1. Chapter 13 CAPM and APT Investments
© K. Cuthbertson and D. Nitzsche

2. What is the risk free rate?
Quiz
RA = 11.2% βA=.82
RB = 17.6% βB=1.46
What is the risk free rate?
What is the return on the market? What is the Market Risk Premium?
© K. Cuthbertson and D. Nitzsche

3. Learning Objectives
Link between CAPM and mean-variance portfolio theory
Beta as a measure of undiversifiable risk
Linear relationship between expected returns and beta of stocks- SML
Use of CAPM for portfolio construction; for market risk in a portfolio; for estimation of discount factor in DFCF valuation methods, for market timing strategies
© K. Cuthbertson and D. Nitzsche

4. Capital Market Theory: An Overview
Capital market theory extends portfolio theory and develops a model for pricing all risky assets, while capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset based on the systematic risk in the asset

5. CAPM
CAPM states that the expected excess return on a stock is defined by the stock’s market risk beta and by the expected excess return on the market:
(ER-r)=β(ERm –r) or ER=r+β(ERm –r)
© K. Cuthbertson and D. Nitzsche

6. Systematic Risk Risk factors that affect a large number of assets
Also known as non-diversifiable risk or market risk
Examples: changes in GDP, inflation, interest rates, general economic conditions

7. Portfolio Diversification (1)

8. Portfolio Diversification (2)

9. Measuring Systematic Risk
Beta (β) is a measure of systematic risk
Interpreting beta:
β = 1 implies the asset has the same systematic risk as the overall market βm=Cov(Rm; Rm)/σm2
but Cov(Rm; Rm)=σm2
β < 1 implies the asset has less systematic risk than the overall market
β > 1 implies the asset has more systematic risk than the overall market

10. High and Low Betas

11. Portfolio Betas Security Weight Beta A .133 3.69 B .2 0.64 C .267 1.64
Consider the previous example with the following four securities
Security Weight Beta A B C D
What is the portfolio beta?

12. CAPM and SIM
SIM is statistical relationship (regression of excess returns of a stock and a benchmark)
The intercept of the regression line of SIM is a performance measure Jensen’s alpha
© K. Cuthbertson and D. Nitzsche

13. Market Index in the SIM
Copyright © 2010 Nelson

14. Security Market Line
CAPM is an asset pricing equation that explains the systematic risk and the role of diversification
E(Ri) = Rf + βi(Rm-Rf)
Rearrange CAPM in terms of market risk
Calculate beta on historical stock returns or from financial information vendor
Return averages from historical data serve as estimates of expected returns
© K. Cuthbertson and D. Nitzsche

15. The larger is βi, the larger is the CAPM expected return ERi
Figure 1 : Security market line (SML)
Expected/Average
Returns
SML
Q (buy)
14% M
13%
SML/CAPM
return, ERP P 9%
T (sell)
r = 5%
Average historic return for S 4%
S (sell)
Beta, βi
0.5 1
1.2
The larger is βi, the larger is the CAPM expected return ERi
© K. Cuthbertson and D. Nitzsche

16. Matrix
Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column
© K. Cuthbertson and D. Nitzsche

17. Applications of CAPM Market timing Portfolio construction
Value at risk
Performance measure
Treynor measure for excess return (uses market risk β)
Sharpe measure (uses total risk σ)
Jansen’s α
© K. Cuthbertson and D. Nitzsche

18. Two Fund Separation and CML
© K. Cuthbertson and D. Nitzsche

19. Return and Risk of Two Fund Portfolio
Return is weighted average of Risk free rate and market return; portfolio weights sum to one
Rp= wRf (Rf) + (1- wRf )(Rm)
Risk on this portfolio is also weighted average (covariance zero; σRf =0
σRp = wRf (σRf ) + (1- wRf )(σ Rm )
© K. Cuthbertson and D. Nitzsche

20. Using the CML to Invest: An Example
How much to invest in the riskless security?
11.5%= wRF (4%) + (1-wRF )(9%)
wRF= -0.5
The investment strategy is to borrow 50% and invest 150% of equity in the market portfolio
Copyright © 2010 Nelson

