How to Calculate Realized & Implied Volatility and Why it's Important - Christopher Quill

so as you can probably tell from the slide there my name is Christopher quill I'm the Institute statistical analyst I also help produce some of the educational content that we do with Anton and I run the research and reports through the website so we have a bunch of like macro research and risk reports and data that we sell through the work through the website as well and I run that what I'm going to talk about today is the importance of volatility how you can measure it and some of its uses okay so it's going to be some of the concepts might be a little bit similar to some of the things that Raj has already discussed but hopefully that just adds some more value as well to what I'm going to say so before we begin all the spreadsheets and supplementary material that you see in today's lecture will be made available to you afterwards all you need to do is send us a message through the contact form on our website and I put the links up there so you guys can just write that down if you don't know the website already and basically the the format of this talk is going to be half of it's going to be a traditional kind of PowerPoint presentation and then we're going to move over to an Excel workshop type format where I'm going to go through practical examples of calculating both realized and implied volatility so why are we actually bothered about volatility so let's first off start by defining what it is so in terms of trading and investing all it is is it refers to the fluctuations in asset prices in asset returns and it's essential for us to actually think about volatility both in terms of risk and reward or opportunity and it's actually a very common mistake to overlook the opportunity or the reward aspect of volatility and only think about the risk aspects so if we didn't actually have volatility in asset prices then there wouldn't actually be no real chance for us to generate portfolio return so we actually require it we need volatility in order to generate returns and by analyzing asset volatility we can think about it in in a number of different ways so like I said in terms of risk or reward or opportunity we can also think about it in terms of the market environment so what's actually telling us about the market environment how how much uncertainty is there in the market that we're looking at and if you think back to Raj's presentation implied volatility is high and low for a reason and that gives us an insight into the market environment what I want to actually drill home to you guys today is thinking about volatility in terms of opportunity a bit more than risk because I think you're all probably fairly familiar with thinking about volatility in terms of risk and one of the most important things to consider in terms of opportunity is thinking about volatility in terms of profitable time horizons for investments and I'm actually going to talk about that a bit more in a few slides time the other uses for volatility is thinking about things like profit targets and risk limits which probably thinks you're more aware of so I'm talking there about position limits leverage limits stop losses things like that and again I'll talk about that I'll mention that in a few slides time and again going back to Raj's presentation having an understanding of volatility and being able to analyze it can help you structure your trade ideas through options instead of the underlying and that can give you a marginal benefit so it can help you create effectively a cost-effective asymmetric payoff so that's a bit of background about volatility what I want to do now is actually get you thinking about risk and reward and particularly a risk reward kind of ratio and what I'm going to do is basically were going to play a little game I'm going to get some audience participation going and it's a very simple game it's going to be a fair coin toss so you get a 50% chance of it landing on heads 50% chance of the coin landing on tails and I'm going to give you two options in option a you get $200 for every heads but you give me $100 for every tails or an option B you get $25 for every coin toss so I just let you think about that for a moment and then I'll ask you guys by a show of hands which option you'd rather go for and we'll talk about the outcome okay so who thinks option A put your hands up okay and what about option B all right so there's some non-participants I think but but yeah so basically you guys went for a as a whole and in this game that's actually the correct answer that's the rational choice the reason being that the expected return per coin toss is higher for option a so we calculate expected return simply by taking the probability of an outcome times the payoff of that outcome so you can see for choice a there it's $200 times 50% for heads plus minus $100 because you give me $100 for every tails times fifty percent fifty dollars per coin toss that's your expected return whereas an option B it's only $25 which is guaranteed every coin toss now what if I change the game slightly and this time give you two new options okay option a you get $300 for every heads but you give me a hundred and fifty dollars for every tails or you can have option B you get 75 dollars for every coin toss so again I'll leave you for a couple of moments to think about it and then show of hands we'll go through the answers okay so who's going for option A this time okay yeah and option B okay this time this is pretty close but it's probably marginally option B does anyone have anything to say about how the game has changed option C they're equal okay so the expected return you mean is the same in both options okay so does that mean that we're indifferent as to which option we choose does anyone I have an answer for that yep gum right yeah