Hi everybody. Uh, my name is Russell jude uh, from the company edged designations. Mm cf a charter holder. Um, I always get asked by a lot of people. Um, and I have a few other designations as well because, um, as part of what we teach, we teach cf a frm kaya. So I didn't think it would look very professional for the teacher not to have the same designations is what we're teaching. So I've got a few others as well, but people always ask which one do you put first? Yeah. And I'm not favoring the CF A guys at all, but I always put the one first round lecturing. So because I'm with you guys today. Okay, We get cf a first. Okay. Um, and we put the kyliyah and therefore ems in the chartered accountants a little bit towards the back end for today, but no less important that All important. Okay. Welcome everybody and thank you for for your time. I know it's uh, everyone's given up a lot of their hard earned time to be with us today. Okay. The topic that was selected, I'm not sure who does this election, but it's uh, apparently it's a, is a democratic process. So this is obviously what people preferred or wanted for today's session. So where we go. Um, it's Fintech in investment management. Okay. For those that are familiar with the cf valuable, two syllables. This is where it comes from. Fintech in investment management. Okay. It is made up of two readings in um, cf A level two. Well, I'm not talking about CFR level two for the 2021 syllabus uh, for the 2022 syllables, no changes at all. Other than where exactly where it sits in terms of its reading number, but no change other than that. And it's made up of um to specific readings. Okay. In terms of the CF level two syllables, it's made up of a reading called machine learning, followed by big data. Those are the two readings in machine learning and big data. In terms of today's class, I'm going to be focusing a lot more on the machine learning side of things. The big data um aspects um is quite detailed, quite technical and you're gonna laugh when I start with machine learning and you say, well, this is technical and detailed as well. Yes, I know. Okay. But unfortunately, or fortunately makes no uh, no difference. But we need to get into the specifics a little bit. Okay. As we go through Fintech, it's a very wide diverse topic. Fintech. And it's not, it's not easily explainable in terms of, you know, you can't say well, you know, and I was, I was a little bit, I had to give it a bit of thought when I spoke with with the Cf, a society. When the topic, Fintech came up to see exactly what's in there. Okay. And what the reference to Fintech was because um, I hope I don't talk out of turn here, but if I had my own way and I wasn't constricted in a sense to to uh to this being a refresher topic in terms of cf a specific material. Okay. Which as I mentioned earlier was machine learning and Big Data. Um There's some lovely interesting stuff that we can also talk about in terms of Fintech but we're gonna have to leave that to the back end, see how much time we have as we come to the conclusion of the presentation, once we've covered the more specific cf readings being machine learning and a little bit of big data as well. Because when you look at Fintech, Fintech is a massive massive topic. It's a massive innovation and it's a massive topic. What is Fintech? Okay. We're gonna start off talking about that a little bit and then we're gonna move straight guys into machine learning. Um We're gonna break machine learning down into uh supervised unsupervised. Okay. As well as deep learning, the three major categories where we look at in terms of supervised learning. Okay. Um We'll talk about algorithms as well. Okay. And how algorithm and then fits into a machine learning. Okay. Um And we'll hopefully we'll do a little bit of a practical Fintech applications as well. We'll see how we go for time guys. Obviously the topic. Fintech is massive, massive, massive. Okay, I don't know if I'm allowed to say this on a c f a presentation but We were here for education Assumption No one will mind. Um but for those that as we go through the presentation, this type of information, this type of um topic resonates with you. There is a lovely designation. Unfortunately don't offer it. It's not free advertising. Okay. We don't offer it. Um but it is, it is a specifically uh, Fintech type designation which is called FDP financial data processing. It falls interestingly under the chi a banner that they they started that it looks like I haven't done it myself so I can't give too much credit or otherwise to it. But if those are interested to just just to take a look as well, if you want to further your studies in this particular topic, it's a specific designation called FTp on this type of information. Okay. Now let's just jump it straight away because our time is short. Okay. Um and there's so much wonderful stuff that we could cover. Um and we'll see how we go for for time as to what we're gonna be discussing. But we'll do first thing first we'll talk about what we the actual cf A readings okay. Which by the way, if you were if you are in CFL level two or you've covered CFR level two before um this is reading seven and eight Machine learning and big data. Okay. Just a little quick one guys, what is Fintech? We'll do our best to give you a description. Okay. And one would have to take the word Fintech and break it down into two Fin, which is finance and tech, which is the technology site. Okay. And it's a term that describes any kind of financial technology Okay. Which is using technology within the financial services area and anywhere from businesses to consumers. Okay. Um now you could you could for example, take a bank. Okay. Uh an old fashioned bank. And if you guys have seen that lovely discovery discovery bank advert which shows a very old school looking bank, an old school looking banker. Okay. And take that bank as it stood an ad tech, a technology aspect to that. And then well that's Fintech, isn't it? Okay. So remember it's not such a uh it's not an overly complicated topic. It really means taking uh fin finance area, anything in that nature, financial services and giving it a tech component as well. Okay, when we started talking about this guys and hopefully it back and we'll get a bit of time as well. Then you introduce all these fancy things, smart contracts. Bitcoin. I'm sure everybody's heard of this latest one called N. F. T. Non fungible poke ins, tokenization i C E O s. You're probably most familiar with our pos initial public offerings. This one is called an Rco an initial coin offering. Yes. So there's some lovely lovely stuff coming up guys and let us jump straight in but just to preempt what we're going to be doing next. Now I'll turn the slide over over here guys is, as I said earlier, we're going to be uh putting most of our focus on the actual cf reading because remember this is a refreshed a series that we're doing over here guys, obviously I'm going to stick more to the cf a content, which in and of itself is lovely as well, quite technical, but very important. Of course guys that we get the understanding of what we're doing before we can then because remember if you can understand the technology behind what we're doing well, then you can apply to anything, can't you? Okay, so we're gonna be spending most of our time guys today on the back end of the technology side. Machine learning algorithms, supervised versus unsupervised learning um and all that kind of good stuff. Okay. Uh as I said, it is a little technical, we're gonna try what I've tried to do specifically for this presentation is to untech nickel a little bit to make it as simple as possible because unless you specifically need the very technical aspect of it. Okay. Um then it's good enough just to have an understanding of it to be able to, to work forward. Okay. We talk about machine learning, that's, that's the very first part. And again, guys, we break the topic machine learning down into two. Machine learning is actually like it, we're going to teach the computer to think. Okay, good. And the reason that we do that guys is because for the most part we work with vast amounts of data most most people as you get into a financial type of environment, a bank and insurer anything of that nature. The amount of information