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 portfolio of thirty mutual funds’ monthly performance from 12/ /2010 – net of the Rf for that month
A long term series from
Mutual funds are believed to include all principal asset classes as per S&P

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

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

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
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. 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

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 ; 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
EXAMPLE ONLY
Change in Beta
+30%
-24%
Base

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

17. Variation in 12 month Betas from 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 ; observations each

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

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
Long term, Beta values vary significantly for individual assets
Source: Yahoo Finance, Analisis Lambda * Rolling 36 month Betas vs 12, 24, 36 and 48 month Betas

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

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 makers as a measure of risk.

25. Systematic Risk (Beta) X Beta R2 = Contribution to Total 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 ret
75% of S&P
125% of S&P
Random
Dephased S&P
Mix

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. Other investors might be classified as:
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
230%
66%

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

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

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

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

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

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

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