Comparing the Asset Allocation Methods

Asset Allocation
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Asset Allocation In comparing the asset allocation methods, performance considerations were made while assuming the other factors of consideration, such as personal goals, risk appetite, and types of investment horizon, were constant. While allowing only one input tuning parameter, various risk allocation methods were compared to a specific uncertainty set. From the results, strategies performances were compared using the methods. The results indicate that the out-of-sample Sharpe ratio and in-sample Sharpe ratio for the Bayes-Stein with no-short-sale constraints gave the highest turnover value. However, the optimum number of asset investments must be medium for it to give the best turnover. A high asset number gave a low turnover value, and a low asset number also gave a low value for turnover, while a medium number of assets gave the highest value. For these reasons, using Bayes-Stein with no-short sale and risk-free assets with low asset numbers was considered the best method. However, estimations were not enough to reach a meaningful conclusion about the most relevant asset allocation strategy, and data were generated to compare performance. The following light-tailed distribution of the simulated data was obtained by using a loading vector B for N = 9 risky assets and simulating a noise covariance matrix for all N = 9 risky assets.   Light-tailed distribution   Where the risk-free rate , , and   Using  ,  a T-distribution of heavy-tailed distribution was determined as below.   Heavy-tailed distribution The above excess return is of the risky asset N=10, and the histogram of the heavy-tailed distribution is apparent from the density considerations since the distribution is heavy around 0. Using these two distributions, the performance of the risky asset and risk-free asset allocation methods were compared, and the results are shown in the tables below. In determining the values, the following formulas were used: Rebalancing:    Sample-based unbiased mean-variance:   Sample-based unbiased mean-variance:   Bayes-Stein:   Minimum-variance:   Sample-based mean-variance with no-short sale constraints:   Bayes-Stein with no short sale:   Minimum-variance with no short sale:   Uncertainty in mean with box uncertainty set:   Uncertainty in mean with ellipsoid uncertainty:   Distribution robust:   Case 1. With normal distribution. N = 10, M = 120, T = 2400 In this case, the number of assets was kept low, while the number of observations used for training was high. Normal distribution of the assets was used during training. Case 1: Normal Distribution Case 2: t-distribution. N = 10, M = 120, T = 2400 In this case, the number of assets was kept low, while the number of observations used for training was high. However, the type of distribution was changed to increase the risk-free asset's chances.   Case 3: N = 10, M = 500, T = 2400 In this case, the number of assets was kept low while the number of observations used for training was increased, and normal distribution was used.