Portfolio Optimization Across Risk, Returns, and Climate - MATLAB
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      Portfolio Optimization Across Risk, Returns, and Climate

      Bob Meindl, MathWorks

      Learn how to leverage portfolio optimization models in conjunction with climate data while balancing the demands of transparency, scalability, and model risk management. Climate data and optimization can impact the bottom line of organizations by tilting portfolios in a targeted way. Building advanced analytics and machine learning models on top of these factor repositories of climate data can improve business decisions. Some tasks that stand to gain the most from such improvements include risk mitigation, trading opportunity identification, customer goal-based investing, and forecasting risk across complex multibillion-dollar instrument portfolios. However, implementation at scale and with compliance is daunting to most financial institutions at all levels of Assets Under Management (AUM).

      Published: 31 Aug 2021

      Hi, this is Bob Meindl from The MathWorks and thank you for joining us for a really timely session on portfolio optimization across risk returns and climate. We will be starting in a few minutes. I just want to remind you to please ask questions in the Q&A. If we have time at the end, we will answer as many as we can. And if not, we'll be glad to follow up and with that, I'd like to turn it over to Riley LeFrancois.

      Thanks Bob, this is Riley LeFrancois. I'm a financial services account manager here at The MathWorks and thanks, everyone, for joining us. And, like Bob said, this is a very timely session, as you've been hearing a lot about climate risk in the news lately, so we'll have our lead financial engineer Marshall Alphonso presenting on that today. As Bob mentioned, please feel free to populate any questions in the Q&A and we'll do our best to get to those. If not we'll be happy to follow up with you afterwards and spend a bit more time on those. We will also be forwarding out the slide deck after 2:00, so you can have that for reference. Without any further delay though I'll hand things over to Marshall and we'll get started. Thank you.

      Thanks Riley, and thanks [AUDIO OUT]. Welcome everyone to a very interesting session. So from a logistics standpoint, we're going to be doing about an hour or so on the site and there's going to be a lot of material in this presentation. And so to kick things off I'm actually going to turn off my video and I'm going to keep going from here. Bob quick sound check. Can you guys hear me?

      You're good.

      Loud and clear.

      Excellent. All right. Welcome everyone to portfolio optimization across risk returns and climate. As everyone knows this is a very important topic that's hitting all our financial institutions today. And so on actually cap [AUDIO OUT] quote that you're seeing up here says-- if I translate that-- this basically talks about the future-- and I'm going to start with the translation here. This came out of the United Nations Special Report that basically says it's not merely important to foresee the future, but to actually bring it about. And you're going to see why this is relevant as we go through the talk.

      So let's start with the basic agenda. What is climate change and why should I care? Now what is climate change? I'm going to put it through-- I'm going to basically help you understand it through-- the lens of finance. So you might see some sort of climate change physiology. I'm kind of mixing in two different fields here. But the geophysics of what's going on in the world is going to be relevant to us understanding how we can infuse that data into our thinking.

      So the simplest definition-- and this is sort of like my summarization of the definition-- is that the change in the temperature of the Earth with significant financial ramifications. And how the financial ramifications actually come about can take different forms and you'll see that as well. So to start with, if you think about the world, and you think about our ozone layer and everything-- and this is not meant to tell you what the science is, I'm just stating what we understand. Solar energy comes in and bounces out of the atmosphere normally.

      If you have some molecules such as carbon dioxide nitric oxide, methane and other hydrofluorocarbons, then what ends up happening is the solar energy bounces around inside and heats up the Earth. This is a natural process within the Earth. But what ends up happening is, if you end up building up any of the core greenhouse gases, GHGs, carbon dioxide, [AUDIO OUT] methane et cetera, that's when you start seeing heating up. That's when you start seeing physical risks that are impacting a variety of things such as floods and forest fires and things like that in South America. And that's when you have to start thinking about the financial ramifications of this.

      So let's use this information to actually understand what this looks like through the lens of the central banks. Now there is a specific Bank Group called NGFS. NGFS is a membership organization which consists of 95 banks and 15 observers. So you can see here-- you're welcome to go through this page-- there's a lot of banks over here. And I've had the privilege to go out there and meet a lot of them in person, pre- COVID, and understand how they look at the world.

      Now let's take a look at the models that they've built. I've built a little application here and you'll notice it's actually sitting inside a web page. I built an application in MATLAB to help us look at the data. And we're going to start with a very simple question that a central bank may think about, and you may be thinking about, when it comes to how does climate change impact my portfolio? So the first question is, do different integrated assessment models, which are the models that the central banks are producing, are they all in agreement? Do they produce the same sort of results?

