OUTPERFORMING STOCK INDICES USING PROXIES FOR RISK AND

RETURNS

Vashishta BhaskarDuquesne University

Presented at QWAFAFEWSeptember 9, 2014

Introduction Efficient markets Implications for investors Active equity portfolio

management strategies Empirical results of sort by factor

methodologies Expansion of existing quantitative

techniques

Efficient Markets

A market in which security prices rapidly reflect all available information

Random walk (short term) Provide positive return (long term) Expected Returns are a function of

Size, Relative Value (value-growth), Risk and Momentum

Implications for Investors and Money Managers

Risk tolerance Diversification Passive investing

Buy & hold portfolios Indexing

Active Equity Investing

Fundamental Analysis Top-down Bottom-up

Technical indicators Identify Attributes that provide

superior returns

Empirical Results of Factor Based Strategies – Sort methodology

Fama-French 1992 study concluded that small market equity portfolios performed better than large equity;

And, higher book-to-market performed better than lower book-to-market.

Adapted from What Works on Wall Street. Size Effect 1952-2003

Market Capitalization Return % Standard Deviation

Sharpe Ratio

<25 million 28.12 47.51 0.63

25 million to <100 million

15.96 30.75 0.46

100 million to <250 million

13.72 24.85 0.46

250 million to < 500 million

13.56 21.46 0.47

500 million to <1 billion 12.18 19.34 0.44

>= 1 billion 11.75 16.98 0.45

Market Leaders* 13.52 17.37 0.54Adapted from What Works on Wall Street pgs. 61-62*Market leaders defined as: non-utility, market cap > avg., cf > avg., sales > 50% of avg. from COMPUSTAT.

Returns: Russell Indices 2004-2013

Summary Statistics - Russell.fld 12/1994-12/2013

Arithmetic Mean (%)

Geometric Mean

(%)

Standard

Deviation (%)

Sharpe

Ratio

N Positiv

e Period

s

Average Decline

(%)

Maximum

Decline (%)

Ending Index Value

Russell 2000 TR 11.07 9.27 19.67

0.5627 13 -12.87 -34.82 58,914

Russell 2500 TR 12.61 10.77 19.69

0.6405 16 -14.53 -36.79

77,3430

Russell 1000 TR 11.31 9.38 19.85

0.5699 16 -37.17 -37.6

60,0728

Returns by Cap 250M – 1B1B–5B and > 5B. (1994-2013)

Arithmetic Mean

(%)

Geometric Mean

(%)

Standard Deviatio

n (%)Sharpe Ratio

N Positive Periods

Average

Decline (%)

Maximum

Decline (%)

Ending Index Value

Small Cap 10.96 8.86 21.29 0.515 13 -12.65 -40.62 54,589Mid Cap 12.69 10.86 19.88 0.638 14 -15.33 -34.89 78,634Large Cap 12.55 10.56 20 0.6278 15 -34.8 -40.16 74,458

High 100 CAPX and Low 100 CAPX Portfolio Returns by Cap

Arithmetic Mean (%)

Geometric Mean

(%)

Standard Deviatio

n (%)

Sharpe

Ratio

N Positiv

e Period

s

Average Decline

(%)

Maximum

Decline (%)

Ending Index Value

Small CapHigh CAPX 100 28.46 24.08 34.00

0.8371 16 -14.48 -41.06

748,374

Small Cap Low CAPX 100 5.81 3.22 22.93

0.2535 11 -27.13 -53.79 18,834

Mid Cap High CAPX 100 22.76 19.59 27.51

0.8272 17 -16.1 -43.51

358,013

Mid Cap Low CAPX 100 8.29 6.35 19.79 0.419 12 -21.28 -50.47 34,250Large Cap High CAPX 100 16.41 14.12 22.61

0.7259 15 -21.12 -37.36

140,449

Large Cap Low CAPX 100 7.84 5.42 21.36

0.3671 14 -47.34 -50.46 28,729

Small Cap High CAPX – Low CAPX

 Return Small Cap Small Cap High CAPX minus

 Period EndHigh CAPX Low CAPX Low CAPX

Dec94 1.15% -10.68% 11.83%Dec95 30.75% 28.12% 2.63%

Dec96 34.96% 19.93% 15.03%

Dec97 39.13% 17.16% 21.98%

Dec98 -7.54% -15.00% 7.45%

Dec99 31.37% 35.98% -4.62%

Dec00 34.58% -16.65% 51.23%

Dec01 11.88% -6.28% 18.16%

Dec02 0.93% -18.60% 19.53%

Dec03 73.35% 43.32% 30.03%

Dec04 50.68% 8.80% 41.89%

Dec05 28.81% -4.81% 33.63%

Dec06 38.40% 11.36% 27.05%

Dec07 22.16% -15.04% 37.20%

Dec08 -41.06% -45.61% 4.55%

Dec09 118.92% 29.06% 89.86%

Dec10 48.88% 13.89% 34.98%

Dec11 -5.97% -15.53% 9.56%

Dec12 7.33% 18.62% -11.29%

Dec13 54.90% 30.89% 24.01%

Why Z – Score?

