Capital Asset Price Model
Suppose we are in….
The Land of All Assets
The end result of our time spent in the Land of All Assets was that an investor in the Mean-Variance World would complete the following process to construct her or his optimal portfolio: 1) The investor would first estimate the various inputs needed to build the Old Efficient Frontier. The inputs that the investor needs to estimate are the expected returns and the variances of all the risky assets, and all of the covariance terms across all of the risky assets. 2) Using these estimates, the investor would then construct the Old Efficient Frontier. This requires that the investor use the algorithm we discussed in class, where the investor would: o Pick a return: for instance, 10%. o Find all of the portfolios that have an expected return of 10%. o Of these portfolios, choose the portfolio with the lowest risk and plot that point on the risk/return graph. o Pick another return: for instance, 11%. o Find all of the portfolios that have an expected return of 11%. o Of these portfolios, choose the portfolio with the lowest risk and plot that point on the risk/return graph. o Repeat until the investor has drawn out the entire Old Efficient Frontier. 3) Having built the Old Efficient Frontier, the investor would then construct the New Efficient Frontier by drawing the line from the risk-free asset through the tangent portfolio (Portfolio M) and beyond.
At this stage the investor would have a picture that looks like:
New Efficient Frontier Return (expected return)
Old Efficient Frontier Portfolio M Expected Return on Portfolio M
Risk-free
Standard Deviation of Portfolio M
Risk (standard deviation)
The equation of this line is:
E(R M ) − R F E(R Portfolio ) = R F + * SD Portfolio SD M
Bodie, Kane, and Marcus refer to this as the Capital Allocation Line.
Notice that we have our first inkling of a link between risk and return. On the right-hand side, the independent variable is risk (the standard
The Land of All Assets
The end result of our time spent in the Land of All Assets was that an investor in the Mean-Variance World would complete the following process to construct her or his optimal portfolio: 1) The investor would first estimate the various inputs needed to build the Old Efficient Frontier. The inputs that the investor needs to estimate are the expected returns and the variances of all the risky assets, and all of the covariance terms across all of the risky assets. 2) Using these estimates, the investor would then construct the Old Efficient Frontier. This requires that the investor use the algorithm we discussed in class, where the investor would: o Pick a return: for instance, 10%. o Find all of the portfolios that have an expected return of 10%. o Of these portfolios, choose the portfolio with the lowest risk and plot that point on the risk/return graph. o Pick another return: for instance, 11%. o Find all of the portfolios that have an expected return of 11%. o Of these portfolios, choose the portfolio with the lowest risk and plot that point on the risk/return graph. o Repeat until the investor has drawn out the entire Old Efficient Frontier. 3) Having built the Old Efficient Frontier, the investor would then construct the New Efficient Frontier by drawing the line from the risk-free asset through the tangent portfolio (Portfolio M) and beyond.
At this stage the investor would have a picture that looks like:
New Efficient Frontier Return (expected return)
Old Efficient Frontier Portfolio M Expected Return on Portfolio M
Risk-free
Standard Deviation of Portfolio M
Risk (standard deviation)
The equation of this line is:
E(R M ) − R F E(R Portfolio ) = R F + * SD Portfolio SD M
Bodie, Kane, and Marcus refer to this as the Capital Allocation Line.
Notice that we have our first inkling of a link between risk and return. On the right-hand side, the independent variable is risk (the standard