      And let's look specifically at a very popular macroeconomic measure when it comes to climate change, which is GDP, which is, sort of, the productivity of the world and other macroeconomic variables. And you can see there's different models out there. There's GCAM, IMAGE, and we'll come back to these models themselves and we'll touch on why, and how, to interpret these models. But for now, let's look at baseline scenario.

      So according to baseline scenario, off of forecasts of GDP over 100 years-- so you can see there's 100 years here-- so over 100 years, all the models seem to agree that there's an upward transition expected to happen in Europe. What about the United States? In the United States they're all more-- there's a lot more agreement on that.

      The European one, maybe, due to Brexit and the long term ramifications of that, maybe that's a bit too short term. But you could think about how Europe's going to evolve, Latin America, you can see [AUDIO OUT] occurring right here. But look at our reference policy, which is sort of a moderately regulated world, then you see that the GDP is still going up and there's a little bit of disagreement in terms of the model themselves USA and Europe, just to give you a feel for things. So with regards to GDP, there doesn't seem to be much difference whether using a baseline policy or a reference policy. And what happens if we go to a stringent policy and you can see there's not much of a change either.

      Where we start to see changes is in the area of forecasting greenhouse gases. And those could have physical ramifications too. For example, the Chicago Mercantile Exchange where you're dealing with futures contracts, where you're dealing with oil contracts on the exchange. So if you had a baseline policy a lot of the models are a little bit all over the place, especially for, let's take, carbon dioxide.

      You can see the models-- this REMIND model, right here, it says it goes up, but then it comes down. The actual amount of emissions of carbon dioxide goes down. Methane is a little bit all over the place. What happens if you switch over to a reference policy? You can start to see that all the models start to appear to go down. What about a stringent policy? They all indicate that over 100 years we're able to reduce our overall greenhouse gases. Now this is a very simple example, just to kind of give you a feel for some of the data that we're going to be working with as we start to think about the ramifications of climate change.

      So why should you care? I'm showcasing some data. I think you should care because climate change may not be directly impacting you today, but climate regulation is percolating through our economy. And that's a very important consideration when you start looking at how should you tilt your portfolios to basically account for the kind of regulation that might be coming your way.

      Let's take a step back. I was thinking about how do we frame the challenges around this problem? And one way of doing it is I've actually taken inspiration from SIFMA which is the Securities Industry and Financial Market Association. And you'll notice this is their roadmap that they put together. Where today-- I'm just highlighting a few things here-- what they're saying is we're in a stage of unclear taxonomies regarding climate data. Data is limited and not congruent, inconsistent standards, which makes it very challenging. If you're familiar with working with market data, we know that one of the biggest challenges we have in doing any kind of modeling is getting our data under control.

      And we're in a phase right now from 2021 to 2023 we're expecting there to be sector transition pathways, well-aligned definitions and taxonomies, and dataset standardization across companies. And so that's when we can start to take advantage of it. And I like to think of that next phase, after 2023, as the optimization phase. Data is now easily available, we have a variety of products, a lot of the industry is finalized in terms of their mergers and acquisitions, in terms of bringing on board the right partners for their organization, and they're really trying to optimize to compete as financial institutions.

      So what are the business questions that we're going to be dealing with here? The first one, we saw a little bit of, is the data itself. What climate models are relevant? A lot of these questions came about from discussions I've been having over the last few years with a variety of different financial institutions. What climate models are relevant to my portfolio? How do we translate the climate data into discount factors to discount risk in future cash flows? In the portfolio construction area, one of the questions that's very common is, how do I tilt my portfolios to account for climate risks? What are the right optimization algorithms? How will my portfolio evolve with climate policy?

      Stress testing is obviously a very important consideration. What are the right climate scenarios to look at? What's the right way to systematically think about shocks to our portfolio? And explainability in governance is always key to helping us get our models through production. What I'm going to focus on is just these three questions right here. What climate models are relevant to my portfolio? And how do we tilt our portfolio? The optimization problem. The climate data problem and optimization problem. And from the mathematics perspective the optimization problem is a very challenging problem. And the way I've seen a lot of people approach it is they're approaching it with brute force, but that's a very costly affair especially when you start scaling up into the cloud.

      So lets actually frame the problem, the mathematics of the optimization, problem for a second. So how do we think about tilting our portfolios, accounting for climate data? So when you start thinking about mandates, there's a lot of incentive structures built into our mandated benchmarks at the top level of our portfolios. So that I think of as fund level, asset level, mandates. There's portfolio level. So once you aggregate all the different portfolios together across the different onshore offshore accounts, the different currency accounts, you end up with attribution benchmarks that are relevant for incentivizing, through tracking error, the portfolios to move or tilt the portfolio a certain way. And then, finally, at a security level, you might think of concentration limits when you start to look at how things flow that way.

