Figures & data
Figure 1. Cumulative returns of momentum-sorted naïve and optimised portfolios over the period January 2002 until October 2021.
![Figure 1. Cumulative returns of momentum-sorted naïve and optimised portfolios over the period January 2002 until October 2021.](/cms/asset/26d589b1-ae60-43e2-bb09-d508c78315f3/oaef_a_2231662_f0001_oc.jpg)
Table 1. Monthly average excess return and Sharpe ratios of naive and optimised momentum-sorted quintile portfolios from January 2002 to October 2021. Momentum is proxied by cumulative returns over the previous 252 trading days, skipping the most recent 21 days, and the risk-free rate proxied by 91-day SA government T-bill. Average returns are expressed monthly in excess of risk-free proxy with “***”, “**” and “*” indicating statistical significance at the 1%, 5% and 10% levels
Figure 2. Cumulative returns of value-sorted naïve and optimised portfolios from January 2002 to October 2021.
![Figure 2. Cumulative returns of value-sorted naïve and optimised portfolios from January 2002 to October 2021.](/cms/asset/160f1ce3-44b5-4bdf-a589-21f3d0375dd6/oaef_a_2231662_f0002_oc.jpg)
Table 2. Monthly average excess return and Sharpe ratios of naive and optimised value-sorted quintile portfolios from January 2002 to October 2021. Value is proxied by earnings yield adjusted for look-ahead bias by lagging accounting data by 63 days. Average returns expressed monthly in excess of risk-free proxy with “***”, “**” and “*” indicating statistical significance at the 1%, 5% and 10% levels
Figure 3. Cumulative returns of size-sorted naïve and optimised portfolios from January 2002 to October 2021.
![Figure 3. Cumulative returns of size-sorted naïve and optimised portfolios from January 2002 to October 2021.](/cms/asset/49caf68b-8e0f-4469-88e5-ad9e088ed94a/oaef_a_2231662_f0003_oc.jpg)
Table 3. Monthly average excess return and Sharpe ratios of naive and optimised size-sorted quintile portfolios from January 2002 to October 2021. Value is proxied by earnings yield adjusted for look-ahead bias by lagging accounting data by 63 days. Average returns expressed monthly in excess of risk-free proxy with “***”, “**” and “*” indicating statistical significance at the 1%, 5% and 10% levels
Figure 4. Cumulative performance of momentum, value, and size naïve and optimised factor premiums over the period January 2002 until October 2021.
![Figure 4. Cumulative performance of momentum, value, and size naïve and optimised factor premiums over the period January 2002 until October 2021.](/cms/asset/cf615586-a6d9-4cfb-86f0-7c3c1ef142c1/oaef_a_2231662_f0004_oc.jpg)
Table 4. Average monthly excess returns (factor premiums) and Sharpe ratios across naive and optimised across momentum, value, and style extreme quintiles. “***”, “**” and “*” indicate statistical significance at the 1%, 5% and 10% levels
Figure 5a. Returns-based style analysis per Sharpe (Citation1991) on naive long-only momentum (Q1) using naïve value, growth, and small- and large-cap quintile returns.
![Figure 5a. Returns-based style analysis per Sharpe (Citation1991) on naive long-only momentum (Q1) using naïve value, growth, and small- and large-cap quintile returns.](/cms/asset/afefa833-8bb7-4205-b5db-c7cf9cc9bf9a/oaef_a_2231662_f0005a_oc.jpg)
Figure 5b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only momentum (Q1) using optimised value, growth, and small- and large-cap quintile returns.
![Figure 5b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only momentum (Q1) using optimised value, growth, and small- and large-cap quintile returns.](/cms/asset/afbc6401-16ff-4c9f-a7a2-2d7996a34eea/oaef_a_2231662_f0005b_oc.jpg)
Figure 7a. Returns-based style analysis per Sharpe (Citation1991) on naïve long-only value (Q1) against naive winner, loser, and small- and large-cap quintile returns.
![Figure 7a. Returns-based style analysis per Sharpe (Citation1991) on naïve long-only value (Q1) against naive winner, loser, and small- and large-cap quintile returns.](/cms/asset/0ecb534e-9ef5-47fd-8842-c11f3ac8e4e8/oaef_a_2231662_f0007a_oc.jpg)
Figure 7b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only value (Q1) against optimised winner, loser, and small- and large-cap quintile returns.
![Figure 7b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only value (Q1) against optimised winner, loser, and small- and large-cap quintile returns.](/cms/asset/ae9688fd-b341-46d0-a0d3-4f50eeb5ceda/oaef_a_2231662_f0007b_oc.jpg)
Figure 9b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only size (Q1) against optimised winner, loser, and small- and large-cap quintile returns.
![Figure 9b. Returns-based style analysis per Sharpe (Citation1991) on optimised long-only size (Q1) against optimised winner, loser, and small- and large-cap quintile returns.](/cms/asset/e3080fd3-8cdd-4542-a307-1bc875173024/oaef_a_2231662_f0009b_oc.jpg)
Figure 9a. Returns-based style analysis per Sharpe (Citation1991) on naïve long-only size (Q1) against naive winner, loser, value, and growth quintile returns.
![Figure 9a. Returns-based style analysis per Sharpe (Citation1991) on naïve long-only size (Q1) against naive winner, loser, value, and growth quintile returns.](/cms/asset/7894e46e-a119-4385-9ea9-3edcb887dc61/oaef_a_2231662_f0009a_oc.jpg)