Questions tagged [tracking-error]

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What is the correct method to maximize information ratio ex ante of a 150/50 portfolio against the S&P500

I have no problem forecasting and minimize ex ante information ratio for a market neutral portfolio, because the benchmark is just zero and you are just minimizing portfolio variance while maximizing ...
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Minimizing tracking error for a 150 / 50 portfolio against the S&P500

I am trying to minimize tracking error ex-ante for a 150 / 50 portfolio, eg. it is 150 units long, 50 units short and market exposure of 100 units. It uses all 500 stock in the S&P500. I've ...
xxanissrxx's user avatar
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"fix" a sample covariance matrix which is not positive semidefinite by using daily returns instead of monthly

In the portfolio optimization problem at hand, one of the constraints is that the tracking error should not be greater than $\gamma$. The constraint is therefore: $(\textbf{x}-\textbf{w})^\mathrm{T}\...
D. B.'s user avatar
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Methods for Constructing Mimicking Portfolios for Observable Factors

I've created some macroeconomic factors (e.g. analogs of real GDP growth) that I believe have explanatory power for asset returns. By a factor here, I mean a stationary time-series of real numbers. I'...
rubikscube09's user avatar
-2 votes
1 answer
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Industry best practice for minimizing tracking error [closed]

Lets say I have an alpha generating model that forecasts expected returns for SP500 stocks. I formulate a portfolio with 100 stocks having the highest expected return. What is the simplest way of ...
helloimgeorgia's user avatar
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How do you explain consistently making money with discrete hedging a call option?

In a backtest I did, I'm selling a call option and buying a delta amount of the underlying (calculated using implied vol). Now I know in the limit case of continuous hedging I end up paying a PnL ...
user121416's user avatar
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Constructing a Replicating Portfolio : Regression on Individual Constituents or their Average?

I would like to replicate a portfolio of stocks $S_1, \cdots, S_n$ using other instruments, $X_1, \cdots, X_m$. Using the letters above with a subscript $t$ to denote the forward returns over some ...
rubikscube09's user avatar
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1 answer
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Delta hedging error in B-S (hedging with implied vol) question

I have been thinking about this for a while and am at my wits end. Now assume I am pricing a call at implied vol $s$, whereas the realized volatility is $σ$. Let $C$ be the incorrect pricing function. ...
Arshdeep's user avatar
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How to calculate Annualized tracking error of an Index fund given daily historical data?

Let's say I have Fund A and Benchmark B and the daily data for both, stretching back 5 years. To find the Annualized Tracking Error (ATE), would this method be correct: Compute percentage change of A'...
SamuraiJack's user avatar
2 votes
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154 views

Active risk and tracking error (from AQR paper)

From this paper (https://www.aqr.com/Insights/Research/Alternative-Thinking/Was-That-Intentional-Ways-to-Improve-Your-Active-Risk) I would like to know how to solve for the amount of active risk (i.e. ...
Jeweller89's user avatar
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Tracking error and index tracking

Let's say I want to replicate an index like S&P500. People generally minimize a mathematical notion called tracking error which is nothing else than the standard deviation between the index's ...
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1 answer
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How to calculate a position's contribution to its portfolio's tracking error?

Say we have assets X (with weight $w_a$) and Y (with weight $w_y$) in a portfolio. X and B returns are correlated: $Cov(R_x, R_y)\neq 0$. The portfolio's tracking error is: $std(R_p - R_b) = std((w_x*(...
hartmut's user avatar
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1 answer
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Dax 30 Portfolio optimisation

Let's say I have a return forecast for each stock in the DAX index. I also have a covariance matrix for these 30 stocks. I want to solve for the 30 weights by maximising the forecast portfolio return,...
cune's user avatar
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1 answer
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N Needed for Statistically significant tracking error

Let's say I have the tracking error calculation for a portfolio: How would I determine the N-obervations required for a statistically significant tracking error? Alternatively, how would I determine ...
jason m's user avatar
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1 answer
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Marginal contribution to Tracking error

I'm trying to calculate Marginal contribution to Tracking error. I would use the following formula: MCTE(asset i)=TE(excess return asset i vs.benchmark)* Beta(excess return asset i vs. benchmark AND ...
Anton's user avatar
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1 answer
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Why is it better to use evolutionary algorithms than OLS for solving index tracking problem?

I am currently using different optimization algorithms for finding constrained portfolio that best replicate choosen index. So i have a optimization task to minimize tracking error. I wonder why every ...
SquintRook's user avatar
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1 answer
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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 ...
tweedi's user avatar
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2 votes
1 answer
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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 ...
trock2000's user avatar
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1 answer
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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 ...
tweedi's user avatar
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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 ...
Wouter Adolfsen's user avatar
2 votes
3 answers
4k 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 ...
rmacey's user avatar
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1 answer
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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 ...
Fabian Tan's user avatar
2 votes
1 answer
1k 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 ...
mHelpMe's user avatar
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1 answer
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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 $TE$: $$TE = \sqrt{(1-R^2)} \times \sigma$$ ...
MSFinanceStudent's user avatar
3 votes
2 answers
5k 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 $...
user1627466's user avatar
2 votes
1 answer
142 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< ...
Freewind's user avatar
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4 votes
3 answers
14k 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 ...
GT213's user avatar
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2 votes
0 answers
74 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-...
tr_ad's user avatar
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2 votes
1 answer
20k 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: ...
mHelpMe's user avatar
  • 259
2 votes
1 answer
3k 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'...
finstats's user avatar
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2 votes
1 answer
751 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 - ...
Mariska's user avatar
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1 vote
1 answer
2k 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 ...
mHelpMe's user avatar
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11 votes
1 answer
2k views

Minimum Variance and Minimum Tracking Error portfolio 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 ...
Richi Wa's user avatar
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4 votes
1 answer
896 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 ...
Centesima's user avatar
6 votes
2 answers
6k 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 ...
SRKX's user avatar
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