is massive is massive and we can't manage that information guys without the use in the help of a computer. Okay. No better case in point guys I know how many of you were following the story but the J. C. The chinese berg stock exchange opened a little bit late yesterday being Wednesday. Um The system kind of like uh you know I don't have enough to be able to comment fairly or unfairly about it but the system seemed to crash. Not to be able to cope with the massive volumes that were pushed through the system the day before they on Tuesday. So the stock exchange opened a little bit late in on Wednesday. Okay again vast amounts of data, vast amounts of trading. We can't do this kind of stuff and without the use of computers. Okay good. So machine learning then. Okay is we teach the machine we teach the computer to learn. Okay we're gonna go through all the videos, ways of learning, supervised unsupervised etcetera. Okay And then once the computer is learned and we'll talk about what it means for the computer to learn. Okay then the decision making process can be automated and done in a much much easier way. Okay good. What the computer will do guys is it will work with the data. Okay. And once I understand that data then I can say okay, well I understand what I'm doing now with this particular data. Okay. And we call it making generalizations about the structure of the data. Whatever data is that I can understand that and it can take it forward to other uh other data. Okay good. The machine will learn. Okay we'll make predictions. And guys, I want to see this. You can see a little bit why this falls into cf A level to the con section because a minute what are we doing over here? We're getting the machine to learn. Okay. Such that it can make predictions based on the data without the help of humans. And remember a big portion of cf A. Level two. Okay. Is regression analysis. Okay. Making use of ordinary least squares methodology. Regression analysis. Both simple and multiple regression time series data. All of that. Okay. It's part of what we've seen. CFR Level two. Okay. And then of course this is a continuation. Is trying to use machines to help us make those regressions and predictions. Okay. How does an algorithm amongst humans? Heard of an algorithm? Okay. Um that we use as part of the machine learning process. Okay. And an algorithm simply it's a set of rules. Okay. That the computer follows. Okay. In terms of uh its calculations or other other kind of problem solving methodologies okay. That the computer goes through and is able to learn via those processes, we just call it an algorithm that it's fancy name. Okay? Now that we're getting involved in the actual machine learning process guys, we're gonna break machine learning down into three. Okay, supervised unsupervised. And then deep learning. And of course guys as we move further and further down the process into deep learning, deep learning takes us all the way through to ai okay, we'll get we'll get to to that violence towards the end of this particular picture. Okay. We start off over here guys. Okay guys feel free at any point in time was proposed questions if it does get technical or anything of that nature. Okay, well you just need an explanation. Just please feel free. Of course there is a question box there for you. Please feel free to make use of that as well. Okay. We start off with supervised learning. Supervised learning. And I'm sure everybody that has been involved in C. F. A. In some form or not or any other kind of quantum course is very familiar with the X. Variable and the Y variable. Okay. And almost a little bit like the dependent variable which is your Y variable. Okay. And your independent variable is your X variable. Okay. And what we do with remember as part of any kind of regression, what are you trying to do? Okay, as part of a regression you're saying? Okay, well the dependent variable. Okay. Which is always going to be your wife is equal to what we'll normally, I'm just gonna make hope. It doesn't sound too technical. You normally got your be Oh your B. O. Is your um uh where it kicks in your intercept? Okay. Often people call it the cut as well, where it cuts into the graph plus, Okay. B one is my slope. Okay. And we are always times that by X. And X is obviously the independent variable. I could put this obviously guys, if I so wish into a bracket over there. Okay. But what do we see over here? We see that the Y which is your dependent variable? Okay. Okay. And we can use that to predict contrary, what are we predicting? Okay. Based on based on my B. O. Which is my intercept? My B. One which is my slope which which we correct my slope times X. Which of course is my independent variable. And remember guys, the minute I move from simple regression to multiple regression, you can have X one X two. You can have many many independent variables. What we do know over here with supervised learning. Okay. Is what we do is we try and we teach the computer to think. Okay, so what we do over here. Okay. We we we we you know, I'll show you here, we've got it. Okay. Again just let's get the terminology, we're using an algorithm, Okay that works out the relationship or the patterns between my two variables. My X. Variable. Okay. Remember X. Variable is what I put into the system. And what comes out a set of output is the Y. Variable. Okay? Um and the computer learns this pattern because we're teaching that we're teaching the computer how to get to this pattern. Okay um how do we do that? We give the computer labeled a label, data set. Okay. And we say to the computer here is your input. This is what you should get out. Now learn that. Okay. Almost like teaching, you know teaching a child in a sense you're saying well this is what goes in, this is what's supposed to go out and next time it happens. Well now, you know the process and the computer now has has learned, okay. The computer can now in for the pattern between inputs and outputs because you've taught it okay. The difference between the various inputs and the outputs. Okay. And the beauty about this is now once the computers learnt okay in a supervised manner because you've given the computer both the inputs and the outputs, okay. The computers now learned the pattern. Okay now it can predict the values. Okay? Um If you put new inputs into the system now I can say, okay well I've seen I know what to do now. So what will the computer do? It will take the values of your new input and it will predict the output for you. Okay. So but first we need to teach it. That's why it's called supervised learning. First thing we teach the computer, how do we teach him? We give him what we call labeled data. We give them the X. And we give them the Y. And not only do we give him the two, but we teach the computer the relationship between the two. Okay. Such that in the future the computer can use that to predict when I when I then only give him an input. Okay. That the computer can then work out the output. It can you see as we move forward guys, what's going to be one of the most commonly used algorithms under supervised learning will be regression analysis. Okay. Because what what do we do with regression analysis? Exactly what I've shown you in the picture over here guys is we trying to work out what the output is? Okay. Based on what the input is, the input is going to be my X. Variable? Yeah. Good. Okay. And obviously here's an example of supervised learning is multiple regression in their weaker. Okay, good. I'm gonna go over the page. I hope that makes makes sense to people. As I say, this is probably not language and most of us are familiar with being in CFO, most of us are familiar more with. If I started to talk about Gordon? Growth model. Okay. We're building blocks models? I'm sure everyone so that we know about? Okay, so this is probably a little bit out of people's comfort zone. So we take it very slowly and it's just trying to get a sense overall of what we do. So that supervised learning. Okay, breaks it down main into two major categories guys, which is regression problems. Okay. And regression. We've spoken about uh in detail also we look at classification problems. Okay and classification is exactly that. Okay. The target, which is my wife variable is I'm going to use the word is either