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

Diversification

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

The Problem with Betas

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

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 asset classes as per S&P

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% 0.14AGG US Bonds 0.21% 1% 719% 0.05OIL Crude Oil -1.00% 12% -1199% 1.11IGE Natural Resources (Inc Oil) 0.39% 8% 2126% 1.10GSG Commodities Index -0.76% 9% -1140% 0.84VNQ US Real Estate 0.06% 11% 16956% 1.49RWX International Real Estate -0.95% 8% -864% 1.28EEM Emerging Markets 0.80% 9% 1136% 1.38EFA Europe, Australasia, Far East -0.29% 7% -2560% 1.17VB US Small Cap Stocks 0.19% 8% 4043% 1.24VV US Large Cap Stocks -0.12% 6% -5081% 1.01VO US Mid Cap Stocks 0.09% 7% 7555% 1.16DOW Dow Jones Ind Average -0.23% 5% -2330% 0.90S&P Standard and Poors 500 -0.34% 6% -1727% 1.00IXIC NASDAQ 0.19% 7% 3645% 1.12VGK European Stocks -0.19% 8% -4062% 1.24VPL Pacific Rim Stocks -0.20% 7% -3239% 1.00EWJ Japanese Stocks -0.66% 6% -867% 0.81JXI Global Utilities -0.46% 5% -1170% 0.76IXJ Global Health Care -0.30% 5% -1697% 0.69EXI Global Industrials 27.49% 8% 28% 1.25IXG Global Fin Services -0.96% 10% -1048% 1.58IAU GOLD 1.38% 6% 426% 0.05IXC Global Energy 0.13% 7% 5586% 0.99IXP Global Telecom 0.22% 6% 2663% 0.80IXN Global Technology 0.15% 7% 4930% 1.17MXI Global Materials 0.54% 9% 1695% 1.36IGF Global Infrastructure -0.89% 8% -843% 1.04KXI Global Consumer Staples 0.20% 5% 2353% 0.69

RXI Global Consumer Discretionary -0.19% 7% -3807% 1.14

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

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

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

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

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

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)

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.938 R Square 0.881 Adjusted R Square 0.872 Standard Error 0.138 Observations 32.000

ANOVAdf 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

Relative

Volatility

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

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

EXAMPLE ONLY

+30%

-24%

Change in Beta

Base

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

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

Smbl ONE year Betas Calculator 2,010 2,009 2,008 Mean Std Dev StdDev/MeanTIPs Inflation-protected Treasuries TIPs (0.06) 0.14 0.25 0.11 0.16 141%AGG US Bonds AGG (0.09) 0.12 0.07 0.03 0.11 355%OIL Crude Oil OIL 1.34 0.87 1.76 1.33 0.44 33%IGE Natural Resources (Inc Oil) IGE 1.06 0.97 1.31 1.11 0.18 16%GSG Commodities Index GSG 1.01 0.61 1.28 0.97 0.34 35%VNQ US Real Estate VNQ 0.95 1.83 1.60 1.46 0.46 31%RWX International Real Estate RWX 0.99 1.33 1.25 1.19 0.18 15%EEM Emerging Markets EEM 1.18 1.26 1.38 1.28 0.10 8%EFA Europe, Australasia, Far East EFA 1.17 1.21 1.11 1.16 0.05 4%VB US Small Cap Stocks VB 1.23 1.26 1.31 1.27 0.04 3%VV US Large Cap Stocks VV 1.01 0.99 1.01 1.01 0.01 1%VO US Mid Cap Stocks VO 1.09 1.04 1.29 1.14 0.13 12%DOW Dow Jones Ind Average DOW 0.90 0.98 0.84 0.90 0.07 8%S&P Standard and Poors 500 SP 1.00 1.00 1.00 1.00 - 0%IXIC NASDAQ IXIC 1.23 0.89 1.22 1.11 0.19 17%VGK European Stocks VGK 1.26 1.27 1.14 1.22 0.07 6%VPL Pacific Rim Stocks VPL 0.88 1.09 0.96 0.98 0.10 11%EWJ Japanese Stocks EWJ 0.68 1.00 0.80 0.82 0.16 20%JXI Global Utilities JXI 0.70 0.84 0.73 0.76 0.07 9%IXJ Global Health Care IXJ 0.55 0.83 0.59 0.66 0.15 23%EXI Global Industrials EXI 1.26 1.37 1.16 1.26 0.11 8%IXG Global Fin Services IXG 1.21 2.00 1.40 1.54 0.42 27%IAU GOLD IAU (0.15) (0.05) 0.05 (0.05) 0.10 -207%IXC Global Energy IXC 1.25 0.80 1.11 1.05 0.23 22%IXP Global Telecom IXP 0.79 0.69 0.78 0.75 0.06 7%IXN Global Technology IXN 1.31 0.89 1.29 1.16 0.24 21%MXI Global Materials MXI 1.34 1.27 1.33 1.31 0.04 3%IGF Global Infrastructure IGF 0.94 1.11 0.95 1.00 0.09 9%KXI Global Consumer Staples KXI 0.68 0.72 0.68 0.69 0.03 4%