      Let's actually take a look at a demonstration here, just to understand what this could potentially look like. And what I've built is a little [AUDIO OUT] here that allows me to optimize my portfolio. So I'm going to open up a little application. And this is a [AUDIO OUT] optimization problem. Now this is meant to set the stage on how to start thinking about infusing in some of the climate data that we saw early on in our portfolios themselves. So what you see at the top over here is a whole series of bonds. These are bonds out of the Merrill Lynch high yield index. And so you can see there's a lot of these bonds available for me to choose from. There's zero weights on all of them. One of the strategies that is very common in the industry is a replication strategy. Whoops, I meant to open a slightly different one here. Let me open up the ESG one. The ESG flavored version of this.

      OK so this is actually running on my cloud right now. This is my Amazon Cloud Infrastructure so I have enough compute power up there to run this. So what we have here is all of the different ticker symbols, ALLY, et cetera. We have some sort of ESG scores associated with these different tickers, bank of America, et cetera. The question is, can I choose high yield bonds that basically replicate these different [AUDIO OUT] The yield to worst, spread to worst, and modified duration to worst. And in this case, I'm actually going to use a very simple-- I built this demo quite a few years ago actually-- but I'm going to give you a flavor for things by infusing in the ESG scores, without giving you all the details right now. We'll come back to how we actually use that.

      So what this did was it took the high yield bonds and actually allocated a certain percentage. 2.5% to ALLY bank, RBS, et cetera. And so you can see here, this is the portfolio that's been selected out of all my bond portfolios. And you can see that the portfolio itself is replicating the high yield index over here. With a yield to worst that matches up, a spread to worst that's matching up, and a modified duration to worst that's matching up. Now from a climate perspective, there's a variety of scenarios that you can use to stress test this portfolio, or the expected future cash flows, by discounting things such as interest rates, and looking at how the cash flows are impacted by that. And so you can see that the actual cash flows are being impacted by incorporating in some of the climate factors that are going to be relevant to us going into the future.

      One other thing you could do is then look at attribution. That's a very important thing at the mandate level, what's really driving these returns. And you can always look at the returns themselves and try to get a sense of what's going on, or look at the VaR numbers as well, so I put that into the portfolio. So I can see here there's a minus 3.8% loss. And you can start thinking about, how does my climate portfolio itself get impacted by the actual climate factors themselves?

      Now the business of optimization is quite complicated. One of the biggest challenges with optimization is the overfit to the paths over time. The explanation, how do you communicate with governance teams, is quite challenging. We work very closely with some of our Tier one partners, Tier one bank partners, to help them take their optimization models and climate and help them get that through governance. And what ends up happening is a lot of groups arbitrarily, for example, use fmincon or some sort of choice of optimizer. And what ends up happening, once you start scaling the problem, is a lot of wasted compute cycles. The other challenge with doing that is you don't end up with necessarily a global minimum. You end up with sort of a localized minimum, depending on your initial start point.

      Forecasting is impossible and long term predictions are extremely unrealistic. How do you start incorporating those in to your optimization problem? So one of the problems that we've dealt with over the last few years is with asset managers in which you have a variety of different portfolios and they want to optimize against the benchmark. So as opposed to the traditional benchmarking model which is like the Fama-French style model, maybe you can incorporate in some sort of ESG factors. And then you're trying to minimize the optimization problem against some sort of objective function such as, tracking error, Sharpe ratio, volatility, information ratio, et cetera subject to a variety of constraints. And this constraint landscape gets very complicated, very quickly. And you're going to get a glimpse into that today.

      So it's easy enough to get your model through governance. But one of the challenges I see is when you're starting to use it and retrain those models, that's when things get complicated. Because the governance team always ask the question, where are your parameters coming from? Did you really truly converge? How are you making sure you're not overfitting to history? How are you using climate data? Those are really challenging problems and those are the kinds of things that we're going to look at in terms of how we begin to approach this problem.

      All right. So let's take a step back now. We saw a few demos already but what I'd like to do is actually take a step back and look at the Climate Framework itself that's being put out there. And you see this percolating through a lot of our presentations that are coming from the industry, whether you're talking to consultancies or whether you're looking at internal groups. A lot of them use very similar structure.

      I think of it in two big buckets. There are physical risks and there are transition risks. The physical risks you can think of as you're going to the doctor and you have chronic pain. Stuff that sort of systematically are percolating through your body. Oh my back is hurting or something's hurting. You can think of the Earth in a similar way. You can think of chronic pain is like a sea levels are rising. But it's not a direct impact to our financial institutions. On the acute side, you can think of floods, hurricanes, direct impacts, as other risk factors that are harder to model, but the insurance industry has been doing it for years.

