Ch. Risk and Return:II

1. Efficient portfolio Def: portfolios that provide the highest expected return for any degree of risk, or the lowest degree of risk for any expected return. If an investor produces potential portfolios with securities, he or she would generate feasible or attainable sets of portfolios in terms of risk and return (Page 81, Figure 3-3). Efficient frontier: In Figure 3-3, the boundary line BCDE is called the efficient frontier (or set). The portfolios on the efficient frontier are efficient portfolios.

(source: Intermediate Financial Management by Brigham and Daves, 9 th edition) Expected Portfolio Return, r p Risk,  p Efficient Set Feasible Set

Risk/Return in difference curves: curves showing investor’s attitude toward risk and return trade-off. That is, an investor is indifferent with any combination of risk and return on the curve. But if the curve is steeper, the investor is more risk averse. Optimal portfolio for an investor. Optimal portfolio is an tangency point between efficient frontier and indifference curve of the investor.

(source: Intermediate Financial Management by Brigham and Daves, 9 th edition) IB2IB2 IB1IB1 IA2IA2 IA1IA1 Optimal Portfolio Investor A Expected Return, r p

2. Capital market line and security market line What will happen if a risk free (riskless) asset is included? We can obtain new portfolio sets composed of a risk free (riskless) asset and a risky asset portfolio. These new portfolios are better than old efficient portfolios (or set) without riskless asset. Furthermore if an investor is allowed to borrow and lend at the riskless rate, he or she would generate new better attainable efficient portfolio set (frontier) and new tangent point with indifference curve.

(source: Intermediate Financial Management by Brigham and Daves, 9 th edition)

r RF MM Risk,  p I1I1 I2I2 CML R = Optimal Portfolio. R. M rRrR rMrM RR ^ ^ Expected Return, r p

If the market is in equilibrium, every investor would know a M portfolio generating a new better attainable efficient portfolio sets. He or she would include the M portfolio. It is called a market portfolio composed of every risky securities/assets available in the market. In Figure 3-6, the line r RF MZ is called “Capital Market Line.” The line shows a relationship between risks and returns of efficient portfolios. The optimal portfolio (R) for any investor is a tangency point between the CML and the indifference curves.

CML equation = E.g) if risk free (riskless) rate is 10%, a market portfolio return is 15%, a standard deviation of the market portfolio is 15% and a standard deviation of the efficient portfolio is 10%, what would be the expected return of the efficient portfolio?

More about CML and efficient portfolios: - Risk is measured by the standard deviation of the portfolio - Slop of CML reflects the aggregate attitude of investors toward risk. - Efficient portfolios are supposedly well diversified. They would have only market (systematic) risk. - Relationship between the market portfolio and its standard deviation. Difference between SML and CML -SML tells us an individual stock’s an required rate of return whereas CML tells an required rate of return of an efficient portfolio.

SML uses a beta coefficient as a measure of the risk. CML uses a standard deviation of the portfolio as a measure of the risk. 3. Calculating Beta Coefficient in CAPM or SML (1) Scatter plot chart (2) Regression Results -Market model:

- Theoretically correct model: (3) Implications of return and risk -Jensen alpha : intercept in a CAPM regression of excess returns. -Sharpe’ s ratio : -Treynor’ s ratio :

(4) additional insights - estimated returns in CAMP and SML assume that the past return and risk relationship would be consistent in the future. - beta is a measure of relative market risk. Actual market risk measure is - total risk (variance) = market risk + diversifiable risk =

- beta in future : Adjusted beta: 0.67*(historical bets)+0.33*0.1 Fundamental beta: adjusted to reflect the change of operating performance. 4. Arbitrage Pricing Theory (APT model) -CAPM is a single factor model. But the return/risk relationship may be a function of more than one factor. -In 1976, Ross proposed APT with several economic factors.

Here, r1 is a portfolio only sensitive to economic factor 1. Advantages of using APT model - multi-economic factors model - APT need fewer assumptions than CAPM - APT does not assume that all investors hold the market portfolio. But it is not easy to interpret the factor analyses and to find a portfolio only sensitive to one economic factor.

5. Fama-French three factor models They hypothesized that three factors largely determine the required rate of return: 6. Behavior finance It assumes that people are not expected to behave rationally with their investments. E.g) overconfidence, biased self-attribution, etc Stock prices reflect those irrational but predictable human behavior.