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These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link.

Hi my name is patrick boyle welcome back to my youtube channel where we’re going to learn all about derivatives and quantitative finance if this is the first video you’re watching make sure that you click the subscribe button to see more content like this this video is the last one in a series on the topic of risk management i’ve put them all together in a

Playlist i’ve actually done two playlists one does risk management in general and the other one that is var so sort of a subset that just relates to var because a lot of people are interested in that as a standalone topic and so the link to those playlist is above by the end of this video you’ll understand some of the difficulties involved in risk managing a

Portfolio that contains derivatives or even just a portfolio that’s actively traded and you may be quite surprised by some of the things you learn ok so let’s get straight into it many of the ideas we’ve talked about up until now things like var for example are based around the idea of managing the risk in a static portfolio and by a static portfolio i mean a

Portfolio whose constituents do not change in the real world many investors are much more active than that but any activity or even planned activity so things like stop orders that are in the book can dramatically change the risk of a portfolio the first thing we’ll need to talk about unfortunately is distributions now most of the people watching this video are i

Imagined reasonably financially sophisticated in fact also a bit of an aside i’d love if you could tell me a bit about yourselves in the comment section below as it would be really useful to me to know what kind of people and what kind of backgrounds my audience have so tell me a bit about yourselves below but for now i’m just gonna assume that you guys are already

Aware that stock markets and most investment products are not loved normally distributed but let’s talk about how active trading affects the distribution that an investor actually will have in their portfolio many investors or investment educators like to encourage people to use stop-loss orders in order to risk manage their portfolios if you don’t know what a

Stop-loss order is click on the link above to watch my video on order times the argument given is usually that if you put a stop loss order in that’s let’s say five or ten percent away from where the market is right now that you’ll end up capping how much you can lose but still have unlimited upside essentially people argue that you’re chopping off the left tail

Of the distribution some will tell you that it’s irresponsible and foolish to trade without stop orders at first this may sound like it makes sense and a lot of investors imagine that a portfolio with a stop-loss order in the books will have a distribution like the one that you can see on the screen right now obviously that would be great if that was the case more

Sophisticated investors understand that an order that’s close to the market is actually more likely to be traded and that’s just because of the random movements in the market if it’s moving up and down just unrounded it’s a news or on you know it’s had a few good days as a few bad days that could actually trigger one of your stop orders and knock you out so when

People understand that they might then picture the distribution as looking like what you see on the screen right now which shows the most likely event as being stopped out but nonetheless you truncate or cut off the left part of the distribution and keep all of the upside but let’s think a little bit more about this let’s say that you put a stop loss in that’s 5%

Below where the market is right now it won’t necessarily work every time the market falls because sometimes a stock might gap down right and so even though your stop-loss was 5% below the market if the bad news was announced overnight for example the stuff might open down 20% and so you lose way more than the five percent that you thought you had limited your losses

Two examples of that would be things like september 11th where the stock market didn’t open and then it opened a few days later down quite a lot another more important issue is that you will be losing a lot of your winners so let’s think about this the idea that you’re just cutting off the losses is untrue because a lot of your biggest winners will say the ones

Went up to three four hundred percent maybe they first went down five ten or fifteen percent and then went up a lot right and so the problem is that it’s not just saving you from losses but it might be preventing some of your big winners from happening too so actually when you put a stop loss in the books the problem is that it’s just gonna entirely change your

Distribution of returns and not just change that one tail of it that you’re sort of probably hoping it will do so what you see up on the screen right now is the actual distribution that you get from having a stop loss order in the books and as you can see by far the most likely event is that you’re gonna get stopped out you are still getting some left tail risk

Way less than before obviously but you’re still getting some and you’ve equally lost an awful lot of your winners as you can see there and you have a distribution that let’s be really honest here it’s very very far from a log normal distribution so a lot of the other risk management ideas that are then gonna be overlaid on this portfolio will be entirely inappropriate

For it because they assume a lot normally distributed return series okay so now that we understand how a simple stop order can impact the distribution of returns in your portfolio you can probably see how any real trading activity in a portfolio is going to give you a portfolio that is far from being log normally distributed so that means almost anything if

You’re taking some wins off the table when the market moves up a little bit or if you’re adding on dips or just anything that you might do like that is gonna really change the distribution of returns in your portfolio i’m sure that once you understand that you can also imagine that a portfolio containing derivatives is also going to be far from being normally

Distributed and thus that a lot of the basic ideas of simple risk management are wholly inappropriate for portfolios that are actively traded or portfolios that contain derivatives many portfolios do contain derivatives such as futures options and swaps in the case of the derivative on an equity we know how to devar of the equity over a one day horizon at the 99

Percent confidence level we just need to find the volatility of its return and multiply its square root by the product of today’s stock price and the confidence factor but how can we find the var of the derivative on this stock one approach is to link the derivative to the underlying stock and use the standard var method to do this we use a pricing method such as

The black scholes model to calculate delta which gives us a way to translate the derivative portfolio into the stock portfolio delta tells us how the derivatives price changes when the stock price changes a small amount so using our estimate of the stock’s volatility we could calculate var as we did before by multiplying delta times the square root of the stocks

Volatility times the confidence factor an obvious drawback to this method is that it will only work when stock price changes are small for larger changes delta itself can change dramatically leading to inaccurate var estimates thus we need to account for how delta changes which is known as gamma and that of course complicates the overall analysis to deal with this

Complication risk managers often use monte carlo analysis if you don’t know what this is i’ve linked to my video on that topic using the volatility and covariance estimates for the derivatives underlying assets as well as a pricing tool risk managers can then look at the largest loss the derivative will sustain for 99 percent of the likely outcomes let’s suppose this

Loss is $100 then the var of the derivative over a one-day horizon at the 99% confidence level is $100 this monte carlo approach can be applied to other portfolios with short volatility payoff such as merger arbitrage and event-driven strategies as i mentioned early on in this risk management series there are whole books that have been written on topics that i’m

Covering in a few sentences but hopefully this videos helped you think a bit about how modern quantitative risk management works and about the problems faced by risk managers hopefully it’s opened a few eyes as to how much small changes in how a portfolio is managed can affect the distribution of returns and the risks faced by investors often things that seem like

Simple solutions like stop-loss orders require greater thought than you might at first realize it’s time now for you to hit the like and subscribe buttons all of this content comes from my book which is called trading and pricing financial derivatives and that is linked to below have a great day and tune in next week for another video on derivatives and quantitative finance bye you

Transcribed from video

How do you risk manage portfolios that contain financial derivatives? By Patrick Boyle