Currency Index Weights and Constructing a Custom FX Index

Summary

The document asks how currency index formulas select their component pairs and weights, and how to build a dollar index from a chosen set of exchange rates. It supplies example formulas for dollar and euro indexes, then asks how to estimate a constant and pair exponents for a custom basket. It also questions why the same currency pair can have different exponents in separate indexes.

No answer or estimation procedure is included, so the document does not establish how the published weights were derived or whether they have a direct economic interpretation. In particular, the suggested expectation that weights on a shared pair should sum to one is left unresolved. The formulas show that index construction involves both pair orientation and chosen exponents, but the source provides no data, fitting criterion, or evidence to judge alternative baskets. It is therefore useful as a framing of index design questions rather than a complete method for calculating weights.

Key ideas

• A currency index can be represented as a constant multiplied by exchange rates raised to pair-specific exponents.
• The document asks how to estimate weights for a custom basket of currency pairs.
• Pair orientation affects the sign and interpretation of an exponent.
• The source gives no method or evidence for deriving index weights, leaving the questions unanswered.

Tags

# Calculating currency indexes weights?


# Calculating currency indexes weights?












I was looking at this formulas:

```
USD_INDEX= 50.14348112 × EURUSD^-0.576 × USDJPY^0.136 × GBPUSD^-0.119 × USDCAD^0.091 × USDSEK^0.042 × USDCHF^0.036
```

and

```
EUR_INDEX =  34.38805726 x (EURUSD^(0.3155) x EURGBP^(0.3056) x EURJPY^(0.1891) x EURCHF^(0.1113) x EURSEK^(0.0785))
```

I was wondering why those currencies where chosen and how could I calculate, for example, the USD_INDEX if I use other currency pairs? For example:

```
USD_INDEX = CONST * EURUSD^A * GBPUSD^B * USDJPY^C * USDCAD^D * AUDUSD^E * NZDUSD^F * USDCHF^G
```

How could I determine/estimate `CONST, A, B, C, D, E, F` and `G`?

Also, I was kinda surprised that for `USD_INDEX` the `EURUSD` constant was `-0.576` and the `EUR_INDEX` the EURUSD constant was `0.3155`. I would have expected that the second one was 1 minus the first one, so the sum of both of them adds 1.

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.