Expected return from Corporate Bonds = Risk free rate + bond risk premium

Expected Return from Equity = Company specific bond rate +

equity risk premium Z score model and calculation provided at the end of this presenation

50 Stock portfolios based on high and low Z scores

Arithmetic Mean

(%)

Geometric Mean

(%)

Standard

Deviation (%)

Sharpe

Ratio

N Positiv

e Period

s

Average Decline

(%)

Maximum Decline

(%)Ending

Index Value

Small Cap High CAPX High Z 50 32.75 27.96 37.55

0.8721 15 -10.22 -35.88 1,385,930

Small Cap High CAPX Low Z 50 24.67 20.12 32.98

0.7483 15 -16.27 -45.14 391,135

Mid Cap High CAPX High Z 50 29.78 26.07 32.19

0.9251 19 -37.01 -37.01 1,028,754

Mid Cap High CAPX Low Z 50 15.14 12.32 25.06

0.6043 14 -15.11 -43.97 102,201

Large Cap High CAPX High Z 50 18.33 16.04 22.21

0.8254 15 -18.53 -39.14 195,975

Large Cap High CAPX Low Z 50 14.51 11.85 25.46

0.5698 14 -22.75 -36.85 93,915.37

Z Score effects   Small Cap Small Cap High z - Low Z  High CAPX High CAPX  High Z Low Z  50 50

Return thru    Dec94 6.09% -2.43% 8.52%Dec95 29.86% 35.64% -5.78%Dec96 36.03% 34.08% 1.95%Dec97 46.46% 30.49% 15.96%Dec98 -5.06% -15.39% 10.33%Dec99 49.14% 23.78% 25.37%Dec00 37.11% 44.47% -7.36%Dec01 24.80% -2.36% 27.16%Dec02 -4.86% 5.39% -10.25%Dec03 67.24% 69.87% -2.63%Dec04 52.48% 50.29% 2.19%Dec05 31.38% 21.57% 9.81%Dec06 50.60% 32.26% 18.34%Dec07 21.41% 27.10% -5.69%Dec08 -35.88% -45.14% 9.26%Dec09 147.21% 91.94% 55.27%Dec10 53.78% 38.82% 14.96%Dec11 -1.97% -15.11% 13.14%Dec12 12.29% 0.04% 12.24%Dec13 46.29% 69.09% -22.80%

  Arithmetic Mean

(%)

Geometric Mean (%)

Standard Deviation

(%)

Sharpe Ratio

N Positive Periods

N Negative Periods

Average Decline (%)

Maximum Decline (%) Starting Index =

10.,000

Ending Index Value

Large Cap 12.55 10.56 20.00 0.6278 15 5 -34.80 -40.16 74,458.7836

Large Cap High CAPX 100 16.41 14.12 22.61 0.7259 15 5 -21.12 -37.36 140,448.9883

Large Cap High CAPX High Z 50

18.33 16.04 22.21 0.8254 15 5 -18.53 -39.14 195,975.8426

Large Cap High CAPX Low Z 50

14.51 11.85 25.46 0.5698 14 6 -22.75 -36.85 93,915.3658

Large Cap Low CAPX 100 7.84 5.42 21.36 0.3671 14 6 -47.34 -50.46 28,728.8504

Mid Cap 12.69 10.86 19.88 0.6380 14 6 -15.33 -34.89 78,634.6707

Mid Cap High CAPX 100 22.76 19.59 27.51 0.8272 17 3 -16.10 -43.51 358,013.2837

Mid Cap High CAPX High Z 50

29.78 26.07 32.19 0.9251 19 1 -37.01 -37.01 1,028,754.4758

Mid Cap High CAPX Low Z 50 15.14 12.32 25.06 0.6043 14 6 -15.11 -43.97 102,201.3356

Mid Cap Low CAPX 100 8.29 6.35 19.79 0.4190 12 8 -21.28 -50.47 34,250.1741

Small Cap 10.96 8.86 21.29 0.5150 13 7 -12.65 -40.62 54,589.6128

Small Cap High Capx 100 28.46 24.08 34.00 0.8371 16 4 -14.48 -41.06 748,374.3280

Small Cap High CAPX High Z 50

32.75 27.96 37.55 0.8721 15 5 -10.22 -35.88 1,385,930.5502

Small Cap High CAPX Low Z 50

24.67 20.12 32.98 0.7483 15 5 -16.27 -45.14 391,135.1867

Small Cap Low CAPX 100 5.81 3.22 22.93 0.2535 11 9 -27.13 -53.79 18,833.9723

Summary Statistics - 12/1994-12/2013

Limited conclusions and further research CAPX is indicative of future returns Z score can be used as a further

discriminant as a proxy for risk There are additional factors such as

value and momentum that can be incorporated in an overall strategy

Scaled CAPX or items such as retention ratio may be useful