Explain in detail the concept of the mean-variance optimal portfolio approach of Markowitz. Use graphs and simple formulas to support your qualitative arguments.
ALT: The optimal complete portfolio $w_{cp}$ is
$w_{cp}=y*w_{TP}$ and $w_{rf} = 1-y$
$w_{cp}$ is on the Capital Allocation Line
if $y < 1$: $w_{cp}$ between $r_f$ and $w_{TP}$
$y= 1: w_{cp} = w_{TP}$
$y>1: w_{cp}$ above $w_{TP}$. The investor borrows money
Assume a risk-averse investor invests as suggested by Markowitz. The investor reveals that his complete portfolio is a 200/100 portfolio, meaning, the investor invests 200% of his wealth into the tangency portfolio and borrows the additional 100% at the risk-free rate. If the Sharpe ratio of the Tangency portfolio is 1.0 and its volatility is 30%, how large is the revealed degree of risk aversion of the investor? How large needs risk aversion to be so that the investor invests only 50% into the Tangency portfolio?
Assumption: volatility = standard deviation ????
The optimal fraction of wealth employee i invests into the TP portfolio is: $y_i^* = \frac{SR_{TP}}{\gamma_i *\sigma_{TP}}$
Hence, $\gamma_i=\frac{SR_{TP}}{y_i^**\sigma_{TP}}$
In the first case:
$y_i^* = 2, Var = 0.3, SR = 1$
risk aversion is: $\frac{1}{2 \times 0.3} = 1.6667$