Introduction to Risk Parity and Budgeting

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Ἥλιος Βουρδουμπάς
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1 Introduction to Risk Parity and Budgeting Chapter 3 Risk-Based Indexation c Thierry Roncalli & CRC Press Evry University & Lyxor Asset Management, France Instructors may find the description of the book at the following addresses: May 22, 2013 Introduction to Risk Parity and Budgeting Risk-Based Indexation 1 / 22

2 Table 3.1, Page 158 Table: Weight and risk concentration of several equity indices (June 29, 2012) Weights Risk contributions Ticker L(x) L(x) G (x) G (x) 10% 25% 50% 10% 25% 50% SX5P SX5E INDU BEL DAX CAC AEX HSI HSCEI SMI NKY UKX SXXE SPX MEXBOL IBEX SXXP SPTSX NDX TWSE TPX KOSPI Introduction to Risk Parity and Budgeting Risk-Based Indexation 2 / 22

3 Figure 3.1, Page 158 Figure: Lorenz curve of several equity indices (June 29, 2012) Introduction to Risk Parity and Budgeting Risk-Based Indexation 3 / 22

4 Figure 3.2, Page 162 Figure: Performance of the RAFI index since January 2000 Introduction to Risk Parity and Budgeting Risk-Based Indexation 4 / 22

5 Figure 3.3, Page 163 Figure: Illustration of the diversification effect of AW indices Introduction to Risk Parity and Budgeting Risk-Based Indexation 5 / 22

6 Figure 3.4, Page 165 Figure: Location of the minimum variance portfolio in the efficient frontier Introduction to Risk Parity and Budgeting Risk-Based Indexation 6 / 22

7 Tables 3.2 & 3.3, Page 166 Table: Unconstrained minimum variance portfolios Asset ρ 20% 0% 20% 50% 70% 90% 99% σ (x ) Table: Long-only minimum variance portfolios Asset ρ 20% 0% 20% 50% 70% 90% 99% σ (x ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 7 / 22

8 Tables 3.4 & 3.5, Page 168 & 171 Table: Composition of the MV portfolio x Asset β i βi i Unconstrained Long-only Volatility Table: Composition of the MDP Unconstrained Long-only Asset xi ρ (e i,x ) xi ρ (e i,x ) σ (x ) DR (x ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 8 / 22

9 Table 3.6, Page 175 Table: Weights and risk contributions (Example 26) Asset EW MV MDP ERC x i RC i x i RC i x i RC i x i RC i H (x) σ (x) DR (x) H (RC ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 9 / 22

10 Table 3.7, Page 176 Table: Weights and risk contributions (Example 27) Asset EW MV MDP ERC x i RC i x i RC i x i RC i x i RC i H (x) σ (x) DR (x) H (RC ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 10 / 22

11 Table 3.8, Page 177 Table: Weights and risk contributions (Example 28) EW MV MDP ERC Asset x i RC i x i RC i x i RC i x i RC i H (x) σ (x) DR (x) H (RC ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 11 / 22

12 Table 3.9, Page 178 Table: Weights and risk contributions (Example 29) EW MV MDP ERC Asset x i RC i x i RC i x i RC i x i RC i H (x) σ (x) DR (x) H (RC ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 12 / 22

13 Table 3.10, Page 179 Table: Weights and risk contributions (Example 30) EW MV MDP ERC Asset x i RC i x i RC i x i RC i x i RC i H (x) σ (x) DR (x) H (RC ) Introduction to Risk Parity and Budgeting Risk-Based Indexation 13 / 22

14 Figure 3.5, Page 180 Figure: Weight of the first two assets in AW portfolios (Example 31) Introduction to Risk Parity and Budgeting Risk-Based Indexation 14 / 22

15 Figure 3.6, Page 180 Figure: Weight with respect to the asset beta β i (Example 32) Introduction to Risk Parity and Budgeting Risk-Based Indexation 15 / 22

16 Table 3.11, Page 182 Table: Main statistics of AW indexations (Jan Sep. 2012) CW EW MV MDP ERC µ (x) σ (x) SR(x r) σ (x b) IR(x b) M DD (x) γ 1 (x) γ 2 (x) (x) γ1 γ2 (x) ρ (x b) β (x b) Introduction to Risk Parity and Budgeting Risk-Based Indexation 16 / 22

17 Table 3.12, Page 182 Table: Simulated performance of AW portfolios by year (in %) Year CW EW MV MDP ERC Introduction to Risk Parity and Budgeting Risk-Based Indexation 17 / 22

18 Figure 3.7, Page 183 Figure: Concentration statistics of AW portfolios Introduction to Risk Parity and Budgeting Risk-Based Indexation 18 / 22

19 Table 3.13, Page 184 Table: Annualized monthly turnover of AW portfolios (in %) Lag EW ERC MV MDP 10% 5% 10% 5% 1M M M Y Y Y Introduction to Risk Parity and Budgeting Risk-Based Indexation 19 / 22

20 Figure 3.8, Page 185 Figure: Concentration statistics of constrained MV and MDP indexations Introduction to Risk Parity and Budgeting Risk-Based Indexation 20 / 22

21 Table 3.14, Page 185 Table: Main statistics of constrained MV and MDP indexations (Jan Sep. 2012) MV MDP 10% 5% 10% 5% µ (x) σ (x) SR(x r) σ (x b) IR(x b) M DD (x) γ 1 (x) γ 2 (x) γ1 (x) γ2 (x) ρ (x b) β (x b) Introduction to Risk Parity and Budgeting Risk-Based Indexation 21 / 22

22 Table 3.15, Page 187 Table: Influence of the covariance estimator EMP CCM RMT CCS FSE Statistic ERC MV MDP 10% 5% 10% 5% τ (x) G (x) G (RC ) IR(x b) τ (x) G (x) G (RC ) IR(x b) τ (x) G (x) G (RC ) IR(x b) τ (x) G (x) G (RC ) IR(x b) τ (x) G (x) G (RC ) IR(x b) Introduction to Risk Parity and Budgeting Risk-Based Indexation 22 / 22

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