrics, strategies and taxes for ETF portfolios: from the basics to models from research, with formulas, worked examples to recalculate and evidence from the literature. Every article leads to the matching tool in Portfolio Lab.
Return and risk
How to measure return, how to measure risk and how the two belong together.
CAGR: how to calculate the average annual return correctlyWhat CAGR (compound annual growth rate) is, how to calculate it, and why the simple average of annual returns is misleading, with formulas and worked examples.Basics8 min readCompound interest: how returns on returns make wealth growCompound interest explained simply: the formula, examples with a lump sum and monthly contributions, the rule of 72, the effect of costs and inflation, and what the research says.Basics8 min readCorrelation and diversification: why mixing assets reduces riskCorrelation shows how closely two investments move together. How it lowers a portfolio's risk, where diversification ends and how to measure it. With examples.Basics8 min readMaximum drawdown: the largest loss from a peakMaximum drawdown shows the largest loss in value from peak to trough. Calculation, example, recovery time, Ulcer Index and why a −50% loss needs a 100% gain to recover.Basics8 min readSharpe ratio: return per unit of riskThe Sharpe ratio measures the excess return over the risk-free rate per unit of volatility. Formula, worked example, good values, estimation error and common mistakes.Basics11 min readVolatility: how much a portfolio fluctuatesVolatility is the standard deviation of returns. How to calculate and annualize it (√12, √252), what it tells you, how it changes over time and where its limits lie.Basics8 min readBeta and alpha: how closely a fund moves with the marketBeta measures how strongly a fund reacts to market moves, alpha the return beyond that. Calculation by regression, a worked example, R², capture ratios and the Treynor ratio.In depth7 min readDividend strategies and dividend ETFs under scrutiny: irrelevance, factors, risksDividend investing under scrutiny: Miller-Modigliani, the free dividends fallacy, homemade dividends, value and sector tilts, dividend cuts and yield traps.In depth12 min readHistorical stress testing: how to apply past crises to your portfolio todayHistorical stress testing explained: apply crises such as 2008, 2020 or 2022 to today's portfolio, by replaying returns or via factors and betas, with a worked example.In depth10 min readRisk metrics beyond the Sharpe ratio: Treynor, Calmar, Omega, Ulcer Index and moreTreynor ratio, Calmar ratio, Omega, Ulcer Index, gain/loss ratio and M² explained: formulas, one shared worked example and when to use which risk-adjusted metric.In depth7 min readSkewness and kurtosis: why market crashes are more frequent than the normal distribution saysSkewness and kurtosis describe the asymmetry and fat tails of returns. Formulas, a worked example, Cornish-Fisher VaR and what research shows about crash risk.In depth7 min readSortino ratio and Calmar ratio: measuring downside riskThe Sortino ratio divides return only by downside volatility, the Calmar ratio by the maximum drawdown. Formulas, worked examples, variants and when to use which.In depth7 min readStock market seasonality: Sell in May, the January effect and how to test calendar effectsSell in May, the January effect, turn of the month, Santa Claus rally: what research shows on stock market seasonality, how to test calendar effects and what switching costs.In depth11 min readTime-weighted and money-weighted return: what measures what?Time-weighted return (TWR) measures the fund, money-weighted return (IRR) the investor. Formulas, a worked example, Modified Dietz and why the two often diverge.In depth8 min readTracking error and information ratio: deviation from the indexTracking error measures how far a fund deviates from its index, the information ratio whether that pays off. Formulas, examples, causes in ETFs and the statistics.In depth7 min readValue at risk and conditional VaR: how much you could lose in a bad caseValue at risk (VaR) is the loss that will not be exceeded with, e.g., 95% probability; CVaR is the average loss beyond that point. Explained with worked examples.In depth7 min readVolatility drag: why volatility costs you returnThe more an investment fluctuates, the further its growth falls below its average return. Volatility drag with formula, examples, diversification return and leveraged ETFs.In depth8 min readBond math: calculating price, yield, duration, convexity and spreadsBond math with worked examples: price and accrued interest, yield to maturity, spot and forward rates, duration, convexity, Z-spread, carry and breakeven inflation.Advanced12 min readDeflated Sharpe ratio: how much skill is in a Sharpe ratio?The deflated Sharpe ratio explained: standard error with skewness and kurtosis, probabilistic Sharpe ratio, minimum track record length and haircut, with a worked example.Advanced10 min readMomentum crashes: why momentum collapses rarely but violently, and what volatility scaling and crowding measures showMomentum crashes explained: time-varying betas after bear markets, Daniel/Moskowitz and Barroso/Santa-Clara, the 2007 quant meltdown, comomentum and volatility scaling.Advanced9 min readRisk contribution: breaking portfolio risk down into its partsRisk contribution shows how much each asset contributes to portfolio volatility. Marginal contribution, Euler decomposition, examples with 60/40 and risk budgets.Advanced9 min readScenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency riskScenario analysis and stress tests explained: beta, duration, DV01, spread duration, FX delta, historical and hypothetical scenarios, reverse stress tests, an example.Advanced15 min readStock-bond correlation: regimes, drivers and what it means for 60/40, risk parity and hedgingStock-bond correlation for advanced investors: why it changes sign, inflation versus growth shocks, the impact on 60/40 and risk parity, and estimation error.Advanced12 min readTail hedging: what put protection costs, when it pays off and what short-vol strategies teachTail hedging for advanced investors: put costs vs. the crash payoff, the volatility risk premium, the Spitznagel vs. AQR debate, Volmageddon 2018 and alternatives.Advanced12 min read
Portfolio and strategy
Allocating, rebalancing, optimizing and planning for retirement.
