What's the difference between Sharpe and Sortino ratios?

Sharpe uses total volatility (standard deviation of all returns) in the denominator. Sortino uses downside deviation only — the volatility of negative returns. Sortino acknowledges that investors don't dislike upside volatility, so it's often a more honest measure of unpleasant risk. For portfolios with positive skew, Sortino is meaningfully higher than Sharpe.

What is a good Sharpe ratio?

A long-term Sharpe ratio above 1.0 is generally considered good for a diversified portfolio. The S&P 500 historically runs 0.4 to 0.7. Sustained Sharpe above 2.0 over multi-year periods is exceptionally rare and usually indicates either skill, leverage, or sample-size noise.

What is a good R-squared for a portfolio?

It depends on what you're trying to achieve. If you want diversified market exposure with minimal active risk, R² near 0.95 vs your benchmark is fine. If you're paying for stock-picking skill, R² above 0.95 is a red flag — you might be 'closet indexing' (paying active fees for passive performance). Foliolytic flags portfolios with R² > 0.95 and low active share.

Why does Foliolytic use real Treasury yields instead of a fixed risk-free rate?

Many calculators use a static 2% or 3% as the risk-free rate, which produces wildly inaccurate Sharpe and Sortino ratios in environments where T-bill yields are 5%. Foliolytic pulls actual 3-month U.S. Treasury bill yields from FRED for the exact period your portfolio was active, matching the methodology used by institutional asset managers.

Portfolio Analytics Glossary

Q: What's the difference between time-weighted, money-weighted, and dollar-weighted returns?

Time-weighted return (TWR) measures the return of the asset itself, ignoring the size or timing of contributions and withdrawals — it's the standard for evaluating fund managers. Money-weighted return (also called dollar-weighted return, equivalent to XIRR) weighs each return period by the amount of money invested at that time, reflecting the actual dollar experience of an investor. The two diverge whenever you add or withdraw money: a fund with TWR of 10% can give a poorly-timed investor an XIRR of only 4%.

Last updated: April 28, 2026

Plain-English definitions of 52+ portfolio analytics terms — from Sharpe and XIRR to Hurst exponents and Probabilistic Sharpe Ratio. Every term cross-linked to the relevant calculator.

Quick Answer

What's the difference between time-weighted, money-weighted, and dollar-weighted returns?

Time-weighted return (TWR) measures the return of the asset itself, ignoring the size or timing of your contributions and withdrawals — it's how funds report their performance. Money-weighted return (also called dollar-weighted return, equivalent to XIRR) weights each return period by the amount of money you had invested at that time, reflecting your actual dollar experience. The two diverge whenever cash flows happen on uneven dates: a fund with TWR of 10% can give a poorly-timed investor an XIRR of only 4%.

TWR = the asset's return · XIRR = your actual return

A

Active Return

The portion of a portfolio's return that comes from active management decisions, calculated as the portfolio's return minus its benchmark's return over the same period. A positive active return means the manager beat the market; a negative active return means the index would have done better.

Active Return = R_portfolio - R_benchmark

If you are paying for active management (or paying yourself in time), active return is the only number that justifies the cost. Persistently negative active return is the strongest argument for indexing.

Alpha (Jensen's)

Jensen's alpha is the return a portfolio earned above what its beta-adjusted exposure to the market would have predicted. It isolates skill from leverage. A portfolio that returned 15% with a beta of 1.5 in a year the market did 10% has alpha of zero — all the excess came from extra market exposure.

α = R_p - [R_f + β·(R_m - R_f)]

Alpha is the cleanest measure of stock-picking or allocation skill. Long-term positive alpha is exceptionally rare and is the gold standard for evaluating active managers.

See also: → Portfolio Alpha Calculator Beta R-Squared CAPM

Annualized Return

A return expressed as if compounded over a full year, allowing comparison between investments held for different lengths of time. Foliolytic uses geometric (CAGR-style) annualization, which is the only mathematically correct method for multi-period returns.

R_annual = (1 + R_total)^(365/days_held) - 1

Reporting a 30% return without annualizing tells you nothing — was it over 6 months (60% annualized) or 6 years (4.5% annualized)? Always demand the annualized figure.

