Nomura Holdings, Inc. · TSE:8604
Nomura — Technical Presentation (May 2015)
39 slides from Nomura's technical presentation, May 10, 2015
Slide 1: Advances in Quantitative Meta-Strategies
ADVANCES IN QUANTITATIVE META-STRATEGIES Marcos López de Prado Lawrence Berkeley National Laboratory Computational Research Division
Slide 2: Key Points
Key Points • Quantitative Meta-Strategies (QMS) are quantitative strategies designed to manage investment strategies. • As a field, QMS is the mathematical study of the decisions made by the supervisor of a team of investment managers, regardless of whether their investment style is systematic or di
Slide 3: Section I: The Art & Science of Investing
SECTION I The Art & Science of Investing
Slide 4: Investing is Not an Art
Investing is Not an Art • Popular view: Investing is an Art because… – It does not follow fixed rules (…unlike Art!) – Like a sport or game, excellence cannot be taught, but it can only be learned through practice. • Reality: Sports, Games, Arts increasingly rely on Math. Any game can be studied mat
Slide 5: Investing is Not an Academic Endeavor
Investing is Not an Academic Endeavor • Academic view: Like physical objects, Markets follow fundamental principles that can be studied. • Reality: Investing differs from Physics in several aspects: – There are no “laboratories”: We cannot reproduce experiments under controlled conditions. – Low sig
Slide 6: Investing is an Industrial Science
Investing is an Industrial Science • In contrast with Academic Finance: – Financial firms can conduct research in terms analogous to Scientific laboratories. E.g., deploy an execution algorithm and experiment with alternative configurations (market interaction). – Financial firms can control for the
Slide 7: Section II: Strategy Selection / PM Hiring
SECTION II Strategy Selection / PM Hiring
Slide 8: Strategy Selection Under Multiple Testing
Strategy Selection Under Multiple Testing • PROPOSITION #1: Suppose N independent trials following a Normal distribution, with mean 𝐸 𝑆𝑅𝑛 = 0 and variance 𝑉 𝑆𝑅𝑛 . Then, the expected maximum Sharpe Ratio is 𝐸 𝑚𝑎𝑥 𝑆𝑅𝑛 1 1 −1 ≈ 𝑉 𝑆𝑅𝑛 1 − 𝛾 𝑍 −1 1− + 𝛾𝑍 −1 1− 𝑒 𝑁 𝑁 where 𝜸 is…
Slide 9: Expected Maximum Sharpe Ratio
Backtest Overfitting 7 Expected Maximum Sharpe Ratio as the 6 number of independent trials N Expected Maximum Sharpe Ratio 5 grows, for 𝐸 𝑆𝑅𝑛 = 0 4 and 𝑉 𝑆𝑅𝑛 ∈ 1,4 . 3 Searching for empirical 2 findings regardless of their theoretical basis 1 is likely to magnify the 1 1 E max 𝑆𝑅𝑛 ≈ V…
Slide 10: The Backtest Overfitting Simulation Tool
The Backtest Overfitting Simulation Tool An “optimized” investment strategy (in blue) making steady profit while the The same investment strategy performs underlying trading instrument (in green) poorly on a different sample of the same gyrates in price. It is trivial to make trading instrument. Fin
Slide 11: The Deflated Sharpe Ratio (1/2)
The Deflated Sharpe Ratio (1/2) • The Deflated Sharpe Ratio (DSR) corrects the inflationary effect of multiple trials, non-normal returns and shorter sample lengths: 𝑆𝑅 − 𝑆𝑅0 𝑇−1 𝐷𝑆𝑅 ≡ 𝑃𝑆𝑅 𝑆𝑅0 = 𝑍 𝛾 −1 2 1 − 𝛾3 𝑆𝑅 + 4 𝑆𝑅 4 where −1 1 −1 1 𝑆𝑅0 = 𝑉 𝑆𝑅𝑛 1−𝛾 𝑍 1− + 𝛾𝑍 1−…
Slide 12: The Deflated Sharpe Ratio (2/2)
The Deflated Sharpe Ratio (2/2) • The standard Sharpe Ratio (SR) is computed as a function of two estimates: – Mean of returns – Standard deviation of returns. • DSR deflates SR by taking into consideration five additional variables (it packs more information): – The non-Normality of the returns 𝛾3
Slide 13: Numerical Example (1/2)