RXI Global Consumer Discretionary RXI 1.19 1.13 1.00 1.11 0.10 9%Median 1.01 1.00 1.11 1.08 0.11 10%

… 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

One solution is to use longer term Betas, 36 to 48 month Betas vs 12 month Betas

ONE year Betas Calculator Mean Std Dev StdDev/Mean Mean Std Dev StdDev/MeanInflation-protected Treasuries TIPs 0.11 0.16 141% 0.15 0.08 50%

US Bonds AGG 0.03 0.11 355% 0.05 0.01 23%Crude Oil OIL 1.33 0.44 33% 1.27 0.33 26%

Natural Resources (Inc Oil) IGE 1.11 0.18 16% 1.13 0.13 11%Commodities Index GSG 0.97 0.34 35% 0.94 0.23 25%

US Real Estate VNQ 1.46 0.46 31% 1.52 0.06 4%International Real Estate RWX 1.19 0.18 15% 1.25 0.04 3%

Emerging Markets EEM 1.28 0.10 8% 1.35 0.06 5%Europe, Australasia, Far East EFA 1.16 0.05 4% 1.17 0.04 4%

US Small Cap Stocks VB 1.27 0.04 3% 1.26 0.03 3%US Large Cap Stocks VV 1.01 0.01 1% 1.01 0.00 0%

US Mid Cap Stocks VO 1.14 0.13 12% 1.17 0.10 8%Dow Jones Ind Average DOW 0.90 0.07 8% 0.90 0.04 5%

Standard and Poors 500 SP 1.00 - 0% 1.00 - 0%NASDAQ IXIC 1.11 0.19 17% 1.12 0.08 7%

European Stocks VGK 1.22 0.07 6% 1.23 0.06 5%Pacific Rim Stocks VPL 0.98 0.10 11% 1.00 0.03 3%

Japanese Stocks EWJ 0.82 0.16 20% 0.83 0.03 4%Global Utilities JXI 0.76 0.07 9% 0.76 0.02 3%

Global Health Care IXJ 0.66 0.15 23% 0.68 0.06 9%Global Industrials EXI 1.26 0.11 8% 1.25 0.07 5%

Global Fin Services IXG 1.54 0.42 27% 1.57 0.13 8%GOLD IAU (0.05) 0.10 -207% 0.01 0.06 438%

Global Energy IXC 1.05 0.23 22% 1.02 0.06 6%Global Telecom IXP 0.75 0.06 7% 0.77 0.03 4%

Global Technology IXN 1.16 0.24 21% 1.18 0.09 8%Global Materials MXI 1.31 0.04 3% 1.34 0.02 2%

Global Infrastructure IGF 1.00 0.09 9% 1.02 0.05 5%Global Consumer Staples KXI 0.69 0.03 4% 0.69 0.01 2%Global Consumer

Discretionary RXI 1.11 0.10 9% 1.11 0.08 7%Median 1.08 0.11 10% 1.07 0.06 5%

12 to 48 month BetasOne Year Betas

Source: Yahoo Finance, Analisis Lambda

More Stable Betas

Over the long term, however, even 36 month Betas are not stable

Source: Yahoo Finance, Analisis Lambda

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

Analisis of Betas Asset Class Minimum Maximum Mean Std Dev Std/Mean Minimum Maximum Mean Std Dev Std/Mean

Inflation-protected Treasuries 0.07 0.25 0.15 0.08 50% (0.33) 0.18 (0.03) 0.08 -231%US Bonds 0.04 0.07 0.05 0.01 23% (0.18) 0.28 (0.01) 0.10 -1626%

Natural Resources (Inc Oil) 1.01 1.31 1.13 0.13 11% 0.54 1.42 0.80 0.20 25%US Real Estate 1.47 1.60 1.52 0.06 4% (0.09) 0.11 0.00 0.03 680%

