The document discusses interactive visualization techniques and mathematical models used in finance, specifically portfolio optimization and understanding data analytics. It covers the constant expected return (CER) model and minimum variance portfolios, along with practical implications for data aggregation and performance measurement. Additionally, it references relevant literature and tools for visualization and data analysis.

1. Interactive Visualization
in Human Time
Mike Martinez
www.ociweb.com
@brillozon
StampedeCon 2015
July 15-16, 2015
Saint Louis, MO

2. Several forms

3. Several forms

4. Long History

5. Clarify Intuitions
d
dx
f (x) = lim
h→ 0
f (x+h)−f (x)
h

6. Clarify Intuitions
∫
a
b
f (x)dx = lim
n→ ∞
∑
i=1
n
(b−a
n
f (a+(b−a
n )i)
)

7. Information Dense

8. Hidden Insights

9. Shapes of Data

10. Data Analytics

11. Data Exploration

12. Interactive Visualization

13. Brushing and Linking

14. Response Times

15. there's your problem
Data
analytics
Processing Times
Storage Sizes
aggregation
network
Query Times
Network latency
And capacityWrite Times
Query Times Write Times
Selection Times
Rendering Times

16. Level of Detail
MoreDetail
Discrete /
Continuous
Hierarchical

17. Financial Engineering
Math? Lolwut!

18. Portfolio Theory
Constant Expected Return (CER) model:
Ri t ∼ iid N (μ i ,σ i
2
); i = 1,...,N ( assets)
t = 1,...,T (time)
^SRi =
^μ i − rf
^σ i
Minimum Variance Portfolio:
^m =
^Σ −1
⋅1
1
T
⋅^Σ
−1
⋅1
;
^m is portfolio weightings
such that ^m
T
⋅1 = 1
^μ p, ^m = ^m
T
^μ ; p is portfolio
^σ p , ^m = ( ^mT
⋅^Σ⋅^m)
1
2
^σ p , ^m1 , ^m2
2
= ^m1
T
⋅^Σ⋅ ^m2 = ^m2
T
⋅^Σ⋅ ^m1
Markowitz Algorithm to find Efficient Frontier:
min
x
σ p , x
2
= ^x
T
⋅^Σ⋅^x
μ p , x = xT
⋅μ = μ p
0
xT
⋅1 = 1
constraint for no short sales: xi≥0
Tangency Portfolio:
^t =
^Σ
−1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
; ^t is portfolio weightings
max
^t
μ p ,t − rf
σ p ,t
; such that ^t
T
⋅1 = 1

19. CER model
Constant Expected Return (CER) model:
Ri t ∼ iid N (μ i ,σ i
2
); i = 1,...,N ( assets)
t = 1,...,T (time)
^SRi =
^μ i − rf
^σ i
Minimum Variance Portfolio:
^m =
^Σ
−1
⋅1
1
T
⋅^Σ
−1
⋅1
;
^m is portfolio weightings
such that ^m
T
⋅1 = 1
^μ p, ^m = ^mT
^μ ; p is portfolio
^σ p , ^m = ( ^m
T
⋅^Σ⋅^m)
1
2
^σ p , ^m1 , ^m2
2
= ^m1
T
⋅^Σ⋅ ^m2 = ^m2
T
⋅^Σ⋅ ^m1
Markowitz Algorithm to find Efficient Frontier:
min
x
σ p , x
2
= ^xT
⋅^Σ⋅^x
μ p , x = x
T
⋅μ = μ p
0
x
T
⋅1 = 1
constraint for no short sales: xi≥0
Tangency Portfolio:
^t =
^Σ −1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
; ^t is portfolio weightings
max
^t
μ p ,t − rf
σ p ,t
; such that ^tT
⋅1 = 1Constant Expected Return (CER) model:
Rit ∼ iid N (μ i,σ i
2
); i = 1,..., N ( assets)
t = 1,...,T (time)
t1
t2
t3
t4
Ri2
Ri3 Ri4
Rit
= (Rit
– Ri(t-1)
)/ Ri(t-1)

