annual excess returns from CAPM on monthly total returns

Question

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):

1. 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.)
2. 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?
3. 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?
4. 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?
5. 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.)
6. 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?
7. 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 1

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.