How Portfolio Rebalancing Changes Average Daily Returns
Summary
The document explains why two calculations of a two-stock portfolio’s average daily return can differ. One method takes each stock’s average return and combines them using fixed portfolio weights. That calculation represents a portfolio whose weights are maintained over time, which generally requires periodic rebalancing.
The alternative starts with capital allocated at the chosen weights and lets each holding’s value change with its own returns. The weights then drift as one stock gains or loses relative to the other, so the resulting portfolio return reflects a buy-and-hold allocation rather than constant weights. The small difference between the reported averages is attributed to these distinct assumptions, not necessarily to an arithmetic error. Which method is appropriate depends on the portfolio management policy; the answer does not assess transaction costs, timing conventions, or other implementation details.
Key ideas
- Combining average asset returns with fixed weights represents a portfolio maintained at those weights.
- A buy-and-hold portfolio’s weights change as its holdings earn different returns.
- Different rebalancing assumptions can produce different average portfolio returns.
- The correct calculation depends on whether the investor rebalances or lets weights drift.
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# Differences Between Portfolio Daily Average Returns # Differences Between Portfolio Daily Average Returns I have a doubt about the average daily return for a 2 stock porfolio. I have the data of both stock returns over a 1511 day period. I used 2 approachs to calculate the average return. In the first one, I calculated the average of the returns of each individual stock over the 1511 days period, then I used the formula $Average Return = (Weight 1*Return 1)+(Weight2*Return2)$ I'm getting 0.058% In the second approach, I assumed a starting capital ammount, choose the same weights, and calculated the daily increase on the starting capital over the 1511 period. I calculated the returns for every day and got the average of those. The solution was 0.056%. Is the second approach incorrect? Why are those differences found? ## Answer by mark leeds (score 0) https://quant.stackexchange.com/a/42970 In the first case, you are assuming the weights are fixed. I guess one half to each weight. In the second case, the weights start out equal, but, since you're using a starting capital, the weights are changing at each time, t, implicitly, depending on the returns of the two stocks up to time t. This is because, when you multiply the capital by the return of the respective stock, the capital goes up ( or down) in proportion to what the cumulative return was up to that point. So, given that your numbers are pretty close, you're probably doing things correctly and the difference is due to what I explained above. The method you want to use all depends on how exact you want to be. Is the manager gonna be re-weighting his portfolio every day so that his weights truly are constant through out the investment period. Or is he just letting them start out that way and letting capital appreciation do whatever it does over time ? It's all about the assumptions you want to make. I hope that helps some.
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