Calculating Ex Ante Tracking Error
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it indicates how closely a portfolio follows the index to which it is benchmarked. The best measure ex ante tracking error excel is the standard deviation of the difference between the portfolio and ex-ante tracking error models index returns. Many portfolios are managed to a benchmark, typically an index. Some portfolios are expected to ex ante tracking error definition replicate, before trading and other costs, the returns of an index exactly (e.g., an index fund), while others are expected to 'actively manage' the portfolio by deviating slightly
Ex Ante Vs Ex Post Tracking Error
from the index in order to generate active returns. Tracking error is a measure of the deviation from the benchmark; the aforementioned index fund would have a tracking error close to zero, while an actively managed portfolio would normally have a higher tracking error. Thus the tracking error does not include any risk (return) that is merely ex ante beta formula a function of the market's movement. In addition to risk (return) from specific stock selection or industry and factor "bets," it can also include risk (return) from market timing decisions. Dividing portfolio active return by portfolio tracking error gives the information ratio, which is a risk adjusted performance measure. Contents 1 Definition 1.1 Formulas 1.2 Interpretation 2 Examples 3 References 4 External links Definition[edit] If tracking error is measured historically, it is called 'realized' or 'ex post' tracking error. If a model is used to predict tracking error, it is called 'ex ante' tracking error. Ex-post tracking error is more useful for reporting performance, whereas ex-ante tracking error is generally used by portfolio managers to control risk. Various types of ex-ante tracking error models exist, from simple equity models which use beta as a primary determinant to more complicated multi-factor fixed income models. In a factor model of a portfolio, the non-systematic risk (i.e., the standard deviation of the residuals) is called "tracking error" in the
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Annualized Tracking Error Formula
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Ex Ante Tracking Error Example
a question and answer site for finance professionals and academics. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers https://en.wikipedia.org/wiki/Tracking_error are voted up and rise to the top ex ante tracking error correlation between funds up vote 2 down vote favorite I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold the same stocks. I would like to examine the correlation of the ex-ante http://quant.stackexchange.com/questions/11101/ex-ante-tracking-error-correlation-between-funds between the two funds. I know I can calculate the ex-ante tracking error as below, te = sqrt((port_wgt - bm_wgt)' * cov_matrix * (port_wgt - bm_wgt)) I also know the correlation is calculated by p = cov(x,y) / stdev(x) * stdev(y) I was wondering the best way to calculate the ex ante correlation between the two funds? Is there a relationship between the two funds weights that I can make use of? Update I should have mentioned that the two portfolios are sub portfolios and are combined into one portfolio. So I wanted to see the correlation of the ex ante tracking error between the two sub portfolio's. I realised I can do the following, port_wgts - number_of_companies x 2 matrix cov_matrix - number_of_companies x number_of_companies matrix so the below line will return a 2x2 covariance matrix. port_wgts' * cov_matrix * prt_wgts So I have the variances of both sub portfolios - taking the square root of this gives me the tracking error for both. Convert the 2 X 2 covariance matrix to a correlation matrix by the following D = Diag(cov_matrix)^(1/2) corr_matrix = D^-1 * cov_matrix * D^-1 So I now have the correlation between the two sub portfolios jus
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 http://www.investinganswers.com/financial-dictionary/mutual-funds-etfs/tracking-error-4970 first is to 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 tracking error follows: How it works (Example): 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 ante tracking error XYZ Company mutual fund had a 0.5% tracking 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 port
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