And the last video we created 100000 random portfolios and we plotted them here in red and black we
have our six stocks and we can actually see that by creating portfolios we can realize risk and return
profiles that cannot be realized by a single stock.
So let's focus here on the Coca-Cola stock.
And at least from an historical point of view it was not efficient to just hold the Coca-Cola stock
because keeping the risk constant.
So this is a risk.
There are actually many portfolios that gives us a higher return.
So here are many portfolios with the same risk and higher return and keeping the return constant.
So this is year the return.
There are many portfolios that realize that the same return at a lower risk.
So these portfolios here this is the portfolio effect and we will examine this in much more detail in
the next section.
But for the time being the question is whether we can rank our portfolios here from best performing
to worst performing with a metric that incorporates a risk and return.
And we actually might think of a ratio that simply divides the return by the risk and the higher the
ratios or the more return we get for a unit of risk the better the performance of the portfolio and
actually with this approach we are quite close to the most frequently used risk adjusted performance
metric for financial instruments.
The ESOP ratio and instead of dividing the portfolio return by the portfolio risk we first attacked
the risk free return from the portfolio return.
So we have other portfolio return minus the risk free return.
And this is actually called the excess return or that return premium over the risk free rate.
And then we divide the excess return by the portfolio risk taking.
So to say we calculate the excess return per unit of risk and at a first glance this looks quite arbitrary.
So why do we not just the divide return by risk.
And I can give you the answer and a very simple graphical intuition in the next videos.
But for the time being let's focus on the risk free return and the risk free asset
and actually there's no completely a risk free asset.
But as an approximation government bonds issued by a highly stable countries like the US or Germany
are deemed to be a risk free.
So that's almost the surplus and risk that these countries will not repay their obligations.
And now in our example of is the risk free asset.
So in our portfolio analysis of U.S. stocks we are considering a five year time period from the end
of 2013 to the end of two 18 and therefore a five year U.S. government bond or Treasury note where we
lend money from the end of 2013 to the end of two 18 would be considered as a risk free asset because
it's almost 100 percent certain that we get our money back at the end of two.
And that we get to the predefined coupon or interest payment and the coupon is approximately the return
of this risk free asset.
So if we had invested into a five year Treasury note at the end of 213 we would have realized a coupon
or a return of about one point seven percent.
And that's the risk free return.
And by definition the risk free asset has zero risk.
So this is our formula father Sharpe ratio and we defined that the risk free return this one point seven
percent and the risk free risk is zero.
And then we are creating here a list risk free where at the first position we offer the risk free return
and at the second position we have the risk free risk so this was an introduction on these Sharpe ratio
and in the next video we are calculating the sharp ratio for our portfolios.
And then we have a closer look how our portfolios performed in terms of risk and return.
So I hope to see there by.