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8

You should consider an unsupervised learning algorithm such as K-nearest neighbor ('KNN'). KNN will measure the distance amongst the observations in your space. You can and probably should consider alternative distance functions (besides euclidean) particularly if you are clustering on features such as returns which have outliers. There are quite a few ...


7

An index is just an abstract concept and does not hold securities. Hence no source of revenue from lending them. A portfolio mirroring an index holds the securities and can in fact generate revenue by loaning the securities to others wanting to short the stocks. This provides a positive bias. That is often offset by a negative bias when the index ...


5

In general, it depends on the particular ETF, and should be checked in the prospectus, but one standard way (e.g. SPY) is to do it on a daily basis based on NAV published after the close. E.g. NAV per share = X$, so the expenses taken out would be X*0.03/(100*252). Again usually ETF's have cash component (with aggregated dividends etc), so there's no problem ...


5

Quant Guy's answer is quite informative for your question already. Just to add few other things: instead of figuring out the choice of features by your own brain, you could also use machine learning techniques to help in extracting the 'features' for your specific purpose, e.g. risk modeling or returns forecasting or portfolio construction as mentioned by ...


5

Are there any other mechanisms at play here which might explain this kind of tracking error? Dirk is right, you often lend the titles internally or not, etc. You can also write calls for your index, this is not orthodox, but it's ETF, there is no orthodoxy there... Edit : With the graph and given the outperforming is seasonnal (around May), I think we ...


4

There is a good article in Seeking Alpha but if you did a Google Search you probably found it already. Some ETF's work through swaps with a counterpart, but you will never know who the counter-part is. As you said it depends on the type of ETF, with a UCITS ETF you're not supposed to have a big counter-part risk as you own the underlyings, when it's ...


4

I would look to run a pre-optimization routine over the whole universe of 200+ ETFs. I would use this pre-optimization to reduce the universe to a cardinality that provides optimal diversification effects. You can do that by first looking at pair-wise correlations and then also run optimizations to reduce portfolio variance by utilizing the covariance ...


3

Here couple ETFs that may satisfy what you are looking for: http://www.quant-shares.com/etf-list/ http://www.etc.db.com/GBR/ENG/Institutional/Downloads/ISIN/Factsheets/GB00B4N0QN94 http://guggenheiminvestments.com/products/etf/wmcr http://etfdb.com/type/investment-style/high-beta/ Those include ETFs with a momentum approach, mean-reversion approach, ...


3

It depends on your ETF. Some have synthetic exposure to the index sold by a sponsor (ie someone give them exactly the performance of the index) but this has a cost (a constant / deterministic drag on the NAV of your ETF which doesn't appear in your tracking error). Futures on the other hand have basis, are sensitive to changes in implied dividends and ...


3

It depends a lot on the structure of the ETF, it could be : * In the "terms and conditions" of the (highly possible) total return swap of the fund * Portfolio insurance * Option combination (or cap & floor) I think it's in the swap details, already saw that a few times.


3

In my mind, there are two questions here: 1) How does DB make money given a zero expense ratio? This is covered by Dirk and Lliane. Basically, DB gets cheap funding and stock loan fees in return for paying marketing / index / hedging costs. The ETF investor gets zero expense ratio in return for taking DB credit risk. 2) Why does it look like the etf ...


3

Unless explicitly mentioned, iShares ETFs do not apply any currency hedging directly. (See the factsheet for the case of IJPN. The base currency is USD merely because it is the common currency for a set of identical funds offered in many different versions around the world. At the end of each day they mark their books in USD, converting their ...


3

To answer your questions: 1) Yes, the above table is correct 2) Your results are correct except..... 1X loss = 9.6%. When you combine both positive and negative changes, it is the MEDIAN value that is of interest. Here are some links: http://www.futuresmag.com/Issues/2010/March-2010/Pages/Trading-with-leveraged-and-iinverse-ETFs.aspx ...