yeah so that that's the idea that I'm getting out you're right you're exactly right in saying that the expected return for both options is the same okay but actually it doesn't mean that we should be indifferent to the choice here because this time in option B for the same return we have much less volatility and that's your sort of risk reward payoff so think about it this way what if you chose option A and I changed the game after the first two coin tosses let's say they were tails both time you now only $300 and I'm like yeah okay I'll just stop the game that's that priced into effectively the volatility okay that's the risk of option a so hopefully that that's clear and that gets you thinking about risk reward in general and thinking about probabilities and in the next slide I've got a cumulative dollar profit just simulated of what might happen with option A and B and hopefully that clears this up even further option a is clearly more volatile they both have the same expected return option B is basically just a straight line up I'd happily leverage all my worldly possessions into investing in option B if I could but in option A I might not because if tails comes up let's say a couple of times I may lose all my positions so that was thinking about volatility in terms of risk okay so now I want to move on to talking about volatility and opportunity in terms of opportunity so the most important question to ask yourself here is is there enough volatility in the asset that I'm looking at over the time horizon that I'm considering for investment to actually significantly overcome transaction cost some brokerage costs okay and if there isn't then I have two options option A and by far the most important option this is probably one of the most important things I want you to take away from this lecture is we can increase our time horizon for investment okay that effectively increases the volatility and hence the opportunity of the trade because everyone knows a monthly volatility is higher than weekly volatility and daily volatility etc the other way to do that is actually through leverage but that comes within an inherent risk and it also increases the transaction costs so option a is far more important if the volatility is low you need to think about extending the time horizon of investment to essentially gain more opportunity to profit so let's just conclude this opening section here about volatility we're thinking about it in terms of risk and reward okay the risk stuff you're probably familiar with but I just go through a couple of them now so it's things like setting leverage limits stop losses position limits portfolio limits so let's say that leverage as an example if the assets more volatile than another asset you're likely to have a leverage limit that's actually lower and that that same sort of theory applies to position limits as well more volatile assets you're reasonably likely to have a limit a position limit that's slow it's lower and it can apply to starter positions as well if you think about it in terms of stop losses and profit targets okay assets that are more volatile will generally have wider you should have wider stop losses and profit targets the reason being is that you need to allow for the normal fluctuation of the asset price so you don't want to get stopped out too early you don't wanna get whipsawed so you need to allow for that and like I've said earlier in the presentation the most important thing that I want to take you to take away from thinking about volatility from this lecture is thinking about it in terms of opportunity okay so that's gauging opportunities and profitable time horizons ask yourself that question is the volatility high enough to overcome transaction costs over the time period that you're considering with that investment time horizon and again going back to Raj's presentation you can also think about volatility in terms of helping you structure trade ideas through options to increase the marginal benefit of the trade okay with and instead of just buying or selling the underlying so that's the background on volatility okay that's why it's important and those are some those are some reasons that some ways in which you can actually use volatility so how do you actually measure volatility or we can actually be measured in a number of ways okay so you can think about volatility you can measure volatility in terms of standard deviations beta drawdowns averaged three ranges there's multiple ways to think about volatility what we're going to do and it's the it's the sort of generally defined way of looking at volatility in the investment management industry is to think about it in terms of a standard deviation and we're going to look at the standard deviation calculation in slightly more detail in a moment I know you're all excited about that and we're going to then move on to a practical example of calculating realized volatility which we've already talked about a bit in Raj's presentation and so on and also more importantly implied volatility the reason why it's slightly more important to think about or calculate implied volatility is because that's a forward-looking measure the reason why it's a forward-looking measure of volatility is because options have a future expiry and so market makers have priced in the volatility that they think that the underlying is going to have over that period whereas calculating realize volatility is historical because we use a sort of historical prices to do so so let's look at the standard deviation calculation in a little bit more detail there it is exciting stuff fortunately you don't actually need to understand that equation as it is there at all okay this is a typical example of a mathematical formula that is far more perplexing or looks far more perplexing than it acts is so I don't think it's important that