The document discusses limitations of using the beta coefficient to evaluate risk and discusses developing a "Total Beta" measure to better capture risk. It notes that beta values can vary significantly over time and have low correlation values (R2). It proposes that total beta considers both systematic risk (beta x R2) and idiosyncratic risk (standard deviation of asset/market x (1-R2)). For non-diversified investors or assets evaluated independently, total beta may better reflect risk rather than just beta. The concept is illustrated using hypothetical "fantasy assets" and analyzing their risks under total beta versus just beta.

1. Student’s concepts on Beta, Private
Company Valuation and Portfolio
Diversification

2.  Objective: to understand the valuation of companies
and the principles of diversification of equity assets
in order to translate these principles to private
company valuation and implications for the
diversification strategy of private company
stockholders and investors

3. The Problem with Betas

4. From Wikipedia:
 In finance, the Beta (β) of a stock or portfolio is a number describing
the relation of its returns with that of the financial market as a
whole.[1]
 An asset has a Beta of zero if its returns change independently of
changes in the market's returns. A positive beta means that the
asset's returns generally follow the market's returns, in the sense that
they both tend to be above their respective averages together, or
both tend to be below their respective averages together. A negative
beta means that the asset's returns generally move opposite the
market's returns: one will tend to be above its average when the
other is below its average.[2]
 The beta coefficient is a key parameter in the capital asset pricing
model (CAPM). It measures the part of the asset's statistical variance
that cannot be removed by the diversification provided by the
portfolio of many risky assets, because of the correlation of its
returns with the returns of the other assets that are in the portfolio.
Beta can be estimated for individual companies using regression
analysis against a stock market index.
 Diversified investors can diversify away Non Systemic Risk but have
to handle Systemic Risk which is not diversifiable

5. To analyze financial asset behavior we constructed two
portfolios
A. A portfolio of thirty mutual funds’ monthly
performance from 12/2006-11/2010 – net of the
Rf for that month
B. A long term series from 1988 - 2009
 Mutual funds are believed to include all principal

6. A. Thirty mutual funds’ monthly performance from 12/2006-
11/2010 – net of the Rf for that month
 Mutual funds are believed to include all principal asset classes as per S&P
SIM ASSET
Monthly
return net of
Rf
Standard
Deviation of
returns Sdev/Mean Beta
TIPs Inflation-protected Treasuries 0.15% 2% 1651% 0.14
AGG US Bonds 0.21% 1% 719% 0.05
OIL Crude Oil -1.00% 12% -1199% 1.11
IGE Natural Resources (Inc Oil) 0.39% 8% 2126% 1.10
GSG Commodities Index -0.76% 9% -1140% 0.84
VNQ US Real Estate 0.06% 11% 16956% 1.49
RWX International Real Estate -0.95% 8% -864% 1.28
EEM Emerging Markets 0.80% 9% 1136% 1.38
EFA Europe, Australasia, Far East -0.29% 7% -2560% 1.17
VB US Small Cap Stocks 0.19% 8% 4043% 1.24
VV US Large Cap Stocks -0.12% 6% -5081% 1.01
VO US Mid Cap Stocks 0.09% 7% 7555% 1.16
DOW Dow Jones Ind Average -0.23% 5% -2330% 0.90
S&P Standard and Poors 500 -0.34% 6% -1727% 1.00
IXIC NASDAQ 0.19% 7% 3645% 1.12
VGK European Stocks -0.19% 8% -4062% 1.24
VPL Pacific Rim Stocks -0.20% 7% -3239% 1.00
EWJ Japanese Stocks -0.66% 6% -867% 0.81
JXI Global Utilities -0.46% 5% -1170% 0.76
IXJ Global Health Care -0.30% 5% -1697% 0.69
EXI Global Industrials 27.49% 8% 28% 1.25
IXG Global Fin Services -0.96% 10% -1048% 1.58
IAU GOLD 1.38% 6% 426% 0.05
IXC Global Energy 0.13% 7% 5586% 0.99
IXP Global Telecom 0.22% 6% 2663% 0.80
IXN Global Technology 0.15% 7% 4930% 1.17
MXI Global Materials 0.54% 9% 1695% 1.36
IGF Global Infrastructure -0.89% 8% -843% 1.04
KXI Global Consumer Staples 0.20% 5% 2353% 0.69
RXI Global Consumer Discretionary -0.19% 7% -3807% 1.14

