 How's it guys, it's MJ and in this video, we are going to be talking About the valuation of investments. So previous video is on fundamental share analysis and now we've moved on to valuation of investments This is going to be quite a technical video quite a difficult Well, I find this material quite difficult quite confusing But let's go through it slowly and hopefully we can figure this out Remember, this is me studying out loud. I might make mistakes So feel free to correct me in the comment section below and Yeah, enjoy the video. So valuation of investments Why is this important because this is how you can actually make a lot of money? If you know whether a share is overvalued or undervalued or whether any asset for that matter is over undervalued You can make money. So if it's over or undervalued You can make money if it's overvalued you want to sell it if it's undervalued you want to buy it Provided you have the liquidity to do so So how do we determine the value of an investment? There's many different different ways to do it, but traditionally one of the simple methods is to look at the cash flows and So when we've got our cash flows We've got two main cash flows We've got the income and We've got the capital Income return and capital return Okay, and the idea is you have an asset and It's going to give you an annuity payment. So let's say let's just make up a number Five rent today plus five rent tomorrow plus five rent the following day plus When you sell it off for say a hundred The thing is each of these values are at a different moment in time and So remember what we spoke about in one of the very early videos was that I'd rather have five rent today than five rent tomorrow And so there needs to be an interest component on all of these things That are projected into the future Now depending on what the Interest is that's going to determine the price So what I want to do in this video is focus on Interest and we're going to see how by changing interest rates You change the value of every single asset in the world So it's quite important, but it is also terribly confusing I mean when you start looking at interest rates, someone says ooh interest rates We know it's a there's one number that the government or the central bank sets, but from that we get things like spot yields We get bond yields We get forward rates We get coupon rates and Then to make it even more complicated is that these things have different names as well So spot yield is also known as your zero rate your bond yield is also known as your gross redemption yield You know, it does get terribly confusing. There's so many of these things And there are various formulas to see how they all link up to each other and stuff like that I Don't know. Should we should we talk about how how the yields are? Or like between each other, I think maybe let's give a quick example quick example so The way to do it is that let's say we have something that's in two years time Okay We would discount it by two years. So let's say it's a hundred and we're discounting it by two years This would be the spot rates at year two or we can use forward rates where it's 100 V1 V2 and that is the forward rate for year one Which is actually equal to the spot yield for year one and the forward rate for year two so for instance if this was say 6.45 Then we could expect that this one to be around say six and this one to be around 6.9 roughly roughly And this is forward rates and this is spot rates But there's a lot of different weird formulas you can get into it what I want to start talking about is These financial instruments all these assets we create around interest rates and what are their values? so What many of you guys are wondering is that well interest rates? this has got a big impact on our asset price and Interest rate movements are uncertain so how do we mitigate that risk and There's various things that we can buy we can buy an Interest rate future and an interest rate forward, but they like to confuse us with their jargon So that's called a forward rate agreement Now what is interesting is these guys are identical in the sense that you're agreeing on the interest rate in the future But there are a few little twerks that make their values different. So interest rate futures these are done Over the counter. I don't know. Sorry not over the counter. They're exchanged Okay, exchange controlled so because they done with an exchange these ones are done over the counter Because they done with an exchange they standardize and there's some sort of clearing house in between them which means they are going to be daily margins, which means there are cash flows and Depending on how your asset is correlated to the invest interest rate That's going to determine whether this one is more valuable than this one And you have to adjust them if you want to find the price between them using some sort of thing known as the convexity Adjustment But what is interesting is that we've created these these Instruments around interest rates, which we have made up and This is why it gets complicated because it's not telling that you can just think about intuitively This stuff is difficult because it's based on things that we have made up and I mean Interest rates futures the stuff is important for say arbitrage pricing although I feel like arbitrage pricing We've covered enough in the earlier subjects Arbitrage, I mean it doesn't really exist for that long in the market because it does get closed up basically Two assets that have the identical payoffs and identical risks will have exactly the same Price that's that's the principle of arbitrage And you can use that principle in order to determine the values of these various instruments that we're talking about another interesting one is Interest rate swaps So you could be earning a fixed interest rate but you might want exposure to a variable interest rate and There isn't a financial instrument that allows you to swap them And you're it's basically taking a long position in one bond and taking a short position in another bond But it's packaged nicely and you have a swap What else don't want to talk to you guys a bounce Hedging so I mean you know you would use these swaps these interest rates forwards for a thing known as hedging Okay hedging is something we're going to be talking a lot about later But hedging is when you engage in a trade in order to reduce a risk The risk that you're normally trying to reduce is say market risk Although in this instance, it would be the interest rate risk An idea is that you buy a product that moves in the opposite direction to your current asset So that if there's a change your net effect is Still says the same. So let's say for instance, we have this asset over here if these interest rates Increase okay, the value of my asset is going to decrease because the time value of money is going to make these guys worth less Which means I will knock to now take out a interest rate derivative that will have a positive Exposure to the interest rate so that when the interest rate increases I make money on the instrument and that money that I've made there covers the amount that I've lost on my asset price So that's what you'd want to do and seeing that all assets are linked to the interest