I do not understand why you would use the benchmarks prices to do a rebased series. instead of using a return series and using the beta of the stock as a scalar. Since not all stocks are contributing equally to the index (market cap weights) or all equally affected by the index (beta).
Also, there is a side effect of normalizing things unequally, as in the price of the single stock will be highly variable (say from 50-500 USD) they will be reduced unequally but rather proportionally according to their closing price.
Intelligent thought provoking questions from a pure quant
Price versus returns:
Return series would work fine as well. The method is agnostic.
Benchmark:
Managers are assessed on the excess returns versus a benchmark. Short-sellers are measured against the inverse of the index. Absolute players are measured in absolute. This can however be decomposed in outperformance over the index on the long side and underperformance vis-a-vis its inverse on the short side. Therefore, the use of a benchmark is simply a practical convention.
Your points on market cap and Beta are well noted. To be perfectly honest, i have never tried stripping Beta and market cap. This conflicts with a belief developed more than a decade ago
Market cap:
In practice, managers love to fish in the small mid caps pond. Pick a few 2-3 baggers and a star stockpicker is born. Meanwhile, they like to short boring stuff. Long small mid/Short big boring works wonders in bull markets, but not in bear phases. Racy stuff is not a fertile ground for short sellers: borrow is hard to locate, bid/ask spread is wide enough to dock a super tanker, liquidity evaporates. Above all else, liquidity drives small caps performance. Bottom line, market cap matters.
High Beta stocks lead the pack on the way up and down as well. Beta has another interesting property. When hedging Long and Short books, bull markets are characterised by high Long/ low Short: racy stocks as tech Long/utilities, foods Short. Net Beta and net exposure are both positive. In sideways to down markets, reverse the trade low Beta Long/high Beta Short. Net exposure remains marginally positive, while net Beta turns negative. Net Beta is a much more accurate reflection of a manager's bullishness/bearishness than net exposure.
Beta neutral, whilst fashionably interesting, leads to different types of strategies, something which robustness remains to be tested.
This is why stripping off Beta does not intuitively make much sense (at least to me). Once again, it may be a limiting belief. As a married man, being told i am wrong is part of the fun
I would invite you to test your theory and please let me know.
Normalizing effect:
Valid point. Relative returns may be more accurate. This can become rapidly computationally intense. The course is challenging enough.
Once again, thanks for those thought provoking questions. You made my day!
Thank you for the detailed reply Laurent, I will have to put my theory to the test. The thought-provoking ideas flowed both ways on this one. I excited to get my hands dirty on equities and test out a few of these theories.