20. Efficient Frontier
Constant Expected Return (CER) model:
Ri t ∼ iid N (μ i ,σ i
2
); i = 1,...,N ( assets)
t = 1,...,T (time)
^SRi =
^μ i − rf
^σ i
Minimum Variance Portfolio:
^m =
^Σ
−1
⋅1
1T
⋅^Σ −1
⋅1
;
^m is portfolio weightings
such that ^m
T
⋅1 = 1
^μ p, ^m = ^m
T
^μ ; p is portfolio
^σ p , ^m = ( ^m
T
⋅^Σ⋅^m)
1
2
^σ p , ^m1 , ^m2
2
= ^m1
T
⋅^Σ⋅ ^m2 = ^m2
T
⋅^Σ⋅ ^m1
Markowitz Algorithm to find Efficient Frontier:
min
x
σ p , x
2
= ^xT
⋅^Σ⋅^x
μ p , x = x
T
⋅μ = μ p
0
xT
⋅1 = 1
constraint for no short sales: xi≥0
Tangency Portfolio:
^t =
^Σ
−1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
; ^t is portfolio weightings
max
^t
μ p ,t − rf
σ p ,t
; such that ^tT
⋅1 = 1
Return
Risk
Feasible portfolios
Efficient Frontier:
min
x
σ p, x
2
= ^x
T
⋅^Σ⋅^x ; μ p, x = x
T
⋅μ = μ p
0
x

21. Minimum variance
Constant Expected Return (CER) model:
Ri t ∼ iid N (μ i ,σ i
2
); i = 1,...,N ( assets)
t = 1,...,T (time)
^SRi =
^μ i − rf
^σ i
Minimum Variance Portfolio:
^m =
^Σ
−1
⋅1
1
T
⋅^Σ
−1
⋅1
;
^m is portfolio weightings
such that ^m
T
⋅1 = 1
^μ p, ^m = ^mT
^μ ; p is portfolio
^σ p , ^m = ( ^m
T
⋅^Σ⋅^m)
1
2
^σ p , ^m1 , ^m2
2
= ^m1
T
⋅^Σ⋅ ^m2 = ^m2
T
⋅^Σ⋅ ^m1
Markowitz Algorithm to find Efficient Frontier:
min
x
σ p , x
2
= ^xT
⋅^Σ⋅^x
μ p , x = x
T
⋅μ = μ p
0
x
T
⋅1 = 1
constraint for no short sales: xi≥0
Tangency Portfolio:
^t =
^Σ −1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
; ^t is portfolio weightings
max
^t
μ p ,t − rf
σ p ,t
; such that ^tT
⋅1 = 1
Minimum Variance Portfolio:
^m =
^Σ
−1
⋅1
1T
⋅^Σ −1
⋅1
Return
Risk
Feasible portfolios

22. Tangency
Constant Expected Return (CER) model:
Ri t ∼ iid N (μ i ,σ i
2
); i = 1,...,N ( assets)
t = 1,...,T (time)
^SRi =
^μ i − rf
^σ i
Minimum Variance Portfolio:
^m =
^Σ
−1
⋅1
1T
⋅^Σ −1
⋅1
;
^m is portfolio weightings
such that ^m
T
⋅1 = 1
^μ p, ^m = ^m
T
^μ ; p is portfolio
^σ p , ^m = ( ^m
T
⋅^Σ⋅^m)
1
2
^σ p , ^m1 , ^m2
2
= ^m1
T
⋅^Σ⋅ ^m2 = ^m2
T
⋅^Σ⋅ ^m1
Markowitz Algorithm to find Efficient Frontier:
min
x
σ p , x
2
= ^xT
⋅^Σ⋅^x
μ p , x = x
T
⋅μ = μ p
0
xT
⋅1 = 1
constraint for no short sales: xi≥0
Tangency Portfolio:
^t =
^Σ
−1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
; ^t is portfolio weightings
max
^t
μ p ,t − rf
σ p ,t
; such that ^tT
⋅1 = 1Tangency Portfolio:
max
^t
μ p ,t − rf
σ p ,t
; ^t =
^Σ
−1
⋅(μ−rf 1)
1T
⋅^Σ −1
⋅(μ−rf 1)
Return
Risk
Efficient Frontier
Feasible portfolios
Sharpe Ratio
Risk free
return

23. Co-variance
sample co-variance of n observations of k variables:
qjk =
1
n−1
∑
i=1
n
(xij − ¯x j)(xik − ¯xk )
where: ¯xj =
1
n
∑
i=1
n
xij and ¯xk =
1
n
∑
i=1
n
xik

