Understand every number and every tool

CAGR expresses an investment's growth as a single annualized rate, computed as (ending / starting)^(1 / years) − 1. It answers: “what constant yearly return would produce this result?”

Because it is a geometric (compounded) rate, CAGR is NOT the simple average of the yearly returns — it accounts for compounding and is always less than or equal to the arithmetic average when returns vary. It smooths over the bumps, so two portfolios with the same CAGR can still have very different year-to-year volatility and drawdowns.

Volatility is the standard deviation of periodic returns, annualized by multiplying the monthly standard deviation by √12. A higher number means returns are more spread out and less predictable.

It treats upside and downside moves the same, so a portfolio that occasionally jumps sharply higher can look just as “volatile” as one that drops. For a downside-only view, see downside deviation and the Sortino ratio.

Maximum drawdown measures the worst loss an investor would have endured if they bought at a peak and held through the lowest following point. It is expressed as a negative percentage from peak to trough.

Drawdown captures the emotional and practical pain of an investment in a way volatility doesn't — a −50% drawdown requires a +100% gain just to break even. Informed Portfolio measures it on the time-weighted equity curve.

Risk contribution decomposes total portfolio volatility into the part attributable to each holding, accounting for both its weight and how it co-moves with everything else. The contributions sum to the portfolio's volatility.

A position can have a small weight but a large risk contribution (if it's volatile and correlated with the rest), or a large weight but small risk contribution (like bonds in a stock-heavy mix). Comparing weight to risk contribution reveals where risk is really concentrated.

The Sharpe ratio divides a portfolio's excess return (return minus the risk-free rate) by its volatility, then annualizes it. It tells you how much reward you received for each unit of risk taken.

As a rough guide, under ~1 is modest, around 1 is solid, and above 2 is excellent — but the figure depends heavily on the period and the risk-free rate used. Because it uses total volatility, it penalizes large upside swings as well as downside ones; the Sortino ratio addresses that.

The Sortino ratio is a variation of the Sharpe ratio that divides excess return by downside deviation instead of total volatility. By ignoring upside swings, it rewards portfolios that are volatile only when going up.

It is often a fairer measure for strategies with asymmetric returns. A higher Sortino ratio indicates better return per unit of harmful risk.

The Calmar ratio divides the compound annual growth rate by the absolute value of the maximum drawdown. It frames performance in terms of the worst loss an investor had to stomach.

A higher Calmar ratio means more annual return for each unit of peak-to-trough decline. It is popular for evaluating strategies where deep drawdowns are a primary concern.

Beta is the slope from regressing the portfolio's excess returns on the benchmark's excess returns (the CAPM model). It measures systematic (market) risk.

A beta of 1.0 means the portfolio tends to move one-for-one with the benchmark; 1.5 means it tends to move 50% more (up and down); 0.5 means it moves half as much; a negative beta means it tends to move opposite the benchmark. Beta says nothing about total risk — a high-beta fund can still have low overall volatility if it's well diversified.

Alpha is the intercept of the CAPM regression: the annualized return a portfolio earned beyond what its benchmark exposure (beta) would predict. Positive alpha suggests outperformance after adjusting for market risk; negative alpha suggests underperformance.

Alpha is sensitive to the benchmark and period chosen, and historical alpha does not reliably persist into the future.

R-squared ranges from 0 to 1 and measures how much of a portfolio's variation is explained by the benchmark. An R-squared near 1 means the portfolio closely tracks the benchmark, so its beta and alpha are meaningful. A low R-squared means the benchmark explains little, so beta/alpha against it should be interpreted cautiously.

Correlation measures the linear relationship between two assets' returns on a scale from −1 to +1. It is the foundation of diversification: combining assets that are weakly or negatively correlated can reduce a portfolio's overall volatility without necessarily reducing expected return.

Correlations are not constant — pairs that usually diversify can spike toward +1 during market stress, exactly when diversification is needed most. The Rolling Correlations tool shows how they change over time.

The efficient frontier, from Modern Portfolio Theory, is the curve of optimal portfolios — for any given level of risk (volatility), the frontier portfolio offers the highest expected return achievable from the chosen assets. Portfolios below the curve are sub-optimal because you could get more return for the same risk.

Two points are usually highlighted: the minimum-volatility portfolio (leftmost) and the maximum-Sharpe portfolio (the best risk-adjusted mix). The frontier is built from historical estimates, which are uncertain and shift over time.

In a typical 60/40 stock/bond portfolio, stocks are so much more volatile than bonds that they end up driving ~90% of the portfolio's risk — it's far less 'balanced' than it looks.

Risk parity fixes this by giving each asset a weight such that every holding contributes an equal share of total portfolio risk. In practice that means holding more of the calm assets (like bonds) and less of the wild ones (like stocks). The result is usually a steadier ride with smaller drawdowns, though it can lag in roaring bull markets.