60/40 portfolio: the classic mix of equities and bondsThe 60/40 portfolio explained: return and risk in a worked example, why almost all the risk comes from equities, rebalancing, common variants and the main criticism.Basics8 min readAll Weather portfolio: ready for every economic climate?Ray Dalio's All Weather portfolio, Harry Browne's Permanent Portfolio and the Golden Butterfly: the idea, allocations, risk in a worked example, research and criticism.Basics9 min readCore-satellite with a broad core and targeted satellites: costs, tracking error and rulesThe core-satellite strategy explained: core and satellites, weighted TER, portfolio tracking error with correlations, risk budget, rebalancing rules and investor behavior.Basics9 min readDollar-cost averaging: what the average-cost effect really deliversDollar-cost averaging explained: why investing a fixed amount buys at a lower average price, why that is still no extra return, and what research says about DCA vs. lump sum.Basics8 min readHome bias: the preference for your home market and what it costsHome bias explained: how much investors overweight their home market, what it costs in diversification, the reasons research gives and when a home tilt makes sense.Basics8 min readLump sum or dollar-cost averaging: invest a large amount at once or in installments?Lump sum or dollar-cost averaging? Expected return, risk and probabilities compared, with a simulation, research and a decision guide for an inheritance or a bonus.Basics8 min readMarket timing: can you pick the right moment?Market timing explained: what the best and worst trading days do to returns, how often you would need to be right, what studies show and when rules beat gut feeling.Basics8 min readMSCI World vs ACWI vs FTSE All-World: structure, concentration and combinationsMSCI World vs ACWI vs FTSE All-World: countries, holdings, US and tech weights from the factsheets, concentration via the Herfindahl index, Japan in 1989 and combinations.Basics12 min readRebalancing: getting your portfolio back on courseRebalancing resets the weights to the target allocation. How often, with which tolerance bands, what it costs and when it adds return. With examples and research.Basics8 min readSafe withdrawal rate: how good is the 4% rule?The 4% rule says how much you can withdraw from your portfolio each year. Its origins with Bengen, sequence risk in a worked example, perpetual withdrawal rate and flexible rules.Basics8 min readThematic ETFs and hype: what studies, costs and overlaps revealThematic ETFs under scrutiny: launches after the rally, costs, concentration, overlap with a global ETF in an example, fund closures, survivorship bias and a checklist.Basics10 min readActive ETFs: how they work and what they deliverActive ETFs explained: how they differ from index and smart beta ETFs, transparency rules in the US and Ireland, the tax advantage, market size, the alpha required and research.In depth11 min readActive or passive in bonds and commodities: why the rules differ from equitiesActive or passive in bonds and commodities: debt-weighted indices, fallen angels, the credit beta of active bond funds, roll yield, contango and commodity indices.In depth12 min readBuyout funds and management buyouts: how LBOs, MBOs and MBIs workBuyout funds and management buyouts explained: LBO, MBO, MBI, capital structure, sweet equity, an LBO example with MOIC, IRR and value creation bridge, risks and research.In depth10 min readCPPI: portfolio insurance with cushion, floor and multiplierCPPI explained: how the floor, cushion and multiplier drive the equity share, why the strategy wins in trends and loses in choppy markets, plus gap risk and 1987.In depth11 min readEfficient frontier: Markowitz portfolio optimizationThe efficient frontier shows the best expected return for each level of risk: minimum variance, tangency portfolio, estimation error, shrinkage, robust alternatives, examples.In depth8 min readEqual weight vs cap weight: weighting, rebalancing and factor tiltsEqual weight vs cap weight: equal weighting, rebalancing and turnover, tilts toward size, value and reversal, research on 1/N and MSCI World factsheet figures.In depth11 min readEquity allocation by age: rules of thumb, glide paths and what theory saysEquity allocation by age: what lies behind “100 minus age”, how