Please find it below:
“Tracking risk (also called tracking error) is the standard deviation of the deviation of a portfolio’s gross-of-fees total returns from benchmark return. Calculate the tracking risk of the portfolio, stated in percent (give the answer to two decimal places). The table below gives the annual total returns on the MSCI Germany Index from 1993 to 2002. The returns are in the local currency. Use the information in this table to answer Questions 5–10. MSCI Germany Index Total Returns, 1993–2002 Year Return (%) 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 46.21 −6.18 8.04 22.87 45.90 20.32 41.20 −9.53 −17.75 −43.06” Doubts: 1. Tracking error definition is mentioed as std devn for the devn from benchmark…how can we assume benchmark is the mean of the given sample? (This is what they did in Textbook solution) Also, if I key in the data given in the sample in data mode on TI BAII Plus and calc the std devn for that and then subtract each data value from the std devn (Why am I doing this? I interpret std devn of devn like that. Am I incorrect?), I get the same result as the first std devn, which is strange. I mean first you get a std devn for a sample as x; now you subtract all data points in the sample from this value x which appeared as Sx on your TI BA II Plus. Then, you calc the Sx again for the data points obtained in the above step. You land up with “x” again. STRANGE! I think I didn’t give my best to put up my question clearly. Please let me know if I can make it more clear. Source: Ibbotson EnCorr AnalyzerTM. (Institute 392) Institute, CFA. Level I 2013 Volume 1 Ethical and Professional Standards and Quantitative Methods. John Wiley & Sons P&T, 7/3/2012. .
they subtracted the mean of the 10 values - since your sample of 10 returns is returns of the index itself.
deviation = sample return point - mean of the sample
and you need to do that first
and determine the standard deviation of that.
But they are talking about deviation from the benchmark, not from the mean.
since it is the MSCI German Index that you are measuring in the absence of any other info - the benchmark would also be itself.
and tracking error = std deviation of active returns.
Active return = return on portfolio - return of benchmark
so in this case - the return of the benchmark = avg of returns provided (mean of the 10)
active return = return in year 1 - mean return.
and so on.
now use those active returns and calculate the std deviation of the active returns.