1. Portfolio Optimization: Some Practical Considerations
Jim Hwang
CPPIB
4-Oct-2014

2. Disclaimer
All the opinions and views expressed in this presentation and talk are strictly those of the presenter and they do not necessarily reflect those of the institution to which he is affiliated.

3. Contents Overview of the Portfolio Management Process
Optimal Portfolios
Characteristic Portfolio
Minimally Constrained Long-Short (L-S) Portfolio
More Constrained L-S Portfolio
Long-Only Portfolio
Partial L-S Portfolio (130/30)
Constraints, Penalties, Overrides
The Costs of Constraints
Consider Using Penalties Over Constraints
Overrides – What Am I Doing to My Portfolio?
Summary
Glossary
References

4. 1) Overview of the Portfolio Management Process

5. 1. Overview of the Portfolio Management Process
Optimization
Market Model
( σ Model )
Market
Prices
Earn Ests
Financials
Measurement
Performance
Attribution
Risk decomp
Control Models
( α + T-cost Models )

6. Industry Neutralization
A Simple Alpha Model
Univ: US large & mid-caps
Raw Factor:
BP (Book/Price)
Std
Industry Neutralization
Final α

7. Other Assumptions Our Other Tools
Third party structural factor risk model
Risk Factors – e.g., momentum, volatility, leverage …
Industry factors
Single country model – US
Third party optimizer
No transaction costs
The Client
Wants large-mid cap US equity exposure.
Willing to consider long-only or long-short portfolios.
Can tolerate
L-S total risk of 5% and gross gearing of 200% or,
L-O tracking error of 5%.

8. 2) Optimal Portfolios

9. 2a. Optimal Portfolios: The Characteristic Portfolio
A characteristic portfolio has an unit exposure to only one attribute and minimum risk.
Setup: Minimize σp2 s.t. α = 1.
Why isn’t my TC = 1? It should since,
w =σp2 V-1α and
TC = correl (V-1α, w)
Char Ptf
Exp Ret
1.00%
Exp Risk
0.99%
Exp IR
1.01
Trsfr Coeff
0.86
Gross Lvg
121.9%
Net Lvg
-0.4%
Total Long
60.8%
Total Short
-61.2%
# Long
261
# Short
239
Max( |wt| )
2.41%
GICS_Sector
Wgt
Energy
-0.50%
Materials
-0.18%
Industrials
0.63%
Cons Discret
0.53%
Cons Staples
2.20%
Health Care
1.32%
Financials
-3.94%
Info Tech
-0.10%
Telecom Svcs
-0.28%
Utilities
-0.08%
Industry Grp
Wgt
Banks
-1.67%
Div Fncls
-0.14%
Insurance
-3.27%
Real Estate
1.14%

10. 2b. Optimal Portfolios: Minimally Constrained Long-Short Portfolio
Setup: Maximize α s.t. σp = 5%
Long Gearing = Short Gearing = 100%
-10% < wi < 10%
GICS_Sector
Wgt
Energy
-7.20%
Materials
-0.20%
Industrials
-13.88%
Cons Discret
15.18%
Cons Staples
12.63%
Health Care
1.11%
Financials
-8.52%
Info Tech
4.15%
Telecom Svcs
-3.26%
Utilities
0.00%
LS Simple
Exp Ret
3.44%
Exp Risk
5.00%
Exp IR
0.69
Trsfr Coeff
0.68
Gross Lvg
200.0%
Net Lvg
0.0%
Total Long
100.0%
Total Short
-100.0%
# Long
129
# Short 42
Max( |wt| )
10.00%
Am I comfortable with these exposures?
Industry Grp
Wgt
Banks
0.00%
Div Fncls
-9.17%
Insurance
-4.64%
Real Estate
5.29%

11. 2c. Optimal Portfolios: More Constrained Long-Short Portfolio
Setup: Maximize α s.t. σp = 5%
Long Gearing = Short Gearing = 100%
-5% < wi < 5%
-5% < Industry Group < 5%
GICS_Sector
Wgt
Energy
-3.36%
Materials
-0.46%
Industrials
-10.00%
Cons Discret
8.90%
Cons Staples
6.66%
Health Care
4.44%
Financials
-5.74%
Info Tech
4.37%
Telecom Svcs
-4.82%
Utilities
0.00%
LS Constrained
Exp Ret
3.17%
Exp Risk
5.00%
Exp IR
0.63
Trsfr Coeff
0.68
Gross Lvg
200.0%
Net Lvg
0.0%
Total Long
100.0%
Total Short
-100.0%
# Long 29
# Short 33
Max( |wt| )
Am I comfortable with the security concentration? I.e., how much does specific risk contribute to my overall risk?
Industry Grp
Wgt
Banks
0.00%
Div Fncls
-2.95%
Insurance
-4.31%
Real Estate
1.52%

12. 2d. Optimal Portfolios: Long-Only Constrained Portfolio
Setup: Maximize α s.t. σt.e. = 5%
Long-Only
-5% < active_wti < 5%
-5% < active_wtInd Group < 5% LO
Tot Wts
Actv Wts
Exp Ret
1.31%
Exp Risk
4.73%
Exp IR
0.28
Trsfr Coeff
0.30
Gross Lvg
100.0%
187.3%
Net Lvg
0.0%
Total Long
93.6%
Total Short
-93.6%
# Long 23 22
# Short
480
Max( |wt| )
6.17%
5.00%
GICS_Sector
Actv Wgt
Energy
0.34%
Materials
1.72%
Industrials
-2.59%
Cons Discret
12.27%
Cons Staples
6.55%
Health Care
3.64%
Financials
-9.79%
Info Tech
-12.25%
Telecom Svcs
2.91%
Utilities
-2.81%
I hold a 23 stock long-only portfolio. Any stock I own below benchmark weight or do not own is an active underweight.
Industry Grp
Actv Wgt
Banks
-5.00%
Div Fncls
Insurance
2.41%
Real Estate
-2.20%