      Another big area are the transition and policy risks. How are governments going to react to regulating our industry? And so how do we start thinking about incorporating those risks into our portfolio construction costs? So one popular thing that's being done is we're taking a lot of this information. So we're doing a lot of taking a lot of the transition pathways, the integrated assessment models, which is what I showed you early on, infusing it into macro impact type models, along with the chronic climate problems and the acute. One of the areas that the central banks and a variety of other groups are struggling to infuse into-- the institutions are struggling to infuse into-- portfolios is this acute problem. What's happening in the short term is very hard. They're like black swan events. They're very hard to incorporate in. This is stuff that's a little easier to incorporate this is stuff that has a lot of assumptions and are also available for incorporation into our models.

      So to frame the portfolio optimization problem. Let's think about the question of how do we infuse this climate data to achieve our risk and return targets? And the talk that I started with was, what's the right way to optimize our portfolio, given risk returns and climate? And the way I found to help at least frame the problem is I like to think about it in two time frames. The right question is, am I tilting my portfolio in the short term or my tilting my portfolio in the longer term? And you need both. You need tactical asset allocation as well as strategic asset allocation that's happening at different levels. Whether it's macroeconomic type factor tilts or at an asset level factor tilt you need both of them. And that's pretty common with a lot of portfolio management today.

      So let's start with the transition pathways and I'm going to give you a flavor for the transition pathways themselves. We saw a little bit of the let me actually pull that up here, my climate change data model. So the NGFS climate data-- this is all of the different central banks. And we got a glimpse into two questions I asked originally, as to how integrated models do they agree with each other? How do they forecast? But there's a lot more data available to play with and I'm going to give you a little glimpse into that here. So what you see over here is the actual NGFS database.

      So there's a lot of data available for us to look at. And let's start by just looking at all the different models available. So this example right here, or in this database, I can see there is a WITCH, TIAM, REMIND, et cetera, a variety of models available for us to choose from. They're what are known as integrated assessment models. And it's important to understand that each of those models are infused with different types of scenarios, and there's a variety of different scenarios. But the ones I'm going to reference are these three right here. There's a baseline scenario, there's a reference policy scenario in which moderately regulated environment, and then a stringent regulated environment and how it's going to impact our different variables over the next 100 years.

      So in this case, let's look at one model right here. So this is AIM Enduse CH4, so methane gas. Methane is heavier, more dense, than carbon dioxide, CO2. And so this actually traps more greenhouse gas in-- more of the [AUDIO OUT] atmosphere raising our temperature more. We have less of this in the environment, but this is actually-- a large producer of methane gas is agricultural farming industry. So let's look at Asia and CH4 If I look at CH4 as you can see, according to this LIMITS-450 which is the 450 parts per million of carbon dioxide limitations according to the regulations is going to actually have a positive impact in the sense that we're going to reduce our CH4 over 2050. This is how much data is available over here.

      Let's look at a baseline policy. And if I look at the baseline policy, without any regulations, we can see that CH4 is going to actually increase over here. What about carbon dioxide? And so carbon dioxide is also doing something very, very similar according to this database right here. Let's take a look at the United States. And so you can see here, the United States is also increasing. And you can take a look at a variety of different scenarios. You can look at the reference policy scenario, and get a sense for how that's going to impact your actual climate change portfolios.

      So once you start getting familiar with baseline, the regulated environment, or stringently regulated environment and start to get a sense of what data you're dealing with, those really help us get a handle on the next problem that we're going to be dealing with, which is forecasting out key financial indicators such as GDP. So in this case, what happens with GDP? Let's take a look here under our reference policy, moderately regulated environment, it's still going to go up as expected. So that's good. So GDP is not going to go down. I think we as a society are probably going to adapt. But we're not sure how the physical transition risks are going to impact our overall ability to move forward.

      To give you a glimpse into the data that's feeding these models, let's think about what these integrated assessment models do, and how they're built. A lot of them are built in a very similar way. They are macroeconomic models that try to capture, for example, a variety of different dynamics. GDP, population, policies, and other assumptions, with traditional economic outcomes as expected. So for example if I looked at GDP. You can think of GDP as a function of the cost of doing business, the imports, the exports, all the traditional productivity metrics that you could expect. Now you can, if you look at population, let's take actually a specific model here. So there is a variety of models that couple together human and physical systems, Earth systems, to explore economic environmental policies.

