CAGR
How much your portfolio has grown on average each year.
The Compound Annual Growth Rate: the one steady yearly rate that would take your starting value to your ending value over the same period. Ups and downs along the way are smoothed out.
V portfolio value · T length of the period in years
10% means your money grew as if it earned 10% every year, compounded. Being geometric, it accounts for the fact that a 50% loss needs a 100% gain to recover, so it's always at or below the plain average of yearly returns.
CAPM Expected Return
The expected yearly return based on the CAPM model.
The Capital Asset Pricing Model prices risk you can't diversify away. It starts from the risk-free rate and adds the market's premium over it, scaled by how strongly your portfolio follows the market (its beta).
Rf risk-free rate · βp your portfolio's beta · E[Rm] the benchmark's expected return
It's what the market should pay you for the market risk you carry, not a forecast. A return well above it means you're beating the model (positive alpha); well below, the risk isn't being paid for.
Volatility
How much your portfolio value fluctuates in a year.
The annualized standard deviation of daily returns: how widely returns scatter around their average, scaled up to a year.
rt daily return · r̄ their mean · n number of days · N trading days per year
With 20% volatility and roughly normal returns, about two years in three land within ±20% of the average return. It counts upside swings as risk too, and says nothing about how deep a crash can go.
Maximum Drawdown
The biggest drop in your portfolio's value from its highest point.
The deepest fall from a running peak to a later trough, before a new peak was set: the worst loss someone who bought at the top would have sat through.
Vt value on day t · the denominator is the highest value reached so far
−30% means at some point the portfolio was worth 30% less than its previous high. It's the gut-check number: could you hold on through that again? Note that recovering from −30% takes a +43% gain.
Value at Risk
There is a 95% chance that your portfolio won't lose more than this amount in a single day.
Value at Risk at 95% confidence: the daily loss that's only exceeded on the worst 5% of days, read off the distribution of past daily returns.
q0.05(r) the 5th percentile of daily returns
2% means on a typical bad day (about one trading day a month) you'd lose 2% or more. It marks where the tail begins, but not how bad the tail gets; that's what CVaR is for.
Conditional Value at Risk
If losses exceed the VaR, this is the average loss you can expect.
Conditional Value at Risk (Expected Shortfall): the average of the daily returns on the days that were worse than the VaR.
r daily return · q0.05(r) the 5th percentile (the VaR threshold)
It answers “when it's bad, how bad?”. Always at least the VaR; a CVaR far above the VaR means fat tails, where rare days hit much harder than the usual bad day.
Sharpe Ratio
How much return you're getting for the risk you're taking.
Excess return over the risk-free rate, per unit of total volatility. The classic measure of risk-adjusted performance.
Rp annual return · Rf risk-free rate · σp annual volatility
Below 0: cash did better. Around 0.5: what broad stock markets tend to deliver over the long run. Above 1: very good. Above 2: exceptional, and worth double-checking the period isn't cherry-picked.
Sortino Ratio
Similar to Sharpe Ratio, but only considers downside risk.
Like Sharpe, but the denominator is downside deviation: only returns below the target count as risk, so big up-days don't penalize you.
σd annualized downside deviation · τ target daily return · N trading days per year
Read it like Sharpe, but it's usually higher. A Sortino much higher than the Sharpe means the volatility is mostly on the upside, which is the good kind.
Calmar Ratio
The return compared to the biggest loss your portfolio has experienced.
Yearly growth divided by the depth of the worst drawdown: how much you earned for the worst pain you had to endure.
CAGR average yearly return · MDD maximum drawdown
1 means a year's growth would have made up for the worst fall. Above 1 is strong; below 0.5, the drawdowns are large next to the growth. It rests on a single worst episode, so longer histories make it fairer.
Jensen's Alpha
How much your portfolio outperformed the market, adjusted for risk.
Jensen's alpha: your actual return minus what CAPM says you should have earned for your market exposure. The part of the return beta doesn't explain.
Rp portfolio return · Rm benchmark return · Rf risk-free rate · βp beta
+3% means the portfolio beat its risk-matched benchmark by 3% a year. Positive alpha is the edge from your picks; negative means a plain mix of the benchmark and cash would have done better.
Beta
How your portfolio's returns move compared to the market.
The slope of your returns against the benchmark's: how much your portfolio tends to move when the market moves 1%.
rp, rm daily returns of the portfolio and the benchmark
1: moves with the market. 1.5: amplifies it, 15% when the market moves 10%. 0.5: half as much. Near 0: unrelated. Below 0: tends to move the opposite way, a hedge.
Treynor Ratio
The return you're getting for each unit of market risk.
Like Sharpe, but it divides by beta instead of volatility: reward per unit of market risk only, the one risk diversification can't remove.
Rp annual return · Rf risk-free rate · βp beta
Compare it to the benchmark's own excess return (its Treynor, with a beta of 1): above it, you're paid more per unit of market risk. It's only meaningful for well-diversified portfolios, and misleading when beta is near zero or negative.
Omega Ratio
The chance of gains compared to the chance of losses.
The total of all gains above a threshold divided by the total of all losses below it. It uses the whole distribution of returns, not just mean and variance.
rt daily return · τ threshold return
Above 1: gains outweigh losses. 1.2 means €1.20 gained for every €1 lost. Because it sees skew and fat tails, it can rank portfolios differently from Sharpe when returns aren't bell-shaped.
R²
How closely your portfolio's returns match the overall market.
The coefficient of determination: the share of your portfolio's ups and downs explained by the benchmark's. It's the squared correlation between the two.
ρ correlation · rp, rm daily returns of the portfolio and the benchmark
0.9 means 90% of the movement is the market's. High R² makes beta and alpha trustworthy; low R² (below about 0.5) means the portfolio dances to its own tune, and those two say little.
Information Ratio
How consistently your portfolio outperforms the benchmark.
Average outperformance of the benchmark divided by tracking error, the volatility of that outperformance. Sharpe, measured against the benchmark instead of cash.
Rp, Rm annual returns · σ(rp − rm) annualized tracking error
Positive: you beat the benchmark. 0.5 is good, above 1 is rare and excellent. A high ratio means steady outperformance; a low one with the same excess return means it came in a few lucky bursts.
Correlation
How much your assets move together: the average correlation of their daily returns, weighted by allocation. The chart shows a trailing year.
The Pearson correlation of daily returns for every pair of assets, averaged with each pair weighted by both assets' allocations, so the big holdings count most.
wi allocation of asset i · ρij correlation of the daily returns of assets i and j
1: everything moves in lockstep, so diversification does nothing. 0: unrelated moves, which cancel out and cut volatility. Below 0: assets offset each other. Correlations tend to jump toward 1 in crashes, just when you need them low.