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!