The Journal of Portfolio Management



Online Appendix: Technical Details on Portfolio ConstructionA portfolio construction process follows multiple steps with different design choices to be made in each step. This Appendix gives additional details for the parsimonious portfolio construction process.Sector AdjustmentFor every raw signal (s) for a given firm, we subtract the median signal for all firms that fall into the same industry/sector. Unscaled WeightsPercentile. This methodology ranks all n equities in the universe using the signal scores for the value metric in question. It then selects the x% of the names in the universe with the best metric to go long and the x% of the names in the universe with the worst metric to go short. The chosen longs (shorts) are weighted equally. In this analysis we apply different values for x with x∈10,25,33,50.Linear. This weighting methodology takes all equities in the universe and ranks them according to the chosen value metric, where a rank of 1 is linked to the lowest score and the highest rank is attributed to the asset with the best score. It then assigns a weight of +100% to the asset with the best score and -100% to the asset with the worst score with a linear tradeoff between score and weight for the assets ranked in-between these two extreme cases. Positive and negative weights are scaled to sum to +100 and -100%, respectively.Z-Score. The Z-Score methodology takes the signal score for all assets in the universe and performs a cross-sectional normalization by subtracting the average cross-sectional score and dividing the de-meaned score by the cross-sectional standard deviation of the score. Logistic. The logistic transformation applies a centered cumulative normal distribution (cdf) on the Z-Score of an asset to determine its weight. This methodology ensures that the weighting of an asset is rather responsive to changes in the signal around the average values but less so to changes to extreme signals. Logit. In the logit weighting methodology the Z-Score of the value signal is used as the starting point. We then scale the Z-Score to ensure that the maximum and minimum weights are reached for a Z-Score of approximately +/-2 which is also the threshold at which the Z-Scores are capped and floored, respectively. Furthermore, the methodology is parametrized to ensure that for Z-Scores of +/-1 the weights are with +/-0.16 rather limited. The logit signal transformation is useful in situations where signals of a lower magnitude do not carry lots of information and it is the more extreme signals that an investor wants to capture in his investments. Scaled WeightsOnce the unscaled weights have been determined, we scale them first pro rata on the positive side to ensure that all positive weights add to +100%. This step is then repeated for the negative weights which are scaled pro rata to add up to -100%. Short ImplementationWe either use the short S&P or short indidividual stocks (signal based) to control market exposure Relative Sizing of Long and Short PositionsHaving determined the weights for the long and the short side of the portfolio, investors frequently resize the total long and short exposures to better control the overall portfolio risk. In this article three different methodologies are used to determine the final investment weights. Cash neutral. A cash neutral portfolio construction methodology is implemented by ensuring that the sum of the absolute value of short weights is equal to the sum of the absolute value of the long weights. Risk neutral. Risk neutral weights are calculated by rescaling the short weights to have the same expected volatility as the long weights. Beta neutral. Another approach is to size the long and short side only as a function of their systematic risk. Such an approach is implementing a beta neutral portfolio construction by determining the S&P 500 beta on the long and the short side. The short side is then scaled to match the absolute value of the beta on the long side.Rebalancing FrequencyFinally, the portfolio is rebalancing in different intervalls: monthly, quarterly or annually. ................
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