Portfolio Weights Between Monthly Rebalances
Summary
The document asks how to calculate daily returns and weights for a stock portfolio that rebalances monthly, using a ranked-beta strategy as context. It distinguishes the weights assigned at the start of a month from the weights that result after the stocks have different returns. Starting weights determine each stock’s initial allocation; as prices move, the holdings’ portfolio shares drift even if no trades occur.
A two-stock example illustrates the update: multiply each prior weight by that stock’s gross return, then divide by the portfolio’s combined gross return to get its new weight. This process can be repeated each day through the month. At the next scheduled rebalance, the portfolio is reset to the newly calculated target weights. The document is framed as a question and supplies no accepted answer, transaction-cost treatment, or discussion of dividend and cash-flow conventions, so implementation details may vary with the return data and backtest definition.
Key ideas
- Monthly rebalancing fixes target weights at the scheduled rebalance date.
- Between rebalances, differing asset returns cause portfolio weights to drift.
- Update each asset’s share by multiplying its prior weight by its gross return and normalizing by the portfolio return.
- Repeat the weight update through the month, then reset to target weights at the next rebalance.
- The example omits implementation details such as transaction costs and cash-flow conventions.
Tags
Full text
# Daily weights and returns of portfolio that rebalances monthly # Daily weights and returns of portfolio that rebalances monthly I am to replicate the Betting against beta strategy by Pedersen and Frazzini. We use daily returns of the stocks and construct two portfolios based on their ranked betas. Weights is also based on the rank and you can think of it as given for this problem. So the problem is that when the portfolios is to rebalance monthly, it means that at the first date of each month we take the already calculated weights and assign them to each stock and multiply it with the returns each day of the month. OR, and this is what I struggle to understand: Will not the weights of the stocks change based on the stocks returns within the month? Because if we invest 1 dollar in the portfolio upon construction and one of the stocks has a weight of 0.05 the first day of the month, we will invest 0.05 dollar in that stock. If the stock increases by 10% this day, we have 0.05*(1+0.1)=0.055 dollar in that stock after that day. So this should represent what we have invested for day two of the month. This continous for the rest of the month for all stocks. Should this be the procedure of all the stocks within each month after it is rebalanced? So you rebalance at the 1 day of the month, invest 1 dollar in the portfolio, and it develops cumulatively throughout the month as stated above? This continues to the next month, where it starts over with the orginal weights that is calculated beforehand. Please help with the understanding :D Example: You have two stocks in the portfolio, with equal weights 0.5 at the start of the month. Day 1, stock 1 has 2% and stock 2 has 3% return. The weights day 2 is then: Stock 1: 0.51.02/(0.51.02+0.5*1.03) = 0.4975 Stock 2: 0.51.03/(0.51.02+0.5*1.03) = 0.5025 Next day: stock 1 has 1% and stock 2 has 2% return Stock 1: 0.49751.01/(0.49751.01+0.5025*1.02) = Stock 2: 0.50251.02/(0.49751.01+0.5025*1.02) = And so it continues until next month, where the original weights the first day is used calculate for day 2 and so on. Is this correct?
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.