Risk-Adjusted Returns: Sharpe, Sortino and Calmar

By now you can measure how much an investment grew (ROI, CAGR) and how scary the ride was (volatility, drawdown). But those two halves only matter together. A 60% gain on a serene ride is a triumph; the same 60% on a stomach-churning rollercoaster is mostly luck. The metrics in this lesson fuse return and risk into a single number — so you can finally answer the question that actually decides quality: was the return worth the risk?

The question this lesson answers

Was the return worth the risk? → Sharpe ratio, Sortino ratio, Calmar ratio

All three divide return by risk. Sharpe and Sortino differ only in which flavor of volatility lands in the denominator; Calmar swaps in a completely different kind of return and risk — more on that below.

Sharpe Ratio: Return Per Unit of Risk

Before you read — take a guess

Guess before reading: two funds delivered the exact same return. What would make one clearly the better investment?

They're identical — same return, same qualityThe one that took less risk to earn that same returnThe one with the higher share priceThe one with the longer name

Return and risk are only meaningful together. Watch two portfolios finish in the exact same place by completely different roads — same destination, wildly different journey:

Same return, different risk

Steady EddieRollercoaster

	Steady Eddie	Rollercoaster
Total return	+60%	+60%
Volatility (risk)	low	high
Sharpe ratio	1.9	0.4

Both portfolios end at +60%. The calm one earns a far higher Sharpe ratio because it took less risk to get there.

The Sharpe ratio captures this in one number: return earned above a risk-free baseline, divided by volatility.

$\text{Sharpe} = \frac{R_p - R_f}{\sigma_p}$

where $R_p$ is the portfolio return, $R_f$ the risk-free rate (roughly a government T-bill), and $\sigma_p$ the volatility — the standard deviation of returns you met in the risk lesson.

Worked example

A fund returns 12%, the risk-free rate is 2%, and volatility is 15%:

$\text{Sharpe} = \frac{12\% - 2\%}{15\%} = \frac{10}{15} \approx 0.67$

Reading the number

Sharpe ratio	Rough verdict
< 0	You’d have done better in T-bills
0 – 1	Acceptable to mediocre
1 – 2	Good
2 – 3	Very good
> 3	Excellent (or too good to be true)

Why subtract the risk-free rate?

You should only get credit for returns above what risk-free cash would have paid. If T-bills yield 2% and your fund made 2%, your risk earned you nothing — and the numerator correctly collapses to zero.

Which statements about the Sharpe ratio are true? Select all that apply.

It penalizes upside volatility as well as downsideHigher means more return per unit of riskIt ignores risk and just ranks raw returnIt subtracts the risk-free rate before dividing

Sortino Ratio: Punishing Only the Bad Volatility

Before you read — take a guess

Guess: the Sortino ratio differs from Sharpe mainly because it…

Only counts downside volatility, ignoring upside swingsAdds beta to the numeratorRemoves the risk-free rate from the formulaUses drawdown instead of return

The Sharpe ratio has one quirk: it penalizes all volatility, including the upside. But nobody complains about a +20% month. The Sortino ratio fixes this by dividing only by downside deviation — the volatility of returns that fell below your target (often zero or the risk-free rate).

$\text{Sortino} = \frac{R_p - R_f}{\sigma_{\text{downside}}}$

Worked example

Same fund: excess return is 10% (12% − 2%). Suppose its downside deviation is only 8% (because most of its volatility came from good months):

$\text{Sortino} = \frac{10\%}{8\%} = 1.25$

Notice it’s higher than the Sharpe of 0.67 — because we stopped punishing the fund for its pleasant surprises. A big gap between Sortino and Sharpe tells you a fund’s volatility is mostly upside (a nice problem to have).

When to use which

Sharpe — the universal default; good for comparing anything, and what most factsheets quote.
Sortino — better when a strategy has lopsided returns (lots of small wins, the occasional loss), e.g. options-selling or trend-following.