Asset Allocation

The percentage breakdown of a portfolio across asset classes — typically stocks, bonds, cash, real estate, commodities, and crypto. Asset allocation is widely considered the single largest determinant of long-term portfolio outcomes, dwarfing individual stock selection.

Brinson, Hood, and Beebower's classic 1986 study estimated that ~90% of pension-fund return variance came from asset allocation, not security selection. For retail investors, getting the allocation right is more important than picking the right stocks within it.

B

BTC-Beta

A portfolio's sensitivity to Bitcoin price moves, calculated the same way as traditional beta but with Bitcoin daily returns substituted for the market index. BTC-beta of 1.5 means the portfolio moves 1.5% for every 1% Bitcoin move on average.

β_BTC = Cov(R_p, R_BTC) / Var(R_BTC)

Crypto correlation has become a meaningful portfolio risk in 2020+. Even portfolios with no direct crypto holdings often exhibit meaningful BTC-beta through tech-heavy stock exposure (MSTR, COIN, semiconductor and growth names).

Batting Average

The percentage of periods (usually months) in which a portfolio outperformed its benchmark. A batting average of 60% means the portfolio beat the benchmark in 60 out of 100 months.

Batting Avg = (months portfolio > benchmark) / total months

Combined with the magnitude of wins/losses (gain-loss ratio), batting average tells you whether outperformance is steady or driven by a few lucky months. A 55% batting average with a 1.5 gain/loss ratio is a much more reliable strategy than a 70% batting average with a 0.4 gain/loss ratio.

Beta

Beta measures how much a portfolio moves relative to the broader market. A beta of 1.0 means the portfolio matches market moves; 1.5 means it amplifies them by 50%; 0.5 means it moves half as much. Beta is calculated by regressing portfolio returns on market returns.

β = Cov(R_p, R_m) / Var(R_m)

Beta tells you how much market exposure you are running. A high-beta portfolio will outperform in bull markets and underperform in bear markets — both by larger margins than the index. Cash and bonds reduce portfolio beta; leverage and growth stocks raise it.

Beta Drift

The change in a portfolio's beta over time, driven by changes in holdings, leverage, or the market correlation of existing positions. A portfolio that started with beta 0.8 and now has beta 1.4 has experienced significant beta drift — its risk profile has changed even if you haven't traded.

Beta drift often happens silently when high-momentum stocks become a larger share of your holdings, or when defensive stocks underperform during a bull run. Periodically rebalancing helps anchor beta to your target.

C

CAGR (Compound Annual Growth Rate)

The constant annualized rate at which an investment would have to grow to reach its end value from its start value, assuming compound interest. CAGR is the geometric mean of period returns and the standard way to report multi-year performance.

CAGR = (V_end / V_start)^(1/years) - 1

CAGR smooths out volatility and gives a single comparable number across investments. It is more honest than arithmetic mean returns, which mathematically overstate compound growth (the gap is roughly half the variance).

CDaR (Conditional Drawdown at Risk)

The average of the worst α% of drawdowns over a period. CDaR(5%) for example is the mean drawdown across the worst 5% of all drawdown observations. Like CVaR but for path-dependent drawdown rather than single-period returns.

CDaR_α = E[Drawdown | Drawdown ≥ VaR_α]

CDaR captures tail-risk in the drawdown distribution, which matters for investors with hard liquidity constraints (retirement, leveraged accounts). A portfolio with low max drawdown but a heavy CDaR has many bad drawdown events even if none hit the absolute worst.

CPI (Consumer Price Index)

The U.S. Bureau of Labor Statistics' headline measure of inflation, tracking the price of a representative basket of goods consumed by urban households. CPI is what most retirement and Treasury Inflation-Protected Securities (TIPS) calculations index against.

Real return calculations subtract CPI growth from nominal return. Foliolytic uses official monthly CPI data going back to 1947 to compute real (inflation-adjusted) returns and validate against TIPS-indexed benchmarks.

See also: Real Return Risk-free Rate

CVaR (Conditional Value at Risk / Expected Shortfall)

The expected loss given that the loss exceeds the VaR threshold. If your 95% VaR is -3% (meaning losses worse than -3% happen 5% of the time), CVaR(95%) tells you the average loss conditional on being in that bad 5% — typically -5% or worse.

