Risk vs Return Calculator
Investing & ReturnsSharpe, Sortino, beta and alpha.
Sharpe ratio: 0.52
Returns & assumptions
Enter past returns separated by commas — e.g. 12, -8, 15, 5, -3, 20.
A market/benchmark series of the same length unlocks beta and alpha.
Comparison portfolios
Asset weighting (two-asset blend)
Risk tolerance score
Risk vs return
Each portfolio plotted by its risk (horizontal) and return (vertical). Points above and to the left of the dashed risk-free line earn more for less risk.
- Yours9.1% · 9.9%
- Conservative5.0% · 6.0%
- Balanced7.5% · 11.0%
- Aggressive10.0% · 17.0%
- Blend6.6% · 10.1%
Return comparison
Expected return of each portfolio.
- Yours9.1%
- Conservative5.0%
- Balanced7.5%
- Aggressive10.0%
- Blend6.6%
Volatility comparison
How much each portfolio's return swings around its average.
- Yours9.9%
- Conservative6.0%
- Balanced11.0%
- Aggressive17.0%
- Blend10.1%
Sharpe ratio comparison
Risk-adjusted return of each portfolio — taller is better.
- Yours0.52
- Conservative0.17
- Balanced0.32
- Aggressive0.35
- Blend0.26
Scenario risk
Volatility of the conservative, balanced and aggressive profiles.
- Conservative6.0%
- Balanced11.0%
- Aggressive17.0%
Return distribution
How often returns of each size occurred, with a normal curve fitted to the mean and volatility. Loss buckets are shaded.
Drawdown (underwater)
Depth below the running peak over time — the deepest point is the maximum drawdown.
How the Sharpe ratio is built
From your return series, step by step:
- Annualized average return9.13%
- Risk-free rate− 4.00%
- Excess return5.13%
- Volatility÷ 9.93%
- Sharpe ratio0.52
Return metrics
| Expected return | 9.13% |
|---|---|
| Excess return | 5.13% |
| Sharpe ratio | 0.52 |
| Sortino ratio | 1.08 |
| Treynor ratio | 4.07 |
| Alpha (Jensen's) | 0.40% |
| M² (risk-adjusted return) | 8.07% |
| Reward-to-risk | 0.92 |
Risk metrics
| Volatility | 9.93% |
|---|---|
| Variance | 98.70 |
| Downside deviation | 4.74% |
| Maximum drawdown | 8.00% |
| Beta | 1.26 |
| Value at risk (95%)· parametric | 7.22% |
| Value at risk (99%)· parametric | 13.99% |
| Probability of a loss· parametric | 17.9% |
Portfolio comparison
| Portfolio | Return | Risk | Sharpe ratio | Reward-to-risk |
|---|---|---|---|---|
| Your portfolio | 9.1% | 9.9% | 0.52 | 0.92 |
| Conservative | 5.0% | 6.0% | 0.17 | 0.83 |
| Balanced | 7.5% | 11.0% | 0.32 | 0.68 |
| Aggressive | 10.0% | 17.0% | 0.35 | 0.59 |
| Asset blend | 6.6% | 10.1% | 0.26 | 0.65 |
Scenario comparison
| Scenario | Return | Risk | Excess return | Sharpe ratio |
|---|---|---|---|---|
| Conservative | 5.0% | 6.0% | 1.0% | 0.17 |
| Balanced | 7.5% | 11.0% | 3.5% | 0.32 |
| Aggressive | 10.0% | 17.0% | 6.0% | 0.35 |
Risk tolerance score
| Volatility component | 35 / 100 |
|---|---|
| Drawdown component | 16 / 100 |
| Downside component | 26 / 100 |
| Total risk score | 27 / 100 |
| Risk band | Conservative |
Asset weighting
Blend two assets and see how diversification lowers risk below the weighted-average volatility.
