Market risk: volatility, correlation, tail

The classic measures — and the three places where they systematically miss in DeFi.

This lesson has had no expert review. It was written for this platform and against the evidence it cites; nobody has gone through it independently.

Learning objectives

You can tell volatility, drawdown and tail risk apart and apply each where it fits.
You can explain why historical measures understate the stress case.

Check your prior knowledge

Answer these for yourself before reading on. Wherever you hesitate is where this lesson pays off.

What does a standard deviation measure, and what not?
Why is a drawdown something other than volatility?
What happens to correlations in a crash?

Core concept

Fact

Three measures, three questions

Volatility answers: how much does it move in the normal case? Drawdown: how deep did it go from peak to trough? Tail risk: how bad does it get in the rare cases volatility precisely does not describe? The three are not interchangeable. Asking for the maximum loss and receiving a volatility is receiving no answer.

Assumption

Short history, overstated calm

Many DeFi assets have a history of months, not decades. Any measure computed from it describes exactly the period it saw — and that period may have contained no crash. A low sigma over ninety days is therefore not a statement about stability but about ninety days. This platform reports sigma for pool yields; the limit is stated explicitly in the metric catalog.

Risk

Correlation is a different thing under stress

Two positions can run independently for months and fall together in a crash — because the same addresses hold both, the same lending markets collateralize both, or the same liquidity carries both. The measured correlation comes from the state in which that connection is inactive. For portfolio arithmetic that means the historical figure is too low, systematically rather than by chance.

Interpretation

Price impact belongs to market risk

In a deep market the exit price is roughly the displayed one. In a thin market it is a function of your own order size — and under stress every market is thinner. A market risk calculation looking only at price moves and omitting your own price impact understates the realizable loss exactly where it occurs.

Definitions

Volatility in the glossary: A dispersion measure of observed value changes over a period.
Drawdown: The decline from a peak to the subsequent trough.
Tail risk: The risk of rare, large deviations that a normal distribution understates.
Basis risk: The risk that a hedge and the hedged position do not move together.

Model

“How choppy is it normally?” → volatility
“How deep did it once go?” → drawdown
“How bad in the rare case?” → tail view, scenario
“What do I get on exit?” → price impact and depth

Which measure answers which question — The fourth question is asked most often and answered with the fourth number least often.

Formulas

Exit value including price impact

realizable value ≈ position × (1 − price decline) × (1 − price impact)

price decline: market move in the scenario
price impact: discount from your own order size relative to depth

Limit: Both factors are correlated under stress: the same move producing the first reduces depth and so increases the second. The multiplicative form is a lower-bound approximation.

Worked example

Two numbers for the same scenario

Position: USD 2m in a pool with USD 18m TVL
Scenario: market decline of 30 %
Price impact on exit: estimated 6 % — an assumption of more market depth than the constant-product approximation in the model below, which gives about 18 % from the same figures

Pure market arithmetic: USD 2m × 0.70 = USD 1.40m. Including price impact: 1.40m × 0.94 ≈ USD 1.32m.

Around USD 80,000 of difference — for a position making up 11 % of the pool.

Reading: The difference grows disproportionately with the share of the pool. That is why a cap on that share is not a liquidity detail but part of market risk management.

Interactive model

The worked example, with movable figures. Estimate first what happens — then check.

Realizable value at exit

Market decline and price impact act one after the other — and price impact grows with the share of the pool.

Estimate first, then check

Estimate first: by how much does the gap between the pure market calculation and the realizable value grow if the position doubles from USD 2m to 4m — does it double too?

The starting values are the worked example's own figures — change one input at a time.

Position

$0$9M

Market decline

Pool TVL (USD)

Internal share cap

What the model does not show: Price decline and price impact are applied independently here. In a falling market liquidity withdraws, so price impact rises inside the scenario itself — the model holds it constant.

Retrieval

It is stable.It moved little in those 90 days; the figure says nothing about behavior in a crash.Tail risk is low.

Because it omits your own price impact on exit — and depth is smaller precisely under stress.Because it uses the wrong price.Because fees are missing.

Exercise on real data

Read sigma's limitations and record why a pool with a short history necessarily has a sigma that says little.

Sigma in the metric catalog →

Find two markets with a similar APY and distinctly different sigma. State in one sentence what the difference says — and what it does not.

Compare two markets' sigma →

Application

You are to quantify the possible loss on a DeFi position for an investment committee. Which number do you give, and with which two qualifiers?

Related case studies

Institutional reading

Bank: What history length does the internal model require — and does the asset meet it?
Insurance: Which scenario, not which metric, carries the calculation?
Asset management: Does the historical correlation between the positions still hold under stress?