The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 588 Friday, March 12, 2004 12:40 PM

588 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 19.13 Factor Exposures of a 50-Stock Portfolio that

Optimally Matches the S&P 500

Risk Index Exposures (Std. Dev.)

Mgd. Bmk. Act. Mgd. Bmk. Act.

Volatility −0.141 −0.084 −0.057 Value −0.072 −0.070 −0.003

Momentum −0.057 −0.064 0.007 Earnings variation −0.058 −0.088 0.029

Size 0.588 0.370 0.217 Leverage −0.206 −0.106 −0.100

Size nonlinearity 0.118 0.106 0.013 Currency sensitivity −0.001 −0.012 0.012

Trading activity −0.101 −0.005 −0.097 Yield 0.114 0.034 0.080

Growth −0.008 −0.045 0.037 Non-EST universe 0.000 0.000 0.000

Earnings yield 0.103 0.034 0.069

Industry Weights (Percent)

Mining and Metals

Gold

Forestry and Paper

Chemicals

Energy Reserves

Oil Refining

Oil Services

Food and Beverages

Alcohol

Tobacco

Home Products

Grocery Stores

Consumer Durables

Motor Vehicles & Parts

Apparel and Textiles

Clothing Stores

Specialty Retail

Department Stores

Constructn. and Real Prop.

Publishing

Media

Hotels

Restaurants

Entertainment

Leisure

Environmental Services

Heavy Electrical Eqp.

Mgd. Bmk. Act. Mgd. Bmk. Act.

0.000

0.000

1.818

2.360

5.068

1.985

1.164

2.518

0.193

1.372

0.899

0.000

0.000

0.000

0.000

0.149

1.965

4.684

0.542

2.492

1.822

1.244

0.371

2.540

0.000

0.000

1.966

0.606

0.161

0.871

2.046

4.297

1.417

0.620

3.780

0.515

0.732

2.435

0.511

0.166

0.621

0.373

0.341

2.721

3.606

0.288

0.778

1.498

0.209

0.542

1.630

0.409

0.220

1.949

−0.606

−0.161

0.947

0.314

0.771

0.568

0.544

−1.261

−0.322

0.641

−1.536

−0.511

−0.166

−0.621

−0.373

−0.191

−0.756

1.078

0.254

1.713

0.323

1.035

−0.171

0.910

−0.409

−0.220

0.017

Heavy Machinery

Industrial Parts

Electric Utility

Gas Utilities

Railroads

Airlines

Truck/Sea/Air Freight

Medical Services

Medical Products

Drugs

Electronic Equipment

Semiconductors

Computer Hardware

Computer Software

Defense and Aerospace

Telephone

Wireless Telecom.

Information Services

Industrial Services

Life/Health Insurance

Property/Casualty Ins.

Banks

Thrifts

Securities and Asst. Mgmt.

Financial Services

Internet

Equity REIT

0.000 0.141 −0.141

1.124 1.469 −0.345

0.000 1.956 −1.956

0.000 0.456 −0.456

0.000 0.373 −0.373

0.000 0.206 −0.206

0.061 0.162 −0.102

1.280 0.789 0.491

3.540 3.599 −0.059

9.861 10.000 −0.140

0.581 1.985 −1.404

4.981 4.509 0.472

4.635 4.129 0.506

6.893 6.256 0.637

1.634 1.336 0.297

3.859 3.680 0.180

1.976 1.565 0.411

0.802 2.698 −1.896

0.806 0.670 0.136

0.403 0.938 −0.535

2.134 2.541 −0.407

8.369 7.580 0.788

0.000 0.362 −0.362

2.595 2.017 0.577

6.380 6.321 0.059

0.736 0.725 0.011

2.199 0.193 2.006

Note: Mgd = Managed; Bmk = S&P 500 (the benchmark); Act = Active = Managed

− Benchmark

Source: Exhibit 13.10 in Frank J. Fabozzi, Frank J. Jones, and Raman Vardharaj,

“Multi-Factor Risk Models,” Chapter 13 in Frank J. Fabozzi and Harry M.

Markowitz (eds.), The Theory and Practice of Investment Management (Hoboken,

NJ: John Wiley & Sons, 2002).