| Asset | Weight | Return | Risk |
|---|---|---|---|
| Asset 1 | 60% | 9.0% | 16.0% |
| Asset 2 | 40% | 3.0% | 5.0% |
| Asset blend | 100% | 6.6% | 10.10% |
| Weighted-average volatility | 11.60% | ||
| Diversification benefit | 1.50% | ||
Drawdown summary
| Maximum drawdown | 8.00% |
|---|---|
| Peak value | 19,510 |
| Trough value | 13,104 |
| Final value | 19,510 |
| Best period | 21.0% |
| Worst period | -8.0% |
| Positive periods | 75% |
Formulas
The core risk-adjusted performance measures this calculator uses:
Sharpe = (Rp − Rf) ÷ σExcess return over the risk-free rate, divided by total volatility (standard deviation).
Sortino = (Rp − MAR) ÷ σdLike the Sharpe ratio, but divided by downside deviation — penalizing only returns below your target (MAR).
β = Cov(Rp, Rm) ÷ Var(Rm)Covariance of the portfolio with the benchmark, divided by the benchmark's variance — its sensitivity to the market.
α = Rp − [Rf + β(Rm − Rf)]Actual return minus the return CAPM predicts for the portfolio's beta — the value added beyond market risk.
Worked example
Suppose a portfolio averages 9% a year with 14% volatility while the risk-free rate is 4%. Its excess return is 5%, so its Sharpe ratio is 5 ÷ 14 ≈ 0.36 — about a third of a unit of return for each unit of risk. A second portfolio earning 11% with 24% volatility looks better on return alone, but its Sharpe ratio of (11 − 4) ÷ 24 ≈ 0.29 is lower: it pays less per unit of risk. The Sharpe ratio is what lets you compare them fairly.
With your numbers
Your portfolio averages 9.13% a year with 9.93% volatility. Against a 4.00% risk-free rate that is 5.13% of excess return — a Sharpe ratio of 0.52. Its deepest peak-to-trough fall along the way was 8.00%.
Key terms
- Expected return
- The average return you anticipate — here the arithmetic mean of your return series, annualized.
- Volatility (standard deviation)
- How much returns swing around their average. Higher volatility means a wider, less predictable range of outcomes.
- Sharpe ratio
- Excess return over the risk-free rate per unit of total volatility — the standard measure of risk-adjusted return.
- Sortino ratio
- A Sharpe ratio that counts only downside volatility, so it doesn't penalize large upside swings.
- Beta
- How strongly the portfolio moves with its benchmark. Beta 1 matches the market; above 1 amplifies it, below 1 dampens it.
- Alpha
- Return earned above (or below) what the portfolio's beta and the market justify — a gauge of skill or edge.
- Maximum drawdown
- The largest fall from a peak to a later trough — the worst loss an investor holding from the high would have endured.
- Diversification
- Combining assets that don't move in lockstep, which lowers portfolio volatility below the average of the parts.
Know what this estimate is based on
- Jurisdiction
- General mathematical model
- Scope and limitations
- Scenario model, not a forecast. Returns, volatility, inflation, fees, and taxes are assumptions and actual investment outcomes can be lower or negative.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Enter your portfolio's past returns as a comma-separated list — for example 13, -2, 18, 9, -8, 21, 7, 15 — and choose whether they are annual, quarterly, monthly or daily so the calculator can annualize them correctly.
- 02
Optionally paste a benchmark or market return series of the same length to unlock beta, alpha and the Treynor ratio, then set the risk-free rate and your target return (MAR) used for the downside metrics.
- 03
Read the risk-adjusted results — Sharpe and Sortino ratios, volatility, beta, alpha, maximum drawdown, value-at-risk and a 0–100 risk score — and study the risk-return scatter, the return distribution and the drawdown chart.
- 04
Tune the conservative, balanced and aggressive comparison portfolios and the two-asset blend to see them ranked side by side, then save scenarios or copy a share link that reopens the exact analysis.
Formula
Annualized mean return = average periodic return × periods per year. Annualized volatility = sample standard deviation × √(periods per year). Sharpe ratio = (annual return − risk-free rate) ÷ annual volatility. Sortino uses downside deviation instead of total volatility. For two assets, variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ. Beta = covariance(portfolio, benchmark) ÷ benchmark variance; alpha is the return left after the beta-adjusted benchmark return.