24. Portfolio Performance

25. Portfolio Allocations

26. Aggregation
A&B C&D E&F G&H
A B C D E F G H
A&B&C&D E&F&G&H
all
D & (E&F) & G
Aggregated
data
Raw
data
Store precomputed
“tiles” of data
O(log2
nn) operations
to combine nn arbitrary
raw data elements

27. Aggregating Data

28. Commutative Operations
3, 4, 8
2, 6, 7
4, 7, 10, 3
1, 5
Sum,count: {30,6}
Average: 5
Sum,count: {24,4}
Average: 6
Sum,count: {15,3}
Average: 5
Sum,count: {15,3}
Average: 5
Sum,count: {6,2}
Average: 3
Sum,count: {30,6}
Average: 4.5
Sum,count: {60,12}
Average: 4.75
Wrong!
Associative
(grouping)
Commutative
(order)
Sum
Count
Average
Associative
Commutative
X
X
X
X
X

29. Covariance aggregation
Covariance values:
N * (N – 1) / 2
For each time sample
For 10,000 stocks tracking a daily
Close over 10 years this can reach
100,000,000,000 individual values
instrument
instrument
time
*
* * * * * * * * * *
* *
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* *
* *
* *
* *
*
*
*
*
*
*
*
*
*
*
*
*
*
� is a set of two time series(u,v)
aggregating the two subsets �1,�2
μ u, 1,μ v ,1 ,μ u,2 ,μ v ,2 are the means of u,v
on �1 ,�2 respectively
n = n1+n2
δ u, 2,1 = μ u, 2−μ u, 1
δ v , 2,1 = μ v ,2−μ v ,1
C
2,�
= C
2,�1
+ C
2,�2
+
n1 n2
n
δ u,2,1 δ v ,2,1
also recall that in general: μ = μ 1+n2
δ 2,1
n

31. References
● Articles
– Alexander Mordvintsev, Christopher Olah, Mike Tyka. Inceptionism: going deeper into Neural Networks. June 17, 2015
(http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html)
– Zhicheng Liu, Jeffery Heer.
Effects of latency on interactive visual analysis. August 12, 2014
(http://istc-bigdata.org/index.php/effects-of-latency-on-interactive-visual-analysis/)
– Pébay, Phillipe, “Formulas for Robust, One-Pass Parallel Computation of Covariances and Arbitrary-Order Statistical Moments”, 2008
(http://prod.sandia.gov/techlib/access-control.cgi/2008/086212.pdf)
Java Implementation in Apache Hive as org.apache.hadoop.hive.ql.udf.generic.GenericUDAFCovariance
(https://hive.apache.org/javadocs/r0.10.0/api/org/apache/hadoop/hive/ql/udf/generic/GenericUDAFCovariance.html)
● GitHub
– Slide charts (slides 5, 6, 9, 10, 11, 13, 16(partial), 23, 24, 25):
https://github.com/oci-labs/StampedeCon-2015
– Visualization tool (slide 15):
● https://github.com/uwdata/imMens
● Links
– Ggobi: http://www.ggobi.org/
● Books
– Edward R. Tufte. The Visual Display of Quantitative Information. 2001

32. Copyrights
● Slide 2
– Www.cartoonstock.com
(https://www.cartoonstock.com/cartoonview.asp?catref=mbcn2693)
● Slide 4
– CC BY 2.0
(https://www.flickr.com/photos/jackversloot/2563365462)
● Slide 7
– CC BY-SA 4.0
(https://en.wikipedia.org/wiki/Charles_Joseph_Minard#/media/File:Minard_map_of_napoleon.png)
● Slide 8
– Alexander Mordvintsev, Christopher Olah, Mike Tyka.
Inceptionism: going deeper into Neural Networks.
June 17, 2015
(http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html)
Accessed June 21, 2015
● Slide 12
– CC BY 2.0
(https://www.flickr.com/photos/jurvetson/4182789146/)
● Slide 16
– Congress – public domain
(http://media-3.web.britannica.com/eb-media//97/149697-050-05A96268.jpg)
– Chair – public domain
(https://openclipart.org/detail/3817/man-in-chair)
● Slide 17
– CC BY 2.0
(https://www.flickr.com/photos/frontierofficial/16122472323/)
● Slide 30
CC BY 2.0 (https://www.flickr.com/photos/fliegender/396848298/)
x