rates You can imagine that this is a massive market For these interest rates derivatives Although hedging is not a silver bullet. I mean you do introduce something known as basis risk basis risk is when the hedging tool that you're using doesn't completely Eliminate the risk and there's still some sort of residual Although we would expect basis risk to be less than the the main risk If it was higher then you wouldn't actually want to hedge because hedging also introduces Maybe a credit risk and a few other smaller things as well Which are you get basis risk if there's not the perfect customized? instrument for you or if you're actually uncertain on what final dates you need Then I mean there's there's this whole optimal hedge ratio And there's all the math that you can go on behind it, but I think what I want to do for the remainder of this video is Just Just talk about empirical characteristics of asset prices and how humanity has stuffed up around that So let's get a color. This is gonna be fun. Okay So asset prices So remember what I showed you at the bottom we built some sort of little model that has oh That has like Income return and capital return Well the idea is that people build these these cash flow models or these models to determine the price of the asset And they get quite complicated and they feel like they can accurately predict asset price movements when changes to certain things happen However, they rely on a bunch of assumptions Which I don't know why that people came up with this because they really are dumb They sounded reasonable at the time but with empirical evidence It's shown that they it's not the case at all. So for for instance asset price was some of the assumptions include that the That the that the increments so the changes in in asset prices are Normal, so if we take the log value of the asset price We believe that the changes will be normal now normal is remember from the normal curve It looks something like that and what's lovely about this normal curve is that it makes the mathematics very easy It makes a computer friendly and people can understand it and the math is all tangible and all that type of stuff However, when you actually look at what really does happen Okay, you get this type of curve which is known as Lepto Kurtik and that means that for the majority of the time it's going to be less volatile Then what we think on average, but there's also going to be these fat tails Which can absolutely cause havoc So and this is why we were a little bit blind to the world recession is because we thought oh these extreme events have got a Very small probability or meanwhile they had a much larger probability But this type of curve over here is very difficult to model And so people still try and get away with these normal curves Specifically credit rating agencies. I mean there's one thing known as copulas Which is two-dimensional statistical distributions that were normal in nature People presented this to the credit rating agencies to guarantee why they should get triple A ratings credit rating agencies didn't understand the mathematics behind this I don't blame them because neither do I and So they stamped triple A on it, but it wasn't normally distributed. It was more leptocurtic There was this message bubble It did blow up everything and we had this massive world recession because of humanity's stupidity to Make a model with an assumption that does not link up with the empirical evidence. So yeah, we only have ourselves to blame Another thing that's quite interesting is that the increments not only do they not change normally But they're not independent. So we also assume that these things are independent and What's interesting about this is because there is some sort of, you know, autoregressive You know in reliance on the past and all that type of stuff. It does kind of make people You know flirt now with technical analysis something which I don't like But the fact that this assumption breaks it down Does give room for this style of trading? But this is also calls Havoc with the models because there's things that have happened which weren't supposed to happen And that's the thing is when you start adding all these assumptions that are wrong together The effect magnifies and like I said, that's why we had this massive, you know You know, we'll give these instruments triple A rating credit Rating agencies totally stuffed up and we had the world recession And Final one is constancy of parameters. So they believe that the parameters are constant And this one's also this is very dumb very very dumb and there's no excuse why we should do it So what they're saying is Things like your drift or your average and your volatility that they're constant But unknown parameters that once you figure them out, you can then model them. Okay Back in like the seventeen hundreds. Okay, this is like 300 years ago a guy called Bayes Was famous for saying he wasn't even like a statistician. He's whole life. He only did it like in his later years He was like maybe these parameters are random variables and so we got this whole thing known as Bayesian Statistics, which is brilliant because that's what a lot of artificial intelligence is based on and it actually is a much more accurate way Of looking at things. So I think these models that we use to price assets are really dumb And they have left the door open for new ones that can incorporate Bayesian statistics and have maybe more of an artificial intelligent nature to them But then I mean sure there's a lot more that we can be said on this subject But now this you can see this is why it's important to be to have all the mathematical background that actual Science provides you with that, you know, why do we do three years of mathematical statistics? Well, because in valuing these things I mean you need to also know something about Cointegration which we'll talk about in a much later video Cross-correlation and and all these other things that that haunt Asset prices and make it a lot more complicated than we initially think it to be But the reason why they use these models is because like I said, they're such a big market for them They need to trade them very quickly. They need to have a standard, you know way to to push these things out So they can't go really Complex will be spent too much time trying to be accurate because that's going to cost business But that's good news for you. That means that if you can develop a better asset pricing model You can make a lot of money Trading these instruments that are based on interest rates, which are made up So there is an opportunity to make money in the sense if you are smart and if you do understand statistics and Mathematics better than the credit rating agencies, although after this whole world recession I'm almost sure that These creating agencies will have invested a lot more time and brainpower into understanding How models actually are supposed to work But here we go. This is this is the difficult part of finance This is the cloudy part of finance Yeah, this confuses a lot of people. So if I have lost you along the way, I do apologize But feel free to ask questions in the comment section below Otherwise, thanks guys so much for watching and I'll see you next time. Cheers