Example
A portfolio returning 8% with 12% volatility when the risk-free rate is 2% has a Sharpe ratio of (8% − 2%) ÷ 12% = 0.50. For a 60/40 blend of assets returning 8% and 5%, the expected return is 6.8%; its volatility also depends on both volatilities and their correlation.
Definitions
- Volatility
- Annualized sample standard deviation of the return series.
- Sharpe ratio
- Excess return above the risk-free rate per unit of total volatility.
- Sortino ratio
- Excess return above a target per unit of downside deviation.
- Beta
- Sensitivity of portfolio returns to benchmark returns, estimated from covariance and benchmark variance.
- Maximum drawdown
- The largest percentage fall from a running portfolio peak to a later trough.
Good to know
The trade-off at the heart of investing
Every investment decision is a negotiation between two forces that pull in opposite directions: return, the reward you hope to earn, and risk, the uncertainty you must accept to earn it. The iron rule of markets is that you cannot reliably raise expected return without also raising risk — if a higher return were available for the same risk, buyers would crowd in until the bargain disappeared. That is why a savings account, a bond fund and a basket of growth stocks sit on a rising line: each step up in expected return comes with a wider range of possible outcomes. The whole purpose of this calculator is to put a number on both sides of that bargain at once, so you stop judging an investment by its return alone. A portfolio that earned 9.13% a year, like the default series here, sounds impressive until you learn it did so with 9.93% volatility and an 8% peak-to-trough drawdown; a quieter holding that earned 7% with half the volatility may have been the better deal for the risk taken. Return tells you how far you travelled; risk tells you how rough the road was. Reading them together — through ratios that divide reward by risk — is what separates disciplined investing from chasing the biggest headline number, and it is the single habit that most improves long-run results.
Volatility, variance and standard deviation
Risk has many faces, but the workhorse measure is volatility: how widely your returns scatter around their average. The calculator quantifies it with the standard deviation of your return series, using the sample formula that divides by one less than the number of observations — the convention statisticians use when estimating future risk from a limited history. Variance is simply that same dispersion before taking the square root, expressed in awkward squared-percent units, which is why standard deviation, in plain percentage points, is the figure usually quoted. On the default series the volatility works out to 9.93% a year. Crucially, volatility scales with the square root of time, not linearly: if you feed the tool monthly returns it annualizes the volatility by multiplying by the square root of twelve, while the average return is annualized by multiplying by twelve. That asymmetry is why a fund's monthly numbers always look calmer than its annual ones. Standard deviation is intuitive — about two-thirds of returns land within one of it of the average in a normal world, and roughly nineteen in twenty within two — but it has a blind spot: it treats a thrilling 20% gain as exactly as 'risky' as a painful 20% loss. That even-handedness is mathematically tidy but emotionally wrong, and it is the reason the downside-focused measures that follow exist.
The Sharpe ratio: reward for the risk you take
The Sharpe ratio, devised by Nobel laureate William Sharpe, is the most widely used measure of risk-adjusted return, and it answers a deceptively simple question: how much extra return did you earn for each unit of volatility you endured? It takes your return, subtracts the risk-free rate — what you could have earned in a short-term government bond with no risk — and divides the result by your volatility. The subtraction matters, because only the return above the risk-free rate is genuine compensation for taking risk; the rest you could have had for free. On the default series, a 9.13% return less a 4% risk-free rate leaves 5.13% of excess return, which divided by 9.93% volatility gives a Sharpe ratio of 0.52. As a rough guide, a Sharpe ratio below 1.0 is unremarkable, around 1.0 is solid, above 2.0 is excellent, and a negative figure means you earned less than the risk-free rate while taking on risk — the worst of both worlds. The ratio's great strength is that it lets you compare wildly different investments on a level field: a calm bond fund and a volatile tech stock can be ranked by how efficiently each turns risk into reward. Its weakness is that it counts upside and downside volatility alike, which the next measure sets out to fix.
