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Base-Year Price Normalization in the S&P Dynamic Asset Exchange

Article Quant Q&A · Author: user2188190
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Summary

The document clarifies how to interpret asset prices normalized to 100 at the end of the preceding year. The answer describes simple rebasing: divide each later price by its value on the base date and multiply by 100. This expresses subsequent price changes relative to a common starting level, much like a price index or deflator. It is distinct from standardizing a random variable by subtracting its mean and dividing by its standard deviation.

The exchange also raises a separate issue about calculating changes in two assets from their correlation. Correlation alone does not determine either asset’s realized price change; additional price data or a model for those changes is needed. The discussion is brief and does not explain the paper’s full exchange methodology or provide a worked example, so it resolves the normalization question more clearly than the broader replication problem.

Key ideas

  • Rebasing sets each asset’s value to 100 at a chosen base date by scaling its prices relative to that date.
  • This price-index convention is different from mean and standard deviation normalization.
  • Correlation describes how two assets move together but does not reveal their individual realized price changes.
  • Replicating the exchange method requires the paper’s full formulas and suitable asset price data.

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Multi-assetStatistics
Full text
# Pricing Assets in the S&P Dynamic Asset Exchange


# Pricing Assets in the S&P Dynamic Asset Exchange












I am attempting to recreate the S&P Dynamic Asset Exchange using the methodology outlined in this paper.

I am struggling to 'normalize' the prices of the assets properly. On page 6 of the aforementioned paper,

Price A(t) = Price of asset A normalized to equal 100 on the last trading day of the preceding year

Price B(t) = Price of asset B normalized to equal 100 on the last trading day of the preceding year

-- What methodology is implied for 'normalize' -- the standard Random Variable normalization? (Random Variable - Mean)/(Standard Deviation)? Or is there an alternative method?

## Answer by Karol J. Piczak (score 1, accepted)

https://quant.stackexchange.com/a/8317

I think in this case no fancy normalization techniques are implied. At least from what I understand from the cited part, they just scale the variables so that they are equal to 100 in the base period (end of preceding year) - something like computing a deflator, commonplace in macro analysis.

## Answer by Rick (score -1)

https://quant.stackexchange.com/a/8504

On page 6 of the document there is the formula "Ct_DeltaAB = Equation #1 evaluated for changes in Price A and Price B". How can I know what the changes are in Price A and Price B? I know the correlation between A and B but that does not mean that I can derive the changes of A and B. How do I solve this problem?

Rick

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.