CAPM Estimation with Monthly Returns: Frequency, Currency, and Benchmarks
Summary
The document raises practical questions about estimating portfolio betas with monthly CAPM returns, including whether monthly excess returns should be compounded for annual reporting, whether shorter months deserve different weights, and how to handle instruments with incomplete histories. It also asks about using a changing monthly Treasury bill rate, translating internationally invested Swedish portfolios and benchmarks into a common currency, and choosing between broad global or more representative market benchmarks.
The response advises using trading days for analysis, treating the stated pre-crisis sample as a usable baseline while also seeking data that include crisis conditions, and considering omission of instruments with very short records instead of making complex adjustments. It accepts monthly risk-free observations as reasonable given their relatively low volatility, recommends currency consistency, and suggests comparing portfolio-appropriate benchmarks alongside a broad index. The exchange leaves some original questions unanswered and offers informal guidance rather than a full CAPM procedure.
Key ideas
- Estimate CAPM relationships at the return frequency used for the analysis and distinguish that from annual reporting.
- Use trading days when constructing return observations, according to the response.
- Short instrument histories may be excluded rather than adjusted through complex methods.
- Express portfolio and benchmark returns in a common currency when comparing them.
- Compare benchmarks that reflect portfolio exposures, potentially including a broader market index.
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# annual excess returns from CAPM on monthly total returns # annual excess returns from CAPM on monthly total returns I want to calculate annual excess returns on portfolios using monthly returns for a CAPM (for the assets in the portfolio as well as for the benchmark), in order to have more information on the correlations, more precise betas. I have a few questions about this (may justify separate postings): - Because the CAPM comes from monthly correlations, I shall calculate excess returns for each month, right? But if I only have year-end snapshots of portfolios, I should chain the monthly excess returns up (compound them) and multiply the initial value with each surprise return? Is this essentially the same as doing the annual calculation? (I suspect an argument about integrating a continuous price process into some return observations anyway.) - Is it standard practice to adjust (slightly) for shorter months having somewhat less information on the correlations? Shall I weight by the number of days or only trading days before return dates? - I do not have a principled approach on which time period to use for the beta-calculation. The observations are from 1999-2007, and it was already hard to get returns for only these year, so I do not use retrospective, historical returns. This is defensible, right? - Relatedly, some instruments end trading during these years, or start only later. Those betas should be adjusted somehow to acknowledge less information about them? Or the point estimate is just the point estimate? - Is it OK to use the monthly T-bill rate as the risk-free rate, changing from month to month? (I have average SAY yields with day-counting on the ACT/360 -- which I shall correct for, I presume.) - All these portfolios are Swedish. Is it good practice to include the currency risk in the correlations with expressing all returns (incl. the benchmark) in SEK? - Many holdings are diversified internationally, but not completely. Is it appealing to use an MSCI all-world benchmark (MSCI ACWI IMI GR USD converted into SEK) as people "should" diversify, so all extra risk is, well, extra, so it makes much more sense to compare everything to an MSCI World (viz. developed markets only) benchmark? Thanks a lot! ## Answer by Dom (score 2) https://quant.stackexchange.com/a/10892 2) you only take trading days for your analysis because taking in account days on which no price changes took place would shift results in a wrong direction. For exmple, you mostly take 250 trading days p.a. 3) Your time interval up to 2007 is okay and excludes the financial crisis, which is a non-normal circumstance. Therefore, your time interval can be regarded as representing the usual case. If possible, try to get some data which includes the financial crisis in order to get an impression of how the capm performs during extreme market conditions. 4) If you want to add adjustments, it will get complex very fast. The second problem is that whoever supervises your analysis might not accept your adjustments. If instruments have a very short data track, maybe leave them out. 5) Should be OK, however if you can get daily data, it is always the better way. But as the volatility is quite low in those rates compared to stock quotes, switching to monthly data is legitimate. 6) I do not fully understand what you mean. If everything is in Swedish, why convert it into another currency? However, if you add a benchmark in another currency, you have to express all time series in the same currency, of course. To do so, get daily FX data and convert the stock quotes every day into the corresponding benchmark currency (or vice versa). 7) Try to include benchmarks, which represent your portfolio more than the MSCI World. You can still include him and see what the broader diversification changes return and risk. I hope that helps a bit. Sorry if I didn't fully understand some questions.
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