Total Fund Asset Allocation to Maximize Sharpe Ratio

Hi, friends. Welcome back to another episode of Peer Connections, the podcast series brought to you by the Global Peer Financing Association, also known as GPFA. These podcasts offer our GPFA members and global beneficial owner friends a forum for information sharing and discussion on topics most important to them. And we hope you, our listeners, appreciate the insights, best practices, and transparency offered from our members and industry friends about securities, finance, or related investment areas. Now, let's get into the episode. So thank you all and thank you GPFA for inviting us. Today, we're going to be talking about a recent paper that we published called Financial Anomalies in Asset Allocation, Risk Mitigation with Cross-Sectional Equity Strategies. This is one of the several academic research projects that we have worked on over the past one to two years with our co-authors. What we will do is I'll provide a brief introduction first, and then I'm going to pass it over to my co-authors. Marco will take us through some of the details. And finally, White One is going to wrap it up for us at the end. Before I start, I just want to mention that this piece of research reflects our academic interests and not necessarily an initiative by our employer. So what we did is we studied how financial anomalies, also known as equity-style factors, can complement a portfolio during periods of stress. They could be recession, portfolio drawdown, high inflation, and whatnot. And the reason we do this is that while many studies in the past have focused on style factors, they mostly focus on the individual characteristics. And there's a few studies that focus on how they complement the portfolio and specifically during periods of stress. And I'm just going to provide a few key findings first. So like many others, we find that several style factors provide counter-signical behavior. in addition to providing strong expected return, we find that those style factors not only improve the Sharpe ratio of a portfolio, but they actually can further reduce losses during periods of stress. And Marco is going to provide you with more details on that. But interestingly, I find this probably the most interesting one is that when you look at individual performance for individual factors, you find that the dispersion of their performance is much larger during periods of stress than during boom times. So what this means is this really suggests the importance of building a portfolio of factors when you do asset allocation, rather than relying on single or only a several implementation of a different factor. So with that, I'm going to pass it over to Mark to give you guys more details. Over to you, Marco. Okay, thanks, Jackie. Well, what I'm going to do is, Jackie mentioned it, I'm going to walk you through some of the most important results that we have in our study. And I want to start really with the motivation that led us to write this study. And as we know, all traditional portfolios experience periods of stress. For example, in the paper, we consider the traditional 60-40 portfolio of equities and bonds, a portfolio of equities, income and commodities, a risk-positive portfolio of stock and bonds, an all-equity portfolio, and we even tried other what we call traditional portfolios. and all these portfolios no matter how you diversify at the end of the day they're gonna have periods of large drawdowns that are periods of distress where they're going to have large losses avoiding such drawdowns is of course something that we all try for and it is greatly beneficial if we could avoid those losses now the problem with traditional risk mitigation tools such as the food options is that they create a trap in expected occurrence so there are many studies have found that at the end of the day these type of you know traditional risk mitigation tools like buying a food option at the end of the day the drug outweighs the benefits of buying the risk mitigation tool so now what we did is we essentially had a large data set of cross-sectional anomalies in the equity returns we have used it for other studies that we have and i want to be clear that when we say financial anomalies really we're only talking about financial anomalies in in the cross-section of equity and defense. So it's essentially long-short portfolios of equity. And we pretty much asked ourselves, well, can these anomalies actually help us mitigate risk? And as Jackie mentioned, in the summary, the answer is going to be yes. And I'm going to walk you through how we did it. So the first thing that we did is simple. We take these large data sets of anomalies and we categorize them into different buckets. We choose five different categories following some recent research. And we have momentum anomalies. Again, when we talk about momentum here, this is cross-sectional momentum. Buy the winners, sell the losers. We're not talking about time period momentum. We have intangible, the value, value versus growth, profitability investment. So we have these five categories. For each category, we have many anomalies in each category. And what we do is, okay, let's look at average return, the distribution of average return during expansionary periods and during recessionary periods. And there are a couple of interesting results. The first result that stands out right away is that the dispersion of the average returns across anomalies is actually gradated during recessions rather than expansions. In particular, we start the analysis by looking at NBER recessions, so the recessions as classified by the National Bureau