This document summarizes a presentation on using predictive analytics for portfolio management and risk analysis. It discusses using state-space models to identify structural breaks in time series data from financial markets in real-time. This allows for alpha generation and risk management. It also describes implementing cluster and cointegration analysis on big data in parallel using GPUs for efficiency. The analysis identifies coherency and group membership between assets.

1. Predictive Analytics for Alpha Generation and Risk Management
Yigal Jhirad
March 19, 2015
NVIDIA GTC 2015: Deep Learning and AI Conference
Silicon Valley

2. 2
GTC 2015: Table of Contents
I. State-Space Models: State Instantiation
— Portfolio and Risk Management: Big Data/Real Time Sensitivity
— Applications - Cluster and Cointegration Analysis, Factor
Optimization
II. Parallel Implementation
— Coherence, Correlation, Cointegration, Clustering
III. Summary
IV. Author Biographies
DISCLAIMER: This presentation is for information purposes only. The presenter accepts no liability for the content of
this presentation, or for the consequences of any actions taken on the basis of the information provided. Although the
information in this presentation is considered to be accurate, this is not a representation that it is complete or should be
relied upon as a sole resource, as the information contained herein is subject to change.

3. 3
GTC 2015: State-Space Models
 Portfolio/Risk Management
— Financials markets display discrete dynamic micro states and regimes
– Traditional valuation techniques may not be as effective, e.g. Options markets – Implied
Volatility vs. Jump Diffusion Regime Shifts
— Big Data : Time Series Tick Data, Interday and Intraday
— Predictive Analytics: Identifying Structural Breaks
— Alpha Generation, Risk Management, Market Impact
 Parallel Processing: APL/CPU and CUDA/GPU physics based modeling exploit hardware efficiently
— Array Based Processing paradigm Matrix/Vector thought process is key
— APL is a programming language whose quantum data object is an array, which is
fundamental to parallel processing and can leverage parallel processing across CPU’s
— CUDA leverages GPU Hardware
 Application in Econometrics and Applied Mathematics
— Monte Carlo Simulations — Fourier Analysis
— Principal Components — Optimization
— Cluster Analysis — Cointegration

4. 4
GTC 2015: Cluster & Cointegration Analysis
 Cluster Analysis: A multivariate technique designed to identify relationships and cohesion
— Factor Analysis, Risk Model Development
 Correlation Analysis: Pairwise analysis of data across assets. Each pairwise comparison can be run in parallel.
— Use Correlation or Cointegration as primary input to cluster analysis
— Apply proprietary signal filter to remove selected data and reduce spurious correlations

5. 5
Quantitative Cluster Analysis: Correlation
Application example: Correlation function removing N/A values
 Correlation measures the direction and strength of a linear relationship between variables. The Pearson
product moment correlation between two variables X and Y is calculated as:
 For N assets there are unique correlation pairs
 Given an N x M matrix A in which each row is a list of returns for a particular equity, return an N x N
matrix R in which each element is the scalar result of correlating each row of A to every other
— Each element of A may be an N/A value
— When processing a pair of rows, the calculation must include neither each N/A value nor the
corresponding element in the other row. This requires evaluating each pair separately.
— As a result the increased computational demand is more effectively implemented through a
parallel processing solution. As the matrix size increases the benefits of parallel processing become
more significant.

6. 6
Cluster Analysis: Configuration
 Hardware Constraints
— Compute capability: 3.5
— Warp size: 32
— Number of shared memory banks: 32
— Coalescence capacity (4-byte words): 128 bytes = 32 contiguous words
— Max blocks / warps / threads per multiprocessor: 16 / 64 / 2048
— Max registers per multiprocessor: 64K
— Max shared memory per multiprocessor: 48K
 Software Constraints/Response
— Run 32 independent correlations per block for output coalescence
— Read 32 prices/returns per correlation for input coalescence
— Registers used per thread: 33 => max 15 blocks per SM @ 4 warps per block
— Shared memory used per block: 256 + 384 per warp => max 16 blocks per SM @ 4 warps per block
— Thread block configuration: 4 x 32 => 15 blocks / 60 warps / 1920 threads per SM
Tesla K20c

