"Life Cycle" Hypothesis of Saving: Aggregate ... - Arabictrader.com

296 Miscellanea
r
l 2
RAP(2)
Marker Line
l 1
r 1
P
P M
l M
RAP(M) = r M
s M s
RAP(1)
r f
Figure 12.1
RAP: Total and risk-adjusted return
Legend:
y-axis: r = return; x-axis: s = standard deviation = risk
P 0 = a portfolio of risk-free assets with the risk-free rate of return, r f ;
P i = portfolio i with total return r i , risk s i , and risk-adjusted performance RAP(i);
where:
P M = the market portfolio;
P 1 = portfolio 1;
P 2 = portfolio 2; and
RAP(i) = the risk-adjusted performance of portfolio i
or unlevering a portfolio moves it up or down along its leverage opportunity line
to alternative levels of standard deviation and total and excess return. Levering
a portfolio by d i % increases the standard deviation as well as the excess return
of that portfolio by the same d i %.
The points on a portfolio’s leverage opportunity line l i represent portfolio i at
various levels of d i . Any point on l i that is to the right of the initial portfolio P i
constitutes borrowing and levering the portfolio (with a positive value for d i ).
Any point on l i that to the left of the original portfolio P i represents lending and
unlevering the portfolio (with a negative value for d i ). The market leverage line
l M (or “market line”) is a straight line from the risk-free rate to point P M , representing
the market trade-off between risk and return. Notice that the slope of any
portfolio’s leverage opportunity line is that portfolio’s Sharpe ratio S i = (r i - r f )/s i .
Thus, from the graph it is easy to identify the portfolio with the highest return
per unit of risk as that with the steepest slope or greatest Sharpe ratio (P 2 in figure
12.1). Moreover, the graph can be used to compute RAP(i) and demonstrate its