      Let's look at one of the models which is WITCH. A model that integrates a unified framework bringing in the elements. I think this is the easiest one to explain. The WITCH model basically takes a very simplistic idea of population growth. If you can predict population growth-- if you go back in history, there was about two million people, went to 20 million, 200 million people, and then you're talking about billions of people and that sort of exists. It turns out they use that as part of the WITCH model to forecast out utilization of resources, and how we're draining the different resources that are critical to our energy production industries. The model then balances out as a dynamic equation, a set of dynamic equations, that are then solved to produce the actual forecast that we see today.

      Now let's actually see if we can use MATLAB to build our own versions of these models for GDP. So this is one of the first challenges that you have is taking the climate data, the transition risk data, and mapping it to actual financial impact data that you're going to be able to utilize as part of your portfolio. So this simple example right here, we're going to run a hypothetical stress testing tool. And this tool right now is built to take in a fixed income portfolio and stress it out.

      So let's start thinking about the mapping of the climate data to the actual-- our portfolios, themselves. And there's a variety of ways to do it. I'm going to show you the first way, which is using simple ways of discounting our future cash flows. These are all corporate bonds. And if you had to do a very simple stress test I could value and stress this portfolio after doing a fit. So I fit my corporate-- my yields-- right here with a Nelson Siegel type fit. I'm able to use a parallel shift over here, stress out my portfolio, there's about 10,000 bonds over here. And I revalue.

      So, just revalue, using the pricing functionality out of our financial instruments toolbox, I revalued my portfolio resulting in about $271,000, for the cost of this portfolio, had I bought one of all my instruments. With a shift in the yield curve, in a positive direction, my overall portfolio because of the maturity date right here would lose 6%. OK? So that's the baseline. We're starting with a very simple sort of parallel shift.

      But let's actually think about sort of a climate stress. And so let's think about stressing out this portfolio. And so when we start thinking about stressing out the portfolio-- What we see here is, when talk about a traditional stress, the yield at different points along the term structure might move by a little bit. Typically beta-adjusted by some sort of relationship that would be captured through something like a covariance structure. So in this case, for example, had I moved my five year yields a little bit, everything else readjusts. And you can ask the question, how would that impact this portfolio? Let me move that a little bit, that was a slight shift here, you'd have lost about 6.8%. Because there's about a 1% shift, very similar to what I had done before.

      What happens if I switch to a baseline climate stress scenario? And so you can see here, everything is adjusted. And in this case, given the regulated environment-- this is a very hotly debated topic-- I had a chance to, before speaking to you, had a chance to speak to some of the economists out of some of the hedge funds that we're dealing with and tried to get a sense on what their thinking is around interest rates. And that's a good question for you. How are the policy risks, in the short term, going to be balanced out by the physical transition risks, which we're seeing in the news today, and also the social media risk of the news articles going to impact the regulated interest rate environment? How is the government going to respond? Are they going to lower or raise interest rates to counterbalance the different economic forces that are going on?

      In this case, a simple baseline scenario, infusing in some of the climate data we saw earlier, results in a 2% loss in my portfolio. Had I chosen a moderately regulated environment, stressed out my portfolio, it turns out we actually had a gain. Obviously this portfolio is custom to what's actually within the walls of this portfolio. I could also look at a stringently regulated environment. And you can see here, the yields are going down and the losses are going to go up. Sorry, the gains are going to go up here. In this case, a positive gain on my portfolio.

      Now what's actually happening under the hood is important. And this is what I want to spend some time on here. When we start thinking about the mapping of financial impacts, it's important to think about the different ways of forecasting out these transition risks. Because now we're not looking at the past, we're looking in the future, and we're asking ourselves, how do we infuse future scenarios into our climate portfolios? And so, if I had invested $100 today, how is $100 going to be impacted by hurricanes that are hitting us, or sea levels rising, or temperatures basically affecting emerging markets in a certain way, then we need to break it out into forecasting and now-casting.

      And I'm actually stealing the word now cast from meteorology. Meteorology has this concept of short term forecasting something that we would look at in the short term. Forecasting on the other hand, is sort of a macro or long term forecast and the other group that stole the same meteorological term is the Federal Reserve. They actually have a now cast model that we built out in MATLAB as well. And you can look up the now cast code that's available in MATLAB and it's available online.

      Let's start with a long term forecast. And I'm going to take a little bit of a journey into the forecasting problem itself, to take account of a variety of the different macroeconomic variables and start to think about how do we forecast that as an input into our optimizer.

