Concepts on Beta, Valuation and Diversification v6
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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.
![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](https://image.slidesharecdn.com/bcdf60ae-95c6-4880-9a30-9220a6e089e9-150212182937-conversion-gate02/85/Concepts-on-Beta-Valuation-and-Diversification-v6-4-320.jpg)
Concepts on Beta, Valuation and Diversification v6
- 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