0. Capital Market Theory

1. Capital Market Theory: An Overview
Capital market theory extends portfolio theory and develops a model for pricing all risky assets
Capital asset pricing model (CAPM) will allow you to determine the required rate of return for any risky asset

2. Capital Asset Pricing Model (CAPM)
The asset pricing models aim to use the concepts of portfolio valuation and market equilibrium in order to determine the market price for risk and appropriate measure of risk for a single asset.
Capital Asset Pricing Model (CAPM) has an observation that the returns on a financial asset increase with the risk. CAPM concerns two types of risk namely unsystematic and systematic risks. The central principle of the CAPM is that, systematic risk, as measured by beta, is the only factor affecting the level of return.

3. Capital Asset Pricing Model (CAPM)
The Capital Asset Pricing Model (CAPM) was developed independently by Sharpe (1964), Lintner (1965) and Mossin (1966) as a financial model of the relation of risk to expected return for the practical world of finance.
CAPM originally depends on the mean variance theory which was demonstrated by Markowitz’s portfolio selection model (1952) aiming higher average returns with lower risk.

4. CAPM assumptions Assumptions:
All investors have homogenous expectations about asset returns and what the uncertain future holds for them.
All investors are risk averse and they operate in the market rationally and perceive utility in terms of expected return.
Investors are price takers
They cannot influence the market individually

5. CAPM assumptions (cont’d)
Investors look only one period ahead
All securities are highly divisible for instance they can be traded in small parcels (Elton and Gruber, 1995, p.294).
All investors can lend and borrow unlimited amount of funds at the risk-free rate of return.
All investors have equal and costless access to information
There are no taxes or commission costs

6. The Efficient Set for Many Securities
return
Individual Assets P
Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.

7. The Efficient Set for Many Securities
return
minimum variance portfolio
Individual Assets P
Given the opportunity set we can identify the minimum variance portfolio.

8. The Efficient Set for Many Securities
return
efficient frontier
minimum variance portfolio
Individual Assets P
The section of the opportunity set above the minimum variance portfolio is the efficient frontier.

9. 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

10. Optimal Risky Portfolio with a Risk-Free Asset
return
100% stocks rf
100% bonds 
In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills

11. Combining a Risk-Free Asset with a Risky Portfolio
Expected return
the weighted average of the two returns
This is a linear relationship

12. Combining a Risk-Free Asset with a Risky Portfolio
Standard deviation
The expected variance for a two-asset portfolio is
Substituting the risk-free asset for Security 1, and the risky asset for Security 2, this formula would become
Since we know that the variance of the risk-free asset is zero and the correlation between the risk-free asset and any risky asset i is zero we can adjust the formula

13. Combining a Risk-Free Asset with a Risky Portfolio
Given the variance formula
the standard deviation is
Therefore, the standard deviation of a portfolio that combines the risk-free asset with risky assets is the linear proportion of the standard deviation of the risky asset portfolio.

14. Combining a Risk-Free Asset with a Risky Portfolio
Since both the expected return and the standard deviation of return for such a portfolio are linear combinations, a graph of possible portfolio returns and risks looks like a straight line between the two assets.

15. Capital Market Line (CML)
return
efficient frontier rf P
With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope

16. Market Equilibrium
return
CML
efficient frontier M rf P
With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.

17. The CML and 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
Risk averse investors will lend part of the portfolio at the risk-free rate and invest the remainder in the market portfolio

18. Portfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient Frontier
CML
Borrowing
Lending M
RFR

19. 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
Therefore this portfolio must include ALL RISKY ASSETS

20. The Market Portfolio
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

21. Systematic Risk Only systematic risk remains in the market portfolio
Systematic risk is the variability in all risky assets caused by macroeconomic variables
Systematic risk can be measured by the standard deviation of returns of the market portfolio and can change over time

22. Examples of Macroeconomic Factors Affecting Systematic Risk
Variability in growth of money supply
Interest rate volatility
Variability in
industrial production
corporate earnings
cash flow

23. Capital Asset Pricing Model

24. The Capital Asset Pricing Model: Expected Return and Risk
The existence of a risk-free asset resulted in deriving a capital market line (CML) that became the relevant frontier
An asset’s covariance with the market portfolio is the relevant risk measure
This can be used to determine an appropriate expected rate of return on a risky asset - the capital asset pricing model (CAPM)

25. The Capital Asset Pricing Model: Expected Return and Risk
CAPM indicates what should be the expected or required rates of return on risky assets
This helps to value an asset by providing an appropriate discount rate to use in dividend valuation models
You can compare an estimated rate of return to the required rate of return implied by CAPM - over/under valued ?

26. Fundamental Risk/Return Relationship Revisited
CAPM
Market model versus CAPM
Note on the CAPM assumptions
Stationarity of beta

27. CAPM The more risk you carry, the greater the expected return:
Assume bi = 0, then the expected return is Rf.
Assume bi = 1, then

28. Relationship Between Risk & Expected Return
1.0

29. CAPM (cont’d) The CAPM deals with expectations about the future
Excess returns on a particular stock are directly related to:
The beta of the stock (only consider systematic risk)
The expected excess return on the market

30. Market Model Versus CAPM
The market model is an ex post model
It describes past price behavior
The CAPM is an ex ante model
It predicts what a value should be

31. Market Model Versus CAPM (cont’d)
The market model is:

32. Jensen's alpha
Jensen's alpha was first used as a measure in the evaluation of mutual fund managers by Michael Jensen in 1968.
The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset.

33. Jensen's alpha
This is based on the concept that riskier assets should have higher expected returns than less risky assets.
If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "abnormal returns".
Investors are constantly seeking investments that have higher alpha.

34. Jensen's alpha
Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]
Rit : the realized return (on the portfolio)
Rmt : the market return
Rf : the risk-free rate of return
: the beta of the portfolio.

35. Note on the CAPM Assumptions
Several assumptions are unrealistic:
People pay taxes and commissions
Many people look ahead more than one period
Not all investors forecast the same distribution
Theory is useful to the extent that it helps us learn more about the way the world acts
Empirical testing shows that the CAPM works reasonably well

36. Stationarity of Beta Beta is not stationary
Evidence that weekly betas are less than monthly betas, especially for high-beta stocks
Evidence that the stationarity of beta increases as the estimation period increases
The informed investment manager knows that betas change

37. Equity Risk Premium
Equity risk premium refers to the difference in the average return between stocks and some measure of the risk-free rate
The equity risk premium in the CAPM is the excess expected return on the market
Some researchers are proposing that the size of the equity risk premium is shrinking