      Now this is a little bit of a very new, hot off the presses, a really new model that we've built. It's not even in MATLAB yet. So I'm going to give you a glimpse into it and I'm sure if there's any questions, please feel free to reach out to us and we're happy to have a deeper dive into the modeling itself and the forecasting itself. Now when we started this talk we started with a black box model. In the sense of, we're using prebuilt models that the central banks are producing. In this example, I'm actually using the MATLAB econometrics functionality out of the box. This is one of the great things about MATLAB, you have a lot of prebuilt functionality. In this case, I'm using the econometrics toolbox with all their prebuilt multivariant, vector autoregressive models, Markov switching models, that are really, really powerful when you start to do any kind of modeling.

      There are different ways to think about it, but let's start with looking at the data available to us. This is just US Treasury yield curve data between 1972 and December 2000. So in addition to it, I have three macroeconomic factors that are all going to be impacted by climate change. In this case, CU represents the manufacturing capacity utilization, FFR represents the federal funds rate, and the PI represents the price of inflation. And the question for us is, how will climate change impact our manufacturing capacity utilization? And talking to the economists they're like, oh that's a silly question. It's cyclical factor and I'm not expecting any kind of impact. And so what they do care about, though, is GDP.

      They definitely care about sort of the impact of climate change on GDP, which is a measure of our productivity at a corporate level, at a sector level, at a National level, at a global level. But for now, just to illustrate the concept right here I'm going to give you a sense of how to start thinking about these in the context of a climate stress scenario. And you can think of, if I did stress out these things, you can think of basically stressing this out by shifting it, a basic point up or down, once you have a prebuilt model or once you have a trained model.

      The first model I'm going to start with is an autoregressive model that kind of forecasts out what your yield curves are going to look like. Now the model I'm going to use here is a model, which basically forecasts out yield, decomposing yields, in terms of three components the level of the slope and the curvature of the model. Now notice there's a little t over here on each of those parameters. So there's a level, there's a slope, and this is curvature. So as opposed to assuming it's a one time estimation or regression process, with lambda as well, there's a lambda term in here, it is not just a one time estimation process. You can actually think of it as a function of time, so you're actually estimating, through an autoregressive process, how the level of the slope and the curvature are going to actually shift.

      Without getting into the details of the math, which we're happy to do with you, let's actually go and fix the vector autoregressive model here. And so you can see here we're doing it two separate ways. This is the first way, which is the blue line right here, which is the 2-step process essentially does a simple regression. It just basically loops through all the different slices of the yield curve to actually estimate what the level slope and curvature looks like. Let me actually expand this out here. What you can see here is the vector autoregressive process itself. Now what you see over here is a vector autoregressive estimates on the parameters. So you can see the betas themselves are about the same for both the models. It might be slightly off on this, or slightly different, and the State Space model versus the vector autoregressive model.

      Now the State Space model is a very powerful model though. The simple regression model is good for a starting point. The reason I personally like the State Space model is because you can now infuse the ability to forecast and predict the future. And so what we did then is we took the State Space model and we augmented that with macroeconomic factors. So the three factors that I mentioned, the manufacturing cross utilization. And you can see now that the vector autoregressive and State Space are the same. For the macro enhanced one, this is just showing you the three adjustments on the level, slope, and curvature, you end up with basically the ability to forecast out the future by infusing in macroeconomics into your model.

      Now how is this related to climate change? I have two models that we built in MATLAB. So the first thing I'm going to do is forecast out my yields. And according to the macro infused model if I Zoom into the end right here, you can see that the macro infused model appears to be going up. Let me zoom out again. It seems to be going up. And that's basically telling me that this is our expectations on the yields themselves. They're going to go up.

      Now when you start thinking about the mapping of the yields, with the climate data, you can expect that, when you slice and dice it, the yield forecasts are going to basically produce a variety of different sort of scenarios, beta adjusting their yields themselves. This is the yield curve. And the question is, how do you actually forecast those or stress test the yield curve? Well that's exactly what we did early on. With the climate stress scenarios you can take that yield curve as a stress scenario and then stress out your yield curve to produce what your expectations are on your portfolio itself. So this is a little bit of a glimpse into the forecasting piece of it.

      Now let's actually take a different stab here. I wanted to spend some time on this but I think I'm going to skip this example just in the interest of time. We do have the ability to forecast out. We have some very powerful functionality with deep learning. You can basically forecast out GDP infusing in the climate variables to be able to do the carbon pricing adjustments, the expectations on your interest rates, et cetera, that might be worth discussing. We also have an econometrics app that's very powerful. But let's actually take a look at sort of the second piece, which is a now casting piece.

      And in this case right here, another way to look at it is not just a discount curve for infusing in climate change, is we can think about ESG because it's very popular in the industry now in confusing and identifying ESG scores like I showed you in the beginning, can be used to tilt the portfolio one way or another. So in that example, let's actually pull that up here. On my simple, ESG example here, actually I'm going to pull it up in MATLAB.