CVaR_α = E[Loss | Loss ≥ VaR_α]

CVaR (also called Expected Shortfall) is mathematically coherent in ways VaR is not — it satisfies subadditivity, meaning combining two portfolios cannot increase total CVaR. Most modern risk frameworks (Basel III for banks) prefer CVaR over VaR.

Calmar Ratio

A risk-adjusted return measure that divides annualized return by the worst (maximum) drawdown over the period. A Calmar ratio of 1.0 means the portfolio gained as much per year on average as its worst peak-to-trough fall.

Calmar = Annual Return / |Max Drawdown|

Calmar is popular with trend-followers and CTAs because drawdown captures path risk that volatility alone misses. A portfolio with low standard deviation but a single brutal 50% drawdown looks fine on Sharpe but terrible on Calmar.

Capture Ratio (Up/Down)

Two paired metrics: up-capture is the percentage of the benchmark's gains a portfolio captured during up months; down-capture is the percentage of the benchmark's losses it captured during down months. The dream profile is high up-capture, low down-capture.

Up-Capture = R_p / R_m (when R_m > 0)
Down-Capture = R_p / R_m (when R_m < 0)

Capture ratios reveal asymmetric performance that single-number metrics hide. A defensive equity strategy might capture 90% of upside and only 60% of downside — far better than its raw beta suggests.

See also: Beta Batting Average Alpha (Jensen's)

Carhart 4-factor

Mark Carhart's 1997 extension of the Fama-French 3-factor model, adding momentum (UMD = up-minus-down) as a fourth factor alongside market, size (SMB), and value (HML). The model tries to explain mutual fund returns through systematic factor exposures.

R_p - R_f = α + β_MKT·(R_m - R_f) + β_SMB·SMB + β_HML·HML + β_UMD·UMD + ε

After fitting Carhart 4-factor, the residual alpha is much smaller for most active managers — most apparent skill turned out to be tilted exposure to size, value, or momentum factors that anyone could have replicated with cheap ETFs.

D

Diversification Score

Foliolytic's composite score (0–100) measuring how spread-out a portfolio is across uncorrelated holdings. The score combines the effective number of holdings (HHI-based), sector concentration, country/region weights, and pairwise correlations.

A diversification score above 80 typically requires 20+ holdings across multiple sectors and at least some non-equity exposure (bonds, gold, REITs). Crypto-only portfolios usually score 30–50 because crypto assets are highly correlated with each other.

See also: Asset Allocation Beta R-Squared

Dollar-Weighted Return

Another name for money-weighted return, which weights each return period by the amount of money invested at that time. Equivalent to XIRR — the IRR that solves for the discount rate making the NPV of all cash flows equal zero.

Dollar-weighted return matters because it reflects the actual dollars-and-cents experience of an investor who added or withdrew money over time. If you bought heavily at the top, your dollar-weighted return will be lower than the fund's published time-weighted return.

Downside Deviation

The standard deviation of returns that fall below a target threshold (usually zero or the risk-free rate), ignoring upside volatility entirely. Used as the denominator in the Sortino ratio.

DD = sqrt( (1/n) · Σ min(R_i - T, 0)² )

Downside deviation acknowledges that investors don't dislike upside volatility — they only dislike losing money. By measuring only negative deviations, it gives a more honest picture of unpleasant risk.

Drawdown

The peak-to-trough percentage decline of a portfolio between any two points. A portfolio that hit $100k, fell to $80k, and recovered to $90k experienced a 20% drawdown. Drawdowns are the most psychologically painful aspect of investing and the main reason investors abandon strategies.

DD_t = (V_t / max(V_s for s ≤ t)) - 1

Drawdown captures path risk that variance-based metrics can miss. A portfolio with two 30% drawdowns can have lower realized volatility than one with continuous 1% daily noise but is psychologically much harder to hold.

E

Excess Return

A portfolio's return minus the risk-free rate. Excess return is what you earn for taking risk above what you could earn riskless in T-bills. The numerator of the Sharpe ratio is excess return.

Excess Return = R_p - R_f

Reporting a 7% return in a year T-bills paid 5% is misleading — the excess return was only 2%. In high-rate environments, the gap between nominal returns and excess returns matters substantially.

Expected Shortfall

Synonym for CVaR. The expected magnitude of loss given that the loss exceeds VaR. Preferred over VaR by modern regulators because it is mathematically coherent and reveals tail-risk severity that VaR alone hides.

