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The authors demonstrated in earlier papers that a maximal predictability portfolio (MPP) using a dynamic strategy leads to a significantly better ex-post performance than the one based on a static strategy and the index. In this paper, we will consider a maximal predictability portfolio subject to transaction cost. To reduce transaction cost, we employ turnover constraint. It will be shown that this approach leads to a significantly better performance than the standard MPP and the index.

In this paper, we will propose a practical method for improving the performance of a maximal predictability portfolio (MPP) model proposed by Lo and MacKinlay and later extended by the authors. We will employ an alternative version of MPP using absolute deviation instead of variance as a measure of fitting and apply a dynamic strategy for choosing the set of factors which fits best to the market data. It will be shown that this approach leads to a significantly better performance than the standard MPP and the index.

Assume that $n$ mobile sensors are thrown uniformly and independently at random with the uniform distribution on the unit interval. We study the expected sum over all sensors $i$ from $1$ to $n,$ where the contribution of the $i^{\mathrm{\text{th}}}$ sensor is its displacement from the current location to the anchor equidistant point $t_i=\frac{i}{n}-\frac{1}{2n},$ raised to the $a^{\mathrm{\text{th}}}$ power, when $a$ is an odd natural number.

As a consequence, we derive the following asymptotic identity. Fix $a$ positive integer. Let $X_{i:n}$ denote the $i^{\mathrm{\text{th}}}$ order statistic from a random sample of size $n$ from the Uniform$(0,1)$ population. Then