a category orginal remember orginal is just an order. Okay. Does't necessarily just sister for example, in a race, 10 people run a race. The orginal is where they come in order. It doesn't give you much more than that, does it? Okay. Um okay, okay. And all that. It does a classification model and will break things down into distinct categories. Okay, this goes into that category. For example, I wish you to laugh with my students when I used to teach them about orginal and cf valuable one and I would tell them, let's say for example, um uh I run a race a running race against a well known athletes. I'm sure you all know Hussein, bolt, probably quite a quick chap. Okay. And I run a race against him. Okay, now if we're looking at an orginal measure, the orginal measure will just say okay, there was two of you in the race. Who came first? Who came second? Okay. Not a question really, is it? So Hussein came first and I came second but it doesn't give you more information than that. Just it just gives you categories or orders. Okay. So in classification problem what I'm trying to do is I'm trying to say, okay who are the top five athletes? Who are the bottom five athletes? Okay. Doesn't matter for example that the first athlete ran the race in under 10 seconds and the second athlete took about 25 seconds. That's not of interest to me essentially. I'm just trying to classify them into major areas and that's why we call it the output over here. Okay. The input will be all the races. We put all the all the different people that ran the race in there. The output is we classify them, we classify them into let's say first quartile, second quartile etcetera etcetera. Okay. For example guys we're looking at a fraud detection model, we're not looking how much fraud or what was the details of the fraud. What I'm saying to you is yes or no. So the outcome is okay I'm gonna put all my numbers in all the data into the computer into the algorithm and this algorithm must come out and say yes, fraud or no fraud and other is what has it done? It's classified for me, classified into a yes a fraud or know of fraud. Okay. And again, when we see these words yes or no or just to classify into those things. The word that should come to my heart is binary. Yeah. Finally say yes or no. Okay. Very not not much gray in the middle. It's black or it's white. It's a yes there was a fraud. I know there's no fraud. Okay. Good. Another lovely time thing that you can use classification problems for guys is ratings. Okay. Remember the rating could be also orginal. It's an order for example when you're looking to rate. Okay, a particular bond issue. Well a triple A rating is a very good investment type rating. Okay. A C writing not so good D rating, default. And again, the computer can do that for you because it acts as a classifier. It takes everything that you put into it all the data and remember again all the data that you put into it get is the all my exes I put everything in all the data in. Okay. Well hoping to get get uh why variable some kind of output out from there. Okay, let us move on a little bit over here. And guys by the way, when we as we move through the program. Okay. I'm gonna be spending more time going on specific. We started with a bit of a general introduction to supervised Unsupervised and deep learning. And then we move on to talk about specific cases of each one. So we can still do quite a bit of work on each of these specific algorithms. Okay. We then move forward over here guys to unsupervised. Okay. Unsupervised learning. Okay. And we look over here and unsupervised learning, it doesn't work with like what what we spoke about before. Remember the key word for supervised learning was labeled data? Okay. In other words, I give the computer okay? Um the X. And the Y. And I teach it to learn here. I don't yeah, I don't give it. Okay? Um anything I just give it the input. I put all the inputs in all the exes in. Okay. I don't give it the wise, I don't tell the computer what the answer is. Okay. How does this do for now? What does the computer need to do now? The computer must discover the structure on its own when it was supervised learning. Okay. I taught the computer what kind of conclusion and needed to have. Okay. Could I gave the computer the exes. Okay. I got the computer input and I told the computer what the output for the target was as well. Yeah, I'm not giving the computer the target. Okay. I'm saying here's all the inputs. Computer take all the inputs. Like all the exes. And you tell me you come up with what you believe the answer to be Okay. And of course guys, because I'm not giving the computer the answer. The computer is gonna have to work out the structure of the data by itself and based on that. Okay. And using unsupervised learning is very good. Okay for two kinds of things exploring new data sets because we don't have the answers yet. Anyway, it's a brand new data set. So what difference does it make him? I've tried working out myself with the computer, does it for me? Okay. So then why on earth would I use a computer generally? Because the data is too large or too complex for a human minds to to visualize. So I plug into the computer and what again, just guys, there's a bit of a revision. What am I plug into the computer? I can't give the computer all the exes. Okay. And I tell the computer come out with what is the target come out with an answer. Do something with this data for me. Okay, good. Um we look at two important things that specifically unsupervised learning deals with number one I mentioned reduction. Okay. And dimension reduction is, and we'll see there's some lovely um uses to this as well. Okay, particularly as we try and apply this to to finance and investment in terms of dimension reduction. It's all in the words again, there guys is, I'm taking the entire all the various dimensions of this particular data set. I'm trying to reduce them. Okay, and what we're going to come out here, we're gonna see, okay, um is a very lovely kind of system thing if we work with Okay, um particularly if you want to go more in detail, uh if the frm part two guys do this quite a bit called P C. A principal component analysis. Okay. And in P. C. A what happens? Okay? Is it takes all the look at the words principal components, so what principal components does? Okay, a P C a principal component analysis takes all the components. And let's talk, for example, if you're looking now remember uh from cf A level two and also goes in to see available to you as well when we're looking at a factor model, for example, a multi factor model as opposed to a single factor model, like the cap model. But if you're looking at a multi factor model for example, okay, you might want, will want to know what are those most important factors that drive equity returns? Okay. The principal components can come along and try and break that down for you and so let me show you where the majority what factors are there that are driving the large percentage of your returns and that's called dimension reduction on breaking the total into more manageable parts. So I can come out and say, well, okay, What drives the return? There's 100 factors that drive the equity return but really three of those 100 factors account for 85% of the of the return. So let me just work with those rather. Okay, that's dimension reduction. Okay, we move along over here grass to what we call clustering. Okay and again, this is just taking all my observations and putting them into various groups, similar groups, similar, similar clusters. The computer can do that for us. Okay. And the very last one of my three supervised unsupervised and deep learning in terms of deep learning. Okay. Um you know obviously your most sophisticated algorithms, these when you start to talk about things like hand handprint or fingerprint recognition, face recognition, speech recognition and I don't know how many of you have been asked by your bank recently if you want to authenticate yourselves by a voice and they can do that as well. It's got to be better than the 10 questions that they ask you every time that they want to authenticate you. Okay. Um, if you can just be authenticated by your voice, I'm sure that's a much, much easier pain free approach as opposed to all those questions I've been