Calculating historical returns interested, following, question

pawn

While I await my L3 results, I have been toying with the following question.

Assumes I have 5 years annual returns of 1,000 securities, partitioned in 10 asset classes of 100 securities each.

I am interested in estimating mean and st dev of my ten asset classes.

How would you go about it? For each class would you:

1) calculate the mean returns of all asset in the class, for each year 1, 2 ,3, 4 and 5; and then calculate mean (geometric, I guess) and standard dev of these annual returns;

or

2) calculate geometric mean of each asset in the class over the 5 years; and then calculate mean and st dev of these geometric means.

I'm sure this was covered somewhere in one of the levels, but where?

ll11

I think #1 & #2 will give same value if you use GM everywhere since you are taking equal weigh of everything. For standard deviation if you consider calculating standard deviation in #2 by using portfolio standard deviation formula, which accounts of correlation between assets, then you will get same value of standard deviation in both #1 and #2.

But if you want some fun, then you can play around with standard deviation profile in each asset class. It's quite useful in algorithmic trading and for short term sometimes, you can see if it offers some insight for very long term, that might be good timepass.



Edited 2 time(s). Last edit at Wednesday, August 4, 2010 at 02:28PM by d0pa.

thommo77

For single year periods you should use arithmetic mean, multiple year periods geometric. Alt. #2 doesn't make sense because you'd be taking an arithmetic mean of a geometric mean. You can take geometric means of arithmetic figures, but not the other way around because the geometric mean is a exponential figure whereas arithmetic average is additive.


If you work the two methods out on a spreadsheet you'll find theres a difference between the two which is due to the compounding of interest. It would grow the greater the variability in returns. Think about it, with Alt #2 your taking 1000 stocks and computing their geometric means over 5 yrs; 1000 separate compounding interest rate paths. Whereas with Alt #1 your only taking the geometric mean of 10 separate asset classes.

bpdulog

d0pa, I don't think it makes sense to use geometric mean for the cross section e.g. the average return for a given year across all securities. And in Excel, method 1 & 2 yield different results (ca 5% difference).

F-MBA, yes #1 seems a better approach. Although what makes me wonder is the fact that the annual returns that I calculate have an internal dispersion. But when I calculate the st dev for the asset class (e.g. the st dev of the series of mean annual returns) I never use that internal dispersion, so I am not leveraging all info included in my data set?

Jana, my securities are actually funds (active and passive), hence there is no market weights I can use ... right?

And finally, I came across a statistical approach called (TSCS) which promises to combine a time-series with a cross-sectional analysis, which I believe may be what I need. Anyone familiar with it? is it relevant?

mp3bu

C-uff-A Wrote:
-------------------------------------------------------
> d0pa, I don't think it makes sense to use
> geometric mean for the cross section e.g. the
> average return for a given year across all
> securities. And in Excel, method 1 & 2 yield
> different results (ca 5% difference).


But then, you'll have to normalize it (give weights) with market cap otherwise simple AM of returns means higher weigh for out-sized return and lower weight of lower return, while using GM means taking equal weight for returns. In AM, whenever few of the securities will post high return (say 10 names with 40% return) and rest will post low (90 names with 2% return), in this case AM (5.8) is more then twice the GM (2.6). If few names give outlier returns, they'll screw up AM.