21. Background to Capital Market Theory
Assumptions:
All investors are Markowitz efficient investors who want to target points on the efficient frontier
Investors can borrow or lend any amount of money at the risk-free rate of return (RFR)
All investors have homogeneous expectations; that is, they estimate identical probability distributions for future rates of return
All investors have the same one-period time horizon such as one-month, six months, or one year
Continued…
Copyright © 2010 Nelson

22. Background to Capital Market Theory
Assumptions:
All investments are infinitely divisible, which means that it is possible to buy or sell fractional shares of any asset or portfolio
There are no taxes or transaction costs involved in buying or selling assets
There is no inflation or any change in interest rates, or inflation is fully anticipated
Capital markets are in equilibrium, implying that all investments are properly priced in line with their risk levels
Copyright © 2010 Nelson

23. Background to Capital Market Theory
Development of the Theory
The major factor that allowed portfolio theory to develop into capital market theory is the concept of a risk-free asset
An asset with zero standard deviation
Zero correlation with all other risky assets
Provides the risk-free rate of return (RFR)
Will lie on the vertical axis of a portfolio graph
Copyright © 2010 Nelson

24. Risk-Return Possibilities
One can attain a higher expected return than is available at point M
One can invest along the efficient frontier beyond point M, such as point D
Copyright © 2010 Nelson

25. Risk-Return Possibilities
With the risk-free asset, one can add leverage to the portfolio by borrowing money at the risk-free rate and investing in the risky portfolio at point M to achieve a point like E
Point E dominates point D
One can reduce the investment risk by lending money at the risk-free asset to reach points like C
Copyright © 2010 Nelson

26. Risk, Diversification & the Market Portfolio: The Market Portfolio
Because portfolio M lies at the point of tangency, it has the highest portfolio possibility line
Everybody will want to invest in Portfolio M and borrow or lend to be somewhere on the CML
It must include ALL RISKY ASSETS
Copyright © 2010 Nelson

27. Risk, Diversification & the Market Portfolio: The Market Portfolio
Since the market is in equilibrium, all assets in this portfolio are in proportion to their market values
Because it contains all risky assets, it is a completely diversified portfolio, which means that all the unique risk of individual assets (unsystematic risk) is diversified away
Copyright © 2010 Nelson

28. Risk, Diversification & the Market Portfolio
Systematic Risk
Only systematic risk remains in the market portfolio
Variability in all risky assets caused by macroeconomic variables
Variability in growth of money supply
Interest rate volatility
Variability in factors like (1) industrial production (2) corporate earnings (3) cash flow
Can be measured by standard deviation of returns and can change over time
Copyright © 2010 Nelson

29. Risk, Diversification & the Market Portfolio
How to Measure Diversification
All portfolios on the CML are perfectly positively correlated with each other and with the completely diversified market Portfolio M
A completely diversified portfolio would have a correlation with the market portfolio of +1.00
Complete risk diversification means the elimination of all the unsystematic or unique risk and the systematic risk correlates perfectly with the market portfolio
Copyright © 2010 Nelson

30. Risk, Diversification & the Market Portfolio: Eliminating Unsystematic Risk
The purpose of diversification is to reduce the standard deviation of the total portfolio
This assumes that imperfect correlations exist among securities
Copyright © 2010 Nelson

31. Risk, Diversification & the Market Portfolio
The CML & the Separation Theorem
The CML leads all investors to invest in the M portfolio
Individual investors should differ in position on the CML depending on risk preferences
How an investor gets to a point on the CML is based on financing decisions
Copyright © 2010 Nelson

32. Risk, Diversification & the Market Portfolio
The CML & the Separation Theorem
Risk averse investors will lend at the risk-free rate while investors preferring more risk might borrow funds at the RFR and invest in the market portfolio
The investment decision of choosing the point on CML is separate from the financing decision of reaching there through either lending or borrowing
Copyright © 2010 Nelson

33. Risk, Diversification & the Market Portfolio
A Risk Measure for the CML
The Markowitz portfolio model considers the average covariance with all other assets
The only important consideration is the asset’s covariance with the market portfolio
Copyright © 2010 Nelson