7. B. A long term series from 1988 – 2009, net of Rf
 Mutual funds are believed to include all principal asset classes as per S&P
ASSET
Monthly
returns net of
Rf
Std dev of
returns Std Dev/mean Beta
S&P 500 Index Fund 0.003% 4.26% 124837% 1.00
T Rowe Price Nat Resources Fund 0.115% 5.36% 4666% 0.82
Vanguard Precious Metals Index -0.234% 8.63% -3687% 0.66
Fidelity Select Gold Fund -0.117% 9.76% -8340% 0.47
Gold Mutual Fund -0.459% 10.08% -2195% 0.40
T Rowe Price MMKT Fund -0.376% 0.24% -65% (0.01)
Vanguard TIP Bonds -0.328% 1.34% -407% (0.00)
Vanguard Intermediate USD Bonds -0.201% 1.33% -662% 0.00
Vanguard Long Term USD Bonds -0.163% 2.14% -1310% 0.02
T Rowe Price Int'l Bond Fund -0.045% 2.45% -5505% 0.10
Vanguard Hi Yld Corp Bonds -0.078% 2.16% -2753% 0.29
T Rowe Price Emg Mkt Bond Fund -0.577% 0.86% -148% 0.01
T Rowe Price Large Cap Fund -0.370% 4.03% -1088% 0.81
T Rowe Price Mid Cap Fund -0.605% 2.58% -427% 0.27
T Rowe Price Small Cap Fund -0.560% 5.33% -951% 0.85
Vanguard Energy Fund 0.370% 5.95% 1611% 0.75
Vanguard Health Care Fund 0.562% 3.91% 697% 0.69
T Rowe Price Health Sciences Fund -0.123% 5.00% -4065% 0.58
Health Care Average -0.048% 3.77% -7935% 0.52
T Rowe Price Fin Serv Fund -0.514% 4.01% -780% 0.58
T Rowe Price Media + Comm Fund -0.118% 5.82% -4948% 0.97
Fidelity Comp Tech Fund 0.097% 8.96% 9220% 1.57
Fidelity Utilities Fund -0.015% 4.18% -27672% 0.76
Fidelity Utilities Index -0.607% 3.76% -620% 0.49
Fidelity Lat Am Stox Fund -0.199% 5.47% -2752% 0.66
Vanguard Emerging Markets Stox -0.319% 6.04% -1895% 0.94
Vanguard Euro Stox Fund -0.103% 4.62% -4495% 0.82
Vanguard Pacific Stock Index -0.482% 5.45% -1130% 0.66
Fidelity Mtg Backed Sec Fund -0.390% 0.56% -143% (0.01)
Vanguard US REIT Index -0.577% 0.86% -148% 0.01

8. It is true that Higher Beta Assets have
higher volatility ….

9. …and higher Beta assets have higher
average returns, BUT with a low R2=.167 ….

10. …indicating that higher returns correlate
somewhat with higher volatility, R2=.277

11. Nevertheless, Beta has some shortcomings
which affect Valuations and Investments
 Beta values do not consider Strength of Fit (R2)
which illustrates the degree of correlation between
the regression equation and the market marker
 Beta’s R2 are generally between 0.4 and 0.8, with much
dispersion
 Betas vary – in some cases significantly – over the
medium and long terms and according to the time
span measured

12. Nearly 40% of assets in sample have Betas with R2’s of .7
or below – is Beta a measure of Risk or Correlation?
Beta = Covariance(asset,market)/ variance(market)

13. SUMMARY OUTPUT
Regression Statistics
Multiple R 0.938
R Square 0.881
Adjusted R Square 0.872
Standard Error 0.138
Observations 32.000
ANOVA
df SS MS F Significance F
Regression 2.000 4.073 2.036 106.840 0.000
Residual 29.000 0.553 0.019
Total 31.000 4.625
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%
Intercept (0.094) 0.052 (1.818) 0.079 (0.201) 0.012
R2 vs S&P 0.930 0.090 10.333 0.000 0.746 1.114
stda/stdm 0.334 0.042 7.972 0.000 0.248 0.419
Beta is more a descriptor of correlation with
S&P than intrinsic volatility
Multiple regression analysis for 32 assets shows
that the correlation between the asset and the
S&P influences Beta more than the volatility
Relativ
e
Volatilit
y

14. This low R2 is because 57% of monthly returns fall outside of
the range of +/- 99 % of the mean for each asset….
 Source: Yahoo Finance, Analisis Lambda, based on 30 assets from 2007-2010 ; 40-60
observations each

15. A small reduction/increase in Beta can have
a significant impact on Valuation
 Expected Re= Rf + *(Rm-Rf)
 Re impacts not only the discount rate for the estimated
cash flows, but also the estimation of the perpetuity cash
flows leading to a double impact on values
+30%
-24%
Change in
Beta
Base

16. Most assets show significant variation in 12
month Betas between 2008-2010
 Source: Yahoo Finance, Analisis Lambda, based on 30 assets from 2007-2010 ; 40-60 observations
each

17. Variation in 12 month Betas from 2008-2010 shows a median
Standard Deviation of 10% of the Mean, ranging from – 200% to +
300% ….
 Source: Yahoo Finance, Analisis Lambda
 * Comparison between 12. month Betas during the period