you understand that notation at all but what I do think is useful to you guys is to understand how that calculation works because it will put your mind at ease when you use standard deviation as a measure of volatility so you'll feel more comfortable doing say so I'm going to move over to excel now basically to do the next half of the presentation and we can go through some examples and things okay so this this excel sheet is part of the supplementary material that you'll be able to get hold of after the presentation you'll also be able to get a PDF guide that takes you through a lot of the process that I'm about to go through so you don't need to worry about following every single step but I say just now just try and take away the concepts that I'm talking about so there's six sheets in this spreadsheet the first one is looking at the standard deviation calculation in a bit more detail that's what we'll start with and the second one is calculating realized volatility and then there are three sheets for calculating implied volatility the reason why there's three sheets for that is because it depends on what option you look at as to which calculator you should be using and I'll go into that in a bit more detail later and then the sixth and final sheet that I've got on there is just a bonus sheet I'll quickly show it to you now which I'm not going to have time to go through in this presentation but I wanted to include it for you guys to have a quick look at basically it's just a load of payoff profiles for options to allow you to familiarize yourself with options okay so it's got long put long and short calls and puts and I've also put in some interesting more complex strategies that you can try and implement by by putting calls and puts together putting those profiles payoff profiles together and they're there down the bottom of the sheet so you guys can have a look at that in your own time and see what you think so let's get back on track the standard deviation calculation so here I've got a series of numbers in red okay and we're just going to calculate the standard deviation of this series of numbers to keep things simple how I'm going to explain it is through this chart here so that series of numbers is represented by all the red dots on this chart okay so they are they're the data points and if you think about all measures of volatility they actually all require a reference point to measure volatility around okay so for beta the reference points the market essentially you measure volatility around the market now beta also has a directional component but essentially it is a measure of volatility think about drawdowns the reference point is the previous high you measure the volatility from the previous high for standard deviation it's just the average so the average of the series so that's the starting point of this calculation you calculate the mean of the series I've done that here balance is 6 and in the chart that's illustrated by the blue line and all standard deviation actually does is take the difference between those data points and the average of the series and an average them to get a value for the volatility okay and that's represented by the black lines it's a difference between the data points and the average of the series and if you average those differences you get a measure of volatility you get the standard deviation so to go through that in a little bit more detail you subtract the mean from each number in the series fine they're your differences they're from for each point the thing is if you try and average those numbers now you'll have some trouble in actually obtaining a decent value of volatility because they all net out when you add them up okay because some are below the line and some are above the line so obviously they net out positive and negative values so what you need to do is perform a mathematical manipulation which is square those numbers okay so they all become positive then you can take the average of all the squared numbers so you then get a single sort of number for volatility and then to undo the mathematical manipulation you just square root it and you get about you can standard deviation and if you you can obviously skip all that process in Excel there's a formula for standard deviation we can just sort of double-check it here so equals stdev dot p and then in brackets i can put this series of numbers and you'll see the standard deviation there is exactly the same obviously it just cut out all the steps but the reason why I go through those steps is to basically illustrate how how simple it is it's literally just the average of the differences from average of the series so it's a very simple concept so you should feel comfortable using it and now you know what it actually is so now let's move on to calculating realized volatility and all we're actually going to do is use this formula the standard deviation formula for on historical prices okay so in this sheet in this sheet all i've got here for assets okay the assets are the s py ETFs a S&P 500 ETF I've got a US midterm Treasury ETF a Brazilian stock market ETF and the dollar yen currency pair and all I've got here is five years of monthly returns for each asset and we're just going to calculate the standard deviation for each of those just out of interest I'm going to go through those assets and just see which you think is going to be the most volatile so who thinks by show of hands that the S&P 500 is going to be the most volatile out of those assets no one good okay who thinks the Treasury bond etf is going to be the most volatile of those assets no Brazilian stocks wait ok cool right and what about the dollar yen does anyone think that that has a high volatility okay so let's go through and calculate it now we just use the same formula formula that we did before so stdev P and then in