Questions tagged [tracking-error]

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Relationship between Tracking Error and Beta to benchmark

Analyzing an indexed portfolio, can we say there is any relationship between ex-ante TE and Beta to benchmark? Tracking error is the volatility of the difference in returns between the portfolio and ...
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1answer
90 views

portfolio information ratio calculation on daily returns including hedged strategy results interpretation

I am tasked with calculating the portfolio information ratio on ~15 years of daily portfolio returns and I am finding several approaches online which is quite confusing. The first approach simply ...
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1answer
64 views

Track an index with futures only: what to do with the cash?

Suppose your mandate is to track S&P500. Suppose the mandate size is $ 1,352,500. The contract size of the future is 50, today's index price is 2705. If I buy 10 contracts my exposure will be ...
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0answers
267 views

What to use for Tracking error minimization

What programs/packages can one use to minimize a portfolio's tracking error? What I am trying to do is see what ex post TE, portfolio returns and variance can be achieved when adding CSR constraints ...
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3answers
395 views

Negative variance?

Using the formula w*Cov*t(w) I can generate a negative portfolio variance. What are the implications of a negative variance? Should I just assume it's zero? A negative variance is troublesome ...
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1answer
133 views

Genetic Algorithm - Portfolio Optimization / Index Tracking crossover process

i am currently doing a research on index tracking using Genetic Algorithm (replicating the index using a subset of the index members). This is a new topic to me. I have been reading research paper on ...
2
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1answer
307 views

minimise tracking error whilst reducing number of trades required

I have a portfolio which is a subset of a benchmark. I want to minimise the tracking error between my portfolio and the benchmark. Currently I use APT's risk model to do this. I set it to run for 10 ...
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1answer
401 views

What is the formulat to compute Tracking Error?

I am here for the first time and read quite a few posts before asking this question. In my class, my finance Professor wrote the formula for Tracking Error $TE$: $$TE = \sqrt{(1-R^2)} \times \sigma$$ ...
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2answers
1k views

Ex-Ante Tracking Error : active strategies and the size of the covariance matrix

The most common formula for the ex-ante tracking error is $\sqrt{w^{T}Cw}$, where $w$ is a vector of excess weights relative to the benchmark and $C$ a forecast of covariance matrix. The sums of both $...
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1answer
100 views

How to find coefficient that will minimize the distance between few times series

I have 3 time series X1, X2, X3. I want to find the coefficient (c1, c2) that will minimize the distance between them as follow: $$MIN\sum\sqrt{(X1-(c1*X2+c2*X3))^2}$$ The constrains are: $$-1< ...
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2answers
5k views

How to calculate ex Ante Tracking Error

I'm looking to find the correct way to calculate the ex ante tracking error of a portfolio. If say I have 10 funds, and their historical returns series (used to calculate mean return, standard ...
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0answers
61 views

Subclass Tracking Error

I am currently doing a master program project regarding tracking errors. My assignment is to evaluate following question: How to find out the correlation structure of the passive (=second order/sub-...
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1answer
8k views

How to calculate annualised tracking error?

I have 36 months of relative returns and I need to calculate the annualised tracking error. So, using 36 months of returns is it simply like below: ...
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1answer
2k views

Understanding how to calculate tracking error

I have come across two ways of calculating Tracking Error (TE) but i'm not sure if they are essentially the same. The first way is to calculate the standard deviation of the difference between a fund'...
2
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1answer
540 views

ETFs have lower tracking error than Futures?

I used the daily returns of SPX Index, SPY US Equity, and SPA Index. I then calculate their standard deviation as hedging instruments with respect to SPX Index, i.e., (spx_ret - spy_ret) or (spx_ret - ...
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1answer
1k views

Ex-Ante tracking error how to determine the look back period

I am looking to compare the ex-ante predictions against the post values. I am using a look back period of ranges from 1 year to 5 years to construct my covariance matrix that I am using for my ex-ante ...
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1answer
1k views

Min VaR and Min TE as second order cone program

The quadratic optimization (min variance) $$ w^{T} \Sigma w \rightarrow \text{min}, $$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...
4
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1answer
751 views

How to calculate tracking error given mismatches in available data

Apologies if this is an overly simple question. I have a series of stock returns, and I would like to estimate my portfolio's ex-ante tracking error versus the benchmark (S&P 500) given the ...
6
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2answers
3k views

Which objective function should I choose to minimize tracking error?

Let say I have $n$ assets and their returns over $m$ periods which are represented by a matrix $X \in \mathbb{R}^{m \times n}$, and I have some other asset with return over the same period which is ...