a glide path works and what life-cycle models with human capital have to say about it.In depth7 min readESG ETFs: index rules, ratings, returns and the limits of sustainable fundsESG ETFs explained: exclusion, best-in-class and climate indices, why ESG ratings diverge, carbon intensity, EU Article 8 and 9 funds and the research on returns.In depth12 min readFIRE (Financial Independence, Retire Early): Lean, Fat, Coast and Barista FIREFIRE explained: the FIRE number, savings rate and years to financial independence, Lean, Fat, Coast and Barista FIRE, and safe withdrawal rates for 40 to 50 years.In depth11 min readGold in a portfolio: safe haven, inflation hedge or just shiny?Gold in your portfolio: what gold adds to diversification, whether it protects against inflation, how safe the “safe haven” is, how to hold it and what allocation is common.In depth7 min readInfrastructure investing: equity and debt, revenue models, valuation and researchInfrastructure investing explained: revenue models, core to opportunistic, equity and project finance, DCF with +100 basis points, DSCR, default rates and research.In depth12 min readLeverage in a portfolio: return, risk, costs and margin callsPortfolio leverage explained: how borrowing multiplies return and risk, why growth does not keep pace, when a margin call looms and what leveraged ETFs do differently.In depth12 min readLiquid real assets: inflation protection with tradable real assets in a portfolioLiquid real assets explained: linkers, commodities, gold, REITs and infrastructure as inflation hedges, with inflation beta, research, sleeve design, costs and limits.In depth11 min readMonte Carlo simulation: how safe is your plan?A Monte Carlo simulation runs through thousands of possible futures. Methods, success rate, percentiles, fat tails and bootstrap, with a withdrawal plan example.In depth7 min readPrivate equity explained: strategies, fund structure, fees and what research shows about returnsPrivate equity explained: buyout, growth, venture capital, secondaries and ELTIFs, fund structure, carried interest with a waterfall example, returns and risks from research.In depth10 min readReal estate as an investment: rental property, REITs, open-end funds and private real estateReal estate as an investment: gross and net rental yield, leverage with a worked example, REITs vs private real estate, cap rates, appraisal smoothing and research since 1870.In depth10 min readSequence risk: when the order of returns decides your retirementSequence risk means that once you make withdrawals, the order of returns matters. A worked example, the risk zone around retirement and what helps against it.In depth8 min readStock picking: why individual stocks are so hard to get rightStock picking explained: why most individual stocks lag the market, how many stocks a portfolio needs and how to measure your stock-picking success honestly.In depth9 min readStrategic and tactical asset allocation and the total portfolio approachStrategic and tactical asset allocation explained: target weights, bands, a risk budget for deviations, measuring added value and the total portfolio approach of large funds.In depth12 min readTactical allocation: momentum, dual momentum and trend followingHow momentum rotation, dual momentum, moving averages (the 200-day line) and volatility targeting work, with examples, research and backtest pitfalls.In depth7 min readVenture capital: funding rounds, valuation, the power law and what research knows about returnsVenture capital explained: seed to Series C, pre- and post-money, dilution, liquidation preference, the power law, return studies and access for private investors.In depth12 min readYour whole wealth: total wealth from portfolio, home, human capital and carTotal wealth, not just your portfolio: human capital as the present value of income, home with leverage and costs, car, pension and debt. With a balance sheet and true equity allocation.In depth12 min readAsset-liability management: aligning your wealth with future spendingALM sets your assets against future payments: present value, funded status, duration and required return. How pension funds plan, explained for private investors.Advanced7 min readBasket swaps, total return swaps or futures: building market exposure efficientlyBasket swaps, total return swaps, index