The Sortino ratio and downside risk
Investors do not lie awake worrying about their portfolio going up too much, yet the Sharpe ratio treats upside and downside swings as equally bad. The Sortino ratio corrects this by replacing total volatility with downside deviation — a measure that looks only at returns falling below a target you choose, called the minimum acceptable return or MAR. Returns above the target contribute nothing to the risk figure, while shortfalls below it are squared, averaged over every period, and rooted, so only the painful side of volatility counts. Because it ignores the upside, downside deviation is smaller than total volatility for most portfolios, which makes the Sortino ratio larger than the Sharpe ratio. On the default series, with the target (MAR) set to the 4% risk-free rate, the downside deviation is just 4.74% against 9.93% total volatility, so the Sortino ratio climbs to 1.08 — more than double the 0.52 Sharpe ratio. Lower the target below the risk-free rate and fewer returns fall short of it, so downside deviation shrinks and the ratio rises; raise the target and more returns count as shortfalls, so the ratio falls. The Sortino ratio is especially honest for asymmetric strategies — those that grind out steady gains punctuated by occasional sharp losses — where the Sharpe ratio would unfairly punish the very upside volatility you were hoping for. Use it whenever you care about the risk of falling short of a goal rather than the risk of simply being unpredictable.
Beta and alpha: market risk versus genuine skill
Some of your risk comes from the market as a whole, and some is specific to your choices; beta and alpha separate the two. Beta, calculated as the covariance of your returns with a benchmark divided by the benchmark's variance, measures how much your portfolio amplifies or dampens market moves. A beta of 1.0 means you move in step with the market; the default series, compared against its benchmark, has a beta of 1.26, meaning it has historically swung about a quarter more than the market in both directions. Alpha then asks the deeper question: given that market exposure, did you earn more or less than you should have? The Capital Asset Pricing Model predicts a fair return for any beta — the risk-free rate plus beta times the market's risk premium — and Jensen's alpha is your actual return minus that prediction. The default series shows an alpha of about +0.40%, a small but positive edge: it beat what its market risk alone would justify. Positive alpha is the holy grail, the signature of genuine skill or a real advantage; negative alpha means you bore market risk and were short-changed for it. Beware the naive version of alpha — simply beating the index — which flatters any portfolio that took on extra risk. True alpha, the kind this calculator reports, only credits you for returns you earned beyond the reward your risk-taking already entitled you to.
Maximum drawdown: the pain of the path
Averages and standard deviations describe the scatter of returns, but they say nothing about the order in which those returns arrived, and order is what investors actually live through. Maximum drawdown captures that lived experience: it is the largest fall from a previous peak to a later trough along your portfolio's value path. The calculator compounds your returns into a running balance, marks every new high-water mark, and measures the deepest decline from any peak before a new high was reached. On the default series that worst peak-to-trough fall is 8% — modest, because the series never strung together several bad years. The figure matters because it is the number that breaks investors' nerve. A portfolio can have a wonderful long-run return and a fine Sharpe ratio yet inflict a 50% drawdown along the way, and most people sell near the bottom of a fall that deep, locking in the loss and missing the recovery. Two portfolios with identical volatility can have very different drawdowns depending on whether their losses clustered together or were spread out, which is why drawdown is a distinct and essential risk measure rather than a restatement of volatility. The underwater chart on this page shows the whole history of declines, not just the deepest, so you can see how often and how long the portfolio spent below its previous highs — a far better test of whether you could actually have held on than any single summary number.
