3,991 research outputs found
Sparse and stable Markowitz portfolios
We consider the problem of portfolio selection within the classical Markowitz
mean-variance framework, reformulated as a constrained least-squares regression
problem. We propose to add to the objective function a penalty proportional to
the sum of the absolute values of the portfolio weights. This penalty
regularizes (stabilizes) the optimization problem, encourages sparse portfolios
(i.e. portfolios with only few active positions), and allows to account for
transaction costs. Our approach recovers as special cases the
no-short-positions portfolios, but does allow for short positions in limited
number. We implement this methodology on two benchmark data sets constructed by
Fama and French. Using only a modest amount of training data, we construct
portfolios whose out-of-sample performance, as measured by Sharpe ratio, is
consistently and significantly better than that of the naive evenly-weighted
portfolio which constitutes, as shown in recent literature, a very tough
benchmark.Comment: Better emphasis of main result, new abstract, new examples and
figures. New appendix with full details of algorithm. 17 pages, 6 figure
The repetition threshold for binary rich words
A word of length is rich if it contains nonempty palindromic factors.
An infinite word is rich if all of its finite factors are rich. Baranwal and
Shallit produced an infinite binary rich word with critical exponent
() and conjectured that this was the least
possible critical exponent for infinite binary rich words (i.e., that the
repetition threshold for binary rich words is ). In this article,
we give a structure theorem for infinite binary rich words that avoid
-powers (i.e., repetitions with exponent at least 2.8). As a consequence,
we deduce that the repetition threshold for binary rich words is
, as conjectured by Baranwal and Shallit. This resolves an open
problem of Vesti for the binary alphabet; the problem remains open for larger
alphabets.Comment: 16 page
A rapid procedure for the extraction of genomic DNA from intact Aspergillus spores
Genomic DNA of different species of Aspergillus was prepared from intact spores using the Nucleon MiY kit of Amersham. The method is rapid, does not involve mechanical disruption of the spores nor the use of phenol-chloroform extractions and yields DNA that is suitable for PCR amplification and Southern analysis. The method is also applicable to mycelium ground with glass beads
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