      So this simple example right here it's actually giving you a glimpse into our optimizer. And I was trying to find a way to give you a way of understanding ESG scores. Now to help us, what I did, which you're going to find quite exciting, is in the ESG area there is an organization called Science Based Targets. And Science Based Targets is an organization that basically takes companies and looks at which companies are taking action to actually target a specific classification.

      So you can see here there's 169 pages of companies available for us. Some of them are committed to taking climate action. Some of them actually specified target classifications well below 2 degrees Celsius. And you can actually drill into the details here on view target. All I did was pull all the data in and constructed an ESG score, based on the actual climate policies themselves and the expectations, along with generating an ESG rating. So some of them are highly rated some of them are not as highly rated. So this is just a random portfolio of a handful of them randomly picked out from the bucket. So you can see here, if I click on Rand portfolio, it's actually going to randomly pick different portfolios. I could then click optimize. And what I'm going to do now is for those 340 different portfolios I'm going to optimize the frontier.

      Now it takes a few seconds to do this because this is actually a 340 by 340 covariance structure. But what you end up having here is the actual ESG rated efficient frontier. Sorry, not ESG rated. This actually does not account for any of the ESG rating, this is our baseline efficient frontier. Now what you could do is tilt the portfolio by starting off with a benchmark portfolio. So in this case, I'm going to actually generate a max Sharpe ratio portfolio along the frontier. And it's actually going to construct based on the ESG scores themselves. An ESG calculated portfolio with the Sharpe ratio portfolio as my benchmark. And you can see here how much of an emphasis there is on-- With the Sharpe ratio optimized portfolio, you can see that this is just straight up Sharpe ratio optimization, it's not accounting for the ESG scores at this stage. You can see that there's quite a bit of C and D in terms of our benchmark portfolio itself.

      If you click on optimize, what this is actually doing now is to tilt our portfolio. I'm going to give you a glimpse into the optimization, in a second, of what's going on behind the scenes. But what is actually doing is constructing portfolios by optimizing our portfolio against our target portfolio. Our target portfolio was saying, let's try to optimize the results by targeting a specific weight set that we actually end up having here. And so you can see here there's a sharp tip off as the ESG scores get to a certain point. The trade off between the tracking error, the deviation from the benchmark portfolio, has a significant upward propagation as very significantly deviating from our portfolio itself.

      In addition, when we start looking at the return trade off you can see there is a trade off right here. And this has to do with the diversification benefits that are actually occurring in the way we look at the ESG scores infused into our portfolio itself. You could look at a variety of different portfolios and start to look at the actual ratings themselves. So I could look at the rate-- whoops I didn't mean to click it again. But you could look at the portfolios themselves and get a sense of where do I want to operate my tilt to get a sense of what is the right portfolio blend for me.

      Now we've seen a lot of material in terms of modeling the portfolio and we got a little glimpse into the optimization platform itself. But I'd like to actually give you the power to do this yourself. And we have some great infrastructure that things that's been built and expanded on that really make it very easy to be able to do portfolio optimization. So when we start thinking about infusing in our weight on the portfolio themselves. There's several mathematical formulations out there that allow you to optimize your portfolio to meet your needs.

      But within MATLAB itself I want to show you a very powerful example that gives you a sense of how to build your own version of optimization. So this is a starting point right here. You define what is known as the objective function itself, it's a very simple objective function. But I'm going to give you a very powerful tool. So in this case, this is a three dimensional optimization problem with three components. x one minus Pi squared x2 minus exp of 1 squared x3 of 5.2 squared with the starting point of 0 0 0.

      What we have now is the ability to create a live task. So I can basically click on optimize choosing a live task to optimize. And now we have the ability to very easily optimize this portfolio to meet our needs. So all you have to do is specify this is going be a non-linear, let's choose an unconstrained, just to make things simple. You can choose from constraints, unconstrained. You can choose our-- Let's see here, I need to actually run-- put this in to-- to run this piece right here.

      So let's create the function itself. And we're going to actually choose our function handle that we just created and choose x0 as a starting point. I'm going to choose the current function. I'm going to display the iterations. And I'm going to choose maybe display the objective function. Let's run this piece code. And so what it's doing right now is actually running the optimizer with animated, but there's only three points because it actually converts fairly quickly to the optimal value of minus 5.2 Pi which is about 3 and 2.7, which is exp of one.

      So you have this very powerful capability with the live scripts and the live tasks to really jump start your optimization. But if you are really looking to think about the future and thinking about how would you do this yourself. We have done this in collaboration with other clients. So this [AUDIO OUT] but taken our existing infrastructure. [AUDIO OUT] All you do is create a portfolio object itself. [AUDIO OUT] and you have an object to start with set the solver and you're ready to go.

