Building portfolios based on machine learning predictions

Figures & data

Table 1. Performance of an Equal-Weighted Portfolio vs. Equal-Weighted Benchmark.

Performance measure	n = 10	n = 20	n = 30	n = 40	n = 50	S&P500
Return	14.3	14.5	13.9	14.3	14.3	12.4
Stand dev	23.7	20.4	19.0	18.2	17.5	14.8
Max drawdown	45.5	38.7	36.3	33.2	31.3	22.5
Sharpe ratio	0.60	0.71	0.73	0.78	0.82	0.84
Calmar ratio	0.31	0.38	0.38	0.43	0.46	0.55

Table 1 presents the performance measures of five equal-weighted portfolios built with random forest predictions. In each month, $n$ stocks with the highest predictions are chosen for the portfolio. The data is compared to an equal-weighted portfolio consisting of all stocks from the S&P500 index. The data covers the period from 1/01/2010 to 31/12/2020. Table 1 consists of seven columns: the name of the performance indicator, five columns representing five equal-weighted portfolios consisting of 10 (n = 10), 20 (n = 20), 30 (n = 30), 40 (n = 40), and 50 (n = 50) stocks, and the seventh column that represents an equal-weighted S&P500 portfolio (S&P500). Each row represents a performance measure: annual return (Return), standard deviation (Stand dev), maximum drawdown (Max drawdown), the Sharpe ratio (Sharpe ratio), and the Calmar ratio (Calmar ratio). The first three rows are presented in percentage points (Return, Stand dev, and Max drawdown).

Source: The Authors.

Table 2. Performance of Optimized Portfolios vs. Equal-Weighted portfolios and Equal-Weighted benchmarks.

	n = 25	n = 50	n = 75	n = 100	n = 125	n = 150	n = 175	n = 200	n = 225	n = 250
Panel A: Sharpe ratio
Equal-weighted	0.76	0.82	0.90	0.92	0.92	0.94	0.93	0.94	0.91	0.90
MV-weighted (1 year)	0.77	1.02	1.02	1.05	1.08	1.06	1.08	1.12	1.12	1.13
MV-weighted (2 years)	0.83	0.98	1.01	1.05	1.06	1.03	1.06	1.11	1.13	1.15
MV-weighted (3 years)	0.87	0.99	1.01	1.04	1.06	1.01	1.03	1.09	1.11	1.14
HRP-weighted (1 year)	0.87	1.03	1.05	1.06	1.07	1.12	1.07	1.06	1.01	1.02
HRP-weighted (2 years)	0.90	1.03	1.05	1.07	1.09	1.13	1.10	1.07	1.05	1.05
HRP-weighted (3 years)	0.91	1.04	1.06	1.06	1.10	1.13	1.09	1.08	1.04	1.05
S&P500 equal-weighted	0.84	0.84	0.84	0.84	0.84	0.84	0.84	0.84	0.84	0.84
S&P500	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97
Panel B: Calmar ratio
Equal-weighted	0.39	0.46	0.51	0.54	0.55	0.59	0.59	0.59	0.57	0.58
MV-weighted (1 year)	0.42	0.59	0.63	0.70	0.78	0.76	0.76	0.78	0.78	0.78
MV-weighted (2 years)	0.45	0.56	0.61	0.65	0.68	0.67	0.72	0.76	0.77	0.79
MV-weighted (3 years)	0.50	0.57	0.61	0.64	0.66	0.62	0.65	0.68	0.68	0.69
HRP-weighted (1 year)	0.49	0.61	0.64	0.69	0.71	0.77	0.76	0.76	0.73	0.75
HRP-weighted (2 years)	0.52	0.61	0.64	0.67	0.72	0.78	0.77	0.76	0.75	0.78
HRP-weighted (3 years)	0.53	0.62	0.66	0.66	0.71	0.76	0.75	0.75	0.74	0.77
S&P500 equal-weighted	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55	0.55
S&P500	0.73	0.73	0.73	0.73	0.73	0.73	0.73	0.73	0.73	0.73

