WEBVTT 00:01.010 --> 00:08.330 And the last video we created 100000 random portfolios and we plotted them here in red and black we 00:08.330 --> 00:15.590 have our six stocks and we can actually see that by creating portfolios we can realize risk and return 00:15.590 --> 00:19.550 profiles that cannot be realized by a single stock. 00:20.060 --> 00:23.310 So let's focus here on the Coca-Cola stock. 00:23.480 --> 00:28.880 And at least from an historical point of view it was not efficient to just hold the Coca-Cola stock 00:29.180 --> 00:31.880 because keeping the risk constant. 00:31.880 --> 00:34.260 So this is a risk. 00:34.290 --> 00:38.640 There are actually many portfolios that gives us a higher return. 00:38.660 --> 00:45.440 So here are many portfolios with the same risk and higher return and keeping the return constant. 00:45.440 --> 00:47.120 So this is year the return. 00:47.240 --> 00:51.620 There are many portfolios that realize that the same return at a lower risk. 00:51.620 --> 00:58.520 So these portfolios here this is the portfolio effect and we will examine this in much more detail in 00:58.520 --> 00:59.760 the next section. 00:59.840 --> 01:06.950 But for the time being the question is whether we can rank our portfolios here from best performing 01:06.950 --> 01:12.940 to worst performing with a metric that incorporates a risk and return. 01:13.220 --> 01:19.490 And we actually might think of a ratio that simply divides the return by the risk and the higher the 01:19.490 --> 01:26.960 ratios or the more return we get for a unit of risk the better the performance of the portfolio and 01:26.960 --> 01:33.650 actually with this approach we are quite close to the most frequently used risk adjusted performance 01:33.650 --> 01:35.920 metric for financial instruments. 01:36.080 --> 01:44.940 The ESOP ratio and instead of dividing the portfolio return by the portfolio risk we first attacked 01:44.990 --> 01:48.260 the risk free return from the portfolio return. 01:48.260 --> 01:52.810 So we have other portfolio return minus the risk free return. 01:53.030 --> 01:58.830 And this is actually called the excess return or that return premium over the risk free rate. 01:58.910 --> 02:03.930 And then we divide the excess return by the portfolio risk taking. 02:03.950 --> 02:12.040 So to say we calculate the excess return per unit of risk and at a first glance this looks quite arbitrary. 02:12.420 --> 02:15.600 So why do we not just the divide return by risk. 02:15.600 --> 02:20.910 And I can give you the answer and a very simple graphical intuition in the next videos. 02:21.060 --> 02:26.150 But for the time being let's focus on the risk free return and the risk free asset 02:28.840 --> 02:31.380 and actually there's no completely a risk free asset. 02:31.390 --> 02:37.930 But as an approximation government bonds issued by a highly stable countries like the US or Germany 02:38.340 --> 02:40.290 are deemed to be a risk free. 02:40.330 --> 02:47.090 So that's almost the surplus and risk that these countries will not repay their obligations. 02:47.170 --> 02:50.650 And now in our example of is the risk free asset. 02:50.650 --> 02:57.730 So in our portfolio analysis of U.S. stocks we are considering a five year time period from the end 02:57.730 --> 03:05.710 of 2013 to the end of two 18 and therefore a five year U.S. government bond or Treasury note where we 03:05.710 --> 03:14.920 lend money from the end of 2013 to the end of two 18 would be considered as a risk free asset because 03:14.920 --> 03:20.660 it's almost 100 percent certain that we get our money back at the end of two. 03:21.160 --> 03:27.850 And that we get to the predefined coupon or interest payment and the coupon is approximately the return 03:27.850 --> 03:30.390 of this risk free asset. 03:30.430 --> 03:37.180 So if we had invested into a five year Treasury note at the end of 213 we would have realized a coupon 03:37.210 --> 03:40.330 or a return of about one point seven percent. 03:40.900 --> 03:43.450 And that's the risk free return. 03:43.450 --> 03:47.530 And by definition the risk free asset has zero risk. 03:48.220 --> 03:56.290 So this is our formula father Sharpe ratio and we defined that the risk free return this one point seven 03:56.290 --> 03:59.890 percent and the risk free risk is zero. 04:00.790 --> 04:08.290 And then we are creating here a list risk free where at the first position we offer the risk free return 04:08.770 --> 04:18.220 and at the second position we have the risk free risk so this was an introduction on these Sharpe ratio 04:18.610 --> 04:24.040 and in the next video we are calculating the sharp ratio for our portfolios. 04:24.220 --> 04:30.730 And then we have a closer look how our portfolios performed in terms of risk and return. 04:30.760 --> 04:32.620 So I hope to see there by.