ES_α = E[Loss | Loss ≥ VaR_α]

Two portfolios can have identical VaR but very different Expected Shortfall — one has a sharp threshold, the other has fat tails extending well past it. ES tells you how bad the bad days really are, on average.

F

Fama-French 3/5-factor

Eugene Fama and Kenneth French's factor models extending CAPM. The 3-factor model adds size (SMB) and value (HML) to market beta. The 5-factor model further adds profitability (RMW) and investment (CMA). After fitting these factors, residual alpha is small for almost all active funds.

R_p - R_f = α + β_MKT·MKT + β_SMB·SMB + β_HML·HML [+ β_RMW·RMW + β_CMA·CMA] + ε

Fama-French models are the standard tool for separating skill from style. A small-cap value fund that beat the S&P 500 by 3% per year may have zero alpha after Fama-French — its outperformance came entirely from systematic small-cap and value tilts.

See also: Carhart 4-factor Alpha (Jensen's) Beta

G

Gain/Loss Ratio

The ratio of average gain in winning periods to average loss in losing periods. A gain/loss ratio of 2.0 means the portfolio gains twice as much in winning months as it loses in losing months on average.

G/L = mean(R_i | R_i > 0) / |mean(R_i | R_i < 0)|

A high gain/loss ratio with a modest win rate (40–50%) often beats the inverse — it is the trend-follower's profile. The classic 'cut losses short, let winners run' strategy aims for asymmetric gain/loss ratios.

See also: Profit Factor Win Rate Batting Average

H

Hurst Exponent

A measure of long-range autocorrelation in a time series, between 0 and 1. H = 0.5 indicates a random walk; H > 0.5 indicates persistence (trending behavior); H < 0.5 indicates mean reversion. Computed via rescaled-range (R/S) analysis or detrended fluctuation analysis.

log(R/S) ~ H · log(N) (for window size N)

Hurst exponent helps classify a market regime. A trend-following strategy works in H > 0.5 environments; a mean-reversion strategy works in H < 0.5. Equity indices typically run slightly above 0.5 (modest persistence).

See also: Standard Deviation Beta

I

Information Ratio

Excess return over a benchmark divided by the tracking error (the volatility of that excess return). Information ratio measures the consistency of outperformance. An IR of 0.5 is good for an active equity fund; 1.0+ is exceptional and very rare long-term.

IR = (R_p - R_b) / σ(R_p - R_b)

Unlike Sharpe ratio, which uses the risk-free rate, Information Ratio measures excess return above whatever benchmark the manager promised to beat. It is the right metric for evaluating an active manager who claims to add value over an index.

J

Jensen's Alpha

See Alpha (Jensen's). The intercept term from regressing portfolio excess returns on market excess returns. The portion of return not explained by beta exposure to the market.

α = R_p - [R_f + β·(R_m - R_f)]

A persistent positive Jensen's alpha is the strongest evidence of skill. Survey of mutual funds finds fewer than 10% of active funds have statistically significant positive alpha after fees over multi-decade periods.

K

K-Ratio

A measure of return consistency, calculated by regressing the cumulative log-equity curve on time and dividing the slope by the standard error of the slope, scaled by the square root of the number of observations. Higher K-ratio means a smoother upward equity curve.

K = slope · sqrt(n) / std_error(slope)

K-ratio is preferred by some quant managers because it directly rewards smooth compounding rather than absolute return. A trader with high Sharpe and irregular wins can have a lower K-ratio than a trader with modest returns but a tightly straight equity curve.

See also: Sharpe Ratio Hurst Exponent

Kurtosis

A measure of the 'fat-tailedness' of a return distribution. Normal distributions have kurtosis = 3 (or 'excess kurtosis' = 0). Equity returns typically have excess kurtosis of 3–10, meaning extreme moves happen far more often than a normal distribution would predict.

Kurt = E[(R - μ)^4] / σ^4

Higher kurtosis = more 'black swan' tail risk. The 1987 crash, 2008 collapse, and March 2020 sell-off were all 5+ sigma events under a normal distribution, meaning they should happen roughly once every 10,000+ years. Real markets produce them every decade.

L

Lo-adjusted Sharpe

Andrew Lo's 2002 correction to the standard Sharpe ratio that accounts for serial autocorrelation in returns. Hedge fund returns often exhibit positive autocorrelation due to stale pricing of illiquid assets, which artificially inflates Sharpe ratio.