Diversification: the closest thing to a free lunch
Diversification is the rare strategy that can lower your risk without lowering your expected return, which is why economists call it the only free lunch in investing. The mechanism is correlation: when two assets do not move in perfect lockstep, their ups and downs partly cancel, so a portfolio of both is steadier than either alone. Expected return blends linearly — a 60/40 mix of assets returning 9% and 3% expects 6.6% — but risk does not, because the portfolio's variance depends on how the assets co-move. The asset-weighting panel on this page makes the effect concrete. If the two assets were perfectly correlated you would bear the weighted-average of their volatilities, which for the default blend is 11.6%; in reality, with a correlation below one, the blended volatility falls to about 10.1%, a saving of roughly 1.5 percentage points earned for nothing but holding both. The lower the correlation, the larger the benefit, and assets that are negatively correlated can reduce risk dramatically. The catch worth remembering is that correlations are not fixed: in a crisis, assets that normally move independently often fall together, so the diversification you counted on can shrink at the very moment you need it most. Genuine diversification means combining things driven by different forces — stocks and high-quality bonds, different regions, different return engines — not simply owning many holdings that all dance to the same tune.
Risk tolerance and matching a portfolio to it
All the ratios in the world are useless if a portfolio's risk is more than you can stomach, because the investor who panics and sells in a downturn converts a temporary paper loss into a permanent real one. Risk tolerance is your genuine capacity to hold through volatility and drawdown without abandoning the plan, and it has two parts: the financial ability to absorb losses given your time horizon and cash needs, and the emotional willingness to watch your balance fall without flinching. This calculator distils a portfolio's risk into a single 0–100 score that blends its volatility, its maximum drawdown and its downside deviation, then sorts it into a band from very conservative to very aggressive. The default series scores 27, placing it in the conservative range — a portfolio whose worst year lost 8% and whose deepest drawdown was 8% genuinely is on the calmer end. A volatile growth portfolio with a 22% volatility and a 25% drawdown might score in the high sixties, firmly aggressive. The point of the score is not to chase a high number or a low one, but to find the match between the risk a portfolio takes and the risk you can actually live with over your horizon. A younger investor saving for a distant goal can usually accept a higher band, because time lets drawdowns recover; someone drawing down savings soon should favour a lower band, because they cannot wait out a deep fall.
Reading the numbers together: a worked perspective
No single statistic tells the whole story, and the skill this calculator is meant to build is reading them as a set. Take the default portfolio. Its 9.13% return looks strong, and the scatter plot puts it well above the risk-free line, so it was genuinely rewarded for the risk it took. The 0.52 Sharpe ratio tempers that enthusiasm: the reward per unit of total volatility was only middling, the kind of efficiency you would expect from a concentrated rather than a broadly diversified holding. The 1.08 Sortino ratio rescues the picture somewhat, revealing that much of the volatility was upside the Sharpe ratio unfairly penalised. The beta of 1.26 explains where the risk came from — this portfolio rode the market with extra leverage — while the small positive alpha says it did so slightly better than that market exposure alone would justify. Finally the 8% maximum drawdown confirms that, for all its swings, the portfolio never put the investor through a harrowing fall. Assembled, these numbers describe a market-amplifying portfolio with a modest edge, acceptable efficiency, and tolerable worst-case pain — a coherent profile no single figure could have conveyed. Comparing that full profile against the conservative, balanced and aggressive reference portfolios, plotted on the same chart, is how you decide whether the trade-off it strikes is the one you actually want.
Common mistakes when judging risk and return
The errors investors make with risk are remarkably consistent, and avoiding them is most of the battle. The first is chasing return in isolation, picking the fund with the best recent headline number without asking how much risk produced it — the surest route to buying high and selling low. The second is mistaking volatility for permanent loss: a portfolio that swings does not lose money unless you sell while it is down, so volatility is dangerous mainly to those who cannot hold through it. The third is ignoring drawdown, trusting a smooth long-run average while forgetting that the path there included falls deep enough to shake you out. The fourth is misreading past performance as a forecast; every measure here is computed from history, and history sets expectations rather than guarantees, especially over the short windows most people analyse. The fifth is over-trusting the parametric value-at-risk and normal-curve figures, which assume returns behave like a tidy bell curve when real markets have fat tails — crashes happen far more often than a normal distribution predicts. The sixth is false diversification, owning a dozen holdings that all rise and fall together and mistaking quantity for genuine risk reduction. And the seventh is a mismatch between the portfolio's risk band and your own tolerance, which feels fine in a rising market and catastrophic in a falling one. Treat every figure on this page as a disciplined guide to a sensible range of outcomes, not a promise — diversify across genuinely different return drivers, size your risk to what you can hold through, and let the ratios, not the headlines, drive your decisions.
