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Inverse Problems in Science and Engineering Volume 18, 2010 - Issue 1: Proceedings of the 4th International Conference on Inverse Problems: Modelling and Simulation, May 26th–30th, 2008, held in Fethiye, Turkey

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Determining a stable relationship between hedge fund index HFRI-Equity and S&P 500 behaviour, using filtering and maximum likelihood

Paolo CapelliAkros Alternative Investments SGR, Viale Eginardo 29, 20149 Milano, Italy

Francesca MarianiCERI- Centro di Ricerca Previsione Prevenzione e Controllo dei Rischi Geologici, Università di Roma ‘La Sapienza’, Piazza Umberto Pilozzi 9, 00038 Valmontone (RM), Italy

Maria Cristina RecchioniDipartimento di Scienze Sociali ‘D. Serrani’, Università Politecnica delle Marche, Piazza Martelli 8, 60121Ancona, Italy

Fabio SpinelliInvestment Advisor, Piazza Giovanni Paolo II 15, 22100 Como, Italy

Francesco ZirilliDipartimento di Matematica ‘G. Castelnuovo’, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 2, 00185 Roma, Italy

Pages 83-109 | Received 15 Oct 2008, Accepted 29 May 2009, Published online: 08 Oct 2009

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https://doi.org/10.1080/17415970903234398

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Figure 1. Reconstruction of the parameters ε, θ, χ, γ (in ordinate) of the model (1–3), as a function of the index i (in abscissa) of the last observation time contained in the data window used in the calibration.

Figure 2. Reconstruction of the initial stochastic variance and of the parameters β, (in ordinate) of the model (1–3), as a function of the index i (in abscissa) of the last observation time contained in the data window used in the calibration.

Figure 3. Reconstruction of the correlation coefficients ρ_1,2, ρ_1,3, ρ_2,3 (in ordinate) of the model (1–3), as a function of the index i (in abscissa) of the last observation time contained in the data window used in the calibration.

Table 1. Relative bias of the parameter estimators in the five windows (N_R = 100).

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Table 2. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 100).

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Table 3. Relative bias of the parameter estimators in the five windows (N_R = 1000).

Display Table

Table 4. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 1000).

Display Table

Table 5. Mean of the standard deviations of the relative errors of the components of the estimated vectors and worst standard deviation and parameter where it occurs (N_R = 1000).

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Table 6. Relative bias of the parameter estimators in Set 2 (Period 2) and Set 3 (Period 3).

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Table 7. Relative bias of the correlation coefficients and of the initial stochastic variance in Set 2 (Period 2) and Set 3 (Period 3).

Display Table

Table 8. Quality of the forecasted values of the log-returns x_t and z_t and of the forecasted increment of the hedge fund index established comparing with historical data.

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Figure 4. Histogram of the values taken by (a) ν₁, (b) ν₃ and (c) ν₆.

Figure 4. Histogram of the values taken by (a) ν1, (b) ν3 and (c) ν6.

Figure 5. Forecasted values of the S&P 500 x_t (a) and of the HFRI-Equity z_t (b) 1 month in the future (*) and historical data of the log-return of the indices (□).

Figure 6. Forecasted values of the S&P 500 x_t (a) and of the HFRI-Equity z_t (b) 3 months in the future (*) and historical data of the log-return of the indices (□).

Figure 7. Forecasted values of the S&P 500 x_t (a) and of the HFRI-Equity z_t (b) 6 months in the future (*) and historical data of the log-return of the indices (□).

Table 9. The first 46 monthly data and the forecasted values of the log-returns of the HFRI-Equity index 1 month and 6 months in the future compared with the historical data of the 1 month log-return and of the 6 months log-return .

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Determining a stable relationship between hedge fund index HFRI-Equity and S&P 500 behaviour, using filtering and maximum likelihood

Table 1. Relative bias of the parameter estimators in the five windows (N_R = 100).

Table 2. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 100).

Table 3. Relative bias of the parameter estimators in the five windows (N_R = 1000).

Table 4. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 1000).

Table 5. Mean of the standard deviations of the relative errors of the components of the estimated vectors and worst standard deviation and parameter where it occurs (N_R = 1000).

Table 6. Relative bias of the parameter estimators in Set 2 (Period 2) and Set 3 (Period 3).

Table 7. Relative bias of the correlation coefficients and of the initial stochastic variance in Set 2 (Period 2) and Set 3 (Period 3).

Table 8. Quality of the forecasted values of the log-returns x_t and z_t and of the forecasted increment of the hedge fund index established comparing with historical data.

Table 9. The first 46 monthly data and the forecasted values of the log-returns of the HFRI-Equity index 1 month and 6 months in the future compared with the historical data of the 1 month log-return and of the 6 months log-return .

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Determining a stable relationship between hedge fund index HFRI-Equity and S&P 500 behaviour, using filtering and maximum likelihood

Figures & data

Table 1. Relative bias of the parameter estimators in the five windows (NR = 100).

Table 2. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (NR = 100).

Table 3. Relative bias of the parameter estimators in the five windows (NR = 1000).

Table 4. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (NR = 1000).

Table 5. Mean of the standard deviations of the relative errors of the components of the estimated vectors and worst standard deviation and parameter where it occurs (NR = 1000).

Table 6. Relative bias of the parameter estimators in Set 2 (Period 2) and Set 3 (Period 3).

Table 7. Relative bias of the correlation coefficients and of the initial stochastic variance in Set 2 (Period 2) and Set 3 (Period 3).

Table 8. Quality of the forecasted values of the log-returns xt and zt and of the forecasted increment of the hedge fund index established comparing with historical data.

Table 9. The first 46 monthly data and the forecasted values of the log-returns of the HFRI-Equity index 1 month and 6 months in the future compared with the historical data of the 1 month log-return and of the 6 months log-return .

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Table 1. Relative bias of the parameter estimators in the five windows (N_R = 100).

Table 2. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 100).

Table 3. Relative bias of the parameter estimators in the five windows (N_R = 1000).

Table 4. Relative bias of the correlation coefficients and of the initial stochastic variance in the five windows (N_R = 1000).

Table 5. Mean of the standard deviations of the relative errors of the components of the estimated vectors and worst standard deviation and parameter where it occurs (N_R = 1000).

Table 8. Quality of the forecasted values of the log-returns x_t and z_t and of the forecasted increment of the hedge fund index established comparing with historical data.