Portfolio Returns Across Months: Rebalancing and Log Returns
Summary
The note considers how to calculate monthly and cumulative returns for three stocks and an equally weighted hedge fund portfolio. Its answer emphasizes that portfolio weights matter: an equal-weight allocation at the start does not by itself establish that the portfolio is rebalanced each month. Without a rebalancing rule, applying equal weights anew to every month can produce incorrect fund returns because holdings drift as asset prices change.
For a portfolio explicitly rebalanced to equal weights each month, the answer recommends first computing each month’s portfolio simple return from the weighted asset returns, then converting those portfolio returns to log returns and summing across time. It cautions that portfolio aggregation and time aggregation are different operations. The post also identifies a month-label issue in the proposed calculation. The supplied workings contain questionable logarithms of negative returns, and the answer does not provide a full corrected series, so the exact five-month portfolio result cannot be recovered from this exchange alone.
Key ideas
- Portfolio returns require the asset weights to be specified for each period.
- An equal-weight portfolio is not necessarily rebalanced each month.
- For a monthly rebalanced portfolio, aggregate simple asset returns using the month’s weights first.
- Log returns can then be summed across time for the portfolio’s cumulative log return.
- The answer flags a month-label error and does not supply a complete recalculation.
Tags
Full text
# Portfolio & Asset Returns across Multiple Periods # Portfolio & Asset Returns across Multiple Periods The stocks of CK Tan's, Robertson's, and Tamashimaya are held by the hedge fund SSK. They hold an equally weighted portfolio. The end-of month prices of the stock during five months this year is given as a) Calculate the simple monthly returns of the three stocks. Calculate the log returns. b) Using answers of a), what is the return of the hedge fund SSK for each month? c) Calculate the five-month returns of the three stocks and the hedge fund, respectively. Discuss which returns you would add up. Would appreciate if someone could verify my workings as I'm unsure. Answer: a) b) June returns = (10%+12%+4%)/3 = 8.67% July returns = -17.69% August returns = -2.59% c) For the 3 stocks, the monthly log returns are summed to derive the 5-month returns. The hedge fun returns are calculated by summing the log values of b) CK Tan's = 9.53% - 20.07% + 10.54% + 18.23% = 18.23% Robertson's = 27.76% Takashimaya = -91.63% Hedge fund = ln(8.67%) + ln(-17.69%) + ln(-2.59%) (This is the part I doubt the most) Hedge fund = ln(8.67%- 17.69%- 2.59%) Hedge fund = 5.98% ## Answer by AK88 (score 1) https://quant.stackexchange.com/a/47424 You are missing the weights for `b` and `c`. Since it does not explicitly state that the portfolio is rebalanced each month, it would not be correct to use `1/3` to calculate monthly returns. If you insist using monthly rebalanced equally weighted portfolio, then use simple returns to calculate the Hedge Fund return for each month, convert to log space, and then sum them up. Portfolio additive vs Time additive Be careful. Also, your August return is actually September's return, if you assume monthly rebalanced equal weighted portfolio.
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.