outperforming stock indices using proxies for risk and returns vashishta bhaskar duquesne university...
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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