Plain mean-variance optimization trusts historical average returns, which are noisy — feed it slightly different numbers and it produces wildly different, often absurdly concentrated portfolios.

The Black–Litterman model fixes this. It starts from the 'market-implied' returns reverse-engineered from a neutral or benchmark allocation (a stable, reasonable baseline), then lets you express specific views — e.g., 'I think emerging markets will return 9%' — each with a confidence level. It blends the two into a balanced set of expected returns, so the optimized portfolio tilts gently toward your views instead of lurching to extremes.

Given a neutral or market portfolio and its risk (covariance), you can run optimization 'in reverse' to find the expected returns that would make that exact portfolio optimal. Those are the market-implied (equilibrium) returns.

They serve as a sensible, stable starting point: rather than guessing returns or using noisy historical averages, you begin from what the market already implies and adjust only where you have a genuine view.

A Monte Carlo simulation generates thousands of randomized return paths — drawn from a statistical distribution or resampled from history — to estimate the range of outcomes a portfolio might experience, rather than a single point forecast.

The results are summarized as probabilities and percentile bands (e.g., a 10th–90th percentile “cone”). They are only as good as their assumptions about returns, volatility, and correlations, and real markets exhibit fat tails and regime changes that simple models understate.

The safe withdrawal rate (SWR) answers: 'how much can I pull from my nest egg each year without running dry?'. You take that percent of your starting balance in the first year, then increase that dollar amount with inflation every year after.

The famous '4% rule' came from studying U.S. history: a 4% starting rate survived almost every 30-year retirement. But the right number depends on your time horizon, your mix of stocks and bonds, and — crucially — luck with the order of returns. This lab estimates your personal safe rate from thousands of simulations.

Two retirees can earn the exact same average return over 30 years yet end up worlds apart — because the ORDER of returns matters once you're taking money out.

If the market falls in your first few retirement years, you're selling shares at low prices to fund spending, leaving fewer shares to recover when the market rebounds. That early damage can be permanent. The same poor years happening late in retirement barely matter. This is sequence-of-returns risk, and it's why a big crash right after you retire is so dangerous — and why flexible spending (guardrails) helps.

Guardrails (a simplified Guyton-Klinger approach) make your spending flexible instead of fixed. You set a starting withdrawal rate and two 'rails'. If a market drop pushes your withdrawal rate too high (you're spending too fast), you trim spending by a set amount. If a strong market pushes it too low (you could afford more), you give yourself a raise.

This flexibility dramatically reduces the chance of running out compared with rigid, never-changing withdrawals — at the cost of a variable paycheck.

A stress test deliberately puts your portfolio through bad conditions to reveal hidden risk that long-run averages smooth over. There are two flavors here.

Historical replay runs your exact holdings through real crises — the 2008 financial crisis, the 2020 COVID crash, the 2022 bear market — using actual daily prices, so you see the loss you would have lived through.

Hypothetical shocks ask 'what if?' — for example, what if stocks fell 30% and interest rates rose 2% tomorrow? The tool estimates the hit using each holding's measured sensitivity to stocks and to interest rates. Stress tests are planning tools, not predictions: real crises can be worse, because investments that normally move independently often fall together when panic strikes.

An equity shock is a 'what-if' instant fall in the overall stock market. To translate it into a portfolio impact, each holding is assigned an equity beta — how much it tends to move when the market moves. A fund with a beta of 1 falls about as much as the market; a bond fund with a beta near 0 barely reacts; a leveraged or high-growth fund with a beta above 1 falls more. Multiplying the shock by each holding's beta and weight gives the estimated portfolio drop.

An interest-rate shock asks what happens if yields suddenly rise. Bond prices move opposite to rates: when rates go up, existing bonds (paying the old, lower rate) become less valuable, so their price falls. How much it falls depends on duration — roughly, a bond fund with a 7-year duration loses about 7% if rates rise 1 percentage point. This tool measures each holding's 'rate beta' from history (its typical return per 1-point rise in the 10-year Treasury yield), so bond-heavy portfolios show the larger, realistic hit.

Duration measures interest-rate sensitivity in years. A duration of 7 means a roughly 7% price drop if interest rates rise by one percentage point — and a roughly 7% gain if they fall by one point. Short-term bond funds have low duration (small swings); long-term bond funds have high duration (big swings). It's the single most useful number for understanding how much a rate move will move your bonds.

The price-to-earnings ratio divides the share price by the company's earnings per share over the last year. A P/E of 20 means you're paying $20 for every $1 of annual profit.

There's no universally 'good' P/E: fast-growing companies command high P/Es because investors expect bigger future profits, while slow growers trade cheaply. Compare a P/E to the company's own history, its industry, and its growth rate — not in isolation. A negative or missing P/E means the company isn't currently profitable.

