Laspayres' formula in cryptocurrency analytics

How to Track the Value of Digital Assets

Every cryptocurrency investor would like to understand how the actual value of their portfolio changes. For this purpose, there is a powerful mathematical tool — the Laspeyres Index, which allows tracking price changes for a group of assets while keeping their quantities constant. This method is especially useful in the cryptocurrency market, where volatility requires precise monitoring.

The Essence of the Laspeyres Method

The Laspeyres Index operates on a simple principle: you take a specific set of goods (or in our case — cryptocurrencies) at a particular point in time and record their quantities. Then, you track how their prices change, keeping the quantity fixed. This provides a clear picture of whether a real revaluation of assets has occurred.

This method is used to calculate consumer price indices, which show inflation or deflation in the economy. But its logic is universal and works well for analyzing digital assets.

Mathematical Basis

The Laspeyres formula looks like this:

Laspeyres Index = ∑(Pt × Q0) / ∑(P0 × Q0) × 100

Where:

• ∑ — sum of all elements
• Pt — asset price at the current time
• P0 — asset price in the base period
• Q0 — quantity of the asset fixed in the base period

Interpretation of the result:

• Above 100 — the portfolio value has increased
• Below 100 — the portfolio value has decreased
• Equal to 100 — the value remains unchanged

Practical Calculation Example

Suppose you are tracking a portfolio with two assets in the initial period:

• 2 BTC at $50,000 each
• 10 ETH at $3,000 each

Base portfolio value = (2 × 50,000) + (10 × 3,000) = 100,000 + 30,000 = $130,000

After some time, the prices have changed (at the given time):

• BTC is trading at $88,310 (current price)
• ETH is trading at $2,980 (current price)

Current portfolio value (with the same asset quantities): = (2 × 88,310) + (10 × 2,980) = 176,620 + 29,800 = $206,420

Calculating the Laspeyres Index: = (206,420 / 130,000) × 100 = 158.78

This result indicates that the total value of your asset basket has increased by 58.78% relative to the base period.

Application in Crypto Portfolio Management

In the cryptocurrency market, the Laspeyres Index is especially relevant for investors working with diversified portfolios. By selecting a representative basket — for example, BTC, ETH, and SOL (Solana, current price $125.80) — you can:

• Track overall dynamics — see how your portfolio moves regardless of individual price fluctuations
• Compare periods — assess how the real value of assets has changed between two points in time
• Manage your portfolio more effectively — understand whether rebalancing is needed or if the strategy remains valid

Limitations of the Method

It is important to remember that the Laspeyres Index has a peculiarity: it can overstate inflation because it does not account for substitution of goods with cheaper alternatives. In the cryptocurrency market, this means the index does not reflect capital flows between assets or the emergence of new promising coins.

Conclusion

The Laspeyres Formula is a reliable tool for tracking changes in the value of a group of cryptocurrencies. By fixing the quantity of assets and updating only their prices, you get an objective picture of how your portfolio wealth grows or declines. Although this method has its limitations, for investors holding a stable asset composition, the Laspeyres Index remains a valuable analysis tool.