Comments on Asset Allocation Strategies Based on Penalized Quantile Regression (Bonaccolto, Caporin & Paterlini)

Transcription

1 Comments on Based on Penalized Quantile Regression (Bonaccolto, Caporin & Paterlini) Ensae-Crest 22 March 2016

2 Summary An asset allocation strategy, based on quantile regressions (Bassett et al. 2004), two new performance measures, based on Choquet expected utility functions (Ψ 1 and Ψ 2 ), the promotion of pessimistic views, that forget the most favorable outcomes, Lasso-type penalization to manage large portfolios.

3 Summary An asset allocation strategy, based on quantile regressions (Bassett et al. 2004), two new performance measures, based on Choquet expected utility functions (Ψ 1 and Ψ 2 ), the promotion of pessimistic views, that forget the most favorable outcomes, Lasso-type penalization to manage large portfolios. + a simulations exercise + empirical results based on the SP500 components: the performances of high-quantile based strategies are convincing.

4 General opinion A nice piece of work, with a clear-cut discussion of several recent quantitative techniques in portfolio optimization. Interesting and promising new ideas.

5 General opinion A nice piece of work, with a clear-cut discussion of several recent quantitative techniques in portfolio optimization. Interesting and promising new ideas. The switch from least squares regressions to quantile regressions seems to improve risk-return performances...

6 General opinion A nice piece of work, with a clear-cut discussion of several recent quantitative techniques in portfolio optimization. Interesting and promising new ideas. The switch from least squares regressions to quantile regressions seems to improve risk-return performances......but the choice of the reference quantile α is still questionable. An active stream of the statistical literature has proposed solutions: the globally concerned quantile regression framework (Peng et al. 2014, Zheng et al. 2015). Q1: Any advice to choose α in practice?

7 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components

8 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components (ii) state the portfolio weights

9 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components (ii) state the portfolio weights Härdle et al. (2014) chose only (i), as a preliminary stage. Here, both objectives are promoted simultaneously (one-shot).

10 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components (ii) state the portfolio weights Härdle et al. (2014) chose only (i), as a preliminary stage. Here, both objectives are promoted simultaneously (one-shot). This could be seen as a lack of flexibility: no opportunity to use different quantile levels α for both stages;

11 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components (ii) state the portfolio weights Härdle et al. (2014) chose only (i), as a preliminary stage. Here, both objectives are promoted simultaneously (one-shot). This could be seen as a lack of flexibility: no opportunity to use different quantile levels α for both stages; invoke two different risk measures;

12 L 1 penalization A Lasso procedure may be used to (i) select the relevant portfolio components (ii) state the portfolio weights Härdle et al. (2014) chose only (i), as a preliminary stage. Here, both objectives are promoted simultaneously (one-shot). This could be seen as a lack of flexibility: no opportunity to use different quantile levels α for both stages; invoke two different risk measures; Q2: How can such a strategy be justified?

13 Choice of the numeraire The reference asset seems to be more or less arbitrary. The most correlated asset with the first PCA factor?

14 Choice of the numeraire The reference asset seems to be more or less arbitrary. The most correlated asset with the first PCA factor? This choice may be sensitive, particularly with L 1 norms: the removed assets are those that are highly correlated with the numeraire.

15 Choice of the numeraire The reference asset seems to be more or less arbitrary. The most correlated asset with the first PCA factor? This choice may be sensitive, particularly with L 1 norms: the removed assets are those that are highly correlated with the numeraire. Q3: What is the influence of this choice on the final result?

16 Empirics A rather homogenous and large portfolio: SP500. Considering heterogenous portfolios (stocks+bonds, e.g.) could induce difficulties:

17 Empirics A rather homogenous and large portfolio: SP500. Considering heterogenous portfolios (stocks+bonds, e.g.) could induce difficulties: no obvious choice for the reference asset;

18 Empirics A rather homogenous and large portfolio: SP500. Considering heterogenous portfolios (stocks+bonds, e.g.) could induce difficulties: no obvious choice for the reference asset; the lasso procedure has to be modified: different penalization parameters λ, group-lasso, etc;

19 Empirics A rather homogenous and large portfolio: SP500. Considering heterogenous portfolios (stocks+bonds, e.g.) could induce difficulties: no obvious choice for the reference asset; the lasso procedure has to be modified: different penalization parameters λ, group-lasso, etc; the risk appetite for different asset classes is different and the return distributions are different. Is a single performance measure relevant? Q4: Is it realistic to manage a strongly heterogenous portfolio with such techniques?

