Annualised Tracking Error Formula
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Tracking Error Formula Excel
minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How to calculate annualised tracking error? up vote 0 down vote favorite I have 36 months of relative returns and I need to calculate the annualised tracking error. So, using 36 months of ex ante tracking error formula returns is it simply like below: stdev(36 months of returns) * sqrt(12) Why the sqrt(12)? portfolio-management returns tracking-error share|improve this question edited Nov 3 '15 at 3:32 SRKX♦ 7,31032255 asked Sep 3 '15 at 11:38 mHelpMe 11811 add a comment| 1 Answer 1 active oldest votes up vote 1 down vote $\sqrt{12}$ annualizes monthly deviations. But I don't understand why you measure tracking error with stdev. It should be $$ ATE = \sqrt{\frac{12}{36}\sum_{i=1}^{36}(r_{b,i}-r_{t,i})^2}$$ where $r_{b,i}$ is benchmark return for month $i$ and $r_{t,i}$ is tracking portfolio return for same period. So you shouldn't substract average error inside square. share|improve this answer edited Sep 3 '15 at 13:10 answered Sep 3 '15 at 13:02 hvedrung 1596 This is correct, in particular, for ETFs. The scaling is needed for annualization. The same treatment is also employed for historical volatility estimation based on daily asset prices. –Gordon Nov 2 '15 at 14:42 I think his "returns" are as indicated in the question "relative" returns so they correspond to $\bar{r}_i = r_{t,i} - r_{b,i}
CFA Program CFA Forums CFA General Discussion CFA Level I Forum CFA Level II Forum CFA Level III Forum CFA Hook Up CAIA More in CAIA CAIA Test Prep CAIA Events CAIA Links About the annualized tracking error CAIA Program FRM More in FRM FRM Test Prep FRM Events FRM Links About the FRM calculate tracking error from monthly returns Program Careers Investments Water Cooler Test Prep Test Prep Sections CFA Test Prep CAIA Test Prep FRM Test Prep Calendar AF Deals CFA tracking error formula cfa Test Prep CFA Events CFA Links About the CFA Program Home Forums CFA Forums CFA General Discussion Tracking Error Calculation Tweet Widget Google Plus One Linkedin Share Button Facebook Like Last post whystudy Apr 20th, 2009 6:42pm CFA Charterholder http://quant.stackexchange.com/questions/19599/how-to-calculate-annualised-tracking-error 641 AF Points I have quarterly returns for a fund up to 5 years and also the benchmark mark. meaning I calculation the excess return. How can I calculate the Annualized Tracking Error and why? How does the formula change for monthly returns. Thanks 5 Reasons to Use Wiley in 2016 Reason #2: No Expiration Date. You get free updates until you pass. learn more Share this Facebook Like Google Plus One Linkedin Share Button Tweet Widget kblade Apr http://www.analystforum.com/forums/cfa-forums/cfa-general-discussion/9939876 20th, 2009 7:00pm CFA Charterholder 714 AF Points For annualized tracking error I think you need to take your quarterly returns and multiply them to get annual return annual = (1+q1)(1+q2)(1+q3)(1+q4) do the same for benchmark unless it is already in annual terms then tracking error is standard deviation of (portfolio return - benchmark return) for monthly returns it’s same formula, standard deviation of (portfolio return - benchmark return), just that they are monthly returns not annual to get monthly return take 4th root of your quarterly returns i.e. (1+q)^(1/4) unless you have monthly return for portfolio and benchmark already if you don’t then your tracking error will be same for first 3 months, for the next 3 months, etc. whystudy Apr 20th, 2009 7:07pm CFA Charterholder 641 AF Points kblade Wrote: ——————————————————- > For annualized tracking error I think you need to > take your quarterly returns and multiply them to > get annual return > annual = (1+q1)(1+q2)(1+q3)(1+q4) > do the same for benchmark unless it is already in > annual terms > > then tracking error is standard deviation of > (portfolio return - benchmark return) > > for monthly returns it’s same formula, standard > deviation of (portfolio return - benchmark > return), just that they are monthly returns not > annual > > to get monthly return take 4th root of your > quarterly returns > i.e. (1+q)
the benchmark or index it was meant to mimic or beat. Tracking error is sometimes called active risk. There are two ways to measure tracking error. The first is to http://www.investinganswers.com/financial-dictionary/mutual-funds-etfs/tracking-error-4970 subtract the benchmark's cumulative returns from the portfolio's returns, as follows: Returnp - Returni = Tracking Error Where: p = portfolio i = index or benchmark However, the second way is more common, which is to calculate the standard deviation of the difference in the the portfolio and benchmark returns over time. The formula is as follows: How it works (Example): tracking error Let's assume you invest in the XYZ Company mutual fund, which exists to replicate the Russell 2000 index, both in composition and in returns. If the XYZ Company mutual fund returns 5.5% in a year but the Russell 2000 (the benchmark) returns 5.0%, then using the first formula above, we would say that the XYZ Company mutual fund had a 0.5% tracking tracking error formula error. As time goes by, there will be more periods during which we can compare returns. This is where the second formula becomes more useful. The consistency (or inconsistency) of the "spreads" between the portfolio's returns and the benchmark's returns is what allows analysts to try to predict the portfolio's future performance. If, for example, we knew that the portfolio's annual returns were 0.4% higher than the benchmark 67% of the time during the last five years, we would know that this would probably be the case going forward (assuming the portfolio manager made no major changes). The predictive value of these calculations gets even better when there are more data points and when the analyst accounts for how the portfolio's securities move relative to one another (this is called co-variance). Several factors generally determine a portfolio's tracking error: 1. The degree to which the portfolio and the benchmark have securities in common 2. Differences in market capitalization, timing, investment style, and other fundamental characteristics of the portfolio and the benchmark 3. Differences in the weighting of assets between the portfolio and the benchma
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