brackets you just put the data series in so in this case it goes back five years I'm just going to select the whole column for each asset okay so you guys will see and just copy this formula to the other cells you guys will see that actually you're correct in what you said about the Brazilian stock ETF being the most volatile what we're doing here is calculating the monthly standard deviation because we're looking at monthly returns and what I've done to the side there is actually adjusted those monthly standard deviation values into an annualized value just because that's basically convention in the industry and it also allows us to compare that to implied volatility values which comes out as a annualized standard deviation so what do these numbers actually tell us so number one think about it in terms of what we've already discussed in the presentation so far so both on an individual and a comparative basis think about it in terms of setting risk limits okay so we've established that the Brazilian stock market is the most volatile asset so we're likely to have leverage limits that are lower we're likely to have wider stop losses wider profit targets we're also we can also think about it from the opportunity perspective we can think about it in terms of profitable time horizons for investment you might be able you could say that you could invest in the Brazilian stock index over a shorter time period because all else being equal with your transaction costs you'll be able to more easily overcome them on a shorter period okay what you can also do is think about the standard deviation values in terms of probabilities and what I mean by that is if you were to calculate the sort of empirical distribution of return of these assets what that means is basically looking in a graph of the frequency of the data points that lie within certain ranges okay you might be familiar with the normal distribution which is an example of a probability distribution and looks something like this okay and you could look at those asset returns and it would look something like this curve okay this is the frequency on the left hand side and then effectively data ranges at the bottom and what this says and what this curve is saying is that most of the data data points the returns lie around the mean which you would expect and very few lie in the tails okay and the normal distribution is a fairly decent reflection of asset prices and what you find in the normal distribution is that 68% of the data lies within one standard deviation 95 within 299 within three so you can think about using those standard deviation values in terms of probabilities so you can say things like for the s py ETF here for example on a monthly basis you could say that the s py ETF is unlikely to move by so there's a 70% chance roughly that it will move between plus three and minus three percent around the mean okay so you can think of it like that what there's a couple of things just to quickly know about that so I said that the normal distribution is a pretty decent reflection of asset price returns the thing that's slightly different about asset prices to something like human height which basically follows this distribution exactly is that the tails are fatter generally in the in distribution in the monthly returns and that means that extreme events occur more frequently than the normal distribution would predict okay so the tails are slightly fatter and also there is a negative skew what that means is that negative extremes occur more often than positive extremes and that makes sense when you think about the psychology in the market when there's fear prices tend to move very far very fast so that's realized volatility okay now that was looking at getting an annualized standard deviation from historical return so it's a backward-looking measure now we're going to go over to calculating or implying something called implied volatility which is a forward-looking measure which I've already discussed the reasons why so I said before you've got three calculators in the sheet for implied volatility because it depends on what options you look at more specifically it depends whether the option is American or European in exercise style that has nothing to do with the geographical location of where the option is listed an american-style option you can exercise prior to expiry or up to expiry and a European option you can only exercise at expiry and the other thing that matters when you choose which calculator to use is whether the underlying asset pays dividends and in each of these sheets you'll see some notes which basically tell you which she use for which options so you don't need to worry too much about remembering that all these sheets look pretty much identical the option inputs are in red and all the cell values that you need to input are in light orange okay there's a couple more than there are option inputs because things like the observed option price in the market isn't strictly an option input neither is defining whether it's a call or a perp or it's American in your European in exercise style so they all look very similar and what you'll find at the bottom of each sheet is a bunch of resources which again we're going to go through an example of this so don't worry about this too much but basically these resources will allow you to find the inputs that you need to then back out implied volatility from the option that you're looking at now I'm just going to go through a very simplified version of how you can think about implied volatility how it actually works okay think about it in terms of how bring some inputs which are the option inputs and then they're put into a calculator which produces an option price as Raj was saying all of the inputs bar one volatility are known so there's one unknown and you know all the other inputs you actually