Sharpe_Lo = Sharpe / sqrt( 1 + 2·Σ(1-k/q)·ρ_k )

A hedge fund reporting Sharpe 2.0 with smooth monthly returns might have Lo-adjusted Sharpe closer to 1.2 once serial correlation is removed. The Lo adjustment was made famous by its application to Madoff's books, which showed implausibly smooth returns inconsistent with any real strategy.

M

Maximum Drawdown

The largest peak-to-trough decline a portfolio experienced over its history. A portfolio that hit $100k, fell to $55k, then recovered has a maximum drawdown of -45%, regardless of subsequent recovery.

MaxDD = min over t of [V_t / max(V_s for s ≤ t) - 1]

Max drawdown is the single most important psychological risk metric. The S&P 500's max drawdown was -54% in 2007–2009; -49% in the dot-com crash; -34% in March 2020. Investors typically capitulate (sell) somewhere around -20% to -30%, locking in the loss permanently.

Modigliani-squared (M²)

Franco Modigliani's 1997 measure that converts Sharpe ratio into a directly comparable percentage return. M² rescales a portfolio's return to match the volatility of a benchmark, then subtracts the benchmark's actual return.

M² = Sharpe · σ_benchmark + R_f

Sharpe ratio is unitless, which makes it hard to interpret intuitively ('is 0.8 a lot?'). M² answers in dollars: if you levered or de-levered this portfolio to match the S&P 500's volatility, what return would it have produced? A direct apples-to-apples comparison.

See also: Sharpe Ratio Lo-adjusted Sharpe

Money-Weighted Return

A return that weights each sub-period by the amount of money invested. Equivalent to XIRR. Reflects the actual dollar-experience of an investor making contributions and withdrawals over time, not just price movement of a static $1 invested at start.

0 = Σ CF_i / (1 + MWRR)^(t_i / 365)

Money-weighted return is what you actually earned. Time-weighted return is what the asset itself earned. They diverge whenever you add or withdraw money, especially if your additions/withdrawals were poorly timed.

P

Probabilistic Sharpe Ratio (PSR)

Marcos López de Prado's 2012 extension of Sharpe ratio that returns the probability that the true (population) Sharpe exceeds a benchmark, given the observed sample, accounting for sample size, skew, and kurtosis. PSR = 95% means there is a 95% chance the strategy's true Sharpe exceeds the benchmark.

PSR(SR*) = Φ( (SR_obs - SR*) · sqrt(n-1) / sqrt(1 - γ_3·SR_obs + ((γ_4-1)/4)·SR_obs²) )

Sharpe ratios are noisy at small sample sizes. A 1-year backtest showing Sharpe 2.0 may have PSR(>0) of only 80% — meaning there's a 20% chance the strategy is actually unprofitable. PSR forces you to confront how much your data actually proves.

Profit Factor

The ratio of gross profits to gross losses across all trades or periods. A profit factor of 2.0 means the portfolio earned $2 in winning trades for every $1 it lost in losing trades. Below 1.0 means losses exceeded gains overall.

PF = Σ R_i (where R_i > 0) / |Σ R_i (where R_i < 0)|

Profit factor is widely used in trading-system evaluation. Profitable systems typically run between 1.3 and 2.5; values above 3.0 in a backtest often indicate overfitting and rarely survive live trading.

See also: Gain/Loss Ratio Win Rate Sharpe Ratio

R

R-Squared

The fraction of a portfolio's return variance explained by the benchmark's return variance, between 0 and 1. R² = 1.0 means the portfolio moves in lock-step with the benchmark; R² = 0 means no linear relationship at all.

R² = 1 - SS_residual / SS_total

R² helps interpret beta and alpha. A portfolio with R² of 0.05 vs. the S&P 500 has uncorrelated returns — its beta and alpha numbers are essentially meaningless against that benchmark. A portfolio with R² of 0.99 is effectively a leveraged or de-leveraged S&P 500 — there is no stock-picking happening. Foliolytic's 'closet indexer' badge fires when R² > 0.95 with low active share.

See also: Beta Alpha (Jensen's) Tracking Error

Real Return

Nominal return minus inflation. A portfolio that returned 7% in a year CPI rose 3% had a real return of about 4%. Real return is the only return that grows your purchasing power.