asked many me, I failed many authentications by my bank because they train trick questions as well. Do you own a farm somewhere you think no, how many mortgages have you got on the farm? I don't own a farm. So it's a little bit tricky but it does a deep learning if you can, if uh, if you can automate that process via voice recognition while there we go. This saves the process. Okay. We also talk about in terms of deeply when we talk about reinforced learning. Okay, reinforced the computer reinforces or interact with itself. Okay. Um, this is all part of a are artificial intelligence. Okay. You talk about neural networks. You can see it's becoming very technical neural networks can neural from the brain. Okay, artificial neural networks. Okay. Um, and we'll go through those. But remember a deep learning or much more uh, this type of learning process can either be supervised or unsupervised these, these particular neural networks. Okay, so guys at this point in time we have to just stop and take a breather. What we would say is we've covered supervised unsupervised learning and the third form is deep learning what we do. Now guys, excuse me? As we go through each of those three and I'm gonna try and keep it quite untech nickel. Okay. Although we could get quite deep but of course I want to try and make it as untech nickel as possible. Okay, But we go through each of those methodologies, supervised unsupervised deep learning and we talk specifically about each one's learning algorithm. Okay. And we're going to speak about five different algorithms and uh, supervised learning in the last regression S VM support vector machine kenya's neighbour cart or classification and regression tree. Often just uh, we, we use the acronym cart and ensemble learning and random forest. Okay. As I say guys, I'm gonna put a little bit more information perhaps into these notes then? Uh I'm gonna be going through with you just because of the technical nature of it. I would be happy if we come out of this particular presentation. And I say to you, what is penalized regression? You know, a little bit about it. Of course the technical side, if one wants to take it further, will let each, each person on their own will can study it in greater, greater death. Okay. We started with penalized regression. Okay, uh and penalized regression. Okay. Is um and we see the word penalized. Okay, It's just a normal regression. Okay, what is it called? Penalized regression? Because it takes a lot of the features. Okay. And and makes them more manageable for prediction purpose? Because remember, okay, let's say for example, I'll give you a little bit example over here. Okay. And if I can say to you guys, okay, um let's make it as simple as possible. Okay, so I'm trying to predict C. F. A. We will use what the americans uses an american designation. I'm trying to predict cF grades or marks. Okay, now, if I'm trying to predict marks. Okay, first of all then that would be called my that's my wife variable. Okay, um my dependent variable. In other words, my C. F. A marks are dependent upon what. Okay, well let's look at some of the X. The independent variables let's say for example, one of them would be tom studied in other words how many hours you put into your work? Okay that's your ex. But that could just be X. One. And what else could determine my C. F. A. Grades? Well we could have X. Two. How many hours are slept for X. 3? How much exercise our deserves X. Full. How many kids have I got? Maybe they either bonus or not A better they disturb or not. X. five Blah Blah Blah Blah Blah. You're happy with that? So what penalized regression says? Well I'm trying to use regression. Okay to predict what my wife variable my CFO grades now if I'm trying to use all of these various X. Variables to predict my grades I can't have 100 of them because it just makes the prediction a little bit not manageable so I can get down to a manageable set. So what I'm trying to do with penalized regression. Okay um is try and work out what are the key points? Okay. Probably time studied amount of rest I've had and yes probably exercise as well. Okay. Or the other factors. Sure but they're not I've got to try and get it down to a manageable set okay in order to be able to work with my date. Okay. And there's a lot of other information you guys I'm not going to spend too much more on that. Okay when you look at this concept over here guys called penalized regression. What I've tried to do as well as trying to make it a bit more practical. Okay, is let's just see how this then applies to a business. Okay, well business use. And we have a look over here for example again. Yeah. Oh, um, the algorithm. It's a regression algorithm. Okay. What is it used? Some examples. Okay. What is driving my sales? Okay, remember again, sales is mom okay? My wife, my dependent variable. Other words, sales are dependent upon what many excess competition, prices, distribution, etcetera. These are all my exes and we look at over there. Okay. To optimize price points and estimate product price elasticity. Well, no price elasticity is is just how sensitive the prices to the various components. We can classify our customers on how likely they will repay their loans etcetera, etcetera. Okay, over our page over here, I'm going to another one. Uh so I just did come out a little bit small. Okay. S. VM Support vector machine. Support vector machine fits much more guys into the classification side of things. Okay. And it's also very good for detecting outliers. Okay. And if you look at the example over here, what it does. Okay, is I can see my line over there. That's not being line over there. And what the line does is it puts things into two different in this particular example. Into two separate categories. Remember this is a classification algorithm, I want to take whatever's the bluegill dots over there on the right hand side and the green dots on the left hand side. And I want them in separate parts as if I them separately. We've got two sets of data. Okay. I've got them of course on my X and Y coordinates. Okay. And they've got two different features. Okay, so these different features are the green and the blue data. Okay. And what I do is I put a line in between and then I want my algorithm which brought an S. V. M. A support vector machine. S. VM to take the data and put it in. It's correct spots. Okay. The straight line over there is called a linear classify wines that linear because you can see it's a nice straight line. Of course classify because it put them on either side of the line. Okay, good. And then I come out once I'm done with us with what guys, two sets of data points. Okay and again I'm not gonna go too much more into that. But again, remember spm support vector machine is a a classifier. Where would we use support vector machine guys in terms of business use. Okay. Um things like to predict how many patients the hospital will need to serve in a certain time period. Okay. Um and to predict how likely. Okay, someone is to click on an online advert. Again? You do all this? Yes or no you can see it's quite it classifies into yes, they will click No, they won't etcetera etcetera. You can then come out with your levels of probability how likely they are to click. Okay. We then come up with our third one guys. Remember there are five all together in terms of supervised learning, what this one is called. K nearest neighbor. Can you his neighbor by the way? Okay. Is also a classification algorithm. Okay um and you can see over here. Okay. I've got let's say for example two different classes. I've got my class A in which on my red stars. Okay. And I've got my class B which is my green triangles. Okay um and there we go. Okay now what happens is and you can see over here a new example to classify a new data point is then added. Okay, kenya's neighbour. Okay, well then put that particular new point that I've added into my from into my data set. Okay? Um for example we'll just discuss this in a second. For example, if let's go for K equals three. Okay, what what it does is K nearest neighbors. Okay. Now is equal to three and the algorithm is going to look for its three closest neighbors. Okay, so you can see over there if you look at the picture over here? Yeah. Um and I'm upset to my algorithm do me a favor. I'm