【導(dǎo)讀】businessrisk,financialrisk,liquidityrisk,exchangeraterisk,andcountryrisk.opportunities).firm’senvironment.

　　

【正文】 investor’s highest utility occurs at point Y. Investor Y will expect more return than investor X, but investor Y is also willing to take more risk than investor X. h: Describe and calculate the expected return and variance of a twoasset portfolio. Example: In addition to varying the correlation coefficient we will also vary the expected returns and standard deviations. We also vary the weights representing the percentage of the total funding invested in each stock in the portfolio. Table a: When r1,2 is +1, the risk return relationship is linear. There is no reduction in risk because the term +2W1W2σ1σ2r1,2 is at its maximum positive value. a. perfect positive correlation (r1,2 = +1) R1 R2 σ1 σ2 W1 W2 r1,2 ER σport .15 .10 .18 .12 0 100 +1 .10 .12 .15 .10 .18 .12 .40 .60 +1 .12 .144 .15 .10 .18 .12 .50 .50 +1 .125 .150 .15 .10 .18 .12 .60 .40 +1 .13 .156 .15 .10 .18 .12 100 0 +1 .15 .18 Table b: When r1,2 is 0, the term 2W1W2σ1σ2r1,2 goes to zero. Risk is reduced. b. zero correlation between the returns (r1,2 = 0). R1 R2 σ1 σ2 W1 W2 r1,2 ER σport .15 .10 .18 .12 0 100 0 .10 .12 .15 .10 .18 .12 .40 .60 0 .12 .102 .15 .10 .18 .12 .50 .50 0 .125 .108 .15 .10 .18 .12 .60 .40 0 .13 .118 .15 .10 .18 .12 100 0 0 .15 .18 Table c: When r1,2 is 1, the risk return relationship is linear and the risk actually goes to zero at one point. This happens because the term 2W1W2σ1σ2rr1,2 is at its maximum negative value. c. perfect negative correlation (r1,2 = 1) R1 R2 σ1 σ2 W1 W2 r1,2 ER σport .15 .10 .18 .12 0 100 1 .10 .12 .15 .10 .18 .12 .40 .60 1 .12 .15 .10 .18 .12 .50 .50 1 .125 .03 .15 .10 .18 .12 .60 .40 1 .13 .06 .15 .10 .18 .12 100 0 1 .15 .18 : An Introduction to Asset Pricing Models a: Explain how the presence of a riskfree asset changes the characteristics of the Markowitz efficient frontier. The equation for return and the equation for risk show that the bination of the riskfree asset and the risky asset produces a linear risk/return line. How do you start? First, pick a risky stock or risky portfolio (A). Hint: start with one that is already on the Markowitz efficient frontier since you know that these portfolios dominate everything below them in terms of return offered for risk taken. Now bine the riskfree asset with portfolio A. Remember, the bination of the riskfree asset and portfolio A will be a straight line. Observe that any bination on the line RfA dominates the portfolios below it. But any bination on the line RfB will dominate RfA. Why? Because you always get more return for a given amount of risk. Actually, you can keep getting better portfolios by moving up the efficient frontier. At point M you reach the best bination. The RfM line dominates everything else in terms of return offered for the level of risk taken. b: Identify the market portfolio and describe the role of the market portfolio in the formation of the capital market line (CML). The introduction of a riskfree asset changes the Markowitz efficient frontier into a straight line. This straight efficient frontier line is called the Capital Market Line (CML). Since the line is straight, the math implies that any two assets falling on this line will be perfectly positively correlated with each other. Note: When ra,b = 1 then the equation for risk changes to σport = WAσA + WBσB. A straight line. Investors at point Rf have 100% of their funds invested in the riskfree asset. Investors at point M have 100% of their funds invested in portfolio M. Between Rf and M investors hold both the riskfree asset and portfolio M. This means investors are lending some of their funds (buying the riskfree asset). To the right of M, investors hold more than 100% of portfolio M. This means they are borrowing funds to buy more of portfolio M. This represents a levered position. c: Define and distinguish between systematic and unsystematic risk. When you diversify, if assets are not perfectly correlated, the portfolio’s risk is less than the weighted sum of the risks of the individual securities put into the portfolio. The risk that disappears in the portfolio construction process is called the asset’s diversifiable risk (or unique risk or unsystematic risk). Since the market portfolio contains all risky assets, it must represent the ultimate in diversification. All the risk that can be diversified away must be gone. The risk that is left can not be diversified away since there is nothing left to put into the portfolio. The risk that remains is called the market portfolio’s risk (market risk for short) or nondiversifiable risk or the portfolio’s systematic risk. d: Discuss the security market line (SML) and how it differs from the CML. The proper representation of the risk/return relationship is return vs. systematic risk, you can plot the relationship. Use beta to represent the systematic risk. This graph is called the security market line (SML). The equation of the security market line is: ERstock = Rf + (ERM Rf)Betastock CML plots total risk versus return. SML plots market (or systematic risk) versus return. e: Calculate, using the SML, the value of a security and evaluate whether the security is undervalued, overvalued, or properly valued. Example: Expected market return = 15%, Rf = 7%, BetaA = 1, BetaB = .8, and Beta C = . P now EP end E Div ER Required Return Stock A 25 27 .12 .07 + (1)(.) = .15 Stock B 40 45 .175 .07 + (.8)(.) = .134 Stock C 15 17 .50 .166 (.07 + ()(.) = .166 Stock A is expected to earn 12%, but based on risk should earn 15% under 3% (overpriced). Stock B is expected to earn %, but based on risk should earn % over % (underpriced). Stock C is expected to earn %, but based on risk should earn % on target. Stock A falls below the SML, Stock B falls above the SML, and Stock C falls on the SML. If you