I'd like to investigate if we can observe some level of self-similarity in the distributions of intra-day versus daily returns of stocks and stock indexes.
If the intra-day returns are sampled at 5 minute intervals there would be 78 periods in a trading day, assuming a regular 6.5 hour day. In that case to compare intraday results to day results you'd multiply the 5 min geometric returns, essentially ln(Pn/Pn-1) by 78.
Where you run into issues is when you look at different short-term periods say 1min versus 5min which can have relatively similar returns at times but then vastly different implied daily returns. For instance, if your 5min return was say 0.001% and using the 78 periods it will generate about 0.078% daily and 21.7% annualized (252 days). But one could hypothesize that 5min returns won't look vastly different from say 1min returns and mapping 1min returns using the same approach will result in about 0.39% daily and about 167% annualized returns.
Also, if one was to look at say 24 hour forex or futures markets using the same approach would again result in many more 5min or 1min intervals with vastly different results.
Can you recommend any papers or share some theoretical work of scaling factors to map intra-day returns to daily returns? Thanks in advance!
Typical scaling is, of course, square root, corresponding to the random walk assumption but this is not always accurate.
- Badges
- Science topic
- Similar topics
- Geoscience
- Cartography
- Mapping