Numerical Example (1/2) • An analyst uncovers a daily strategy with annualized SR=2.5, 1 after running N=100 independent trials, where 𝑉 𝑆𝑅𝑛 = , 2 T=1250, 𝛾3 = −3 and 𝛾4 = 10. • QUESTION: Is this a legitimate discovery, at a 95% conf.? • ANSWER: No. There is only a 90% probability that the…
Slide 14: Numerical Example (2/2)
Numerical Example (2/2) 2 1 Should the strategist have 1.8 0.99 made his discovery after 1.6 0.98 running only N=46, then 1.4 0.97 𝐷𝑆𝑅 ≈ 0.9505. SR0, annualized 1.2 0.96 DSR 1 0.95 Non-Normality also played a 0.8 0.94 role in discarding this investment offer: For 𝛾3 = 0.6 0.93 0.4 0, 𝛾4 = 3…
Slide 15: Section III: Portfolio Oversight
SECTION III Portfolio Oversight
Slide 16: Finance and the Theory of Evolution
Finance and the Theory of Evolution • Standard structural break tests (see Maddala and Kim [1999]) attempt to identify a “break” or permanent shift from one regime to another within a time series. • In contrast, the methodology we present here signals the emergence of a new regime as it happens, whi
Slide 17: Action plan
Action plan 1. Apply the EF3M algo for matching the track record’s moments (we have already seen this step). 2. Simulate path scenarios consistent with the matched moments. 3. Derive a distribution of scenarios based on that match. 4. Probability of Divergence (PD): Evaluate what percentile of the d
Slide 18: An Example
An Example • Suppose a mixture of 2 Gaussians with true parameters 𝜇1 , 𝜇2 , 𝜎1 , 𝜎2 , 𝑝 = −0.025, 0.015,0.02,0.01,0.1 . True raw moments 0.014 Moments Origin Mean 1 1.10E-02 0 0.012 2 3.95E-04 2.74E-04 3 2.53E-06 -7.85E-06 4 4.31E-07 5.63E-07 0.01 5 -7.48E-09 -3.28E-08 0.008 Fitted Parameters…
Slide 19: Example 1 (1/2)
Example 1 (1/2) • Reference: Suppose that a PM has a track record consistent with the following Mixture of 2-Gaussians 𝜇1 , 𝜇2 , 𝜎1 , 𝜎2 , 𝑝 = −0.025, 0.015,0.02,0.01,0.1 • Divergence: What would happen if draws from the first Gaussian become more likely? For example, if p=0.2 instead of…
Slide 20: Example 1 (2/2): Probability of Departure
Example 1 (2/2) 0.06 1 0.9 0.04 0.8 That situation 0.02 0.7 is distinct Probability of Departure 0 0.6 from the Return 0.5 approved -0.02 0.4 track-record, -0.04 0.3 and PD slowly -0.06 0.2 but surely 0.1 converges to -0.08 0 0 100 200 300 400 500 600 700 800 900 1000 1. Number of observations Retur
Slide 21: Example 2 (1/2)
Example 2 (1/2) • Reference: Suppose that a PM has a track record consistent with the following Mixture of 2-Gaussians 𝜇1 , 𝜇2 , 𝜎1 , 𝜎2 , 𝑝 = −0.025, 0.015,0.02,0.01,0.1 • Divergence: What would happen if, after capital is allocated, returns are IID Normal, matching the mixture’s mean and…
Slide 22: Example 2 (2/2): Probability of Departure
Example 2 (2/2) 0.08 1 0.06 0.9 PD approaches 0.8 1, although the 0.04 0.7 model cannot Probability of Departure 0.02 0.6 completely Return 0.5 discard the 0 0.4 possibility that -0.02 0.3 these returns in -0.04 0.2 fact were drawn 0.1 from the -0.06 0 0 100 200 300 400 500 600 700 800 900 1000 refe
Slide 23: Example 3 (1/2)
Example 3 (1/2) • Reference: Suppose that a PM has a track record consistent with the following Mixture of 2-Gaussians 𝜇1 , 𝜇2 , 𝜎1 , 𝜎2 , 𝑝 = −0.025, 0.015,0.02,0.01,0.1 • Divergence: What would happen if, after capital is allocated, returns are IID Normal with a mean half the mixture’s and…
Slide 24: Example 3 (2/2): Probability of Departure
Example 3 (2/2) 0.08 1 0.9 PD quickly 0.06 0.8 converges to 1, 0.04 0.7 as the model Probability of Departure 0.02 0.6 recognizes that those Normally Return 0.5 0 0.4 distributed -0.02 0.3 draws do not -0.04 0.2 resemble the 0.1 mixture’s -0.06 0 100 200 300 400 500 600 700 800 900 1000 0 simulated
Slide 25: Section IV: Decommissioning of Strategies / PMs
SECTION IV Decommissioning of Strategies / PMs
Slide 26: The Triple Penance Rule (1/2)