20 Comments on SPT and Mean Reversion: Explaining Theoretical Performances by Observed Market Dynamics (Kumar & Lehalle) Ensae-Crest 22 March 2016 SPT and Mean Reversion

21 Summary Theoretical and empirical comparisons between 1 the Market portfolio (MP, buy and hold ), 2 the Constant Rebalancing Portfolio (CRP), 3 the Entropy Weighted Portfolio (EWP). SPT and Mean Reversion

22 Summary Theoretical and empirical comparisons between 1 the Market portfolio (MP, buy and hold ), 2 the Constant Rebalancing Portfolio (CRP), 3 the Entropy Weighted Portfolio (EWP). Following the Stochastic Portfolio Theory, EWP is the best one. But empirically, this is rather CRP. Extend SPT by adding mean reversion (i.e. OU processes), because CRP strategies sell high, buy low. SPT and Mean Reversion

23 Summary Theoretical and empirical comparisons between 1 the Market portfolio (MP, buy and hold ), 2 the Constant Rebalancing Portfolio (CRP), 3 the Entropy Weighted Portfolio (EWP). Following the Stochastic Portfolio Theory, EWP is the best one. But empirically, this is rather CRP. Extend SPT by adding mean reversion (i.e. OU processes), because CRP strategies sell high, buy low. The stronger the mean-reversion is, the larger is the advantage of CRP and EWP wrt MP. SPT and Mean Reversion

24 General opinion Interesting insights of SPT, starting from empirical observations with typical stock indices. The idea of considering mean-reverting process is tempting. SPT and Mean Reversion

25 General opinion Interesting insights of SPT, starting from empirical observations with typical stock indices. The idea of considering mean-reverting process is tempting. Nonetheless, the paper opens a door and it remains a lot of questions. SPT and Mean Reversion

26 Theory The way the theoretical results are stated may be misleading. 1 They are asymptotic results: T. For a given ɛ > 0, T should be larger than some T 0. Any idea of T 0 (ɛ)? SPT and Mean Reversion

27 Theory The way the theoretical results are stated may be misleading. 1 They are asymptotic results: T. For a given ɛ > 0, T should be larger than some T 0. Any idea of T 0 (ɛ)? 2 Is it correct to say V π (T ) V µ (T ) is roughly the same event as T 1 T 0 γ π(t) dt > 0 when T is large? Thus, their probabilities are similar. SPT and Mean Reversion

28 Theory The way the theoretical results are stated may be misleading. 1 They are asymptotic results: T. For a given ɛ > 0, T should be larger than some T 0. Any idea of T 0 (ɛ)? 2 Is it correct to say V π (T ) V µ (T ) is roughly the same event as T 1 T 0 γ π(t) dt > 0 when T is large? Thus, their probabilities are similar. 3 Even more general processes: Affine Jump Diffusion, multivariate Levy or Hawkes,...? SPT and Mean Reversion

29 Empirics The paper is the beginning of the story. 1 Other asset classes? SPT and Mean Reversion

30 Empirics The paper is the beginning of the story. 1 Other asset classes? 2 Other criteria: minimum variance, mean-variance, risk parity, smart-beta, etc. SPT and Mean Reversion

31 Empirics The paper is the beginning of the story. 1 Other asset classes? 2 Other criteria: minimum variance, mean-variance, risk parity, smart-beta, etc. 3 Is the hierarchy CRP > EWP > MP a general rule, for instance since the end of the Second World War? SPT and Mean Reversion

32 Empirics The paper is the beginning of the story. 1 Other asset classes? 2 Other criteria: minimum variance, mean-variance, risk parity, smart-beta, etc. 3 Is the hierarchy CRP > EWP > MP a general rule, for instance since the end of the Second World War? 4 A hierarchy in terms of returns. What s about risk? Is the hierarchy the same? SPT and Mean Reversion

33 Empirics The paper is the beginning of the story. 1 Other asset classes? 2 Other criteria: minimum variance, mean-variance, risk parity, smart-beta, etc. 3 Is the hierarchy CRP > EWP > MP a general rule, for instance since the end of the Second World War? 4 A hierarchy in terms of returns. What s about risk? Is the hierarchy the same? 5 influence of transaction costs? They are zero for MP! SPT and Mean Reversion