13. 2e. Optimal Portfolios: Partial LS (130/30)Portfolio
Setup: Maximize α s.t. σt.e. = 5%
Long Gearing = 130%, Short Gearing = 30%
-5% < active_wti < 5%
-5% < active_wtInd Group < 5%
GICS_Sector
Actv Wgt
Energy
-5.00%
Materials
2.70%
Industrials
-7.18%
Cons Discret
2.38%
Cons Staples
7.69%
Health Care
6.15%
Financials
-0.33%
Info Tech
-8.60%
Telecom Svcs
5.00%
Utilities
-2.81%
130-30
Tot Wts
Actv Wts
Exp Ret
2.39%
Exp Risk
5.00%
Exp IR
0.48
Trsfr Coeff
0.47
Gross Lvg
160.0%
242.7%
Net Lvg
100.0%
0.0%
Total Long
130.0%
121.4%
Total Short
-30.0%
-121.4%
# Long 35 34
# Short 11
468
Max( |wt| )
6.17%
Industry Grp
Actv Wgt
Banks
-5.00%
Div Fncls
0.44%
Insurance
1.32%
Real Estate
2.91%

14. 3) Constraints, Penalties, Overrides

15. 3a. The Costs of Constraints
Different Portfolio Construction Methodologies
(Base Case)
Characteristic Ptf
IR TC
Value
% Diff v Base
LS Constrained Ptf
IR TC
Value
% Diff v Base -37% -21%
Ptf
IR TC
Value
% Diff v Base -53% -45%
LS Simple Ptf
IR TC
Value
% Diff v Base -32% -21%
Long Only Ptf
IR TC
Value
% Diff v Base -73% -65%

16. 3b. Consider Using Penalties over Constraints
Piecewise Penalties
Utility
Utility
Weight
Weight

17. 3c. Overrides – What Am I Doing to My Portfolio?
You’re in the early stages of the Financial Crisis. Subprime loans are defaulting.
Should you override your model? Which one? How?
You decided that you don’t trust your alpha model on the home builders or the diversified financials. Set these alphas to zero. Optimize and examine your portfolio.
α Override
Long-only portfolio
Long-only portfolio
Alpha
Tot Wt
Actv Wt
Consumer Durables
NKE.US
-.54
0.00%
-0.35%
VFC.US
-.33
-0.14%
. . .
PHM.US
1.10
3.77%
+3.73%
Diversified Finacials
BRKB.US
0.83
-1.76%
AXP.US
-0.76
-0.49%
LM.US
0.61
-0.03%
MS.US
1.09
0.59%
+0.24%
GLW.US
1.08
1.25%
1.11%
Alpha
Tot Wt
Actv Wt
Consumer Durables
NKE.US
-.54
0.00%
-0.35%
. . .
PHM.US
0.00
-0.04%
Diversified Finacials
BRKB.US
0.02%
-1.74%
AXP.US
-0.49%
LM.US
-0.03%
MS.US
GLW.US
1.08
3.41%
2.30%
Why?

18. 4) Summary
Understand the models you are using. Make sure your models and metrics are aligned.
The optimizer is a just a tool. Make sure you have the right problem formulation.
Constraints can be expensive
The long-only constraint is very expensive.
Our examples are even before implementation (e.g., borrowing, trading, etc.)
Consider using penalties instead of constraints.
Be careful of unintended consequences from constraints and overrides.

19. Glossary Alpha: Forecast of excess return.
Factors: Characterizations or attributes that may be used to describe a group of securities and explain its returns. Factors may be fundamental or statistical.
Gearing: The notional exposure of a portfolio to risky assets divided by the total capital invested in the portfolio.
Information Ratio (IR): Measure of risk-adjusted return calculated by dividing active return by active risk.
Leverage: Use of capital in excess of the original investment to structure a portfolio. Gearing and leverage are sometimes used interchangeably.
Neutralization: Eliminating the influence of other factors on a given factor by calculating its orthogonal component.
Return, Active: The return of an asset or a portfolio, relative to a benchmark.
Return, Total: The percentage gain or loss of an asset or a portfolio over a defined period of time. Returns may be calculated ex-ante or measured ex-post.
Risk, Active: The risk of an asset or portfolio, relative to a benchmark.
Risk, Total: Standard deviation of total returns of an asset or portfolio. Risks may be calculated ex-ante or measured ex-post.
Short: Selling securities one doesn’t own with the intent of buying it back in the future at a lower price. Shorting rules vary by countries.
Standardization: Creating a Z-score by subtracting the sample mean and dividing by the sample standard deviation.
Tracking Error: Active risk. These two terms are used interchangeably.
Transfer Coefficient: Correlation of the active weights of the assets in a one’s portfolio to one’s risk-adjusted alpha model. It is a measure of how efficiently research ideas are translated into a portfolio.
Weight, Active The weight of a security in a portfolio, relative to a benchmark.
Weight, Total The currency value of a security in a portfolio divided by the capital invested in the portfolio.

20. References
Active Portfolio Management, 2nd edition, R.C. Grinold & R.N. Kahn, McGraw-Hill, 2000
Linear Algebra and Its Applications, 3rd edition, G. Strang, Harcourt Brace Jovanovich, Publishers 1988
Quantitative Equity Portfolio Management, Modern Techniques and Applications, E.E. Qian, R.H. Hua & E.H. Sorenson, Chapman & Hall / CRC, 2007