Gold trading basics · Lesson 77 of 100

Gold Sortino Ratios: Define the Target and the Downside Denominator

Calculate target downside deviation under an explicit full-sample convention and show how changing the required return changes the result.

Downside Needs A Target: instructional diagram for lesson 77 — CYGURU GOLD · Original lesson schematic. Examples are illustrative.

Downside is defined relative to a target

A Sortino-style ratio compares average return above a selected target with a measure of shortfall below that target. The target can represent a required return under a documented convention; it is not automatically zero or a universal risk-free rate. Different implementations can use different denominators and annualization choices. State the observation frequency, return definition, target and downside-deviation formula before comparing outputs. The purpose is to measure one particular form of variability. It does not imply that every other source of loss, funding stress or uncertainty has been accounted for.

Calculate full-sample target downside deviation

Use invented period returns of −1%, +1%, +2% and +2%, whose arithmetic mean is +1%. Set the target at 0% per period. For the chosen full-sample RMS convention, record min(return minus target, zero) for every observation: −1, 0, 0 and 0 in percentage points. Square them, average over all four observations and take the square root. Downside deviation is sqrt(1/4)=0.5 percentage point. The ratio is (1−0)/0.5=2.0 for the stated period. This is not the result obtained by dividing only by the count of negative observations.

Change the target and recompute every component

Raise the hypothetical required return to 0.5% per period. The shortfall observations become −1.5, 0, 0 and 0; full-sample RMS downside deviation becomes sqrt(2.25/4)=0.75 percentage point. Mean return above target is now 0.5, so the ratio is 0.5/0.75, approximately 0.6667. The underlying return series is unchanged, yet the metric changes materially because the objective changed. Do not compare a zero-target ratio with another strategy’s positive-target ratio as if both were the same risk-adjusted measurement. Preserve target units and period alignment in the worksheet.

Downside target conventions
Quantity	Target 0%	Target 0.5%
Mean above target pp	1	0.5
Squared shortfall sum	1	2.25
Observation divisor	4	4
Downside deviation pp	0.5	0.75
Period ratio	2	0.6667

Full-sample root mean squared target shortfall; no annualization.

Understand how a quiet downside denominator can mislead

If no sample observation falls below the target, the downside denominator can be zero. The resulting undefined or specially handled ratio does not establish the absence of future downside. A short or selectively chosen sample may simply omit adverse states. Illiquid or stale valuations can also suppress observed shortfalls. Report sample size, target-breach count, worst outcomes and the path of equity. A method exposed to rare jumps needs a stress analysis beyond a ratio. The absence of a sampled tail loss is a limitation of the evidence, not a guarantee supplied by the formula.

Separate this statistic from Sharpe and loss probability

Sharpe and Sortino differ in what they place in the denominator and, potentially, which reference enters the numerator. They need not rank the same methods identically. Neither is a direct estimate of the chance of losing on the next trade. A desired target chosen after seeing the results can manufacture a favorable presentation. Annualizing a period ratio also requires explicit assumptions about how the monitored returns behave over time. Keep the unannualized components visible. When the mean is below the target, inspect the negative numerator and the economic outcome rather than mechanically treating a larger negative ratio as a superior opportunity.

Practice task: audit two platform conventions

Reproduce 2.0 at a zero target and 0.6667 at a 0.5% target using all four observations in the RMS denominator. Then calculate what happens if a report divides only by the single below-target observation and explain why that convention differs. Do not label the mismatch a software bug without reading its documentation. Prepare a specification containing target, return frequency, denominator, costs, cash treatment and annualization. Finish by naming one loss scenario that the four observations do not contain. The resulting memo should explain the statistic precisely without turning a favorable downside ratio into a broad claim of safety.

Gold Sortino Ratios: Define the Target and the Downside Denominator

Downside is defined relative to a target

Calculate full-sample target downside deviation

Change the target and recompute every component

Understand how a quiet downside denominator can mislead

Separate this statistic from Sharpe and loss probability

Practice task: audit two platform conventions

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