futures or ETFs: roll costs and implied financing, swap spread, margin, counterparty risk, UCITS rules and a cost comparison.Advanced11 min readBeyond Markowitz: estimation error, noise and true diversificationWhy optimized portfolios disappoint, how much noise there is in correlations and how to measure the true number of independent bets. With examples and evidence.Advanced12 min readBlack-Litterman: incorporating your own views cleanlyBlack-Litterman starts from market-implied returns and blends in your own views according to your confidence. Formulas, worked examples and Idzorek's confidence method.Advanced8 min readHierarchical risk parity: building portfolios from clustersHierarchical risk parity (HRP) weights assets via clusters of correlations instead of the inverse covariance matrix. Algorithm, worked example, research and limitations.Advanced9 min readIndex replication: full replication, optimized sampling and swapsIndex replication explained: full replication, optimized sampling with a risk model, swap ETFs, why fewer securities are enough, costs, counterparty risk and taxes.Advanced12 min readLeveraged ETFs and return stacking: path dependence, costs and researchLeveraged ETFs explained: why daily rebalancing helps in trends and costs in sideways markets, what financing costs, what studies show and how return stacking works.Advanced12 min readLiability-driven investing and cash flow driven investing: covering liabilities with bondsLDI and CDI explained: hedge ratio, interest rate and inflation swaps, cash flow matching with bonds, Redington immunization and the 2022 gilt crisis. With worked examples.Advanced12 min readMeasuring private markets: J-curve, cash flows, smoothing and public proxiesHow to measure private markets: J-curve, capital calls and distributions, IRR, TVPI, DPI, PME and direct alpha, smoothed NAVs, desmoothing and levered public proxies.Advanced12 min readMichaud resampled optimization: more stable portfolio weights through simulationMichaud resampled optimization explained: estimation error, simulated datasets, averaging by rank, an example you can recalculate and what studies say about Bayes and 1/N.Advanced10 min readOverlay management with futures: beta, duration and currency overlays, contract numbers and liquidity needsOverlay management explained: beta and duration overlays with contract formulas, cash equitization, rebalancing via futures, currency overlays, margin, basis risk and roll.Advanced12 min readPairs trading and statistical arbitrage: idea, methods, researchPairs trading explained: the distance method, cointegration, z-score and half-life, what research says about the profits and what risks long/short strategies carry.Advanced13 min readRisk parity: equal risk contributions instead of equal weightsRisk parity spreads risk evenly rather than capital. The risk contribution formula, examples with two and three assets, leverage, research findings and limits.Advanced9 min readTakahashi-Alexander model: forecasting the cash flows of private markets fundsThe Takahashi-Alexander (Yale) model: a fund's capital calls, distributions and NAV from a few parameters, with a worked example, calibration and commitment pacing.Advanced12 min readThe Kelly criterion: how much to bet for maximum growthThe Kelly criterion gives the bet size that makes your wealth grow fastest over the long run. Formulas for bets and stocks, worked examples, half Kelly and the risks.Advanced9 min readTrend following: riding each asset's own trendTrend following buys assets that have risen and sells or avoids falling ones. Time-series momentum, moving averages, managed futures, research and limitations.Advanced9 min read
ETF basics and costs
What an ETF is, what it costs and how index funds are built.
Active or passive investing: ETFs versus fund managersActive or passive? Why most active funds lag their index: Sharpe's arithmetic of active management, costs in a worked example, SPIVA figures and how to check a fund.Basics8 min readETF basics: costs, replication and distributionsWhat matters when choosing an ETF: expense ratio and tracking difference, physical and synthetic replication, how income is handled and fund size. With worked examples.Basics7 min read
Analysis and factors
What is inside funds, which factors drive returns and how bonds react to interest rates.
