Choosing a Valuation Formula for a Shocked Composite Index

Summary

The document compares two ways to revalue a composite index after changing the values of its underlying indices. One formula takes the ratio of shocked to base weighted totals; the other adds each underlying index’s percentage change multiplied by its weight. The central issue is what the weights represent and how the composite is constructed.

The question suggests that the choice may depend on whether weights come from a portfolio regression or another definition, but it does not resolve that issue or provide numerical examples. In general, a ratio of weighted totals is appropriate when the composite level is defined by weighted component values, while a weighted sum of component returns corresponds to a return aggregation under specified weights. The correct mapping depends on index construction and weight conventions, including whether weights are fixed or reset through rebalancing. The document is a conceptual question rather than a complete pricing method, so those details need to be established before implementing either formula.

Key ideas

• The two formulas aggregate shocked component values in different ways.
• A ratio of weighted totals reflects a composite defined from weighted component levels.
• A weighted sum of component returns requires weights with a clear return-aggregation interpretation.
• Rebalancing rules and weight definitions affect how shocks should be propagated.
• The document poses the distinction but does not supply a worked example or definitive answer.

Tags

# Methodologies behind shocking a composite index instrument, what assumption distinguishes these?


# Methodologies behind shocking a composite index instrument, what assumption distinguishes these?












Suppose I have a composite index (rebalancing or non-rebalancing) that at present time has some base value $B_{\text{base}}$ in some base economy. I am in the process of shocking the economy on which my composite index is defined ( changing the index values by different factors) and re-valuating its base value. I went to code the pricing engine for my composite index after shocking and figured the new value should be calculated as $$ B_{\text{shocked}} = B_{\text{base}} \cdot \frac{\sum{\big(\text{index weight}}_{i} \cdot \text{shocked index value}_{i}\big)}{\sum{\big(\text{index weight}}_{i} \cdot \text{base index value}_{i}\big)} $$ But then it occurred to me that were I to only shock certain underlying indices this methodology doesn't quite look correct, and maybe should be $$ B_{\text{shocked}} = B_{\text{base}} \cdot \sum \bigg(\frac{ \text{shocked index value}_{i}}{\text{base index value}_{i}} \cdot \text{index weight}_{i} \bigg) $$

My suspicion is that the methodology should depend on how my weights for each underlying index are defined - whether they are set by regressing on a portfolio for instance or otherwise.

I was wondering if anyone could shed any light on which of these two methodologies should be used for what purposes or more importantly what exactly is the assumption that distinguishes them? I'm having a hard time conceptualizing the distinction beyond the fact that they're different mathematical formulas.

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