also know the output which is the option price so here you end up with an equation with just one unknown okay so you can solve it the option price is observed in the market and that's how we in back out the volatility measure so what actually happens here is we have a calculator for option prices and we put all in all our known inputs in and we put our option price in as well that we observe okay and then we iteratively change the volatility number until the calculator price matches the option price in the market the observed price and once the difference is zero we have our measure of implied volatility again don't worry about following all this 100% right now this will be explained in the PDF it's also explained in the spreadsheets okay so don't worry about some of the concepts I'm I'm covering if you don't get them right away so that's basically how it works so now what I'll do is I'll actually go through a practical example of how you can do this so I'm going to look at the s py ETF which we've already had a quick look at in realized volatility and the first thing that we need to do is actually so I'll just delete these cells so we can go through this process the first thing we need to do is actually define which calculator we're going to use and we do that if you remember by working it by finding whether the option is American or European and exercise style and we also find whether the underlying pays dividends so our first task is just that to find the exercise style of the option and there are a number of ways of doing that you can google around for terms like product specifications or option specifications where it will say that for whatever option you're looking at and usually you'll find those on the exchange website for where the option is listed so we're gonna go on to see BAE comm to actually find the option and don't worry exactly about where I'm clicking it doesn't matter you'll be able to navigate through this yourself and like I said it's in the PDF guides ok so what I'm doing is I'm just finding options on exchange-traded products on this website okay now on this page what you'll see is a link here to basically product specifications and if I click that we'd be able to find which exercise style the option actually has or the options listed on this site actually have we don't actually need to click that to find this out because it says in the next paragraph that they're all american-style so that's the answer to our first question the option that we're looking at for the ESPY why because all of them here have the same american-style exercise is American style so the next question is what does does the underlying actually pay dividends so to find that out all you have to do is go down to the resources section and you can find dividend comm you click on that and you just search for the ticker that you're interested in so in this case it will be SP y SP Y enter that in and it will tell you the dividend situation okay so at the moment it says there's no upcoming dividend payouts so you don't know the discrete value of the next dividend and you don't have an ex dividend date okay but what you do have is a dividend yield and by referring back to the spreadsheet looking in the notes sections you can see there in this calculator we look at options with an american-style exercise feature and with an underlying that pays a dividend yield and that's also our first input that we can put in here so the dividend yield was 2% okay so you put that in that cell there the next thing that we can find out is the spot price of the underlying and we can actually find that out on exactly the same websites a dividend com it's at the top here the spot price is two 15.99 obviously there's loads of ways to find the spot price you can go on any website you want practically but it's there so 215 0.99 so you put that in the spot price cell next we'll find something called the risk-free rate okay this is a bit of a theoretical concept because arguably no interest rates are actually truly risk-free but a decent proxy for it is a short-term US Treasury so what I've got here in the resources section is a link to the US Treasury curve so you can just click that and then we can choose the latest value for a short-term Treasury say one month for three months it doesn't actually particularly matter between these and we can put that interest rate this is an annualized interest rate into the calculator so let's choose naught point naught nine so now basically we've just we just need to find an option that's that's all that's left and when we find an option we'll have the exercise price will have the expiry date of the option and we'll have the observed option price as well in the market so to find the relevant option or a relevant option we go back to the exchange which is the CBOE in this case we'll go down to s py and what you'll be presented with here is effectively an option a list of options commonly known as an option chain and this basically gives you a load of details on calls and puts on the asset that you're looking at with varying strikes and so on so in order to choose a relevant option the first thing that I recommend that you do is choose an expiry that roughly reflects your time horizon for investment ok so in this example I'm just going to look at November options so month or two away and I'm gonna list all options not just options near the money then click view chain and then again it comes up with a massive list from there so there's actually two expire e's here we've got the 4th of november and we've got the 18th i'm going to use the expiration that is the 18th of november so we've got a bunch of options you can enter you can use calls or puts in the calculator it doesn't matter it can it can cope with both and what we've basically got here is in the first column we've got we've got the strike