gonna put a bit of data into here. Okay. And you can see over there is the data being added. That's the question mark. See if I can make us a little bit bigger. Okay so there is the question mark and everyone see that. Okay now I say to the computer you got it you got to tell the computer that's what the K. Stands for. Okay. The case the case stands for how many neighbors do you want? And I've said K equals to three. So the computer then takes the three closest Items or data points that the new data has been added to. So we can see over here what are the three closest ones? Well one star and two triangles. Okay so that's what it now speak up and now it says okay well what's the majority to triangle? What does the computer then do? It says Okay. This new data point that I've added which we've called question mark will get added to. Which data set the question marks because it's closest neighbors are what? Two triangles. Therefore the new data set is more likely to be matched or classified with the two triangles. Okay. Of our page over here guys we move to the next one. I'm not gonna spend too much time over here. Um which is called carts carty's classification and regression tree. Okay. It's very much cart okay um the minute you see the word a tree there is a classification. Classic immigration tree. It becomes very bind and he does it because you're treated as what, as I work through my tree. What am I doing? I'm going that branch or that branch. I moved down to the next branch and I go again, this branch of the next branch. It's very binary in nature. Okay. And I've given you a little bit of example over here guys, I want to take you down the page over here. Due process is a little bit small. Okay. And we start off with the decision tree. Okay. And as you can see the decision tree moves, it's a yes or no. Then I come to new decisions then it's again say yes or no yes or no. Okay, can you see that? That is the that's the decision tree that we work with, but I'm not gonna go too much into detail with that. But that's generally what we're doing over here when I'm looking to if I take you back over here, classification and regression tree. So I stood, I do a bit of a tree and it classifies things into various areas. Once I'm done, if you go down here, this is the fairy final part of the cart. Okay, um, and it breaks it down. You can see by the time I'm finished the tree, it partitions everything for me. Okay, look over here. What does it tell me it says there's 10 cases of companies that did increase their dividends and 10 cases of those that didn't and we can classify them into the various components as per that picture over there that's caught guys. Okay. It does get quite technical guys. I'm not gonna go into the technical nature of it. Okay. But if you look at here is a very interesting business use of cart. Okay. Is in terms of a decision tree. Okay. We can give ourselves a decision framework for hiring new employees. Yeah. Remember what is card do it classifies? So you get a new employee comes into the business. We running through the process and it will come out at the end? Yes, likely to be successful or no. Not likely to be successful. Yeah. Same story. What about a product? If I'm looking to sell a product, we run it through the court process, which is a classification process and we say yes. Is it likely to be sold or not? Okay guys, the last one we look at over here, as you can see, it gets more complicated as we move through the various algorithms. Okay. Um, is ensemble learning and random forest. Okay. And really it's just again, it's a little bit regression. I'm using prediction. Okay. Of a group or ensemble. That's just a group of things to arrive at a prediction. Yeah. And what it does. Okay. It takes the average result from all my various predictions from all my various models. Okay. And it comes out as a bit of an average and why does it do this? The reason it does this? Okay. Because if you're gonna work with a bit of an average, Okay, what can you do? You can reduce the level of noise. Okay. Come out with a more accurate prediction. Okay, good. So it takes all the different models, the ensemble learning the random front, whereas it takes all the various models that we've got put them all together comes out as a bit of an average to try and get you a bit of a more accurate result. Okay and if you have a look over here guys, what models do we talk about? There should be a little bit sounding a little bit familiar by now. S. V M kenya's neighbour here and caught we've looked at those three models already, haven't we? Okay. Now what will this particular algorithm do? Let's say for example, if SV m and k nn predicted the stock will outperform but cart predicts that it will underperform. Well now it's got two against one and ensemble learning Random Forest will come out and say what? No, no, no. Okay. The stock will outperform why? Because two out of the three models have said it'll outperform and remember it takes an average of the models. Okay good. Okay. I'm not gonna spend too much time here guys. Boots, you can see it does can can get a little bit heavy, we've got bootstrapping. Okay. Bootstrap, aggregate aggregating or bagging? Okay, bagging you'll see a lot more guys if you were moving along on two big data, how you work with that data. Okay. And then Random forest as well. Okay. Um just another method or another classifier as well. Okay. I'm not sure if by the time we finished, how you guys are gonna be uh are gonna be thanking thanking me in the C. F. A. Society for giving you Fintech as your as your choice. I'm sure everyone was hoping for more exciting a bit quite kind of stuff. But hey, okay. So we have to go over here. What is the business use perhaps for a Random Forest? Okay. You can predict core volumes and core centers in order to see how much staff you need. You can predict power usage in an electrical distribution grid. Bit of a sensitive point. I think for us here in South Africa, I think our power could blew up yesterday if memory serves, I think my duty. It's called. Okay. And of course the random forests can predict if and our people will be successful or not. Okay. Now I'm gonna move on a little bit over here. We're gonna pick up the speeches to touch so we can get to some some stuff at the back end as well. Just something I suppose where people might have been seeking out a little more. Okay, we now move guys. Okay. Um And I said I do apologize that we had this should not stay supervised. Of course this should say unsupervised machine learning algorithms. My apologies for that. Okay. And the two main unsupervised learning methods are P. C. A. And clustering. I'm not gonna spend more of my time guys here on P. C. A. Which is principal component analysis. Yeah. And you've got clustering there as well under clustering. I've got two of what came means and guys we know what K means. Remember we saw k nearest neighbor. Okay. We've seen a little bit before and hierarchical clustering as well but I want to spend my focus over here guys more on principle component analysis. And remember what peace ea does pc A is a dimension reduce. Er Okay. In other words, if as we mentioned a bit earlier, if you're looking to explain, try and explain. Okay, equity returns. Okay. In terms of let's say for example a multi factor model but the number of models or factors that you've got, so you've got 30 factors that that that are all there in trying to explain away. Okay? Um Equity returns, P. C. A will come along and we'll take that those 30 factors. Okay? and reduce them can good. Okay. And they use this process Pc uses this process of data reduction. Okay? Um And what it does. It's an interesting process but it works with highly correlated features. And what it does is it said, well that features there that features there as well and they're not different features. They're just very highly correlated and it breaks things down. PCH comes and on and it breaks things down into very very few un correlated variables. But that's what you want. Don't you want just a few little variables. Okay. That you can work with. Okay. And you would never get away with talking about guys Pc A. If you didn't speak about what we call Eigen factors, doesn't if you're most familiar with Icann factors with Eigen vectors story and I can values Okay. And these are the very few little remaining variables. Okay. And remember what will come out. Okay. Is perhaps uh three Argon vectors? Okay. You may well have had 30 variables When PCA is finished with you and it has reduced the data. What you've now got is you've got three variables. 