Creating a synthetic index from stock prices

I'm developing an trading strategy for global stocks and I need to construct a synthetic index from the prices of the constituent stocks.

Note - I'm not talking about creating a FTSE100 or S&P500 index - this is market cap based, I'm just looking to create an index from historical prices of a bunch of stocks. The stocks may be in different currencies.

I have a few ideas but not sure which is the best approach.

1) Take the natural log of each price. Then for each day take the average value of the log prices - this is the index value for that day.

2) Create a return series for each stock price series. Then for each day take the average return of all stocks - this is the index value for that day.

3) Convert each price series into an index, in a similar fashion as a NAV calculation, I'm not sure of this method since the stock prices all begin on different days.

I would be interested to hear any alternative approaches / opinions.

 

I like the second approach. Seems most representative to me. I'm not sure how to embody the third idea either, considering difficulties of calculation.

 

(2) is best, by far.

You then need to cumulate up the returns to get the index, but that was implicit I guess. Depending on what you're using the index for you can cumulate in a compound sense I_t = I_t-1 * (1+r_t) or add em up I_t =I_t-1 + r_t Personally I'd use the latter.

There is an improvement to this method which I use myself. That is to divide the daily return of each asset by it's recent volatility. Otherwise the more volatile stocks will dominate the index calculation.

This also creates a more stable index over time with roughly the same volatility. Again this may or may not be what you want. If not, then divide the daily returns by the ratio of their recent volatility to the average recent volatility. Then the changes in overall volatility will be preserved in the index, but you're still taking an average over stocks which accounts for different cross sectional risk.

GAT

 

I have created a few equal-weighted indexes for my own trend following systems.

Of paramount importance is survivor bias. Backtesting/simulations based upon today's data is forward-looking.

 

OK 2) it is then. Thanks @Zestilio and @globalarbtrader

@globalarbtrader - To clarify, create a daily return series for each stock, for each day sum the individual daily returns - this is the index value.

I agree, you don't want the returns of a volatile stock to drown out the returns of less volatile stocks. How would you suggest this is done? Use the stddev(10) of returns or ATR(10) ?

Another question, what approach is used to construct a stock sector index in the industry? So when the daily return on a sector is +10%, I assume they do a simple sum of individual stock daily returns?

@jharmon - yes survivorship bias is important, and is incorporated as best as I can given the data I have.

 

You need to incorporate data on delisted securities.

For sector-based approaches it is more difficult - both delisted stocks and stocks that have previously changed sectors.

 

@jharmon - Yes, I understand delisted securities and their impact. Can you please give me an example of a stock that has changed sector?

 

In the micro-cap area, stocks change sectors quite often as their business interests change.

In the higher cap area, you can have acquisition companies (highly funded shells) that take over other companies.

But you just have reclassifications that occur too... eg.
NASDAQ:ACET (Aceto) went from "Industrials" (GICS subsector Trading Companies & Distributors) to "Health Care" (GICS subsector Health Care Distributors) in 2015 probably because their pharmaceuticals became more dominant than their industrial chemicals.

Spinoffs/mergers also cause these changes too. The classification companies don't always immediately reclassify them too (or reclassify them at different intervals).

 

@globalarbtrader - Thank you for the clarification.

@jharmon - Thanks for the example.

I don't look at micro-cap, instead I look at small cap stock portfolios across exchanges around the world. Getting historical constituent data for some exchanges is tricker than others. Delisting is straightforward, re-classification is much more hassle and needs an element of manual intervention. The former is considered, the latter is not even on my radar