 Hello and welcome to the session in which we would look at kurtosis in skewness which is a deviation from the normal distribution. This topic is covered in essentials or principles of investments as well as the CFA exam. Now these topics are statistical in nature so I will not be going over how they are being computed. I'm going to try to explain how they get used or the meaning of them in a finance or an investment perspective so when you read them in your tax book when you see them in an investment context you understand what does kurtosis and what does skewness means. As always I'm going to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1700 plus accounting, auditing, finance as well as excel tutorial. If you like my lectures please like them, share them, put them in playlists. If they benefit you it means they might benefit other people connect with me on Instagram. On my website farhatlectures.com you will find additional resources to supplement and complement your accounting as well as this finance course. So if you're looking for additional resources check out my website farhatlectures.com. In the prior session we looked at the normal distribution and it's very important that you are familiar with the normal distribution or symmetrical distribution before we look at the session. So the assumption here you understand what a normal distribution is. If not look in the playlist of this chapter or in the prerequisite down in the description and I'll have the playlist. So you understand what a normal distribution it allows to calculate the probability and basically have statistical inferences about the data. It tells us a lot about the central tendency. It tells us that mean, median and mode are equal and that's very important and obviously it is symmetrical. It means 50% of the distribution lie on either side of the graph and we can use a standard deviation as a measure of variation and that's very important because in the prior session we talked a lot about standard deviation. So this is what we know about the symmetrical distribution or to be more specific the normal distribution. Now we're going to be looking at distribution that are not normal. Now how do we know distribution is not normal? We measure that by something called skewness. How skewed it is? So what is the there's one simple formula to compute the skewness and that's taking the mean minus the median divided that by the standard deviation. Now let's think about it. If for a normal distribution we said the mean and the median are equal to each other what happened when we have two numbers and we subtract them from each other and they equal to each other? My four and a half year old would notice the answer is zero. Therefore if we have zero divided by the standard deviation my four year old doesn't know how to devise but I can tell you you'll get a skewness of zero. So if the skewness of the data when you compute the mean the median and you take the mean minus the median if the skewness is zero it means that it is it's a perfect normal distribution. It doesn't have to be zero to be considered normal distribution. It could be 0.5 within minus or plus 0.5 you could still consider it a normal distribution but the point is we can measure that skewness. So the skewness measure the asymmetry of the distribution. What do you mean by the asymmetry? It means it's not symmetrical. It means the middle does not cut it in 50-50. So let's take a look at an example that's not symmetrical. If we look at this graph here this is this data is positively skewed or there is a right, notice see there is a right tail there's a right tail. So what what could be an example of this positive skewed data? For example household income in the US if we look at the household income most of the people they might be making right in this area let's assume this area is 70,000 to 150,000 so the majority of the people will make this much then you have at the end of the tail few people like Bill Gates and Warren Buffett they make millions or billions of dollars therefore the data when you when you draw the graph or when you draw the histogram it's going to look like there's a lot of people on this end which is the fat tail at the end right tail we have a right tail at the end so a positive skewness of a distribution from an investor perspective indicates from an investment perspective that an investor might expect frequent small losses and few large gains if we're looking at returns we have few losses because those are small and large gains this is from an investment perspective so it's more desirable by investors because there's there's a probability to gain a huge profit that can cover those frequent small losses if we are looking from a return perspective if we're looking from a return perspective let's take a look at a negatively skewed or left tail distribution now kind of i'm going to give you a simple example to illustrate the negatively skewed if i gave an exam and most of the students it's an easy exam most of the students that well they got in the 70s 80s okay they they mostly fall here but i have few students only few students that get in their 20s therefore i have few students here so this will be negatively skewed data this is what a negatively skewed data would look like but i forgot to mention that with the positive skewed data the mean the mean notice is greater than the median and the negative skewed the mean is less than the median it's just something you want to be aware of if you did the math it does it does it does show itself so the negative skewness which is the left tail of the distribution indicate that an investor might expect frequent small gains and a few large losses if it's a negatively skewed now in finance whether it's positive or negative we always assume we are dealing with a normal distribution we'll try to make it a normal distribution so that's one thing to when we're looking at the data make sure to know what's the distribution of the data is it because what we do is we assume it's symmetrical so you want to make sure you understand what positive skewed data and negative skewed data is another another another thing that you need to be familiar with when it comes to distribution is the kurtosis of the distribution the kurtosis measure the fatness of the tails or the peakness of the probability distribution relative to that of the normal distribution now the kurtosis basically measure the likelihood of extreme outcome okay so what do we how do first of all can we compute kurtosis kurtosis and the answer is yes we can't compute kurtosis now we're not going to compute kurtosis but if we're looking at a normal distribution it should have a kurtosis of zero so let's take a look here at a kurtosis of kurtosis of zero if we look if we look at these lines notice here line n which is the black line hopefully you can see it this one here has a kurtosis of zero so this likes this looks like a normal distribution okay with the kurtosis of zero and what we call this to be more specific if it has a kurtosis of zero of a normal distribution we call it mesocurtic distribution just the name of it it doesn't really matter because we have three type of kurtosis so the first one is the normal which have a kurtosis of zero now we have something called leptocurtic distribution shows a heavy tail on either sides indicating large outline outliers it's easier to see the leptocurtic not from a tail in this graph from its peakness so if we look at this red line here it has a kurtosis when they compute the kurtosis it's equal to three which is positive when that's the case it's called leptocurtic now what does that mean you cannot see you cannot see the tails but if you i'm going to just assume this is the line here you're going to see that these tails goes across like they have a large outcome large outliers indicate large outliers so an investment leptocurtic distribution if the data looks like this should that investment return may be prone to extreme values on either side so they can go to this side that they can go to the side but notice here it's also it has a peak it has a peak but it is risky it's risky because you could have extreme measures on either side now the orange one right here it has a kurtosis of two well it's still extreme but not as extreme as the as the red line simply put you can say that the the more it peaks the the larger it spreads out basically so it's riskier now we also have we also have what's called platocurtic distribution shows a negative kurtosis so if we're looking at the light blue here the blue and the pink they have negative but let's focus on the pink and the blue so notice here this is the pink and this is the blue looks like a semi circle when we compute those are kind of in a sense they are normal distribution because they're they're all symmetrical if we they're all symmetrical they're all symmetrical whether it's three two one or zero they're all symmetrical but the kurtosis of it is negative reveal a distribution with the flat tails now what does that mean flat tails well if you think about it if you look at the let's look at the semi circle here notice there's a small outliers in the distribution so basically this they don't have large outliers like when we started with the kurtosis of three and I told you that kurtosis spreads out when the kurtosis is negative there's not large outliers and outliers means there's risk there is risk so an investment this type of distribution is desirable for investments because there's a small probability that the investment would experience large return now extreme return not large extreme extreme return now if you want if you're talking about return you want the extreme return to be on the positive but also that extreme return could go on the negative so an investment with a with a large kurtosis which is leptocurtic could have a large positive or a large negative versus a platocurtic distribution the the outliers you don't have large outliers so you don't have your you should not be experiencing extreme return so again those two topics kurtosis kurtosis and skewness they're statistical in nature but we use them in finance so the purpose of this session was just to kind of tell you how we interpret them in a finance context I hope I made the point in the next session we would look at how to measure risk premium to talk we'll talk about risk aversion and we'll measure and talk about the sharpie ratio as always I'm going to ask you to if you like this recording please like it share it if it benefited you it means it might benefit other people share the wealth and don't forget to visit my website farhatlectures.com if you want complement and supplement your accounting or your finance courses such as this course good luck study hard and of course stay safe