How to backtest an ETF portfolio: a guide to portfolio backtestingBacktest an ETF portfolio step by step: find securities, set weights, contributions, rebalancing, costs and proxies, then read the results. With a worked example.Basics12 min readLegendary investors: the investment styles of the most famous investors, from Graham to SimonsLegendary investors at a glance: the styles of Buffett, Soros, Simons and co., how to track their portfolios via 13F filings and why copying them is harder than it looks.Basics12 min readCAPM: the capital asset pricing model and the security market lineThe CAPM explains expected returns through market risk, beta. Formula, security market line, worked example, assumptions, criticism and what the research has found.In depth8 min readDuration: how strongly bonds react to interest ratesModified duration, convexity, key rate duration and spread duration explained simply: how much a bond loses when interest rates rise, with worked examples.In depth9 min readFactor investing: understanding the Fama-French factorsMarket, size, value, profitability, investment and momentum: what the Fama-French factors measure, how a factor regression works and what the research shows.In depth10 min readFundamental analysis: valuing a company like an investorFundamental analysis explained: business model, financial statements, P/E, EV/EBITDA and more, a DCF worked example, the Gordon model, value investing and the research.In depth12 min readLook-through: what is really inside your ETFsLook-through analysis breaks ETFs down into individual stocks, countries and sectors. Overlap, concentration risk and effective number of holdings, with examples.In depth8 min readPortfolio reporting: how to report return, risk, attribution and costs properlyPortfolio reporting explained: time- and money-weighted return, Bailey's benchmark criteria, risk, attribution, cost disclosure, GIPS and the EU's MiFID II and PRIIPs rules.In depth11 min readRFP and mandate awards: how institutional investors select asset managersRFPs and mandate awards explained: the process from RFI to contract, due diligence questionnaires, scoring matrix, tiered fee schedules and what research shows about manager selection.In depth10 min readTechnical analysis, chart patterns and candlesticks from a quant perspectiveTechnical analysis put to a sober test: how to test trends, support levels, chart patterns, candlesticks, RSI, MACD and Bollinger Bands, and what the research shows.In depth11 min readBacktest overfitting: when the past looks too goodWhy so many backtests look too good: data snooping, survivorship bias, look-ahead bias, the deflated Sharpe ratio and the factor zoo, with worked examples and remedies.Advanced10 min readBootstrap: future scenarios from your own historyThe bootstrap resamples historical returns with replacement to build new paths. The simple, block and stationary bootstrap explained, with a worked example and limitations.Advanced9 min readCovariance estimation: why optimizers need shrinkageA covariance matrix estimated from historical returns is full of estimation error. How Ledoit-Wolf shrinkage stabilizes it: formula, worked example, research, limits.Advanced9 min readEvent studies: how to measure and test price reactions to eventsEvent study methodology step by step: estimation window, market model, abnormal return, CAR and BHAR, t, Patell, BMP and rank tests, cross-sectional correlation, worked example.Advanced11 min readMulti-asset attribution: weighting schemes, top-down and bottom-up, currencies and overlaysMulti-asset attribution explained: weighting schemes, exposure instead of market value for futures overlays, multi-level Brinson analysis, Karnosky-Singer currencies, bonds.Advanced12 min readPerformance attribution: Brinson decomposition, factors and linking over timePerformance attribution explained: Brinson allocation, selection and interaction with formulas and an example, Carino and Menchero linking, factor attribution and limitations.Advanced11 min readProbability of backtest overfitting: does the best variant deliver what the backtest promises?The probability of backtest overfitting (PBO) explained: CSCV step by step, the logit of the rank, performance degradation, interpretation and limits, with a worked example.Advanced11 min readRegime models: hidden Markov, Markov switching and moreRegime models explained: hidden Markov model, Hamilton's Markov switching, thresholds, structural breaks and macro regimes. With a worked example, research and the look-ahead trap.Advanced13 min readReturn forecasting models: ARIMA, GARCH, LSTM and machine learningForecasting models put to the test: ARIMA, GARCH, regressions, machine learning and LSTM. What can be predicted, how to test forecasts honestly and what research shows.Advanced12 min readSharpe's style analysis: what a fund really doesWilliam Sharpe's returns-based style analysis finds the mix of indexes that best replicates a fund. Plus selection return, standard errors and a worked example.Advanced9 min readThe low-volatility anomaly and betting against betaLow-volatility stocks have historically delivered similar or higher returns than risky ones. The low-volatility anomaly, betting against beta, explanations and limitations.Advanced9 min read
Markets and valuation
Stock market valuation, interest rates, inflation, bubbles, carry, maritime trade and sentiment in the options market.