Emerging Markets 1.25 1.38 1.35 0.06 5% (0.00) 1.90 0.83 0.63 75%US Small Cap Stocks 1.24 1.31 1.26 0.03 3% (0.00) 1.65 0.71 0.62 87%US Large Cap Stocks 1.00 1.01 1.01 0.00 0% (0.00) 1.19 0.67 0.49 73%

US Mid Cap Stocks 1.06 1.29 1.17 0.10 8% (0.00) 1.40 0.21 0.44 206%European Stocks 1.14 1.28 1.23 0.06 5% (0.00) 1.28 0.75 0.30 40%

Pacific Rim Stocks 0.96 1.02 1.00 0.03 3% 0.00 0.98 0.59 0.24 41%Global Utilities 0.73 0.78 0.76 0.02 3% 0.13 1.09 0.69 0.21 30%

Global Health Care 0.59 0.73 0.68 0.06 9% 0.27 1.20 0.74 0.25 33%Global Fin Services 1.40 1.70 1.57 0.13 8% (0.00) 1.26 0.45 0.47 105%

GOLD (0.08) 0.05 0.01 0.06 438% (0.22) 1.73 0.41 0.52 126%Global Energy 0.98 1.11 1.02 0.06 6% 0.33 1.36 0.76 0.20 27%

Global Technology 1.07 1.29 1.18 0.09 8% 0.89 2.38 1.61 0.37 23%Median Value 1.01 1.19 1.07 0.06 7% (0.00) 1.27 0.68 0.27 41%

(2007-2010) 1987-2009

Long term, Beta values vary significantly for individual assets

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

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

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.

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

ret75% of

S&P125% of

S&P Random Dephased S&P Mix .75+1.25

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

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

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

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

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

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%

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

Cluster analysis and portfolio design

Normally, financial assets are not easily segmented or differentiated…

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

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

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 GAAAAAAAAAAAAAAAAAAAAAAAAAAAAE

T Rowe Price Nat Resources Fund AAAAAAAAAAAAAAAAAAAAAAC B B

Using the shorter term time series, twelve clusters can be developed covering vertical industries and horizontal regions

Case NumberVAR00001 Cluster DistanceGlobal Utilities 19 JXI 1 0.091

Global Telecom 25 IXP 1 0.091Inflation-protected Treasuries 1 TIPs 2 0.056

US Bonds 2 AGG 2 0.056Crude Oil 3 OIL 3 0

Natural Resources (Inc Oil) 4 IGE 4 0.079Global Energy 24 IXC 4 0.079

Commodities Index 5 GSG 5 0US Real Estate 6 VNQ 6 0

Emerging Markets 8 EEM 7 0.116European Stocks 16 VGK 7 0.151Global Materials 27 MXI 7 0.133

GOLD 23 IAU 8 0US Small Cap Stocks 10 VB 9 0.116US Large Cap Stocks 11 VV 9 0.085

US Mid Cap Stocks 12 VO 9 0.085Standard and Poors 500 14 s&p 9 0.097

NASDAQ 15 IXIC 9 0.09Global Industrials 21 EXI 9 0.137

Global Technology 26 IXN 9 0.121Global Consumer Discretionary 30 RXI 9 0.127

Dow Jones Ind Average 13 DOW 10 0.118Global Health Care 20 IXJ 10 0.131

Global Consumer Staples 29 KXI 10 0.1Europe, Australasia, Far East 9 EFA 11 0.108

Pacific Rim Stocks 17 VPL 11 0.052Japanese Stocks 18 EWJ 11 0.126

Global Infrastructure 28 IGF 11 0.096International Real Estate 7 RWX 12 0.12

Global Fin Services 22 IXG 12 0.12

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

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

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

Sample assets in portfolio

EEM – Emerging Markets FundBeta= 1.37; range=14%

Source: Yahoo Finance ; Monthly returns

14% range

JXI – Global Utilities FundBeta= 0.76; range=11%

Source: Yahoo Finance ; Monthly returns

11% range

IXP – Global Telecom FundBeta= 0.80; range=9%

Source: Yahoo Finance ; Monthly returns

9% range

OIL – Global Oil FundBeta= 1.1; range=22%

Source: Yahoo Finance ; Monthly returns

22% range

IAU – Gold FundBeta= 0.05; range=18%

Source: Yahoo Finance ; Monthly returns

18% range