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The Samuelson Effect Is About Returns Volatility, Not Price-Level Volatility

Article Quant Q&A · Author: Ben
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Summary

The document distinguishes the Samuelson effect’s maturity-related volatility pattern from volatility measured directly on futures price levels. The effect concerns returns volatility: nearby commodity contracts are often more volatile than deferred contracts, but this pattern is not universal. The question’s crude oil example reports lower standard deviation for the nearby contract’s prices but higher standard deviation for its returns, illustrating that the chosen data scale changes the comparison.

Price levels can have higher dispersion for deferred contracts simply because those contracts trade at higher prices, as may happen in contango. Seasonal markets such as natural gas or power can also have volatility peaks at particular maturities, while price pressures near the far end of a curve may reverse the usual pattern. The explanation is qualitative; no dataset diagnostics or universal test procedure are provided.

Key ideas

  • The Samuelson effect describes a maturity pattern in returns volatility rather than price-level volatility.
  • Price-level standard deviations can rise with contract prices even when return volatility falls with maturity.
  • Contango can therefore make deferred contracts appear more volatile when comparing price levels.
  • Seasonality and price pressures at the far end of a futures curve can disrupt the typical pattern.
  • The effect is an empirical tendency, not a rule that holds in every commodity market.

Tags

CommoditiesFuturesVolatilityStatistics
Full text
# Samuelson Effect with Prices or Returns?


# Samuelson Effect with Prices or Returns?












I have a crude oil term structure dataset with 12 contracts (CL1-CL12). This makes the term structure approx. 1 year long.

The Samuelson effect states that contracts with a longer time to maturity (CL12 in this case) have a lower volatility than contracts with a small time to maturity (CL1).

For Price Data: The volatility (Standard Deviation) of the nearest contract CL1 (28.93) is less than the 12th nearest CL12 (29.3). The Samuelson Effect would thus NOT hold.

For Return Data: The opposite is true SD of CL1 = 0.06 and SD of CL12 = 0.03. The Samuelson Effect would thus hold.

Questions:

- Is there an explanation for the situation above where the volatility pattern of prices is not the same as the volatility pattern for returns?

- Is the Samuelson Effect measures in prices or return?

## Answer by Juan Ignacio Gil (score 3)

https://quant.stackexchange.com/a/68799

The Samuelson effect refers to returns volatility, and it's not something which holds universally. In commodities with seasonality, as gas or power, you often have more volatility in winter than in summer, which could create an effect in the opposite direction. Or any price tension at the end of the curve could give you a higher volatility than in the lower maturity contracts.

If you try to use prices instead of returns, you will find that in situations with contango the higher prices at the back of the curve imply higher volatility on prices, even if the volatility on returns is lower.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.