Quant analysis of managed funds

Water Cooler Investing
#1

Hi, does anyone know the answer to below, been annoying me all day.

I want to separate out total standard deviation of an actively managed fund into tracking error and standard deviation of the benchmark. So if I have expected st dev of benchmark is x and expected tracking error of fund is y then what is the total expected risk? I thought it would be the same formula as a 2 stock or 2 fund portfolio with the weights = to beta of the fund and (1-beta) of the fund. When I test the below it doesn’t work out.

[beta^2*X^2 + (1-beta)^2*Y^2 + 2*beta*(1-beta)*covar(tracking error return, index return)]^0.5

Any ideas?

#2

It’s late and I’m sleepy and I’ve had a few glasses of wine earlier so I’m not 100% sure right now. But I would think that the covariance between your tracking error and your index return should be zero. So yeah,

Total expected error would equal

[(beta*benchmarkSigma)^2 + ( expectedTrackingError )^2]^(1/2)

That’s for a one-factor model. If you have more than one factor, then you have to add a bunch of covariance terms to adjust for how the different benchmark factors are correlated to each other. By definition, tracking error is uncorrelated with (the jargony word is orthoganal-to) all of the benchmarks.

#3

thanks bcad, I tested your formula and doesn’t add up. Can I send you a simple excel sheet with example? or test it yourself if you have time, just make up fund return and benchmark return for a few period sand try match the total st.dev of the fund to the formula above.

Many thanks, its driving me crazy

#4

I’ll take a look at it, but I need to set up an AF oriented email address first, or you can post yours and I’ll get in touch.

#5

Cheers, mines brookcc@gmail.com.

#6

I always find it easier to work with matrices. The formula should be

B_f*sigma_f*B_f’+sigma_e

where B_f is an nXf matrix of factor exposures, sigma_f is an fXf covariance of factors, and sigma_e is an nXn covariance matrix of the error/residual (n is the number of funds, f is the number of factors).

#7

Btw, I shot you an email, but never heard back. No problem if you aren’t so worried about it anymore, but just to let you know I did try.

#8

Hello,

My opinion you can consultant the expert. they will told you the proper advice.