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
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 deviation of the portfolio). On the left-hand side, the dependent variable is return (the expected return on the portfolio). Thus, we see the idea that the expected return on an investor’s portfolio in some way depends on the amount of risk the investor takes. This is a formula that describes the risk/return tradeoffs the investor faces. 4) Finally, the investor would then use his or her indifference curve to find the optimal portfolio for that investor. Since all of the investors in our world are assumed to be rational, the investor’s optimal portfolio will lie somewhere on the New Efficient Frontier. Thus, the investor’s portfolio will be one of four types of portfolios: 1) Long the just the Risk-Free Asset 2) Long the Risk-Free Asset and long Portfolio M 3) Long just Portfolio M 4) Short the Risk-Free Asset and Long Portfolio M.
While all investors will be in one of these basic portfolios, the various weights and long and short positions are decided by each investor based on his or her attitude toward risk and return (as described by his or her indifference curves). Up to this point we have been discussing a process that originally developed by Harry Markowitz in the 1950s.
Next, we left the Land of All Assets and entered…
THE LAND OF CAPM
The Capital Asset Pricing Model (CAPM) was more-or-less independently developed by William Sharpe, John Lintner, and Jan Mossin in the early 1960s. Essentially, these researchers asked: What happens in the marketplace if everyone behaves in the way described by Markowitz. In other words, Markowitz is telling investors what they should do; CAPM is describing what would happen if investors actually follow Markowitz’s process. There are three main assumptions to the CAPM model: 1) All investors follow Markowitz’s process. 2) All investors have homogenous expectations. That is, they all agree on the inputs to the Markowitz model. They have the same estimates for the expected returns, variances, and covariances of all the...