Price-to-sales divides the company's total market value by its annual revenue. Because it uses sales rather than profit, it still works for young or unprofitable companies where a P/E can't be calculated. A lower P/S is generally cheaper, but high-margin businesses justifiably trade at higher P/S ratios than low-margin ones.

Price-to-book compares the market value to 'book value' — what would theoretically be left for shareholders if the company sold its assets and paid its debts. A P/B near 1 means you're paying about book value; far above 1 means investors expect the company to create value beyond its balance sheet (common for brands and tech). Companies that buy back lots of stock can show a very high P/B (and ROE) because buybacks shrink book equity.

Price-to-operating-cash-flow compares market value to the cash a business actually produces from running its operations. Cash flow is harder to manipulate than reported earnings, so this ratio is a useful sanity check on the P/E — if a company shows healthy profits but weak cash flow, that's worth a closer look.

Earnings yield is simply 1 ÷ P/E, expressed as a percent. A P/E of 20 is a 5% earnings yield. It's handy because you can compare it directly to a bond yield or savings rate: a 5% earnings yield means the business earns 5 cents of profit per year for every dollar of stock you buy. The higher the earnings yield, the cheaper the stock relative to its profits.

Net margin is net income divided by revenue. A 20% net margin means the company turns $0.20 of every sales dollar into bottom-line profit after paying all costs, interest, and taxes. Higher margins indicate pricing power and efficiency; margins vary hugely by industry (software is high, groceries are thin), so compare within an industry.

Return on equity is net income divided by shareholders' equity. A 15% ROE means the company earns $0.15 of profit per year for each $1 of shareholder capital. It's a key measure of how efficiently a business uses the owners' money. Very high ROE can reflect either genuine excellence or heavy debt and buybacks shrinking the equity base — so read it alongside debt-to-equity.

The current ratio divides assets that can become cash within a year (cash, receivables, inventory) by liabilities due within a year. Above 1.0 means more short-term resources than short-term bills — a basic liquidity cushion. Some excellent businesses run below 1 because they collect cash from customers before paying suppliers, so a low ratio isn't always a red flag.

Debt-to-equity compares total liabilities (or just interest-bearing debt) to shareholders' equity. A ratio of 1 means equal debt and equity; higher means the company leans more on borrowed money. Leverage can boost returns in good times but magnifies losses in bad times, so a high ratio means more financial risk — though what's 'high' depends on the industry (utilities carry more debt than software firms).

Dividend yield divides the trailing 12 months of dividends per share by the current price. A 3% yield means $3 of annual dividends for every $100 invested. A very high yield can signal either a bargain or a troubled company whose price has fallen (and whose dividend may be cut), so always check whether the payout is sustainable.

The payout ratio is dividends divided by earnings. A 40% payout means the company returns 40% of its profit to shareholders and reinvests the rest. Low payout ratios leave room to raise the dividend and cushion against bad years; payout ratios near or above 100% mean the company is paying out more than it earns, which often can't last and may signal a future dividend cut.

Dividend growth looks at the trend in a company's payout, not just today's yield. A steadily rising dividend — especially a long streak of consecutive annual increases — signals management's confidence and a shareholder-friendly culture. A modest 2% yield growing 10% a year can be worth more over time than a stagnant 4% yield. We also flag the payout ratio, because growth is only sustainable if the company earns enough to fund it.

Factor analysis explains why a portfolio behaved the way it did by attributing its returns to a handful of well-studied 'factors' — broad forces that have historically driven stock returns. Instead of asking 'did it go up?', it asks 'did it go up because of the overall market, a tilt toward small or cheap or high-momentum or high-quality stocks, or genuine skill?'.

Statistically, it regresses the portfolio's returns on the returns of each factor. The result is a 'loading' (sensitivity) for each factor, an alpha (the part not explained by any factor), and an R² (how much of the portfolio's movement the factors explain together). It's the closest thing to an X-ray of an investment's style.

A factor loading is the slope from regressing a portfolio on a factor — it measures how strongly the portfolio moves with that factor. A market loading near 1 means it moves roughly with the market; a positive size loading means a tilt toward small-cap stocks; a positive value loading means a tilt toward cheap 'value' stocks, and so on.

Loadings near zero mean the portfolio has little exposure to that style. A loading is more trustworthy when its t-statistic is large (roughly above 2 in magnitude).

The t-statistic divides an estimate (like a factor loading or alpha) by its standard error. The larger its magnitude, the less likely the estimate is just noise.

A common rule of thumb: |t| above about 2 means roughly 95% confidence that the true value isn't zero. Small t-stats mean the exposure could plausibly be zero — interpret those loadings with caution.