3, 3 argon victors. But what's beautiful and what's fantastic about this is that these three arkan victor's okay. Will help explain. Probably Okay. -85 of the data, wow. So But you said that there's another 27. Yes, but those are not that meaningful. It may have looked meaningful to you in the beginning. Okay. That there's so many different factors are available but they're not that important. Three of them. Once I go through pc A will help me explain the majority of the variation. Okay. Over our page over here and I'm not gonna spend more time over there. We return a few pages over here and we just look I'm gonna look at this one quite briefly guys, it's called clustering. Clustering is my second. Okay. Um Unsupervised learning methodology or algorithm. Okay. And what what clustering does it makes use of clusters? Here we go to organize various data points. Okay. Um and class is really just a subset of the various observations that I take out of my data set. Okay. Um and once I've put observations into a specific cluster, okay. Those are all said to be quite similar in their nature. Okay. Um Okay. Uh they all work together. Of course, the one once I put them together then they are all, everything within that cluster is quite similar. Okay. The weaker. Okay. I'm not gonna spend much more time over here guys, but there are two over here. There's K means clustering. Okay. And again, you can see guys it does get quite complicated. We've got hyper parameters over non overlapping overlapping clusters. Central Roids but it's not obviously what I'm gonna be spending time on over here guys. What is clustering do for us? Okay, what's a lovely thing that you can do agree with clusters. Things into similar groups. Okay. It can segment customers into groups by distinct characteristics. Okay. So in order, you know, it's uh in order to make sure that you are you are targeting the correct customers? You can use clustering and specifically K means cluster. Okay. And there's a bit on hierarchical clustering. Such a different form of clustering. Okay. Um, similar concept. That's what we saw before in terms of clustering things into similar, similar groups. Okay. I'm gonna move on over here. As you can see we're moving quite quickly now. We've got deep learning over here. We've got neural networks. Deep learning nets and reinforcement learning. Okay. Remember deep learning can be both supervised and unsupervised. Yeah. Talk about neural networks. And look at the difference. And this is this is probably the key over here guys in terms of neural networks and how they differ from normal uh, algorithms. When I look at something called the logistic regression. Look what I've got. I've got inputs and I put simple, I see the input, I know what the output should be. And remember if it was a supervised system that would we would we would call that the labeled data and yeah, we can teach the computer quite nicely when I moved to an artificial and a and M an artificial neural network, I've got inputs. I've got output. Okay. But there's hidden layers in between. That's the key over here. Okay. A little bit black boxes, in a sense is the middle section of your artificial networks and I don't really I can't really see exactly what goes on over there. Okay. But a whole batch of learning does happen over their cars. Okay, good. And just to describe it quickly. There's an input layer that goes in an output layer. Okay and then there's a hidden layer? Remember the hidden layer? Okay. That's where the learning takes place and everything that I put into it, the various inputs are processed. Okay. Based on what we called trained nets. Okay. And what it does is it transforms whatever you put into the system, what we call the inputs into new values. There we go. Okay. As I say I'm not going to spend too much time over there just in terms of the nature of this, you've got deep learning nets. Okay. Same story guys, if you just get and the way I would love everybody to come out of this particular presentation is not to become machine learning experts just yet. Unless of course that is your aim. Okay then there's many many resources and of course you're more than welcome to reach out to me and I will direct you accordingly but if not and you're a charter holder or your a C. F. A candidate and you just want to know a little bit more about machine learning, how it works because of course it is the future. Okay. Um ignore uh machine learning etcetera. Big data at your peril. Okay. Because it is here with us. Okay. And uh just get a sense of someone talks about supervised learning. You know what that means? Unsupervised. You got a sense of a classification, trained data input outputs. Okay. Just have a sense of all that and I think you have been a good position then A deep learning net again we've got three. Why is it a deep learning it because it's got three hidden layers. Okay, remember the hidden layers is where the learning takes place, We don't necessarily get to see that, do we? We see the inputs. Okay. What goes in the final output and then in the middle of the hidden layers, Okay. Which the learning takes place takes a long time to train these. Start off with small data set, you teach the computer, what is looking for, what is trying to find etcetera etcetera. Some of the useful applications of deep learning nets are Recognition problems, credit card fraud detection, processing language and if you guys have used Excel recently, the latest versions of Excel on Microsoft 365 as well as on the New Google stuff as well. Some fantastic stuff out there. And you can like import into google, like a translate function into the Excel function of google's. I know it's not called uh it's called sheets or something like that on google. And you can do now on Excel as well. And that's all much more advanced type of information you teach, the computer is now being taught to process languages too much more advanced than it than it ever was in the past. Okay. And we see the last one over here guys reinforcement learning. Okay, for example, things that the algorithm OK performs actions that maximize the rewards over time. Okay. Take into account of course what we call environmental constraints. Okay? I'm not gonna spend too much time over there. Okay, guys, that then, by the way, if you were um following along, perhaps if you had your cf a notice in front of you, I'm not sure anyone does. Um that is where we would have concluded the section then on machine learning. Okay. And if you want to do more, more detailed uh reference that would have been reading seven on the 2021 C available to syllabus. What I wanna do now guys, is a little bit off topic. Okay. Is Blockchain and how that works. And I, and I see him I see my time is running a little bit. Okay? Um and normally we go to about quarter past two, so we've got about another 15, 20 minutes together, guys. Um and I just want to touch on some of the, you know, I think this is probably where people are a little bit more excited about Fintech or perhaps what you guys thought you would get with Fintech, but of course, as I said, I had to stick a little bit within the cf, refresher series um as that is my job. Okay. Um we look over here guys. Okay. And we talk about Blockchain and financial market innovation. Okay. It's very important by the way. What's very interesting. I I was looking at some of the comments yesterday on, linked in a lot of anger surrounding the fact that the stock market, the Joburg stock market open late yesterday due to various system issues, call them what you will. Okay. Um, and a lot of people were saying, well, you know, the system couldn't handle the volumes. Remember the system was closed on Wednesday, only open late due to excessive trading on the day before being the Tuesday. This this this last Tuesday and what a lot of people said, well, you know, had they been using more of what we call D L T D L T distributed ledger technology? Okay. This would never have happened. Okay. Well, that's sure