1. Corporate Financial Theory
Lecture 2

2. Risk /Return
Return = r = Discount rate = Cost of Capital (COC) r is determined by risk Two Extremes Treasury Notes are risk free = Return is low Junk Bonds are high risk = Return is high

3. Risk
Variance & Standard Deviation
yard sticks that measures risk

4. The Value of an Investment of $1 in 1900
2017 13

5. Rates of Return
Source: Princeton University 14

6. Average Market Risk Premia (by country)

7. Diversification
Diversification is the combining of assets. In financial theory, diversification can reduce risk.
The risk of the combined assets is lower than the risk of the assets held separately.

8. Efficient Frontier Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp % %
Big Corp % %
Standard Deviation = weighted avg = 33.6%
Standard Deviation = Portfolio = %
Return = weighted avg = Portfolio = 17.4%
Additive Standard Deviation (common sense):
= .28 (60%) (40%) = 33.6% WRONG
Real Standard Deviation:

9. Efficient Frontier Let’s Add stock New Corp to the portfolio
Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp % %
Big Corp % %
Standard Deviation = weighted avg = 33.6%
Standard Deviation = Portfolio = %
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio

10. Efficient Frontier Previous Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio % %
New Corp % %
NEW Standard Deviation = weighted avg = 31.80%
NEW Standard Deviation = Portfolio = %
NEW Return = weighted avg = Portfolio = 18.20%

11. Efficient Frontier NOTE: Higher return & Lower risk
Previous Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio % %
New Corp % %
NEW Standard Deviation = weighted avg = %
NEW Standard Deviation = Portfolio = %
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION

12. Portfolio Risk / Return19

13. Efficient Frontier
Return B A
Risk (measured as s)

14. Efficient Frontier
Return B AB A
Risk

15. Efficient Frontier
Return B N AB A
Risk

16. Efficient Frontier
Return B
ABN N AB A
Risk

17. Efficient Frontier Return Goal is to move up and left. WHY? B ABN N AB
Risk

18. Efficient Frontier
The ratio of the risk premium to the standard deviation is called the Sharpe ratio:
Goal is to move up and left.
WHY?

19. Efficient Frontier Return Low Risk High Return High Risk High Return
Low Return
High Risk
Low Return
Risk

20. Efficient Frontier Return Low Risk High Return High Risk High Return
Low Return
High Risk
Low Return
Risk

21. Efficient Frontier
Return B
ABN N AB A
Risk

22. Markowitz Portfolio Theory
Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.
Correlation coefficients make this possible.
The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

23. Efficient Frontier
Each half egg shell represents the possible weighted combinations for two stocks.
The composite of all stock sets constitutes the efficient frontier
Expected Return (%)
Standard Deviation

24. 4 Efficient Portfolios all from the same 10 stocks
Efficient Frontier
4 Efficient Portfolios all from the same 10 stocks

25. Measuring Risk 20

26. Measuring Risk 21

27. Diversification
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.
Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.” 18

28. . Security Market Line rf Return Market Return = rm
Efficient Portfolio
Risk Free
Return = rf
Risk

29. $1 Invested Growth (variable debt)
Leverage Varies to
Match Growth Fund

30. $1 Invested Growth (constant debt)
Leverage set at 20%

31. . Security Market Line rf Return Market Return = rm
Efficient Portfolio
Risk Free
Return = rf
Risk

32. . Security Market Line rf Return Market Return = rm
Efficient Portfolio
Risk Free
Return = rf
1.0
BETA

33. Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.

34. Beta and Unique Risk

35. Beta and Unique Risk
Covariance with the market
Variance of the market

36. Beta

37. . Security Market Line rf Return Risk Free Return =
Security Market Line (SML) rf
BETA

38. Security Market Line rf SML Equation = rf + B ( rm - rf ) Return SML
BETA
1.0
SML Equation = rf + B ( rm - rf )

39. Capital Asset Pricing Model
R = rf + B ( rm - rf )
CAPM

40. Company Cost of Capital
A company’s cost of capital can be compared to the CAPM required return
12.9
5.0
SML
Required
return
Company Cost of Capital
Project Beta
1.13

41. Arbitrage Pricing Theory
Alternative to CAPM

42. Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
( )

43. Three Factor Model Steps
Identify macroeconomic factors that could affect stock returns
Estimate expected risk premium on each factor
( rfactor1 − rf, etc.)
Measure sensitivity of each stock to factors
( b1, b2, etc.)

44. Three Factor Model Three-Factor Model . Factor Sensitivities . CAPM
bmarket
bsize
bbook-to-market
Expected return*
Expected return**
Autos
1.51
.07
0.91
15.7
7.9
Banks
1.16
-.25 .7
11.1
6.2
Chemicals
1.02
-.07
.61
10.2
5.5
Computers
1.43
.22
-.87
6.5
12.8
Construction
1.40
.46
.98
16.6
7.6
Food
.53
-.15
.47
5.8
2.7
Oil and gas
0.85
-.13
0.54
8.5
4.3
Pharmaceuticals
0.50
-.32
1.9
Telecoms
1.05
-.29
-.16
5.7
7.3
Utilities
0.61
-.01
.77
8.4
2.4
The expected return equals the risk-free interest rate plus the factor sensitivities multiplied by the factor risk premia, that is, rf + (bmarket x 7) + (bsize x 3.6) + (bbook-to-market x 5.2)
** Estimated as rf + β(rm – rf), that is rf + β x 7.

45. Beta vs. Average Risk Premium
Testing the CAPM
Beta vs. Average Risk Premium

46. Beta vs. Average Risk Premium
Testing the CAPM
Beta vs. Average Risk Premium

47. Measuring Betas

48. Measuring Betas

49. Measuring Betas

50. Estimated Betas

51. Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5
CLASS YEARS LATER YEARS LATER
10 (High betas)
1 (Low betas)
Source: Sharpe and Cooper (1972)

52. Search for Alpha

53. Diversification
What is true diversification?

54. Harvard Endowment

55. CICF Asset Allocation
March 2015

56. CalPERS Asset Allocation
Source: CalPERS 2005 & March 2015 reportsd

57. CICF Asset Allocation
Source: CICF 2006 Audit Report, CICF Portfolio Review, June 30, 2015

58. Dow Jones C.S. Core HF Index
© Dow Jones Credit Suisse

59. Risk Profile (HF vs Public Cos.)
US Public equities
Hedge Funds
Standard deviation = 17.1%
Return = 7.5%
Sharpe ratio = .43
S&P 500 Index
Note: Assumes a treasury yield of 0.20%
Standard deviation = 7.0%
Return = 8.4%
Sharpe ratio = .81
HFR Fund of Funds Composite Index

60. Private Equity Returns
U.S. Private Equity Fund
Index Summary: End-to-End Pooled Return Net to Limited Partners

61. Private Equity Risk / Return
Cambridge Associates LLC U.S. Private Equity Index®
S&P (1986 – 2012)
Since Inception IRR & Multiples By Fund Vintage Year, Net to Limited Partners as of March 31, 2012, starting with vintage year 1986