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minimum variance portfolio using get_fundamentals()

Something I finally got to work, so I thought I'd throw it out to the masses for critique. --Grant

9 responses

are you sure you are calculating the returns correctly? for me it looks like you are working with price differences (i.e. after taking the diff between consecutive prices, you do not divide by the base price).
furthermore: it looks like the weights do not change from the initial weight (i.e. 0.05). for me it looks like the something is wrong with the scaling the variance/covariance matrix ... as you are calculating them using minute returns, already using the starting weights produces an extremly low variance so that the optimizer seems to stop without actually doing something useful.

just my two cents

Have had that issue with scipy.optimize. You can either adjust the solver's tolerance or scale up the inputs (I prefer the latter). Generally what I do is turn daily variance into annual volatility multiplied by 100 so that small changes in daily variance become obvious to the solver.

Nice, no better way to learn Numpy/Pandas then reading your code.

I used to compute the return in a ugly way this is much better.

ret = np.diff(prices,axis=0) # returns  

How do you organize your codes in Quantopian, whenever I open my algorithms I have a urge to try to organize it, but with a flat list it is kinda hard. Prefix with parameters?

I agree, I don't think np.diff() is computing the returns but only the change in price (not percent change).

Instead you can use the .pct_change() method of a pandas dataframe (as returned by history).

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Or of course the diff of the log-prices.

Thanks for the feedback, all. Here's an update, with:

    prices = history(3*390,'1m','price')  
    ret = 1000000*prices.pct_change().dropna()  
    ret = pd.ewma(ret,span=60).as_matrix(context.stocks)  

I also added leverage tracking.

Some mysteries:

  • Per Matt's advice, the inputs to the optimizer need to be scaled. This is disturbing, since I would think that there would be normalization internal to the optimizer.
  • The leverage jumps up during the backtest, which suggests something is not working as hoped. The portfolio allocation should always sum to 1.
  • Is the variance actually being minimized by the optimizer? This could be checked by solving for the minimum analytically (see http://faculty.washington.edu/ezivot/econ424/portfolioTheoryMatrix.pdf), and the code would probably run faster, too.

Grant

Has anyone managed to get this algorithm to work again after the recent upgrade? My attempts are failing...

Here's an updated version. I changed the np.asarray(args) to np.asarray(args[0]) to prevent the creation of a 3D ndarray.

Thanks Thomas.