R_real ≈ R_nominal - π (or exact: (1+R_nom)/(1+π) - 1)

Over long horizons, inflation matters more than most retail investors realize. A 6% nominal return in 4% inflation is a 2% real return — half what it appears to be. Foliolytic computes real returns using actual monthly CPI data going back to 1947.

Recovery Factor

Total return divided by absolute value of maximum drawdown. A recovery factor of 5.0 means the portfolio earned 5x its worst drawdown in total return.

Recovery Factor = Total Return / |Max Drawdown|

Recovery factor lets you compare strategies with very different risk levels on a common scale. Two strategies with similar Sharpe ratios but very different drawdown profiles will have very different recovery factors — and the higher one is generally easier to hold through bad periods.

See also: Calmar Ratio Maximum Drawdown

Risk-free Rate

The yield on a default-free, short-duration government security — typically the 3-month U.S. Treasury bill in U.S. analysis. Used as the baseline return investors could earn without taking risk, against which all risky returns are compared.

Foliolytic uses actual daily 3-month T-bill yields from FRED, not a fixed 2% or 3% guess. This matters substantially in 2022–2025 environments when T-bill yields exceeded 5% — a 'high-return' portfolio earning 6% has almost no excess return over the riskless alternative.

See also: Sharpe Ratio Excess Return Real Return

S

Sharpe Ratio

The most widely used measure of risk-adjusted return. Excess return per unit of total volatility. Developed by Nobel laureate William F. Sharpe in 1966.

Sharpe = (R_p - R_f) / σ_p

Sharpe penalizes upside and downside volatility equally, which some critics dislike. But its simplicity and ubiquity make it the default 'how good is this' metric. A long-term Sharpe of 0.5 is roughly average for a diversified equity portfolio; 1.0 is excellent; sustained 2.0+ over decades is extraordinary.

Skewness

A measure of the asymmetry of a return distribution. Positive skew means a right tail (occasional large gains, frequent small losses); negative skew means a left tail (occasional large losses, frequent small gains). Equity returns typically have negative skew — crashes are sharper than rallies.

Skew = E[(R - μ)^3] / σ^3

Selling out-of-the-money puts gives positive skew (you collect small premiums and occasionally pay big). Selling out-of-the-money calls (covered calls) gives negative skew. Most popular 'income' strategies are mathematically picking up nickels in front of a steamroller — high win rate, very negative skew.

See also: Kurtosis Standard Deviation

Sortino Ratio

Excess return divided by downside deviation only. Identical to Sharpe except it ignores upside volatility. Created by Frank Sortino in the 1980s as a fix for what he considered a flaw in Sharpe ratio.

Sortino = (R_p - T) / Downside Deviation

Sortino is generally higher than Sharpe for any portfolio with positive skew, and lower for portfolios with negative skew. For investments where upside is desired (most risky assets), Sortino is the more honest measure.

Standard Deviation

The square root of the variance of returns — the canonical measure of dispersion around the mean. Used as a proxy for total risk in Modern Portfolio Theory.

σ = sqrt( E[(R - μ)²] )

Standard deviation is intuitive and easy to compute but is a poor measure of risk for non-normal distributions. Two portfolios with identical 15% annualized standard deviation can have wildly different real-world risk if one has fat tails or negative skew.

Sterling Ratio

Annualized return divided by the average of the worst N drawdowns (typically the worst 3 over a 36-month period), minus a fixed adjustment. A more drawdown-sensitive cousin of the Calmar ratio.

Sterling = Annual Return / (mean of N worst drawdowns - 10%)

Sterling ratio penalizes a series of medium drawdowns more harshly than Calmar does — Calmar only cares about the single worst. For investors who stomach drawdowns poorly, Sterling is often the more relevant evaluation lens.

See also: Calmar Ratio Maximum Drawdown

T

TWR (Time-Weighted Return)

A return calculation that removes the distorting effect of cash flows by computing returns for each sub-period between flows and chain-linking them geometrically. The standard for evaluating fund manager skill — measures the asset's return, not the investor's experience.

TWR = Π_i (1 + R_i) - 1

Mutual funds, ETFs, and managed accounts all report TWR because it isolates the manager's contribution from investor cash-flow timing. If you want to know how a fund's strategy performed, TWR is the right number. If you want to know what you actually earned, use XIRR (money-weighted).