not. I think is, you know, I think, uh, not a fair comment to be honest, because, you know, and this one really knows the details. Um, you know, I I definitely, for one couldn't give a comment on that, but it was interesting, there was a lot of comments on saying, well, that's the systems are all the systems need to change. Let's go to Blockchain. Everyone just talks that Blockchain is going to be the cure for everything, all the ills of the past. Okay. It may or may not be. But let's just talk a little bit about this Blockchain process. Okay. And remember, I can see we're not gonna have time to do everything. But if you just think about Blockchain guys, the last point of Blockchain, If I say to what is one of the applications of Blockchain first of all your settings or Blockchain is really just what it's just a distributed ledger. That's all. Block changes means. Okay, and guys, I think it's important to get the concept right without overly confusing anything, Blockchain is just a ledger, so if all the accountants out there, okay that you're probably smiling at, everyone knows about ledger's, I've got my my my twin boys are in great grade nine at the moment um and they're getting a bit frustrated, they want to get into the more interesting stuff but they're learning about the various ledges. Okay, the cash payments journal. The cash receipts journal. Okay, debtors, ledger, okay just ledges, ledges are just records the books and I had to take her back 100 years. What would you see? I don't know why, I always looks like a bit of an older man doing it, I don't know why. Okay, poring over these books, writing them out in the little various squares that he's got in front of him, that's the ledger recording the transactions. Okay, what's happened now, look at the words, it's so important that we look at this and people don't get confused with Blockchain? Blockchain is simply guys, okay, a digital ledger, that's all. So it's a ledger, its digital, what does it mean that it's digital? It means that it's on the computer, it's not written down anyone on the copy of everybody to see look at the other word. When you look at D. L. T. Distributed ledger technology, what's the other word that we look at? That's quite fantastic. It's distributed now. This is what everyone is excited about. Okay this is one of the key excitement's about Blockchain. Okay, by the way, why why do we call this fancy ledger that we work with all the distributed ledger technology? Why do we call this Blockchain? Why is it why does it have such a fancy name for Blockchain? Will conduct called something else? Because remember how does it work? It's a chain of different blocks that's all fancy. So able to go over here, if I've got one block over here, the first block enters into the into the legend that is just the ledger. So the first guy puts into the letter, he's got an asset, there's your asset sits over there. Now what can happen with an asset? Can be bought or sold that will push it onto the next block. Who bought it? Who sold it? Next block, you can see the ledger just moves on. What is that technology? It's all on the computer. It was it distributed? Okay. There's various types is permission and un permission networks but generate a network for example like Bitcoin. Okay where you can see people buying and selling of these various coins etcetera, various processes. It's all just done on via this process which is a distributed ledger called Blockchain. Why is it so? Fantastic? Well, reasons. Fantastic. First of all, everybody can see it. It's no no no secrets over here. And that's always wonderful when you're dealing with a financial system of sorts, let everybody see it. What's too hard? Okay. We love transparency. So the block chain comes along, particularly when you talk about a permission network, everybody can see it. Okay, so you can see what happened to block one. Why is it called a chain? Because block to can't happen until block one has been done properly. We're gonna call it validated. Okay. We use this capacity term called a consensus mechanism. You know that everybody gets to check it. Okay? But once there once check their once happy that we can go from block one to block too. In other words, the asset not get sold. Okay. We can see if you can see it well because it is distributed. Okay, We didn't move from block to to block three, but again, there needs to be a consensus before that can happen. Okay. And everybody can see it. Everybody can see what is a quarter chain. Look at the chain, everybody can see the chain moving along one by one by one. Things don't happen out of water that happen in an order. They are checked. They are validated. There's a consensus mechanism that works within this. I'm sure you guys have agitate you guys what is the consensus mechanism that relates for example to something like Bitcoin. Okay. What would you tell me? You would say? Remember all the Bitcoin miners and what are the miners doing? So compared to the consensus, That's the checking process then I can move on from step to step to step. Okay. And then it goes from step one to step two to step 32 step for the chain moves on its distributed, everybody gets to see it. And it's just a it's just a ledger. That's why guys, it's all called D. L. T distributed ledger Technology. What's the most famous 1? Blockchain? Blockchain is a distributed ledger. What's one of the famous applications of Blockchain? Well, You've got, Bitcoin is a very famous one. You've also got things. We'll see them in in a minute or two. Guys. You've also got things like aiko initial coin offerings. I'm sure you guys now. I've heard of N. F. T. Non fungible tokens cat, we'll talk about that in a second as well if we have a moment or two. Okay. Um Another word that you might come up with in terms of this distributed ledger and this is uh whether this is a good or bad. Well you can you can decide that yourself, it's called immutable. In other words, Once I moved from block 1 to block too, This new transaction over here in block two. That has now come about. It has been checked. Is immutable can't be changed. We can reverse it exactly 100% by going to block three and doing an equal and opposite transaction but you can't just cancel them out. They are immutable. So that does present a bit of a challenge. Some like it some don't. But guys the beauty about when we talk about DLT distributed ledger, it's quick. Okay. And it's transparent, everyone gets to see it. Okay. And that's why people were saying particularly about yesterday's uh issue on the Joburg stock exchange that perhaps if it was more on a system like this one a DLT we may not have had these issues. Okay. That's not what we're here to discuss cars but keep that in mind. Okay. Um and there's a little bit more over the page for you there guys on DLT? S distributed ledger technology. Okay. Um Okay. And one of the another important components of cryptography okay cryptography. And this is what everybody says about because everyone says, well if everybody can see the data, if everybody can see the ledger and it's open to everybody. Isn't that an unsafe? Well we we we encrypt the data a process is called cryptography. Okay. If an unauthorized person receives it, it's useless to them, they can see it. They can see what they want to see all day, every day. It's useless information to them. Okay. I don't know if you guys walked around about a week ago. There is a massive, massive Bitcoin Uh scandal. I don't know the exact details but if memory serves about $600 million dollars in terms of Bitcoin that were uh that had been uh stolen in a sense. Okay and they were busy negotiating with the thief to return the Bitcoin. So yeah there there there are there are downsides as well as well of course. Okay but cryptography does act as a as a certain protection. Okay another okay um concept guys it's called smart contracts. Okay these are computer programs that almost work on their own, they self execute. Okay um on the conditions, the preconditions given by the various parties. Okay good and they can be used for derivatives and things like that. It's fantastic. Okay you're gonna top this page over here guys, I'm not gonna go through this but we have discussed it uh just by the by Okay and Blockchain is a digital ledger. Okay what is it called? Blockchain, okay