2

I recommend you read the Financial Stability Board report. FT Alphaville provides a nice summary of the report with plenty of links to investigate further.


2

I found this searchable/sortable list: http://www.etftrends.com/etf-analyzer.php . Premium membership is required to sort by inception date, $15/month.


2

MSCI has country indices for developed markets going back to 1970 in many cases and a decent history for emerging markets (starting 1988). iShares has pretty liquid ETFs for many of the most popular countries and regions, such as EAFE (EFA), Emerging Markets (EEM), Japan (EWJ), Germany (EWC), Canada (EWC), etc. Other major indices with very long histories ...


2

When I select assets for a portfolio given an universe, I tend to pick ones that span the beta spectrum, given your selected benchmark. I find that if your portfolio of assets have varying volatility or correlation, you can achieve better diversification. I didn't come up with the idea but it comes from a rotational system's framework from the link below: ...


2

Rather than suggesting alternative clustering techniques, as Quant Guy and Flake have (great advice, btw), I'll offer my thoughts on the method you've proposed. On the characteristics used to cluster stocks: You propose using sample statistics (mean and standard deviation of returns). I would suggest you use the entire return (not price) series. For ...


2

The futures price goes to the spot price as time to maturity declines, not vice-versa. The difference is referred to as basis. That's not really what roll yield is about though. The roll yield aspect is that as the contracts the ETF holds are expiring, they are close to the spot price. However, the next futures contract's price is higher than the price of ...


2

Have you considered using 'incremental' singular value decomposition to calculate your component scores? Each future market move (or increment) forces a recalculation of component scores given the new data. This paper outlines an algorithm to do this Fast Low-Rank Modifications of the Think Singular Value Decomposition This paper develops an identity ...


1

Hedginge/Adjusting would be with the Beta of the inverse ETF. Usually, Long/Short strategy would involve an ETF and a stock in which you would Beta adjust the ETF position. You can use an ETF, I don't see anything wrong with this as long as their is some level of correlation between the Short and the Long. You want them to mean revert in a determined time ...


1

Your approach is a good one. But before you venture too far, you should be aware of issues related to zero eigenvalues (positive semi-definiteness) of your correlation matrix $\mathbf{R}$ or covariance matrix $\mathbf{C}$. Let $p$ be the number of assets, and $t$ the number of, for example, day or bars. You probably have many more times in the time ...


1

The day's net change is typically displayed as the $Close$ to $Close$ difference. So today's close of $\$107.69$, yesterday's close is $\$105.00$. So the net change, $\$107.69 - \$105.00 = \$2.69$. If you were to calculate $Open$ to $Close$, you'd get what you expect, $\$0.74$.


1

The key reason why you observe divergent performance patterns is related mostly to the following: The biggest reason is the different cost to hedge those products. The costs to implement and especially maintain the hedge on the long vs short side can be very different. Either the hedge is implemented through an index replication in which case the manager ...


1

There are three prices to consider when discussing an ETF: the ideal price as represented by the index, the NAV of the fund based on that day's holdings, and the market value traded on a stock exchange. This third price is what you see. In your example, Russell has calculated a cap-weighted value based on the annual membership. Direxion then determines ...


1

I've used the graphical lasso for exactly this kind of thing in the past. You can control the degree of shrinkage, which determines the how tight the clusters become.


1

Even in a perfect world, a 3X leveraged ETF cannot achieve a compound return three times that of the underlying. In the case of periodic discrete rebalancing, we call this effect the "arithmetic of loss and recovery," but even in the limit of continuous rebalancing, this effect does not disappear. Ito's formula tells us that $$\mathrm d ...


1

Your example could be correct but you're on the wrong track. Leveraged ETFs are designed for day trading, it isn't a leveraged 3x position that will return 3x the long term average of the name. The leverage is reweighted each day which will affect your performance. Eg if the market goes 100->99->100 the market is unchanged over 2 days. But a 3x ETF will go ...



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