Replicating Equity Index Returns with Constituent Trades

# Replicating an SP500 index with Python


# Replicating an SP500 index with Python












I am looking for a reference to replicate in Python a stock market index like the SP500, or an ETF like SPY (free-floating) or RSP (equal weighting) with individual stock trades. I searched online and could not find one. I found a short blog post that replicates it in the short-term, without taking into account delistings and survivorship bias.

I asked AI to program one in Python and Yahoo Finance and the returns are biased upward by around 6%. It did not take into account fees, commission, and slippage, but 6% still seems too large for a replication.

Since this is a basic exercise in quantitative finance, I think such a reference is bound to exist and I am not using the right terms for it. I have access to high-quality data in CompuStat and CRSP.

How can I find a reference in Python that replicates an index with stock trades?

### Update

By "replicate with individual trades", I mean that I want to formulate and back-test a trading strategy that buys and sells the constituents of the index, and that the market value of such a portfolio closely follows the index, and has similar metrics: similar total return, Sharpe ratio, maximum draw-down, etc.

## Answer by Alper (score 3, accepted)

https://quant.stackexchange.com/a/85706

Unfortunately, I am not aware of any such program at this time, in Python or another coding language, that does what you are looking for, assuming you have access to all the necessary data. However, I would like to give some pointers in case you decide to write such a program yourself.

First, your simulated portfolio would surely track such an index assuming you "buy" or "sell" the right number of shares of the right stocks at correct dates and times, i.e. closings, "collect" and "distribute" the dividends or subscribe to the rights issues at the same schedule with the index. I think your actual challenge would be to figure out the index rules and parameters which would be akin to calculating the index values yourself over time.

Second, one would need much more data than stock prices to be able to accurately simulate an equity index over time, especially when it is capitalization weighted like S&P 500. S/he would also need to learn well how the relevant data need to be crunched. For an introduction, see the Index Calculation Primer presentation by Roger Bos of S&P from 2000. It is old, but it is rich and unique and covers most of the basics. Then I suggest downloading and reading the latest methodology document for equity indices from the S&P web site.

Third, the smaller the number of index constituents is the easier it would be to simulate it. Of course, an equal weight index would be easier to simulate as you would not need to worry about as many data points as otherwise.

Finally, if you try simulating an ETF tracking a market cap weighted index, you could bypass most of the index methodology by reverse engineering the ETF by for example finding out the number of shares to be bought and sold every day based on the weight of each stock in the ETF at the end of every day. However, I reckon you will still need to keep track of dividends and other corporate actions.

## Answer by Dimitri Vulis (score 2)

https://quant.stackexchange.com/a/85712

Before generative AI, when we couldn't find a ready piece of code, we wrote it ourselves. But now we write a prompt, which looks like a Cobol program, and have an AI LLM generate the code. So I did, and checked that Google Gemini and Grok generate reasonable looking Python. They're certainly much smarter than Citi junior quantdevtards I used to give specs to. As an exercise you may want to improve the prompt to handle bid-offer spreads, and catch more problems/edge cases, such as rounding causing problems.

My prompt is:

```
Write a Python function GenerateRebalancingTradeBlotter that will input the following:
MinWeight and MaxWeight are numbers. Assert that MinWeight is less than or equal to MaxWeight.
The other 3 inputs are pandas dataframes named MarketData, TargetWeights,  and CurrentPositions.
Each dataframe had a "ticker" column.
Dataframe MarketData also has columns price and minimumTradeSize.
Dataframe TargetWeights also has column targetWeight.
Dataframe CurrentPositions also has column CurrentNumberOfShares.
Use is_unique property to assert that the ticker column in every dataframe is unique.
Use pandas method merge to outer join CurrentPositions and TargetWeights on ticker.
Use merge again to left join the result and MarketData on ticker.
Pass a dictionary to a single fillna call to replace NaN by zero in columns TargetWeight, CurrentNumberOfShares, and price, and by one in column  minimumTradeSize.
Assert that the sum of targetWeights does not differ from one by more than 1e-5 and that every targetWeight is either zero or between MinWeight and MaxWeight inclusive.
Assert that price and minimumTradeSize are not zero whenever targetWeights or CurrentNumberOfShares are not zero.
Append column CurrentMarketValue calculated as the product of CurrentNumberOfShares and price.
Calculate TotalMarketValue as the sum of all CurrentMarketValue.
Assert that TotalMarketValue is not zero.
Append column SharesToTrade calculated as follows: if TargetWeight is zero then minus CurrentNumberOfShares otherwise use this formula:  divide CurrentMarketValue by TotalMarketValue, subtract TargetWeight, divide by the product of price and minimumTradeSize, round to nearest integer, and multiply by minimumTradeSize. Do not perform this calculation if TargetWeight is zero.
Return a dataframe containing the ticker and only non-zero SharesToTrade.
Write a short main program to set up test data and to test the function.
```

You will need to pass target weights to this program. Googling, I see several web sites that provide S&P 500 weights, e.g. https://us500.com/tools/data/sp500-companies-by-weight