Risk Metrics5 分で読めます

Downside Deviation — Measuring Only the Bad Swings

Is it right to count a +10% surge and a -10% plunge in a single day equally as 'risk'? What we truly fear isn't rising but falling. Downside deviation was born from exactly that concern.

The unfairness of standard deviation

The most commonly used metric for measuring risk is standard deviation (volatility). It measures how much the price swings around the average.

But standard deviation has a somewhat unfair aspect. It counts upward jumps (surges) and downward jumps (plunges) equally as 'risk.' From an investor's standpoint, however, a surge is welcome, not something to fear.

For example, an asset that steadily rose +2% each and then one day surged +15% has a large standard deviation. So it shows up as 'high volatility, therefore risky.' But no one actually lost money. Downside deviation is meant to correct this point.

What is downside deviation

Downside deviation is a volatility calculated by picking out only the returns that fell 'below' a predefined target return (MAR, Minimum Acceptable Return).

Days that came out better than the target (the upside) are treated as 0 and ignored entirely. Only days that fell short of the target (the downside) are gathered, and it measures how large those shortfalls were on average. In a word, it's 'a standard deviation that measures only the bad swings.'

Here the MAR is up to the investor to set. Commonly, people plug in 0% (the criterion of whether there's a principal loss), the risk-free rate (the standard that you should at least earn as much as a deposit or government bond), or a personal target like 'I need to make at least 5% per year.'

The downside deviation value changes depending on what you set the MAR to. So when looking at downside deviation, you should also check 'what percent the standard was set at.'

How to calculate it (seeing it in numbers)

The formula looks like this.

Downside deviation = √( the average of (target shortfall)² over the whole period )

The calculation order is as follows. ① Subtract the target return (MAR) from each period's return. ② If the value is greater than 0 (target achieved), change it to 0. ③ Square only the values that fell short of the target (negatives). ④ Sum the squared values, divide by the number of periods, then take the square root.

For example, if you set MAR to 0% and the monthly returns were +3%, -4%, +2%, -6%, the only ones used in the calculation are -4% and -6%. The remaining plus months are treated as 0. Downside deviation is thus measuring the size of only 'the pain of the losing months.'

Where did it come from, and where is it used

The idea of downside risk traces back to economist A. D. Roy's 'Safety First' theory in 1952. The idea was that investors want, above all, to avoid the worst-case loss.

The person who refined this into a practical metric was Frank Sortino. In the 1980s he created the 'Sortino Ratio,' which uses downside deviation instead of standard deviation as the denominator.

Sortino Ratio = (return − target return) ÷ downside deviation

Unlike the Sharpe Ratio, which divides by total volatility (standard deviation), the Sortino Ratio divides by only the 'bad swings.' So it reduces the problem of an asset with frequent surges being unfairly rated low.

Downside deviation alone cannot determine good or bad. Even if the value is small, an extreme crash (maximum drawdown) may be hidden, so the habit of looking at it together with maximum drawdown and drawdown duration is important.

よくある質問

Q. Downside deviation or standard deviation—which should I look at?

It's good to look at both. Standard deviation measures both up and down swings to show 'how much it swings overall,' while downside deviation pinpoints only the 'bad swings' that fell below the target. When evaluating an asset that's especially sensitive to losses or has frequent surges, downside deviation is more intuitive. That said, both metrics measure 'average swings,' so they carry different information from the maximum drawdown (MDD), the single worst drawdown—check them together.

Q. What percent should I set the target return (MAR) at?

There's no right answer; it depends on your purpose. Three are commonly used. ① 0% — when you only care about 'loss or not.' ② The risk-free rate (deposit/government bond level) — the standard of 'at least earning as much as a safe asset.' ③ A personal target (e.g., 5% per year) — your financial-goal standard. What matters is that the things you compare must use the same MAR to be compared fairly.

Q. Is a low downside deviation a safe investment?

It only means the 'average pain of declines' is small; it does not guarantee safety. An asset that is calm in normal times but collapses greatly all at once during a crisis can also show a low downside deviation. That's why downside deviation must always be viewed together with 'worst-moment' metrics like maximum drawdown, drawdown duration, and recovery period. This site takes it as a principle to show those bad moments without hiding them.