which is the number after the K in these little codes so the smaller strike is 50 and this goes up remember the spot price is about 215 it goes up to 315 that's the higher strike here and then other things we were interested in are things like the last price and the open interest so we've chosen an expiry date the next thing we need to do to choose something an option that's relevant is pick one that's liquid okay open interest is effectively an indicator for liquidity it's how many contracts are open for that particular option and what you'll generally find is the options that have a strike closer to the spot price so they're called near near the money will have more liquidity okay so we're actually going to use an option that is essentially at the money almost or very near the money so and you can see these open interest values on the right hand side are much larger for for options that are near the money we're just going to use one of those so the reason why we want use a liquid option is basically because it makes the inputs a bit more reliable so I'm going to choose this option here so that's a 215 strike so now we have all the rest of our information we've got the strike price 215 we've got the expiry which was the 18th of November and we can use the last price here as our observed option price which is 5.29 okay so observed option price 5.29 expiry date was the 18th and the exercise price was 215 and what you'll find is once you've put in all those inputs the model price comes up with a value because it has enough inputs to actually calculate an option price okay so that's three point six four and what's going to happen if you remember back to the simplified version of the calculator this price the model price we want to converge to the observed price in the market by only changing the unknown which is the implied volatility once they converge to zero difference we have our annualized standard deviation okay again don't worry if you don't follow that exactly you'll get the PDF guide and there's lots of notes in here as well that you can have a look at so for example let's manually change the volatility from 10% to 12% and watch this sell here the option price at the model option price so increased it's gone up to four point three three it started converging to the observed option price now luckily you don't need to go through a manual process to actually do this you can use a tool in Excel called solver so hopefully it's installed on here okay isn't there this is a good example to go through so if you don't have solver installed you should be able to do this through options don't worry about this because it's in the PDF we'll just install silver so you can use this you can use this tool called silver and it all iteratively changed the volatility basically until those option prices match so we click on silver you'll find the parameters are already set up you don't need to worry about changing those but essentially all it's doing is setting an objective cell to zero to zero minimizing it the cell is the difference between the option prices by changing the volatility and all you do is you click solve came up with a solution press ok and you'll see that the volatility has changed a 14.8% and that is it that's our value of implied volatility it's an annualized standard deviation so you can actually hopefully now do this process yourself and you understand at least how it works you don't need to have a detailed understanding of options exactly to carry out this process all you need is to be able to run the process and interpret what the number means and we interpret what the number means in terms of the presentation the slides I went through at the beginning we could also compare this to the real life's volatility we calculated earlier so the annualized realized volatility over the last 5 years for the s py was 11% so at the moment the the implied volatility in the market is slightly higher and you can you can infer things from that as well in terms of maybe you could shorten your time horizon for investment potentially if you wanted to so you could look for opportunities on a shorter term time horizon you could also create smaller position limits since the volatility has gone up obviously this changes all the time so you don't want to be too reactive but it's certainly useful to keep an eye on so let's just have a quick recap of hopefully what you guys should be able to take away from today so the first thing was the going through the presentation ok it's basically what volatility is how you can use it okay so all the risk and rewards type processes that we that we looked at that's how you can use volatility we then to about standard deviation calculating that in a bit more detail so you actually understand and feel very comfortable using standard deviation as a measure of volatility then we looked at a practical application okay so we went through the processes of calculating realized and implied volatility which you should be able to do now as well yourselves and you can interpret those values in exactly the same way as we covered in the slides so that's all from me you will be able to get the spreadsheet at the end of today you'll be able to get the PDF don't worry if you haven't followed followed everything and make sure to have a look at those bonus bonus option examples as well you'll find some interesting strategies in there that you might like to have a look at but yeah that's all from me so thank you very much for listening [Applause]

Channel: InstituteofTrading

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Keywords: itpm, anton kreil, stocks, volatility, portfolio management, risk management, raj malhotra, options, trading, stock market, christopher quill, forex, money, investing, vix

Id: eqmTHLgZzqQ

Length: 40min 6sec (2406 seconds)

Published: Fri Sep 20 2019