Portfolio Optimization Artificial Intelligence in Finance

Zsolt Bihary (Morgan Stanley)

2013, Budapest

Structuring (Securitization)

Pool of

Loans

Cash-flow Bank

Bank wants to • Get rid of risk • Realize future cash-flow now

Investors

Investors want to • Invest in the long run • with different risk

Structuring (Securitization)

A

B

D

C

Pool of

Loans

Cash-flow

Wate

r-fall

Investors

Investors

Investors

Bonds

Bank

The Structuring Problem

A

B

D

C

Pool of

Loans

Cash-flow

Wate

r-fall

Bonds

How to choose bond sizes? Bank is interested in great bond sizes and high ratings. Regulators seek to limit bond sizes before giving high ratings.

Bank

The Black Box Simulator

A

B

D

C

Black Box Simulator

• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4

INPUT

Bonds

OUTPUT

Structure (bond sizes)

• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result

The Black Box Simulator

A

B

D

C

Black Box Simulator

• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4

INPUT

Bonds

OUTPUT

Structure (bond sizes)

• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result

We want to maximize proceeds, under the constraint that the structure passes all stress-test scenarios.

Nature of the Optimization Problem

• Objective function and constraints evaluated by Black Box (no gradients available)

• Objective function and constraints evaluated simultaneously (unknown constraints)

• Constraints returned as pass/fail Booleans (no differentiable discriminant functions)

• Black Box is very slow (we can afford only 5 iterations)

• We can run Black Box parallel on 20 servers

Synthetic Example

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A bond size

B bond size

A (20%)

B (50%)

D (30%)

Example structure

Synthetic Example

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100

A bond size

B bond size

A (20%)

B (50%)

D (30%)

Example structure

Global optimum

Synthetic Example

0 20 40 60 80 1000

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20

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40

50

60

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80

90

100

A bond size

B bond size

A (20%)

B (50%)

D (30%)

Example structure

Global optimum

Local optimum

Reinforcement Learning

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Reinforcement Learning

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Initially, put down random structures

Reinforcement Learning

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At each iteration, new structures are selected

based on information on previous structures

Reinforcement Learning

0 20 40 60 80 1000

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20

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50

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90

100

At each iteration, new structures are selected

based on information on previous structures

Reinforcement Learning

0 20 40 60 80 1000

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20

30

40

50

60

70

80

90

100

At each iteration, new structures are selected

based on information on previous structures

Reinforcement Learning

0 20 40 60 80 1000

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20

30

40

50

60

70

80

90

100

At each iteration, new structures are selected

based on information on previous structures

Surrogate Model Approach

Initial Random Structures

Surrogate Model New Design Structures

Best Structure Found

Black Box Simulator

Results on Structures

Surrogate Model Approach

Initial Random Structures

Surrogate Model New Design Structures

Best Structure Found

Black Box Simulator

Results on Structures

Objective function:

Linear Regression

Constraints:

Support Vector

Machine (SVM)

Support Vector Machine (SVM)

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100

Gives a surrogate model for the

pass – fail boundary

Support Vector Machine (SVM)

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100

With more points, SVM gives more

and more accurate boundary

Support Vector Machine (SVM)

0 20 40 60 80 1000

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20

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50

60

70

80

90

100

With more points, SVM gives more

and more accurate boundary

Support Vector Machine (SVM)

0 20 40 60 80 1000

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20

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50

60

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90

100

With more points, SVM gives more

and more accurate boundary

Pass Probability

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SVM maps out the pass probability

in structure space

Pass Probability

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With more points, pass probability

map becomes more and more accurate

Pass Probability

0 20 40 60 80 1000

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20

30

40

50

60

70

80

90

100

With more points, pass probability

map becomes more and more accurate

Pass Probability

0 20 40 60 80 1000

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20

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50

60

70

80

90

100

With more points, pass probability

map becomes more and more accurate

Expected Improvement

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Surrogate model maps out the most

promising regions of structure space

Expected Improvement

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100

With more and more points, surrogate

model zeros in to the optimal region

Expected Improvement

0 20 40 60 80 1000

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20

30

40

50

60

70

80

90

100

With more and more points, surrogate

model zeros in to the optimal region

Expected Improvement

0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

With more and more points, surrogate

model zeros in to the optimal region

Conclusion

Using Machine Learning techniques

on the Portfolio Structuring Problem,

we could provide a useful tool

for our structuring business

Thank you for your attention