Currency risk: how exchange rates change your returnCurrency risk for US investors in foreign stocks and bonds: worked examples, fund currency versus the currency of the holdings, the cost of hedging and when it pays off.Basics8 min readPump and dump and penny stocks: how the scam worksPump and dump explained: how fraudsters hype penny stocks with spam, newsletters and social media, who loses, how the law defines it, and the warning signs.Basics10 min readReal return: what is left after inflationThe real return is the return after inflation. Why you should not simply subtract, how to calculate it correctly and what taxes and 30 years do to it. With examples.Basics7 min readWorld portfolio: the whole world in one or two ETFsThe world portfolio explained: MSCI World, MSCI ACWI, FTSE All-World and emerging markets compared, country weights, 70/30 or market weight, research and implementation.Basics9 min readAlternative data: job ads, Reddit, X, satellites and card paymentsAlternative data such as job ads, Reddit, X, satellite images and card payments: what they reveal, what the research shows and where the law and backtests set limits.In depth12 min readCarry trade: earning interest with currencies and bondsThe carry trade explained: earning the interest rate differential with currencies and bonds, interest parity, the forward premium puzzle, crash risk, roll-down and research.In depth13 min readCollectibles as an investment: what art, wine, watches and classic cars really returnCollectibles as an investment: markets, buyer's premium and costs, repeat-sales and hedonic indices, selection bias, returns from studies and a worked example for art.In depth10 min readCrypto in institutional portfolios: access, custody, regulation and risk budgetCrypto for institutional investors: ETPs, futures and direct holdings, custody and MiCA, rules for funds, banks and insurers, and the risk contribution of Bitcoin.In depth12 min readCTAs and managed futures: industry, position sizing, costs and crisis protectionManaged futures and CTAs explained: regulation, position sizing with a volatility target, what 2 and 20 costs, when crisis alpha works and why the 2010s were weak.In depth12 min readDigital assets: tokenization, stablecoins, crypto securities and the digital euroDigital assets explained: tokenization, stablecoins and their reserves, crypto securities, faster settlement, EU rules under MiCA, the digital euro, risks and research.In depth12 min readEquity risk premium: how much more equities return and why it is a puzzleThe equity risk premium is the excess return of stocks over safe assets. Historical values, estimation methods, the equity premium puzzle and what investors can expect.In depth7 min readIndex providers and valuation points: why the same index is calculated differentlyIndex providers compared: how NAV, valuation point, FX fixing and swing pricing work, what sets MSCI, FTSE Russell and Solactive apart, and where bond prices come from.In depth12 min readInsider trading: what is prohibited, what is allowed and what insider purchases revealInsider trading explained: what counts as inside information, SEC Rule 10b-5, Form 4 and 10b5-1 plans, EU directors' dealings, shadow trading and research on insider buying.In depth12 min readMarket expectations: what the yield curve, inflation-linked bonds and options reveal about the futureMarket expectations from market prices: priced-in rate moves from forward rates, breakeven inflation, recession risk from the yield curve and distortion by risk premia.In depth12 min readPrediction markets as bets on events: what they can and cannot doPrediction markets explained: binary contracts, price as probability, LMSR, US regulation, accuracy versus polls, and why fees and interest rates distort prices.In depth12 min readPrivate credit and public credit compared: returns, risks and what the research showsPrivate credit explained: direct lending, unitranche, covenants, comparison with high yield and leveraged loans, fees, smoothed returns and what studies show.In depth12 min readShiller P/E (CAPE): how expensive is the stock market?The Shiller P/E (CAPE) relates price to average earnings over 10 years. How to calculate it, the earnings yield, the Excess CAPE Yield and return forecasts.In depth9 min readShip tracking data and satellite images: what they reveal about commoditiesShip tracking data (AIS) explained: who transmits, what land-based receivers see, how researchers measure seaborne trade in real time and what satellite images of oil tanks reveal.In depth12 min readShort selling, hedge funds and hedging: types and how they workShort selling and hedging explained: securities lending, short squeezes and disclosure rules, hedge fund strategies, hedge ratio, beta and delta hedging with worked examples.In depth13 min readThe efficient market hypothesis: why it is so hard to beat the marketThe efficient market hypothesis says prices reflect available information. Its three forms, the evidence, the counterarguments and what it means for private investors.In depth8 min readVIX: how to read the stock market's fear gaugeWhat the VIX measures, how to convert it into an expected move, and what contango, roll yield, VVIX, SKEW and the volatility premium mean. With worked examples.In depth8 min readYield curve: what the term structure reveals and why an inverted curve is seen as a warning signThe yield curve shows