      But what we've done essentially is extended the object to allow for custom objective handles. Now this is done on a custom basis not it's not part of our core infrastructure but because of the fact that we work very closely with our Tier one banks we're able to do this for them. And what you end up with here is three separate optimization examples. Taking advantage of our newest infrastructure, which is our problem based infrastructure, which is very easy to use to end up with three different efficient frontiers.

      So when you start thinking about your optimization problem don't be limited to fmincon. Start to look at the problem based optimization setup which is very easy to use here to get your optimization workflows up and running. It's as easy as basically running and setting up the problem. Right from the documentation you can set up the variables for the problem. You can set up the objective function here. Whoops I just got off over here somewhere. Either way it's quite easy to set up this problem and actually run through this workflow itself. And you can actually just open up a live script and run through our example to be able to do this.

      All right. Our optimization capabilities are quite extensive. I think when I look at the way people implement things with the fmincon, and some of the basic optimizers, I feel like there's a lot more opportunity to really tilt your portfolios and end up with those global optimals that tilt your portfolio based on the climate factors that are being infused into your thinking. Another important example is in our documentation is a [AUDIO OUT], which I'm seeing a lot of papers out there coming out but it's a type infrastructure able to tilt the portfolios to really meet your needs. And so I would highly recommend that you take a look at that.

      Now where do you go from here? So I started at the beginning with the Securities Industry and Financial Markets example, or vision, that they had that basically said, we're in the phase of growing in which the data is a bit of a challenge. So if you have challenge with data. Let us help you. We have a lot of different expertise. All the way from the original roots of our company we have a lot of expertise in the geophysics area. I've had an opportunity to work in the geophysics area for a variety of different problems myself.

      And we've been using deep learning for those problems for over 20 years. So if you have problems with climate data, come to us. We are happy to help. In the optimization area you've had a glimpse into the optimization capabilities we have here. We have some very powerful capabilities that I feel are being underutilized by the industry, but we do have a significant amount of expertise in that area.

      In addition to that, what is The MathWorks doing? We're actually going out there and making a difference in trying to understand climate change ourselves. We're developing deep partnerships with organizations like MIT. So we're actually part of their group right now in terms of partnering with them to try and figure out what are the right climate models. And what we are doing on the finance team is trying to figure out what are the right climate models, and how do we infuse those into your climate change portfolios.

      So to finally end here. We've covered a lot of ground. We've seen a glimpse into the data. A glimpse into the climate models. And the amazing capabilities of being able to build fairly sophisticated forecasting models using State Space and common type approaches. You've got to see the ability of our functionalities to able to tilt your portfolios in exactly in the direction that may, may help your portfolios take advantage of these different climate effects. Even if you're not a believer in climate change or the climate models, regulation is percolating through the economy and we're here to help. So if you have questions, feel free to reach out. Let us know how we can help. I believe there's a lot of power functionality within MATLAB itself that's being underutilized. And we're doing a lot to really help you get your models all the way from inception all the way to production. And feel free to reach out and I will take a minute here and see if there's any questions that came in on the chat.

      Thanks very much Marshall. This is Riley again. While Marshall's checking out to see if there's any questions, I'm just going to put a little plug-in for our computational finance conference, which will be next month September 27th through the 30th. It'll be about four half day sessions focusing on everything from portfolio optimization to AI, data science, climate risk modeling, risk management, et cetera so keep an eye out for the invite for that and we hope to see you there. And I'll hand it back to Marshall if there are any questions.

      Perfect. Thank you. Looks like there's quite a few questions that have come in here. What I'll start with was one of the questions that came up and I'll end with this as well just because it's in the interest of time and we are happy to get back with you later. How do you come up with the ESG scores? That is the million dollar question. Everyone's looking around to try and figure out how do we come up with the ESG scores themselves.

      Some papers out there are indicating that you have to look at the structural dynamics of the company to be able to tilt their corporate abilities to meet their policy implementation. There was a recent Harvard Business Review that basically said a lot of the ESG scores shouldn't be trusted. So if you have questions specifically about construction of the ESG scores, the way I constructed it was basically a simple support vector machine kind of incorporating some of the financial stability data and tilt to produce the scores that we're seeing over here. So with that Thanks, everyone, for attending. I'm looking forward to answering your questions and helping with your climate questions that you may have going forward.

      Thanks very much Marshall. We will send out the slide deck and, like Marshall said, if there are questions or you have interest in taking a deeper dive, we're happy to do so. So we'll be in touch and thank you all for your time. Appreciate it. Have a great day.

      Thanks everyone.

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