Table 2 presents the Sharpe and Calmar ratios of portfolios with different stock numbers and different construction techniques. This table consists of 11 columns. The first column represents the name of the construction technique. Columns 2-11 demonstrate portfolios with different number $n$ of stocks selected to build them. The rows are organized by panels. Panel A presents portfolio performance measured with the Sharpe ratio. Panel B presents portfolio performance measured with the Calmar ratio. Both panels demonstrate the same portfolio construction techniques represented in nine rows. The first row shows equal-weighted portfolios constructed with the 1/N rule (Equal-weighted). Rows 2-4 show mean-variance optimized portfolios with maximum weight in a single stock at 5%, random forest prediction used as expected returns, and shrunk covariance matrix fed with $d$ days of historical daily stock prices, where $d=365$ days for MV-weighted (1 year), $d=2*365$ days for MV-weighted (2 years), and $d=3*365$ days for MV-weighted (3 years). Rows 5-7 show HRP optimized portfolios with the optimizer fed with $d$ days of historical daily stock prices, where $d=365$ days for HRP-weighted (1 year), $d=2*365$ days for HRP-weighted (2 years), and $d=3*365$ days for HRP-weighted (3 years). Row 8 presents equal-weighted portfolios consisting of all stocks from the S&P500 index. Row 9 presents the results of the S&P500 index. The data covers the period from 1/01/2010 to 31/12/2020.

Source: The Authors.

Figure 1. Equal-Weighted Portfolios vs. SPX500 Equal-Weighted.

This figure presents a line plot between the compounded rate of return and dates. The lines show the compounded total return of two equal-weighted portfolios consisting of 10 stocks (n = 10) and 50 stocks (n = 50) vs. the compounded total return of the equal-weighted S&P500 index. The sample period runs from 01/01/2010 to 31/12/2019.

Source: The Authors.

Figure 2. Optimized Portfolio Performance Depending on the Length of Historical Data.

This figure presents line plots between the Sharpe or Calmar ratios and the number $n$ of stocks in portfolios. The two upper subfigures present the Sharpe ratio on the vertical axis. The two lower subfigures present the Calmar ratio on the vertical axis. The two subfigures on the left demonstrate ratios for the mean-variance (MV) optimized portfolios. The two subfigures on the right demonstrate ratios for the HRP (HRP) optimized portfolios. Optimizers fed with $d=365$ daily historical data are marked as 1-year history. Optimizers fed with $d=2*365$ daily historical data are marked as 2-year history. Optimizers fed with $d=3*365$ daily historical data are marked as 3-year history. The sample period runs from 01/01/2010 to 31/12/2019. The data covers stocks from the S&P500 index.

Source: The Authors.

Figure 3. Portfolio Performance Depending on Creation Technique.

This figure presents line plots between Sharpe or Calmar ratios and the number $n$ of stocks in portfolios. The left subfigure presents the Sharpe ratio on the vertical axis. The right subfigure presents the Calmar ratio on the vertical axis. The equal-weighted line represents portfolios built with the 1/N rule. The MV-weighted (2 years) line represents portfolios built with the mean-variance optimizer using 2 years of daily historical prices. The HRP-weighted (2 years) line represents portfolios built with HRP optimized using 2 years of daily historical prices. The S&P500 equal-weighted broken line represents an equal-weighted portfolio of all stocks from the S&P500 index. The S&P500 dotted line represents the market portfolio of the S&P500 index. Note that for S&P500 equal-weighted and S&P500, all index constituents are taken under consideration; thus, the horizontal axis representing the different number of stocks used to create a portfolio does not impact these constants.

Source: The Authors.

Data availability statement

The data that support the findings of this study are available from Refinitiv. Restrictions apply to the availability of these data, which were used under license for this study. Data are available from the authors on request with the permission of Refinitiv.