yields by maturity. Normal, flat and inverted yield curves, forward rates, the Nelson-Siegel model and what the slope says about recessions.In depth8 min readBasis trades: positive and negative basis in bonds, CDS and futuresThe basis trade explained: CDS-bond basis, negative and positive basis trades, Treasury basis and implied repo rate, cash-and-carry, worked examples, March 2020 and risks.Advanced11 min readCounterparty and issuer risk: CVA, ETCs, certificates and swapsIssuer and counterparty risk explained: certificates, ETNs, ETCs, swap ETFs and securities lending, the CVA formula with a worked example, wrong-way risk, xVA and Basel III.Advanced12 min readDistressed debt: strategies, bankruptcy law, recovery rates and returns when investing in crisesDistressed debt explained: definition, trading and loan-to-own, Chapter 11 and cram-down, absolute priority, recovery rates by seniority, uptiering and the IRR of a distressed bond.Advanced12 min readLiquidity risk: measuring market liquidity, liquidity premiums and the tools of open-ended fundsLiquidity risk for advanced investors: spread, Roll and Amihud measures, liquidity as a risk factor, swing pricing, redemption gates, suspensions and ETFs under stress.Advanced12 min readMarket making and bond trading: spread, inventory, axes, RFQ, cross trades and matrix pricingMarket making explained: spread, inventory risk, adverse selection, bond trading via RFQ, bid and ask axes, portfolio trading, cross trades and matrix pricing, with an example.Advanced11 min readOption pricing: where fair option prices come fromOption pricing for advanced investors: no-arbitrage, Black-Scholes, put-call parity, binomial trees, the Greeks, implied volatility, the smile, exotics and strategies.Advanced13 min readOrder types and execution: from limit orders to MOC, VWAP, TAS and BTICOrder types explained: limit, stop, iceberg, MOO and MOC, closing auction, TWAP, VWAP, POV, ETF trading at NAV, TAS, BTIC and implementation shortfall, with examples.Advanced12 min readPrivate debt in practice: direct lending, unitranche, mezzanine, loan structure and fund vehiclesPrivate debt in practice: strategies from direct lending to mezzanine, margin, OID and covenants, BDCs and evergreen funds, fund leverage and a worked net return calculation.Advanced12 min readSmart indexing: added value for index funds around corporate actions and index changesSmart indexing explained: elections in corporate actions, predicting index changes, what the index effect costs index funds and what the research shows.Advanced11 min readSpeculative bubbles: what they are and how the LPPLS model detects themSpeculative bubbles explained: definitions from Kindleberger to Fama, rational bubbles, Sornette's LPPLS model with tc and oscillations, criticism and alternatives.Advanced12 min readThe index effect: what happens to prices when stocks join or leave an indexThe index effect explained: what happens when a stock joins or leaves a major index, how index reviews work, index fund demand versus trading volume and the research.Advanced10 min read
Methodology
How Portfolio Lab calculates: tool by tool, with all assumptions and defaults.
Backtest methodology: data, process, rebalancing and costsHow the Portfolio Lab backtest calculates: prices with distributions, currencies, rebalancing dates, savings plans, withdrawals, trading costs and time-weighted return.Metrics methodology: how Portfolio Lab measures return and riskAll Portfolio Lab metrics with formulas: CAGR, volatility, Sharpe, Sortino, Calmar, drawdown, VaR, beta, alpha, tracking error, capture ratios and withdrawal rates.Optimization methodology: estimation, objectives, Black-Litterman, resampling and walk-forwardHow Portfolio Lab optimizes: Ledoit-Wolf covariance, eight objective functions, min-CVaR, efficient frontier, Black-Litterman, Michaud resampling and rolling tests.Tactical allocation methodology: how the eleven tactical models workTrend following, dual momentum, rotation (PAA, VAA, DAA, ADM), target volatility, adaptive allocation, CAPE and regime (HMM): signals, defaults, cash, comparison.CPPI backtest: methodologyHow Portfolio Lab calculates CPPI: equities = multiplier × cushion, floor with TIPP and lock-in, review dates, costs, gap risk and the comparison with a constant mix.Carry backtest: methodology for FX and bond carryHow Portfolio Lab calculates carry: forward rates from the rate differential, currency ranking, volatility target, crash filter, costs, and coupon and roll-down for bonds.Long/short and statistical arbitrage: methodologyHow Portfolio Lab computes long/short: pairs trading with hedge ratio and z-score, pair portfolios, Avellaneda/Lee s-score, rank strategies, costs and borrow fee.Monte Carlo methodology: how Portfolio Lab simulates wealth pathsHow the Portfolio Lab Monte Carlo simulation works: bootstrap, block bootstrap, normal and t distribution, contributions, withdrawals, percentiles and success rate.Financial goals methodology: how Portfolio Lab simulates a life planHow the Financial goals page calculates: payment plan, priorities with a reserve, simulated return paths, a glide path between two portfolios and the required savings rate.ALM methodology: how Portfolio Lab measures assets against liabilitiesHow Portfolio Lab's ALM page works: payment schedule, present value and duration of the liabilities, funded status, interest rate risk and the