7. Each pair of rows produces a single correlation
Cluster Analysis: Kernel Operation
Input Output

8. Cluster Analysis: Kernel
Correlation computation
σ 𝑋− ഥ𝑋 𝑌−ത𝑌
σ 𝑋− ഥ𝑋 2
σ 𝑌−ത𝑌 2
Two passes through prices/returns in global memory required
First pass:
• Compute means of 𝑿 and 𝒀 ֜ ഥ𝑿, ഥ𝒀
Second pass:
• Subtract means from 𝑿 and 𝒀 ֜ 𝑿 ́, 𝒀 ́
• Sum 𝑿 ́ × 𝒀 ́, 𝑿 ́ × 𝑿 ́ and 𝒀 ́ × 𝒀 ́ ֜ σ𝑿 ́ 𝒀 ́, σ𝑿 ́2, σ𝒀 ́2
• Multiply resultant σ𝑿 ́ 𝒀 ́ by reciprocal square roots of σ𝑿 ́2 × σ𝒀 ́2

9. Cluster Analysis: Kernel First Pass
Computation of means
(row 33, col 0 of block grid)
 Repeat: read next section of
Prices/Returns into registers
 Ns necessary for NA
handling: “0” where
either Xs or Ys is NA;
“1” where Xs and Ys
are both valid

10. Cluster Analysis: Kernel First Pass
Computation of means
(row 33, col 0 of block grid)
 Repeat: sum values in
registers into shared
memory
+ + +

11. Cluster Analysis: Kernel First Pass
Computation of means
(row 33, col 0 of block grid)
 Sum rows to obtain totals for each row of Prices/Returns
 Save totals to shared memory
 Divide totals by N
Assets
÷ ÷
÷ ÷

12. Cluster Analysis: Kernel Second Pass
Computation of correlations
 Read section of Prices/
Returns into registers (reuse
registers from first pass)
 Ns necessary for NA
handling: “0” where
either Xs or Ys is NA;
“1” where Xs and Ys
are both valid

13. Cluster Analysis: Kernel Second Pass
Computation of correlations
 Subtract means of X and Y
− −

14. Cluster Analysis: Kernel Second Pass
Computation of correlations
 Multiply and sum (reuse
X, Y, N from first pass)
× ×
+ +

15. Cluster Analysis: Kernel Second Pass
Computation of correlations
 Multiply and sum (reuse
X, Y, N from first pass)
×
+

16. Cluster Analysis: Kernel Second Pass
Computation of correlations
 Sum rows to obtain σ of terms for each row of Prices/Returns
σ 𝑋 − ഥ𝑋 𝑌 − ത𝑌
σ 𝑋 − ഥ𝑋 2 σ 𝑌 − ത𝑌 2

17. Cluster Analysis: Kernel Second Pass
Computation of correlations
Assets
rsqrt(X2) × rsqrt(Y2) × XY
σ 𝑋 − ഥ𝑋 𝑌 − ത𝑌
σ 𝑋 − ഥ𝑋 2 σ 𝑌 − ത𝑌 2

18. Cluster Analysis: Kernel
Output to global memory : row 33, col 0 of block grid
Assets
Assets
Assets

19. Host/Global Memory
 Pinned-mapped memory eliminates transfer complexity, reduces overhead
 Kernel processing speed approximately 0.1 seconds for 586 assets × 120 periods
Cluster Analysis: Big Data, Real Time
Input Output

20. Overview
 Data source constantly streaming tick data
 Simple routine periodically aggregates ticks into VWAPs
or returns, producing an array of prices, one per ticker
 VWAPs/returns loaded into one column of input
Prices/Returns matrix in host memory at every interval
 Aggregation by period enables arbitrary real time speed,
limited by speed of GPU kernel algorithm
Cluster Analysis: Big Data, Real Time Streaming
data source
Routine to
periodically
aggregate
ticks into
VWAPs
UPG
To target
application

21. 21
Summary
 Application of State –Space models using Intraday time series data
 Our approach is based on Time Series Cluster Analysis and Optimizations
— Identifying Structural Breaks, Patterns and Signals
— Coherency and Group membership
 Application in Portfolio Management for Alpha Generation and Risk Management

26. 26
Author Biographies
 Yigal D. Jhirad, Senior Vice President, is Director of Quantitative and Derivatives
Strategies and a Portfolio Manager for Cohen & Steers’ options and real assets strategies.
Mr. Jhirad heads the firm’s Investment Risk Committee. He has 26 years of experience.
Prior to joining the firm in 2007, Mr. Jhirad was an executive director in the institutional
equities division of Morgan Stanley, where he headed the company’s portfolio and
derivatives strategies effort. He was responsible for developing, implementing and
marketing quantitative and derivatives products to a broad array of institutional clients,
including hedge funds, active and passive funds, pension funds and endowments. Mr.
Jhirad holds a BS from the Wharton School. He is a Financial Risk Manager (FRM), as
Certified by the Global Association of Risk Professionals.