WEBVTT 00:00.860 --> 00:02.180 Welcome to this lecture. 00:02.180 --> 00:09.210 So here we have our graph with 100000 portfolios and the sharp ratios indicated by the color. 00:09.290 --> 00:15.590 And we also fear that Max Sharpe Ratio portfolio that dislocated on the efficient frontier which is 00:15.590 --> 00:17.350 actually here the curve. 00:17.390 --> 00:24.440 Also we have the risk free asset which is approximated by the five year U.S. Treasury note with one 00:24.440 --> 00:28.180 point seven percent annual return and zero risk. 00:28.250 --> 00:34.580 And in this video we will get a better understanding why the sharp ratio is the most commonly used the 00:34.580 --> 00:41.420 risk return performance metric and we will do this in a very intuitive way by visualizing the SAP ratio 00:41.720 --> 00:48.170 and by getting a reasonable interpretation of the SAP ratio and then in the next section about portfolio 00:48.170 --> 00:54.380 theory and ESA pricing we will in detail examine the practical implications and the practical consequences 00:54.380 --> 00:56.670 of our findings here. 00:56.690 --> 01:04.340 So we have here our risk free asset and we could actually link the risk free asset with any of our portfolios 01:04.340 --> 01:07.750 here by drawing a line. 01:07.760 --> 01:15.530 So for example we could draw a line here to this portfolio or we could also add another line here for 01:15.530 --> 01:22.910 example to this portfolio here and you will see the practical intuition behind these lines in the next 01:22.910 --> 01:23.480 section. 01:23.480 --> 01:28.390 But for the time being that's focused on the graphical intuition here. 01:28.460 --> 01:34.900 And finally we could also draw a line from the risk free asset to the max Sharpe Ratio portfolio. 01:34.910 --> 01:36.350 So let's do this here. 01:36.350 --> 01:42.920 So this is the line linking those two points here and we can actually see geographically that this line 01:43.280 --> 01:46.640 is the attendant to the efficient frontier. 01:46.640 --> 01:53.360 So it actually touches the efficient frontier here and the max sharp racial portfolio. 01:53.360 --> 02:00.260 And therefore this specific line here that links the risk free asset and the max Sharpe Ratio portfolio 02:00.710 --> 02:08.800 is the tango and and therefore the max Sharpe Ratio portfolio is the tango and c portfolio. 02:08.950 --> 02:16.950 And actually one property of the tango and here is uh that uh this is uh the steepest the possible lion. 02:16.990 --> 02:24.070 So if you would draw lines from the risk free asset to each and every portfolio here then here the tango 02:24.070 --> 02:33.490 and lion would be the steepest one and the steepest mean that that actually has the highest slope so 02:33.490 --> 02:42.390 the tango and thus the line with the max slope riot now let's recap some high school math. 02:42.410 --> 02:45.190 And so what is the slope. 02:45.190 --> 02:52.420 And we can calculate the slope of a line by calculating that are y divided by delta x. 02:52.600 --> 02:58.630 So let's have a look first of all on the y axis and we have actually the annualized return on the y 02:58.630 --> 02:59.580 axis. 02:59.920 --> 03:08.440 And for our maximum sharp ratio portfolio the annualized return is somewhere around 25 percent. 03:08.470 --> 03:15.050 So then the delta y is here and then the delta y is actually the portfolio return. 03:15.040 --> 03:21.820 So the 25 percent minus the return of the risk free rate of one point seven percent. 03:21.840 --> 03:24.790 And now let's also go to the x axis. 03:24.910 --> 03:31.250 So the max Sharpe Ratio portfolio has a risk of approximately 20 percent. 03:31.600 --> 03:39.460 And the delta x is actually here which is um the risk of the Max drop raise your portfolio minus the 03:39.460 --> 03:42.850 risk of the risk free asset which is zero. 03:42.850 --> 03:46.770 So delta x is actually the portfolio risk. 03:46.770 --> 03:47.260 All right. 03:47.260 --> 03:49.160 Let's summarize our findings. 03:49.510 --> 03:54.240 And uh so we have uh the slope and uh. 03:54.250 --> 04:02.470 Here the slope of the tank end is actually the portfolio return minus the risk free return which is 04:02.810 --> 04:09.860 the excess return on that return premium and then divided by the portfolio risk. 04:10.180 --> 04:13.120 And this term looks pretty familiar actually. 04:13.150 --> 04:18.220 So a portfolio return minus the risk free rate divided by the portfolio risk. 04:18.410 --> 04:27.610 And this is also the sharp ratio so the sharp ratio of each portfolio here is uh simply the slope of 04:27.610 --> 04:32.270 the line that we can draw from the risk free asset to the portfolio. 04:33.320 --> 04:39.740 And actually the line with uh the highest slope is the line that we can draw from the risk free asset 04:39.740 --> 04:42.160 to the max Sharpe Ratio portfolio. 04:42.530 --> 04:47.720 And this line is also here the tank and to the efficient frontier. 04:47.720 --> 04:54.650 So this is the graphical intervention behind the sharp rise saw and in the next section about the portfolio 04:54.650 --> 05:01.100 theory and ESA pricing you will have a deeper look into the practical implications and the consequences 05:01.100 --> 05:02.960 of this finding here. 05:02.960 --> 05:05.480 So I hope to see you also in the next section by.