because everything is recorded in blocks and when the block is finished and I wanted to go onto the next block they change they linked together. How do we secure the various and look and look here again guys here are your blocks, there starts block number one in my block trade Blockchain is just a digital ledger, so remember going dlt digital ledger technology one of those is Blockchain. Okay and Blockchain then moves. Yes. Strong block number one To Block # two There's Your Chain. Okay and every new blockage you can see it's got a new group of transactions. Okay? And they were secured firmly secured to the previous block cab and I can only move on to the next block once it's been one of the new block. Block number three has been validated. Okay. Via what we call a consensus mechanism contents to meet all the people in the Blockchain agreed to this. Yes. And that makes it a bit more secure, doesn't it? There's also what we call uh cryptography which which uh secures everything as well. Okay. So it's a lovely method. Okay. Again, very good for auditing and checking the trail the audit trail in a sense because you can see exactly where things come from because everything is transparent And nothing can move on until the previous block is all trained together. One is changed to two etc and two can't move on to number three until such time as it's been validated or there's a consensus. Okay. Good. Therefore, and you can't manipulate stuff because you can't go back. Okay? We're always that's immutable. Yeah. And then to do that one person we have to gain control of the majority of remember needs to be validated. So unless one party can gain control over the whole system, unlikely there's too many different people in the system. It's too transparent. Okay. Good. So of course, having said that guys, I'm going to show you this last point, I want to show you the success of a digital DLT. Okay relies on broad network participation in other words, that everyone you don't have one person if you've only got one person involved in the Blockchain. Well he can do what he likes can't because then he's the only person there that moves the train forward. He validates everything. He checks it as well. Okay, that's not a system, is it? Okay, good. And over here guys, if you just wanted to see how does the system work, Okay, how does the transaction get added? Okay. Look here the transaction takes place between a buy and sell and by the way, they don't get confused. That's what we do in life, don't we? We buy and we still there's a buyer and a seller then this transaction is broadcast to all the various parties, all the computers on the network on the Blockchain. Okay then that needs to get validated. Okay, um the details of the transaction as well as the parties. Okay, Once it's been validated, consensus has been achieved then. Okay. The transaction is combined with what happened before that. Okay. To form a new block. Okay. The blocks tend to form and remember what's the keyword over here. Chain. The block of data is linked to the previous blocks. That's what's called a Blockchain. Why is it a Blockchain? The block is just a block. Each transit actually represents A block and it's chained to the previous one then what happens once that's all been agreed and it's all changed and it's all the consensus has been achieved. The transaction is complete and my ledger is updated. Okay and a little bit over here guys this is well can't see my time is running short. Yeah I do wish I could be with you guys a whole afternoon but I'm sure you guys wish to get back to work. Okay. Um So we will just finish off with this particular one over here guys. Um which is obviously everyone's pretty most exciting as cryptocurrencies. Okay. Uh I was I was widely um used a day or two ago um again on on linkedin and there's a lovely thing that said something about uh something related to Fintech which was looked quite exciting. So I clicked on it and it said how would you like to pay for this? Um uh This this class this lecture I'm not actually sure what it was. Um So I'm thinking ok it's probably gonna be priced in dollars or something like that which is fine. Um It said North 0.3 ethereum thinking how am I going to get my hands on ethereum which is one of the cryptocurrencies quite closely linked of course to Bitcoin to be able to purchase and then I ran out of time. So that was that but it's interesting to see that there are purchases now happening out there. Okay There are quite closely linked to both. Bitcoin ethereum and all the various is dodge coy dodge coin. I know how you pronounce it as well. Okay um and yeah okay so um these cryptocurrencies okay things like Bitcoin ethereum has become very popular. Okay and most of these cryptocurrencies use DLT systems digital ledger technologies. Okay in other words everything is recorded, every block is recorded. Everything is. And an amusing one over here guys. Just to be very careful when you start to trade cryptocurrencies if that is your if that is your your game. Be very careful guys because if you trade cryptocurrencies okay. You remember we spoke a little bit about the various ways that we can protect it okay um etcetera etcetera and one of the systems over there. If you forget your password no one's got it you can't find the bank and say please reset my password. It's gone. And people have lost their there's a massive number. I'm not exactly sure what it is. Someone quotes me like a half percentage number not just one or 2% but much more than that of Bitcoin. That's been lost into the system because the passwords are lost and no one can get actually rumor. The system is so well protected. Okay when you when when you put something onto this DLT system it's so well protected that you can't get it out and say well let me just change let me find my bank and ask for my password again. Let me do a reset. Okay. So just be very very careful when you do that. Of course you can also look at Archos guys, which is an initial coin offering. Okay. Um, Smart contracts tokenization. I'm not gonna spend four were already out of time over here guys. Okay. Um, and just before we get to the practice questions, which is the end over there guys. Um, just a little interesting one. Okay. There was a little bit of artwork. I don't know if you guys are familiar with with an artist called people I think is his name who does cartoons and I don't mean disrespectfully, but that is essentially he's His area. Okay. And he put together this most fantastic set of, I think it's 500 different pictures all together in one big picture. And he sold if I think 69 or $70 million dollars via what? An N. F. T. A. Non fungible token. What does it mean? Non fungible means there's not many that you can't exchange them. The only one and the token means that you, whoever bought that much of the water. Okay from people is the owner, the proud owner of that. He is the only one you can make as many copies as you like all day every day. Only one person owns the original piece of artwork. Okay guys. I see. I am, I short of time. I'm gonna leave you at this point, but just before I leave you, let me leave you with my details if anybody wishes to reach out okay? Um leaving my email address at E. B. S. Taxi Rosella, that's age. Okay. Um and we are very proud. We have just set up a brand new um web page. Okay. W w w dot edge uh designations. All one word is a bit long, but at least it describes our business quite nicely. Wh designations dot com. So you take a look if you want anything further there and Vice, please feel free if you wish to. I'll leave you my cell phone number as well. Those that wish to initiate with pleasure with pleasure. Okay, there we go. Please feel free to each other if I can help with anything related guys, thank you so much for being with me this afternoon. Okay and taking your time, your precious time to be with us before this refresher series um which everybody will until we meet again. This was, this was the august series. We'll meet again september time. I'm not sure the exact the topic of that's just yet. We'll wait to hear. But hopefully we will meet again in september for the next series in the refreshing series, wishing everybody a month ahead of health, wealth and happiness and we'll see you all. Then here's everybody