Bayesian Dynamic Factor Models - Department of Statistical Science ...

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(%) 5 0 −5 5 0 (a) Mean−target (m = 0.06%) LM−AF−NT LM−IF−NT CM−IF−NT LM−AF−LT LM−IF−LT CM−IF−LT 0 10 20 30 40 50 60 70 80 90 100 (b) Target−free 0 10 20 30 40 50 60 70 80 90 100 Figure 9: Cumulative returns over 100 business days based on one-step-ahead forecasting for (a) portfolio under the target returns of 0.06% and (b) target-free minimum-variance portfolio. 18
LT models provide averagely 20% less risky portfolios. Table 3 reports average risk ratio of full analyses, indicating that the portfolio variances are likely smaller in the use of LT models, and the ratio tends to be larger in rather more flexible specifications, LM-AF and LM-IF models, than in CM-IF models. These evidence implies that the LTM structure plays a considerably relevant role in reducing predicted investment risk on the portfolio allocation. 0.8 0.6 0.4 0.5 0.4 0.3 (a) Mean−target (m = 0.06%) NT LT 0 20 40 60 80 100 30 20 10 NT/LT 0 20 40 60 80 100 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 (b) Target−free 30 20 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Figure 10: Portfolio risk: Ex-ante portfolio standard deviation, (w ′ tQ twt) 1/2 based on one-stepahead forecasting of LM-AF models for (a) the portfolio under the target return of m = 0.06% (top), and (b) the target-free minimum-variance portfolio (bottom). Time trajectory (left panels) and histogram of the risk ratio for NT model relative to LT model (right panels). The vertical line in the histogram refers to the ratio of one. A further look in the optimized portfolios is the trajectories of portfolio weights based on one- step-ahead and five-step-ahead forecasting, displayed in Figures 11 and 12, respectively. In NT model, the allocation is mainly led by a long position of EUR and short position of CHF. This reflects quite a high correlation between these two currencies in the estimated forecast variance matrix. By contrast, LT model provides milder degree of correlation between those two currencies, yielding smaller proportion of resources allocated to the entire currencies. The lower degree of variation in portfolio weights resulting from the LT models leads to more stable portfolios, which would also reduce transaction costs in reality. 19
Page 1 and 2: Bayesian Dynamic Factor Models: Lat
Page 3 and 4: 2 Dynamic factor models 2.1 Standar
Page 5 and 6: series because process of their lat
Page 7 and 8: process for βit, with µi = µβi
Page 9 and 10: 3 2 1 GBP EUR JPY CAD AUD CHF 2006
Page 11 and 12: 1.0 0.5 β 2,1t (EUR−Factor) 2006
Page 13 and 14: 3 0 Factor1 (f 1t ) −3 2006 2007
Page 15 and 16: 0.5 0.0 β2,1t (EUR−Factor1) 2006
Page 17: • CM-IF: Constant means (ct ≡ c
Page 21 and 22: 0.5 GBP 0.0 0.5 0.0 0.4 0.0 CAD GBP
Page 23 and 24: References Aguilar, O. and West, M.
Page 25: West, M. (2003), “Bayesian factor

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