Welcome to this lecture.
So here we have our graph with 100000 portfolios and the sharp ratios indicated by the color.
And we also fear that Max Sharpe Ratio portfolio that dislocated on the efficient frontier which is
actually here the curve.
Also we have the risk free asset which is approximated by the five year U.S. Treasury note with one
point seven percent annual return and zero risk.
And in this video we will get a better understanding why the sharp ratio is the most commonly used the
risk return performance metric and we will do this in a very intuitive way by visualizing the SAP ratio
and by getting a reasonable interpretation of the SAP ratio and then in the next section about portfolio
theory and ESA pricing we will in detail examine the practical implications and the practical consequences
of our findings here.
So we have here our risk free asset and we could actually link the risk free asset with any of our portfolios
here by drawing a line.
So for example we could draw a line here to this portfolio or we could also add another line here for
example to this portfolio here and you will see the practical intuition behind these lines in the next
section.
But for the time being that's focused on the graphical intuition here.
And finally we could also draw a line from the risk free asset to the max Sharpe Ratio portfolio.
So let's do this here.
So this is the line linking those two points here and we can actually see geographically that this line
is the attendant to the efficient frontier.
So it actually touches the efficient frontier here and the max sharp racial portfolio.
And therefore this specific line here that links the risk free asset and the max Sharpe Ratio portfolio
is the tango and and therefore the max Sharpe Ratio portfolio is the tango and c portfolio.
And actually one property of the tango and here is uh that uh this is uh the steepest the possible lion.
So if you would draw lines from the risk free asset to each and every portfolio here then here the tango
and lion would be the steepest one and the steepest mean that that actually has the highest slope so
the tango and thus the line with the max slope riot now let's recap some high school math.
And so what is the slope.
And we can calculate the slope of a line by calculating that are y divided by delta x.
So let's have a look first of all on the y axis and we have actually the annualized return on the y
axis.
And for our maximum sharp ratio portfolio the annualized return is somewhere around 25 percent.
So then the delta y is here and then the delta y is actually the portfolio return.
So the 25 percent minus the return of the risk free rate of one point seven percent.
And now let's also go to the x axis.
So the max Sharpe Ratio portfolio has a risk of approximately 20 percent.
And the delta x is actually here which is um the risk of the Max drop raise your portfolio minus the
risk of the risk free asset which is zero.
So delta x is actually the portfolio risk.
All right.
Let's summarize our findings.
And uh so we have uh the slope and uh.
Here the slope of the tank end is actually the portfolio return minus the risk free return which is
the excess return on that return premium and then divided by the portfolio risk.
And this term looks pretty familiar actually.
So a portfolio return minus the risk free rate divided by the portfolio risk.
And this is also the sharp ratio so the sharp ratio of each portfolio here is uh simply the slope of
the line that we can draw from the risk free asset to the portfolio.
And actually the line with uh the highest slope is the line that we can draw from the risk free asset
to the max Sharpe Ratio portfolio.
And this line is also here the tank and to the efficient frontier.
So this is the graphical intervention behind the sharp rise saw and in the next section about the portfolio
theory and ESA pricing you will have a deeper look into the practical implications and the consequences
of this finding here.
So I hope to see you also in the next section by.