Chapter 3 of 16

Gold–silver ratio and relative-price risk

Calculate a dimensionally consistent ratio and understand why a historical relationship need not revert on a useful schedule.

3 min read · Original educational chapter

In this chapter

Normalize the units first
A ratio is a relative price, not an anchor
Two-leg positions introduce further risks
A ratio trade is a model choice, not a natural law
Attribute both legs and their common factors
Decision lab: A ratio move does not identify either leg
Worked example
Common mistakes
Check your understanding

Normalize the units first #

A gold–silver ratio compares the prices of equal physical mass in the same currency at a matching time and quality convention. A gold quote per 10 grams and silver quote per kilogram must first be converted to a common mass.

Dividing unmatched screen numbers creates a ratio with the wrong scale. Also check whether both prices are spot, futures of comparable maturity or retail quotes that include different charges.

A ratio is a relative price, not an anchor #

A high ratio means gold is expensive relative to silver under the chosen definition; it does not establish that gold will fall or silver will rise. Either price can move, both can move, and the ratio can remain far from a historical average for a long time.

Historical averages depend on the sample and market regime. Industrial demand, monetary conditions, mine supply and product structure change. A narrative of inevitable mean reversion is not a risk control.

Two-leg positions introduce further risks #

A relative-price position needs appropriate quantities or sensitivities rather than an arbitrary one-lot-versus-one-lot pairing. Currency, financing, contracts and liquidity can also differ. A ratio exposure is not perfectly described by a difference in rupee prices.

Closing or funding one leg while the other remains open can create significant directional exposure. The arithmetic here is a study of relative pricing, not a recommendation to establish a paired position.

A ratio trade is a model choice, not a natural law #

A fixed mass ratio, a matched-notional hedge and a regression beta hedge are different books. A log-price spread or return regression needs a stated estimation window, sampling clock and evaluation horizon. An extreme raw ratio does not prove a stable long-run relation.

A cointegration hypothesis requires appropriate testing and allowance for structural change; correlation of returns does not establish it. A high in-sample fit does not establish a useful out-of-sample spread trade. Retain failures and parameter trials in the research record.

Attribute both legs and their common factors #

Write each leg’s return, notional, multiplier, currency and funding. The same fall in the gold–silver ratio can arise from quite different absolute-price paths. A dollar-neutral pair can still carry macro, volatility, liquidity and local-basis exposures.

Stress the correlation approaching one, changing sign or weakening while each leg’s volatility increases. Separate the economic spread hypothesis from daily cash calls. A relative-value book that appears balanced on a normal-day chart can require cash on both legs at different points in the path.

Decision lab: A ratio move does not identify either leg #

A gold–silver ratio can fall because silver rises, gold falls or both move at different rates. Relative-value exposure requires both positions, units and funding assumptions. A high historical ratio does not identify a deadline for mean reversion.

Construct three fictional price paths producing the same ratio change. Calculate both legs’ P&L and their separate collateral calls. Distinguish a value-neutral hedge from a naive equal-lot position and identify the residual currency and basis risks.

Hypothetical worked example

Remove the thousand-versus-ten mismatch

Fictional gold is ₹60,000 per 10 grams and silver is ₹75,000 per kilogram. Gold per gram is ₹6,000 and silver per gram is ₹75, giving a mass-consistent ratio of 80.

Dividing ₹60,000 by ₹75,000 gives 0.8, which compares different quantities and is not that ratio. If gold later rises 10% while silver rises 20%, the ratio becomes 80 × 1.10 ÷ 1.20 ≈ 73.33.

Both metals rose while the ratio fell. A view on the ratio therefore differs from a view that both metal prices will decline.

Common mistakes

Dividing gold-per-10g by silver-per-kg without conversion.
Assuming an extreme historical ratio must revert before funding runs out.

Check your understanding

Can the gold–silver ratio fall while both prices rise?

Make this chapter useful

Can you defend the reasoning?

Before moving on, answer the self-check in your own words and write why each alternative fails. Use the worked example to test that explanation. Then apply it in the module research task; keep the assumptions and the evidence that could change your answer.

Sources and further reading

Further-reading references from the curriculum source list. Contract sizes, expiry calendars, settlement references, margin parameters and tax treatment can change; verify the current operative documents for the actual product. Worked figures are illustrative, not current quotes.

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