Calmar Ratio: Return Per Unit of Pain

Before you read — take a guess

Guess: the Calmar ratio measures return against…

The worst peak-to-trough drop the fund ever sufferedThe fund's management feeOnly the downside deviation below a targetThe standard deviation of all monthly returns

Sharpe and Sortino both measure risk as wiggle — the standard deviation of returns. The Calmar ratio asks a blunter, more visceral question: for the worst loss you ever had to sit through, how much growth did you get?

$\text{Calmar} = \frac{\text{CAGR}}{\lvert \text{Max Drawdown} \rvert}$

This is where the means part ways. Notice the numerator is CAGR — the compound (geometric) annual growth rate, not the arithmetic average of periodic returns that Sharpe and Sortino use. Compounding experiences the drawdowns, so pairing geometric growth with the worst drawdown keeps the whole ratio grounded in what an investor actually lived through.

Arithmetic vs geometric — the one that trips people up

Sharpe & Sortino put the arithmetic mean of excess returns on top.
Calmar puts CAGR — the geometric mean — on top.

So if you ever heard “one of these uses the geometric mean,” it’s Calmar, not Sortino. Geometric growth is the rate that, compounded each period, reproduces your actual ending wealth; it’s always ≤ the arithmetic mean whenever returns vary.

Worked example

A fund compounds at a CAGR of 12% and, over the same window, its deepest peak-to-trough fall was a max drawdown of 20%:

$\text{Calmar} = \frac{12\%}{20\%} = 0.6$

A Calmar of 0.6 says: for every unit of worst-case pain, you earned 0.6 units of compound growth. Calmar is usually measured over a 3-year window, and a reading above 1.0 is considered strong — your annual growth outran your worst fall.

When to use which

Sharpe — the universal default; penalizes every swing.
Sortino — when upside swings shouldn’t count as “risk.”
Calmar — when the worst-case loss is what would actually scare you out of a position. Popular for hedge funds and trend-following CTAs, where surviving the deepest drawdown matters more than smoothing month-to-month wiggle.

Complete each definition.

Pick the right option for each blank, then check.

The ratio divides excess return by total volatility, while the ratio divides only by deviation, so it rewards strategies whose swings are mostly to the upside.

Putting It Together

Match each term to what it really means.

Pick a term, then click its definition.

Now chunk all three ratios into one picture:

Big picture

Risk-adjusted return ratios

Was the return worth the risk?
- Numerator (shared)
  - Excess return = Rp − Rf
  - Subtracting Rf credits only returns above safe cash
- Sharpe — ÷ total volatility
  - Penalizes every swing, up and down
  - The universal default on factsheets
- Sortino — ÷ downside deviation
  - Penalizes only losing swings
  - Sortino ≫ Sharpe ⇒ volatility is mostly upside
- Calmar — CAGR ÷ max drawdown
  - Numerator is geometric (CAGR), not arithmetic
  - Risk = the worst peak-to-trough fall
  - Above 1.0 over 3 years is strong

All three ask 'was the return worth the risk?' — Sharpe and Sortino share a numerator and differ in the denominator, while Calmar swaps in geometric growth over the worst drawdown.

A mixed recap:

Question 1 of 60 correct

What does the Sharpe ratio actually measure?

The raw return, ignoring how bumpy the ride wasHow much a fund fell from its peakWhether a fund beat its benchmark indexReturn earned above the risk-free rate, per unit of volatility

Check your answer to continue.

Key Takeaways

What to remember

Read return and risk together — a big gain on a brutal ride is luck; a solid return on a calm ride is quality.
Sharpe = excess return ( $R_p - R_f$ ) ÷ total volatility. Higher is better; subtracting the risk-free rate credits only returns above safe cash.
Sortino keeps the same numerator but divides only by downside deviation, so it stops punishing upside swings.
A Sortino much higher than Sharpe means a fund’s volatility is mostly the good kind.
Calmar = CAGR ÷ worst max drawdown — the one ratio with a geometric (compound) numerator, not arithmetic. Above 1.0 over a 3-year window is strong.
The “geometric mean” ratio is Calmar, not Sortino — Sharpe and Sortino both use the arithmetic mean of excess returns.
Use Sharpe as the default; reach for Sortino when returns are lopsided, and Calmar when surviving the worst drawdown is the real concern.