The Triple Penance Rule (1/2) • THEOREM #1: Under IID Normal outcomes, a strategy’s maximum quantile-loss 𝑀𝑎𝑥𝑄𝐿𝛼 for a significance level 𝛼 occurs after 𝑡𝛼∗ observations. Then, the strategy is expected to remain under water for an additional 3𝑡𝛼∗ after the maximum quantile-loss has…
Slide 27: The Triple Penance Rule (2/2)
The Triple Penance Rule (2/2) 5000000 It takes three time longer to recover from the maximum 4000000 quantile-loss (𝑇𝑢𝑊𝛼 ) than the time it took to produce it (𝑡𝛼∗ ), 1 for a given significance level 𝛼 < , regardless of the PM’s 3000000 2 Sharpe ratio. 2000000 𝑇𝑢𝑊𝛼 1000000 Quantile (in…
Slide 28: Example
Example 1 20000000 PM1 has an annual mean and standard deviation of 𝑇𝑢𝑊0.05 [PM1] US$10m (SR=1), and PM2 15000000 has an annual mean of 𝑇𝑢𝑊0.05 [PM2] US$15m and an annual 10000000 standard deviation of US$10m (SR=1.5). Quantile (in US$) 5000000 For a 95% confidence level, PM1 reaches a…
Slide 29: Example
Example 2 2000000 PM1 has an annual mean and standard deviation of 1000000 𝑇𝑢𝑊0.08 𝑃𝑀1 = 𝑇𝑢𝑊0.02 𝑃𝑀2 US$10m (SR=1), and PM2 0 has an annual mean of 0 0.5 1 1.5 2 2.5 US$15m and an annual -1000000 standard deviation of 𝑀𝑎𝑥𝑄𝐿0.08 [𝑃𝑀1] US$10m (SR=1.5). Quantile (in US$) -2000000…
Slide 30: A Better Way to Stop-Out
A Better Way to Stop-Out • Given a realized performance 𝜋𝑡 < 0 and assuming IID Normal returns with mean 𝜇 > 0, the Implied Time Under Water (ITuW) is 𝜋𝑡 2 𝜋𝑡 𝐼𝑇𝑢𝑊𝜋𝑡 = 2 − 2 + 𝑡 𝜇 𝑡 𝜇 • The above equation translates a realized loss into time under water. • It makes sense…
Slide 31: Implications of the Triple Penance Rule
Implications of the Triple Penance Rule 1. It makes possible the translation of drawdowns in terms of time under water. 2. It sets expectations regarding how long it may take to earn performance fee (for a certain confidence level). – The remaining time under water may be so long that withdrawals ar
Slide 32: Section V: Conclusions
SECTION V Conclusions
Slide 33: Pros & Cons of Classic Approaches vs. QMS
Pros & Cons of Classic Approaches vs. QMS Practical Classic approach Quantitative Meta-Strategy Application Interview candidates with SR (or any Design an interview process that recognizes the variables that other performance statistic) and track affect the probability of making the wrong hire: reco
Slide 34: Thanks for Your Attention!
THANKS FOR YOUR ATTENTION! 34
Slide 35: Section VI: The stuff nobody reads
SECTION VI The stuff nobody reads
Slide 36: Bibliography
Bibliography • Bailey, D., J. Borwein, M. López de Prado and J. Zhu (2015): “The Probability of Backtest Overfitting.” Journal of Computational Finance, forthcoming. Available at: http://ssrn.com/abstract=2326253 • Bailey, D., J. Borwein, M. López de Prado and J. Zhu (2014): “Pseudo-Mathematics and
Slide 37: Bio
Bio Marcos López de Prado is Senior Managing Director at Guggenheim Partners. He is also a Research Fellow at Lawrence Berkeley National Laboratory's Computational Research Division (U.S. Department of Energy’s Office of Science), where he conducts unclassified research in the mathematics of large-
Slide 38: Disclaimer
Disclaimer • The views expressed in this document are the authors’ and do not necessarily reflect those of the organizations he is affiliated with. • No investment decision or particular course of action is recommended by this presentation. • All Rights Reserved. 38
Slide 39: Notice
Notice: The research contained in this presentation is the result of a continuing collaboration with David H. Bailey, Berkeley Lab Jon M. Borwein, FRSC, AAAS Matthew Foreman, UC-Irvine The full paper is available at: http://ssrn.com/abstract=2547325 For additional details, please visit: http://ssrn.