18. … even though in periods of S&P declines, R2
values for Betas tend to increase
 Source: Yahoo Finance, Analisis Lambda, based on 30 assets from 2007-2010 ; 40-60 observations
each

19. One solution is to use longer term Betas, 36 to 48
month Betas vs 12 month Betas
 Source: Yahoo Finance, Analisis Lambda
More Stable
Betas

20. Over the long term, however, even 36 month
Betas are not stable
 Source: Yahoo Finance, Analisis Lambda

21. Volatility in 36 month Betas over the Long Term (20 yrs) can be
up to five or six times greater than observable in Short Term
horizon of 3 yrs
 Source: Yahoo Finance, Analisis Lambda * Rolling 36 month Betas vs 12, 24, 36 and 48 month
Betas
Long term, Beta values vary significantly for individual assets

22. We developed Fantasy Assets to illustrate asset descriptions and
understand comparative Asset behavior as to Beta and volatility
Asset A Asset B Asset C Asset D Asset E Asset F Asset G
Minus S&P .2% Fixed ret 75% of S&P 125% of S&P Random Dephased S&P Mix .75+1.25

23. Beta is not a good descriptor for this Fantasy Asset behavior
• Random portfolio has similar Std Dev as S&P, but
low - and negative - Beta
• Assets with low correlation to S&P receive low Betas
• Dephased S&P has same Std Dev and monthly
return as S&P, but low Beta
• Again, assets with low correlation to S&P receive low
Betas

24. We propose the concept of Total Beta to
capture risk more accurately
 Systematic Risk (Beta) X Beta R2 =
Contribution to Total Risk
 Idiosyncratic Risk* X (1-Beta R2) =
Contribution to Total Risk
 Total Beta = Sum of both above
* Idiosyncratic Risk defined as Std Dev of Asset/Std Dev
of S&P (as Market Marker)
Note: this concept is not totally new. Daniel L. McConaughy, PhD; California State University,
Northridge, presented a paper (USASBE_2009_Proceedings-Page0113 ) titled The Cost of
Capital for the Closely-held, Family- Controlled Firm where he outlines the use of volatility of
company Cash flows to that of Market markers as a measure of risk.

25. Using ‘Total Beta’ applied to Fantasy Assets leads to a much better
understanding of their performance taking this into account
 Systematic Risk (Beta) X Beta
R2 = Contribution to Total Risk
 Idiosyncratic Risk* X (1-Beta
R2) = Contribution to Total
Risk
 Total Beta = Sum of both above
* Idiosyncratic Risk defined as Std Dev of
Asset/Std Dev of S&P (as Market
Marker)
•Random portfolio has same
Average Return as S&P with similar
Std Dev, but now has Total Risk in
line with Std Dev
•Dephased S&P has same Average
Return and Std Dev as S&P but now
has similar Total Risk measurement
Asset A Asset B Asset C Asset D Asset E Asset F Asset G
Minus S&P
.2% Fixed
ret
75% of
S&P
125% of
S&P Random Dephased S&P Mix .75+1.25

26. Total Beta evaluation of fantasy asset with Random
returns reflects true risk better than Beta

27. Total Beta evaluation of fantasy asset with returns 1 month
dephased from S&P reflects also true risk better than Beta

28. This could lead to a decision tree in Risk
and portfolio evaluation for clients
What is R2 of
asset Beta
Diversification
of Client
Analysis of
Client
Is client fully
diversified?
No
Low (Use
Total Risk)
High (Use
Beta of Asset)
Yes
Use Beta of
Asset
In case of
standalone
project analysis,
assume no
diversification

29. This concept can also be matched to the investment
horizon of the investor
Time Horizon of
Investor
Short term (less than 3
years)
Not Diversified Use Total Beta
Well Diversified
Adjust Beta by using a
weighed three year
average (3-2-1)
Long term
Use long term Beta
because there is no
excess risk as Investor
should diversify

30. If you are a fully diversified investor, then Beta and the non
diversifiable risk that it represents would probably work fine … Other
investors might not find this as attractive
 Other investors might
be classified as:
 Active investors in firms
– publicly traded or not-
whose portfolio is not
diversified
 Individuals or institutions
looking to evaluate
investments as a stand
alone proposition,
independent of other
portfolio holdings
Summation of Risk
Illustrative Only

31. Non diversified investors should note that StdDev of asset
returns to their Mean is significantly lower than the Std Dev of
their Betas – this validates using Total Beta in certain cases
66
%
230%

