Improving portfolio investment performance with distance‐based portfolio‐combining algorithms

We propose distance‐based portfolio‐combining algorithms to improve out‐of‐sample performance in the presence of estimation errors. Our algorithms use approaches similar to the shrinkage method but with a different weighting scheme: the Euclidean distance. The Euclidean distance of a portfolio is its 2‐norm distance to the in‐sample tangency portfolio. These algorithms aim to construct a portfolio with a small Euclidean distance by making a convex combination of any number of portfolios. We propose three distance‐based portfolio‐combining algorithms: a distance‐based portfolio combination, a distance‐based asset combination, and a distance‐based asset combination with systematic errors (DAc‐S). Each algorithm consists of two steps. First, we predict the Euclidean distance of each portfolio using time‐series forecasting methods. Second, we increase (decrease) the combination level of a portfolio whose predicted Euclidean distance is small (large). We use 11 empirical data sets, and the numerical results show that our proposed algorithms significantly improve the Sharpe ratio with reasonably low portfolio turnovers. This outperformance stems from successfully decreasing the Euclidean distance. Most important, the DAc‐S achieves a significantly high Sharpe ratio and the smallest Euclidean distance.