【正文】 for Risky Assets ? At the time of the investment decision, we know the set of possible outes and the likelihood of each, but we do not know what particular oute will occur. The TradeOff Between Risk and Return Chapter 5 Slide 77 The Demand for Risky Assets ? The risky asset will have a higher expected return than the risk free asset (Rm Rf). ? Otherwise, riskaverse investors would buy only Tbills. The TradeOff Between Risk and Return Chapter 5 Slide 78 The Demand for Risky Assets ? How to allocate savings: b = fraction of savings in the stock market 1 b = fraction in Tbills The Investment Portfolio Chapter 5 Slide 79 The Demand for Risky Assets ? Expected Return: Rp: weighted average of the expected return on the two assets Rp = bRm + (1b)Rf The Investment Portfolio Chapter 5 Slide 80 The Demand for Risky Assets ? Expected Return: If Rm = 12%, Rf = 4%, and b = 1/2 Rp = 1/2(.12) + 1/2(.04) = 8% The Investment Portfolio Chapter 5 Slide 81 The Demand for Risky Assets ? Question ? How risky is their portfolio? The Investment Portfolio Chapter 5 Slide 82 The Demand for Risky Assets ? Risk (standard deviation) of the portfolio is the fraction of the portfolio invested in the risky asset times the standard deviation of that asset: mp b ?? ?The Investment Portfolio Chapter 5 Slide 83 The Demand for Risky Assets ? Determining b: fmp RbbRR )1( ???)( fmfp RRbRR ???The Investor’s Choice Problem Chapter 5 Slide 84 The Demand for Risky Assets ? Determining b: pmfmfpRRRR ??)( ???mpb ?? /?The Investor’s Choice Problem Chapter 5 Slide 85 The Demand for Risky Assets ? Observations 1) The final equation is a budget line describing the trade off between risk and expected return . Risk and the Budget Line )( p?)p(R=+ mfp f pm( R R )R R σσChapter 5 Slide 86 The Demand for Risky Assets ? Observations: 2) Is an equation for a straight line: 3) c o n s t a n t s a r e a n d ,R ,R mfm ?mfm )/R(R S l o p e ???Risk and the Budget Line =+ mfp f pm( R R )R R σσChapter 5 Slide 87 The Demand for Risky Assets ? Observations 3) Expected return, RP, increases as risk increases. 4) The slope is the price of risk or the riskreturn tradeoff. Risk and the Budget Line Chapter 5 Slide 88 Choosing Between Risk and Return 0 p R e tu r n , of D e v i a ti o n Sta n d a r d ?Expected Return,Rp U2 is the optimal choice of those obtainable, since it gives the highest return for a given risk and is tangent to the budget line. Rf Budget Line m?Rm ??R* U2 U1 U3 Chapter 5 Slide 89 Rf Budget line The Choices of Two Different Investors 0 Expected Return,Rp p R e tu r n , of D e v i a ti o n Sta n d a r d ?Given the same budget line, investor A chooses low returnlow risk, while investor B chooses high return high risk. UA RA A?UB RB m?Rm B?Chapter 5 Slide 90 Rf Budget line Buying Stocks on Margin 0 Expected Return,Rp UA RA A?UA: High risk aversion Stock amp