32. Nevertheless, Total Beta still has some shortcomings
common to all volatility based measures
 Total Beta says nothing about fundamental valuation,
such as the current price bid/asked for the stock/asset in
relation to its inherent values, past or projected: ie P/E,
P/Cash Flow; P/Sales, P/Growth, etc.
 In fact, Total Beta, like Beta says nothing about
underlying value drivers such as current or projected
earnings, cash flow, and others.
 It is a ‘rear view mirror’ indicator, not capturing present or
future changes in markets
 For non publicly traded companies and SME’s the Beta
and Total Beta of the overall industry may be irrelevant,
as SME’s may have totally different risk and income
profiles.
 These may require analysis of the volatility and risk
elements particular to that asset’s cash flows

33. Cluster analysis and portfolio
design

34. Normally, financial assets are not easily
segmented or differentiated…

35. …yet the analysis of Beta leads us to study Cluster Analysis as
a tool to group assets before constructing a portfolio

36. Using monthly returns over 20 years and Cluster
Analysis software, assets can indeed be grouped

37. And nine final clusters have a strong relation with the two
dimensional analysis presented in terms of Beta vs Std
Deviation
Gold Mutual Fund AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAE B
GAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC
Fidelity Select Gold Fund AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC
Vanguard Energy Fund AAAAAAAAAAAAAAAAAAAAAAE B B
GAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAC GAAAAAAAAAAAAAAAAAAAAA
T Rowe Price Nat Resources Fund AAAAAAAAAAAAAAAAAAAAAAC B

38. Using the shorter term time series, twelve clusters can be
developed covering vertical industries and horizontal regions
Case NumberVAR00001 Cluster Distance
Global Utilities 19 JXI 1 0.091
Global Telecom 25 IXP 1 0.091
Inflation-protected Treasuries 1 TIPs 2 0.056
US Bonds 2 AGG 2 0.056
Crude Oil 3 OIL 3 0
Natural Resources (Inc Oil) 4 IGE 4 0.079
Global Energy 24 IXC 4 0.079
Commodities Index 5 GSG 5 0
US Real Estate 6 VNQ 6 0
Emerging Markets 8 EEM 7 0.116
European Stocks 16 VGK 7 0.151
Global Materials 27 MXI 7 0.133
GOLD 23 IAU 8 0
US Small Cap Stocks 10 VB 9 0.116
US Large Cap Stocks 11 VV 9 0.085
US Mid Cap Stocks 12 VO 9 0.085
Standard and Poors 500 14 s&p 9 0.097
NASDAQ 15 IXIC 9 0.09
Global Industrials 21 EXI 9 0.137
Global Technology 26 IXN 9 0.121
Global Consumer Discretionary 30 RXI 9 0.127
Dow Jones Ind Average 13 DOW 10 0.118
Global Health Care 20 IXJ 10 0.131
Global Consumer Staples 29 KXI 10 0.1
Europe, Australasia, Far East 9 EFA 11 0.108
Pacific Rim Stocks 17 VPL 11 0.052
Japanese Stocks 18 EWJ 11 0.126
Global Infrastructure 28 IGF 11 0.096
International Real Estate 7 RWX 12 0.12
Global Fin Services 22 IXG 12 0.12

39. The R2 for correlation among assets across
time seems to be high…

40. … in effect equal to that of Beta – but with a
shorter tail

41. This leads to a porfolio construction strategy
 Perform Cluster Analysis for assets, dividing into clusters
 Nine to twelve clusters could be a reasonable analysis point
 Start out determining modified Sharpe ratio for asset classes as per the
cluster strategy
 Modified Sharpe ratio equals Return/Volatility (exclude Rf factor) per cluster
 Take highest modified Sharpe ratio asset or cluster
 Add subsequent asset or clusters considering Sharpe ratios and correlation
with first asset or cluster
 Each subsequent asset should improve overall Sharpe ratio of portfolio
where correlation with other assets is considered
 Final portfolio evaluation should consider:
 Returns
 Sharpe ratio for portfolio
 Standard deviation of portfolio
 Intra asset correlation of portfolio
 BEWARE THAT PORTFOLIOS BASED ON HISTORICAL PERFORMANCE
ARE ALWAYS A REAR VIEW MIRROR VISION

42. Sample assets in portfolio

43. EEM – Emerging Markets Fund
Beta= 1.37; range=14%
Source: Yahoo Finance ; Monthly returns
14% range

44. JXI – Global Utilities Fund
Beta= 0.76; range=11%
Source: Yahoo Finance ; Monthly returns
11% range

45. IXP – Global Telecom Fund
Beta= 0.80; range=9%
Source: Yahoo Finance ; Monthly returns
9% range

46. OIL – Global Oil Fund
Beta= 1.1; range=22%
Source: Yahoo Finance ; Monthly returns
22% range

47. IAU – Gold Fund
Beta= 0.05; range=18%
Source: Yahoo Finance ; Monthly returns
18% range