Frequently asked questions
What is the difference between the Sharpe and Sortino ratios?
Both divide your excess return by a measure of risk, but they define risk differently. The Sharpe ratio uses total volatility — the standard deviation of every return, up and down alike — so it penalizes big gains as much as big losses. The Sortino ratio uses only downside deviation, the spread of returns that fall below your target, so it ignores upside swings and focuses on the volatility that actually hurts. Because most portfolios have some upside volatility, the Sortino ratio is usually the higher of the two. On the calculator's default series the Sharpe ratio is 0.52 while the Sortino ratio is 1.08 — the same returns look roughly twice as good once you stop counting the upside as 'risk'.
Why is my Sharpe ratio below 1.0 even though the portfolio made money?
A Sharpe ratio measures reward per unit of risk, not whether you made money. The default series averages 9.13% a year, comfortably positive, but it does so with 9.93% volatility against a 4% risk-free rate, so each unit of risk only buys about 0.52 units of excess return. A Sharpe ratio around 0.5 is typical for a single stock or a concentrated portfolio; broad, well-diversified portfolios often land between 0.5 and 1.0, and anything sustainably above 1.0 is genuinely good. A low Sharpe ratio is a prompt to ask whether you are being paid enough for the bumps along the way — not a sign the investment lost money.
What does beta of 1.26 and a positive alpha actually mean?
Beta measures how much your portfolio moves with its benchmark. A beta of 1.26 means that when the benchmark rises or falls 10%, your portfolio has historically moved about 12.6% in the same direction — more volatile than the market, amplifying both gains and losses. Alpha is what is left over after accounting for that market exposure: the return you earned above what the Capital Asset Pricing Model predicts for a beta of 1.26. The default series shows an alpha of about +0.40%, meaning it modestly beat the return its market risk alone would justify. Positive alpha hints at skill or an edge; negative alpha means you took market risk and were not fully rewarded for it.
How is maximum drawdown different from volatility?
Volatility describes how much returns scatter around their average in any single period; maximum drawdown describes the worst cumulative journey you would have lived through. The calculator compounds your returns into a value path, tracks the running high-water mark, and reports the largest peak-to-trough fall — 8% on the default series. Two portfolios can share the same volatility yet have very different drawdowns, because drawdown depends on the order of returns, not just their spread. Drawdown is the number that tests your nerve: it is the loss you would have had to sit through, from a previous high, before recovering.
Are the value-at-risk and probability-of-loss figures based on my actual returns?
Those two figures are parametric estimates, clearly labelled as such. They assume your returns follow a normal (bell-curve) distribution with the mean and volatility measured from your series, then read off the probability of a losing year and the loss you would not expect to exceed 95% or 99% of the time. Everything else on the page — the mean, volatility, downside deviation, Sharpe, Sortino, beta, alpha and maximum drawdown — is computed directly from your numbers with no distribution assumption. Real returns have fatter tails than a normal curve, so treat the value-at-risk figures as a useful rule of thumb rather than a precise promise.
What does the diversification benefit in the asset-weighting section show?
It shows the risk you save by combining two assets that do not move in perfect lockstep. If you simply averaged the two volatilities by weight you would get the 'weighted-average volatility' — the risk you would bear if the assets were perfectly correlated. The blended portfolio's actual volatility is lower than that whenever the correlation is below 1, and the gap between the two is the diversification benefit. With the default 60/40 blend the weighted-average volatility is 11.6% but the blended volatility is only about 10.1%, a saving of roughly 1.5 percentage points earned purely by holding assets that zig when the other zags. It is often called the only free lunch in investing.