Thematic Pillar Hub · 20 Published Briefings
Cagr Irr Drawdown Compounding research topics and source records from QuantCalc Tools. Terminal wealth compounds at the geometric mean rather than the arithmetic average; this quantitative hub unifies CAGR vs XIRR return attribution, variance drain, autocorrelation-adjusted Sharpe and Sortino ratios, and path-dependent drawdown math.
A named author is recorded on some briefings in this hub, including Elena Rostova, FRM, CQF . Reviewer records and automated-check status appear on each briefing when available.
Terminal wealth compounds at the geometric mean rather than the arithmetic average; this quantitative hub unifies CAGR vs XIRR return attribution, variance drain, autocorrelation-adjusted Sharpe and Sortino ratios, and path-dependent drawdown math.
Volatility acts as a deterministic compounding tax: derive the exact second- and fourth-order Taylor approximations linking arithmetic mean return, variance drain, skewness, and kurtosis to geometric CAGR.
An active ETF can post a +14.2% Time-Weighted CAGR while its average shareholder loses -4.8% via Money-Weighted XIRR; master exact sub-period linking and dollar-timing gap math.
Standard XIRR Newton-Raphson loops diverge past the r = -100% singularity or return arbitrary roots when cashflows flip sign twice; master Brent-Newton solvers and closed-form MIRR.
Portfolio losses obey a punishing hyperbola: losing 50% requires +100% to break even, while losing 75% requires +300% and 18 years at 8% CAGR; master exact recovery time math.
Multiplying a monthly Sharpe ratio by sqrt(12) assumes strictly IID returns; when stale pricing or illiquid credit marks induce +0.35 AR(1) autocorrelation, naive Sharpe ratios overstate skill by +44.8%!
Dividing squared downside shortfalls only by the count of losing months (N_down) instead of total sample size N corrupts the Sortino Ratio; master exact LPM2 semi-deviation math.
Sharpe and Sortino ratios are invariant to return permutation: shuffling six -4% losing months together creates a -21.7% crater with identical volatility; master Calmar, Sterling, and Ulcer Index math.
Unlike Sharpe (2 moments) or Sortino (LPM2), the Keating-Shadwick Omega Ratio partitions the entire empirical return CDF around threshold tau, embedding every higher moment automatically.
Testing 250 strategy variations on 5 years of random noise guarantees an expected maximum backtest Sharpe Ratio above 1.45 purely by luck; master exact PSR, DSR, and MinTRL equations.
Multiplication is commutative, so reversing 20 annual returns leaves buy-and-hold terminal wealth unchanged; adding constant real withdrawals breaks commutativity and triggers total ruin.
Two volatile assets that each compound at 0.00% standalone geometric CAGR can generate +6.07% annualized CAGR when rebalanced 50/50; derive exact Booth-Fama dispersion harvesting math.
When an index finishes flat (+0.0%) over a volatile year with 32% annualized sigma, a 3x daily-reset ETF loses -26.5% before financing fees; master exact beta slippage and optimal leverage L*.
Institutional benchmark mandates judge active managers on Information Ratio rather than raw Sharpe; derive exact Tracking Error decomposition and the Clarke-de Silva-Thorley Transfer Coefficient law.
When an SR = 1.0 strategy suffers a -22% drawdown over 5 years, is the model broken or behaving normally? Derive exact Magdon-Ismail Brownian Expected Maximum Drawdown scaling laws.
When daily pre-flow portfolio valuations are unavailable on private credit or multi-custodian wealth accounts, Modified Dietz approximates True TWRR by day-weighting external cashflows.
Because annual 20% incentive fees crystallize on up years without rebating losses on down years, a volatile fund with +10% gross CAGR can pay 48% of its cumulative 10-year gains in fees!
When adding a sleeve to a diversified multi-manager book, systematic beta matters more than standalone sigma; master exact Treynor, Jensen Alpha, and Modigliani M-Squared (M2) equations.
Logarithmic returns are additive across time but NOT across portfolio assets; multiplying weights w_i by ln(P_t/P_{t-1}) misstates volatile multi-asset returns and breaks VaR/CAGR models.
Taxing nominal returns in an inflationary regime levies a stealth wealth tax even when real returns are zero; master Fisher exact real CAGR and deferred vs annual turnover tax drag math.
CAGR calculator →
Compound annual growth rate between two values, with a year-by-year projection.
FX forward rate calculator →
Forward exchange rate and forward points from spot and two interest rates (covered interest parity).
Value at Risk (VaR) calculator →
Parametric VaR and Expected Shortfall for a position, at 95% or 99% confidence.
SOFR overnight compounding & carry calculator →
Daily compounded SOFR in arrears (ACT/360), effective annual yield and net levered carry.
Kelly criterion optimal fraction calculator →
Full, Half and Quarter Kelly position sizing, expected edge and geometric log growth rate.
Sharpe & Sortino ratio benchmark calculator →
Risk-adjusted performance across Sharpe ratio, Sortino downside ratio and Information ratio.
Because returns multiply rather than add: (1 + 0.50) * (1 - 0.50) = 1.50 * 0.50 = 0.75, leaving $0.75 per dollar (-13.40% annualized CAGR over 2 years). The +50% gain applied to $1.00, whereas the -50% loss applied to the enlarged $1.50 base (losing $0.75).
Use CAGR (Time-Weighted Return) whenever evaluating a liquid fund manager who does not control when clients deposit or redeem cash. Use XIRR (Money-Weighted IRR) for private equity/venture capital funds where the GP calls and distributes capital at discretion, or to audit your personal dollar wealth experience.
The Sharpe ratio penalizes upside return spikes (+40% months) identically to -40% crashes because standard deviation squares all deviations around the mean. Sortino replaces total sigma with target downside deviation below a Minimum Acceptable Return (MAR), avoiding false penalties on convex upside rallies.
No! Sequence-of-returns risk breaks CAGR invariance once fixed dollar withdrawals begin. Experiencing -20% losses in Years 1–2 while withdrawing living expenses permanently liquidates shares before a Year 8–10 bull market can compound them, depleting a portfolio that had a +7.5% underlying index CAGR.
Use the arithmetic mean ONLY as an unbiased estimator of an unknown single-period expected return (for example, forecasting next year’s 1-year expected return from stationary historical data or feeding single-period Markowitz MVO). Use geometric CAGR whenever measuring realized multi-period wealth growth.
Because 0.5*sigma^2 drops both the (1+A)^2 denominator scaling in the Taylor expansion around A and higher-order skewness/kurtosis terms. For example, alternating +100% and -60% gives A = +20%, sigma = 80%, and exact G = sqrt(2.0 * 0.4) - 1 = -10.56%, whereas A - 0.5*sigma^2 predicts 20% - 32% = -12.00%.