simulation of all portfolios.Factor regression, factor allocation and factor statistics: methodologyHow Portfolio Lab calculates factor regressions: Fama-French models, momentum, bond factors, t-statistics, return attribution, factor allocation and factor statistics.Returns-based style analysis: methodologyHow Portfolio Lab runs Sharpe's style analysis: optimizing the style weights, standard errors, rolling analysis, out-of-sample selection and the style map.Asset analysis: methodology from correlation to cointegrationHow Portfolio Lab calculates correlations, principal components, autocorrelation, the variance ratio, cointegration and the fund comparison as of a common reference date.Look-through: how Portfolio Lab sees inside fundsWhere Portfolio Lab gets a fund's holdings, how it adds up countries, sectors and individual securities across all funds, and how it classifies positions in its taxonomy.Risk factors in the look-through: methodologyHow Portfolio Lab calculates interest rate duration by currency, key rate durations, spread duration by issuer and equity beta from holdings lists and returns.Risk & attribution: methodology of risk decomposition and Brinson attributionHow Portfolio Lab calculates Euler risk contributions, VaR and CVaR, tracking error, factor risk and Brinson-Fachler attribution with Carino and Menchero linking.ESG methodology: sustainability in the look-throughHow Portfolio Lab calculates with freely usable data: shares in companies with coal, oil and gas assets, recorded emissions per company, SFDR and limitations.Asset classes with a long history: methodologyHow Portfolio Lab chains 202 asset classes from funds, index data, synthetic bonds and proxies into long monthly series, handles currencies and deducts fund costs.Macro dashboard and regime analysis: methodologyHow Portfolio Lab prepares macro data for the US, the euro area and Germany, defines six regimes and evaluates portfolios by business cycle, inflation and rate phase.Valuation with the Shiller P/E: methodologyHow Portfolio Lab prepares the US stock market CAPE since 1881, ranks it historically and turns it into a real expected return by regression with Newey-West errors.Volatility dashboard: methodologyHow Portfolio Lab calculates the volatility barometer, VIX maturities, futures curve, VX30, roll yield, Traders-VRP and correlation, and ranks each by percentile.Sentiment: methodology for the fear and greed index, put/call ratio and COTHow Portfolio Lab calculates its own fear and greed index, put/call ratios, COT positioning, financial stress and cross-asset signals, and what came next.Option pricer: how Portfolio Lab values optionsHow the option pricer works: Black-Scholes with cost of carry, binomial trees, barriers, Asians, lookbacks, Greeks, implied volatility, SVI smile and strategies.Bubble indicator (LPPLS): methodologyHow Portfolio Lab computes the LPPLS model: formula, calibration after Filimonov and Sornette, search space, filters, 26 windows, confidence, history and limitations.Regime methodology: how the hidden Markov model worksHow Portfolio Lab computes its hidden Markov model: Baum-Welch, Hamilton filter, smoothing, Viterbi, metrics per regime, BIC and walk-forward in Tactical.Ships at chokepoints (beta): methodologyHow Portfolio Lab counts tankers and cargo ships at Hormuz, Suez, Malacca and more: AIS messages, rectangles, ship type, draft, counting windows and limitations.Data checks: loading, preparing and checking price seriesHow Portfolio Lab loads, cleans and checks price data: jumps, factor-of-100 errors, frozen prices and gaps, with limits per type of security and clear notes.Dimensions methodology: how Portfolio Lab counts independent risksHow Portfolio Lab calculates dimensions: eigenvalues against the Marchenko-Pastur bound, effective number of bets, minimum torsion, absorption ratio and history.Economic pulse: how Portfolio Lab calculates early indicatorsHow the economic pulse works for the US, the euro area and Germany: day-exact year-on-year change, robust z-score without look-ahead, weights and minimum coverage.Methodology of the free calculators: savings plan, withdrawal and leveraged ETFHow Portfolio Lab's free calculators work: a savings plan with compound interest and costs, a withdrawal plan with Monte Carlo and a leveraged ETF with volatility drag.Private markets methodology: analyzing funds, forecasting cash flows, planning commitmentsHow Portfolio Lab calculates private markets funds: XIRR, TVPI and DPI, KS-PME, direct alpha and Long-Nickels, Geltner and GLM desmoothing, forecasting and pacing.Overfitting check and diversification return: the calculations in Backtest and TacticalHow Portfolio Lab calculates the PSR, minimum track record length, deflated Sharpe ratio and probability of backtest overfitting, and decomposes the diversification return.Scenario methodology: how Portfolio Lab runs stress testsHow Portfolio Lab calculates scenarios: regression on seven factors, shocks with conditional expectation, historical crisis windows and a reverse stress test.
Literature
1184 studies and books the articles draw on, from Markowitz (1952) to current factor research.
Glossary
983 terms from A for alpha to Y for yield curve, briefly explained with an example and a link to the detailed article.
The articles explain methods and terms; they are not investment or tax advice. Worked examples are simplified and rounded.