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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:

  1. Is there an explanation for the situation above where the volatility pattern of prices is not the same as the volatility pattern for returns?
  2. Is the Samuelson Effect measures in prices or return?
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  • $\begingroup$ The volatility in prices generally does not make sense because it is not a stationary time series and has (at least locally) strong trends. The volatility of returns is sensible as it is essentially white noise. $\endgroup$ Nov 9, 2021 at 21:22
  • $\begingroup$ In some econometric studies of the Samuelson Hypothesis a volatility estimate $(\ln F_t/F_{t-1})^2$ is produced for every day t in the life of a futures contract, and then these estimates are regressed on the number of days to expiration $T-t$ to see if there is a time trend. HTH $\endgroup$
    – nbbo2
    Nov 10, 2021 at 0:51

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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.

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