Tracking Error

The standard deviation of the difference between a portfolio's returns and its benchmark's returns. Measures how tightly a portfolio shadows its benchmark — a tracking error of 1% means the portfolio's return tends to be within ±1% per year of the benchmark, while 10% means the portfolio frequently deviates substantially.

TE = σ(R_p - R_b)

Index funds aim for tracking error near zero. Active funds typically run 3–8% tracking error. A fund claiming to be active but with sub-1% tracking error is closet indexing — charging active fees for passive performance.

See also: Information Ratio Active Return Beta

Treynor Ratio

Excess return divided by beta, instead of standard deviation. Measures how much excess return a portfolio earned per unit of systematic (market) risk, ignoring firm-specific (diversifiable) risk.

Treynor = (R_p - R_f) / β

Treynor is useful when comparing well-diversified portfolios where idiosyncratic risk has been diversified away. For a single stock or concentrated portfolio with high firm-specific risk, Sharpe is the more appropriate metric.

U

Ulcer Index

Peter Martin's drawdown-based volatility measure: the root-mean-square of percentage drawdowns from running maximums over a window. Unlike maximum drawdown (which captures only the worst), Ulcer Index captures the duration and severity of all drawdowns.

UI = sqrt( (1/n) · Σ DD_i² )

Ulcer Index is the Martin Ratio's denominator and a core metric in technical analysis. A portfolio that spends years underwater has a high Ulcer Index even if its single worst drawdown wasn't catastrophic — a profile that is psychologically miserable to live through.

See also: Maximum Drawdown Drawdown Calmar Ratio

V

Value at Risk (VaR)

The maximum loss expected over a given time horizon at a given confidence level, under normal market conditions. A 1-day 95% VaR of -$3,000 means there is a 95% chance daily losses will be no worse than $3,000 (and a 5% chance they will be worse).

P(Loss > VaR_α) = 1 - α

VaR is the dominant regulatory risk measure (Basel) but has well-known weaknesses: it doesn't tell you how bad the bad days are, only their threshold. CVaR (Expected Shortfall) addresses this by averaging losses beyond the threshold.

Volatility

The annualized standard deviation of returns. Often used interchangeably with standard deviation, though 'volatility' technically refers to the annualized version while 'standard deviation' is the raw period figure.

Volatility_annual = σ_daily · sqrt(252)

Equity index volatility is typically 12–20% per year. Single stocks are usually 25–60%. Crypto runs 60–120% on majors and higher on alts. Bond and cash-like assets run 0–8%. Volatility is the most-used, least-loved risk metric — easy to compute, doesn't capture tail risk.

W

Win Rate

The fraction of trades or periods that were profitable. A 60% win rate means 60 of every 100 trades made money. Closely related to batting average (which compares to a benchmark rather than zero).

Win Rate = (winning periods) / (total periods)

Win rate alone is misleading. A strategy with 90% win rate that gives back 12 months of small gains in one bad month is not a good strategy. Always pair win rate with gain/loss ratio or profit factor to see the full picture.

X

XIRR

Extended Internal Rate of Return — the IRR for irregular cash flows. The discount rate that makes the net present value of all dated cash flows equal zero. Standard money-weighted return measure for portfolios with contributions and withdrawals on arbitrary dates.

0 = Σ CF_i / (1 + XIRR)^( (d_i - d_0) / 365 )

XIRR is the most honest 'what did I actually earn' metric for any portfolio with non-zero cash flows. It is more meaningful than CAGR for investors making periodic contributions because it weighs each contribution by how long it has been invested. Foliolytic computes XIRR using Newton-Raphson with a robust fallback to bisection.

Y

Yield to Maturity

The total annualized return expected if a bond is held to maturity, given current price, coupon, face value, and time remaining. The IRR of the bond's full cash flow stream from purchase to redemption.

Price = Σ Coupon_i / (1+YTM)^t_i + Face / (1+YTM)^N

YTM is the canonical yield measure for bonds. It assumes the investor holds to maturity and reinvests coupons at the YTM rate — both rarely fully true in practice. For floating-rate or callable bonds, yield-to-worst (YTW) is more conservative and more honest.

See also: Risk-free Rate Real Return

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