of Economic Research in the US. But the same result would hold true when we classify a recession as like a period of large drawdown for any of the portfolios that I mentioned before. So it doesn't really matter how you classify a recession as long as it captures like a big drop in traditional portfolios. So what this means is that on average, there is more uncertainty about the outcome of these anomalies, financial anomalies, during a recessionary period, which might seem a bad thing. But actually, when we look at the results closely, what we see is that some of these anomalies take, for example, profitability, they perform considerably better on average using recessionary times. So the dispersion in average returns is larger, but the mean is also quite a bit higher. And there is also another interesting point, which is anomalies have on average positive returns or close to zero in most cases. Therefore, likely there's not going to be a drag on expected return, unlike buying other risk mitigation tools such as food options. So now we have two main points. The average return seems to be counter cyclical. It's higher during recession compared to expansions, but there is a bit of a higher disposition in recessionary times versus expansion. So what we do next, well, how can we exploit this counter-cyclical behavior of anomalies? And the solution is simple, actually. When we want to reduce the disposition but try to preserve the mean, the best way to do it is just to build a portfolio. And that's what we do. So for each category, we build a portfolio of anomalies. So instead of, you know, using one anomaly at a time, what we do is we build a portfolio of anomalies. And so we are going to end up with five portfolios for each category. There is a real advantage of building a portfolio of anomalies. From a theoretical point of view, when we build an anomaly, at the end of the day, we need to use some variables to build these long, short portfolios. And when we try to capture the profitability anomaly, so we want to invest in firms that have robust earnings, for example, well, there are many different variables that we can use to sort these firms. and in the literature, there are many studies that have done it in different ways. Which one is the correct way? Well, we don't know. There is some estimation error. Using the portfolio of anomalies where the profitability anomalies have been built using several methodologies, essentially by building the portfolio, we are able to minimize the idiosyncratic risk coming from the variables that have been chosen. And hopefully the portfolio would capture actually the real characteristic of profitability that we are trying to capture. So I use profitability as an example, but the same logic can be applied to the other four anomalies as well. And to quote Markovits, the famous quote from Markovits, diversification is the only pre-launch and we see it applied even for financial anomalies. So then what comes next? Well, now we have this five portfolio of anomalies. So far, I talked about recession. I also want to mention that when we did the study, we also thought about inflationary period. And we were working on these articles last year before the craziness inflation that we had in the last about 10 months. So this is a very topical today, because now what we can see in our study is there are some anomalies that really help during inflationary time. And one of those is the cross-sectional momentum that seems to perform really well during inflationary time. which is an added result to our paper. So I mentioned the counter cyclical behavior during recession. The cross-sectional momentum seems to help during inflationary times. I mentioned that we built five different portfolios so that we reduce the idiosyncratic risk. Now it's the time to say, okay, well, we have these five portfolios. How much do they help the various portfolios? And what we do is the following. Essentially, we have traditional portfolios. I'm going to use the 60-40 as an example. And then what we do is we add one anomaly, one portfolio of anomalies at a time. So for example, take the 60-40 portfolios, we standardize it to 10% volatility. Then we build a portfolio that is 60-40 plus profitability, where we use weights of 85% on the 60-40, 15% on the profitability factor. Here I'm talking about risk weights. And again, this combined portfolio, we standardize it to 10% volatility to make it compatible to the traditional 60-40. The results are quite interesting because take the 60-40 portfolio on its own. During, say, the stagflation period of the 1970s, it would have lost about 39%. When you pair it with, say, profitability, it would only lose 35%. So, you know, you do have, just by adding the profitability factor, you would have limited your losses during the 1970s inflation period by about 4%. If you use momentum, which is known to help during inflation, the losses would have been 34.6% instead of about 39%. So there is some help that comes by adding these anomalies to the portfolio. And then, of course, do they only help during periods of stress or do they also help on average. Essentially, the question that we wanted to also answer is like, look, they can have a counter-cyclical behavior, but can they also help unconditionally? And what I'm going to do is I'm going to let Zedwan speak about this. So I'll pass this over to Zedwan, who's going to continue on this topic. Thank you, Marco. And thanks to everyone. Good morning and good afternoon, whatever you are. I think just for the continuation of what Marco was talking about, before dragging you into the result, just want to summarize one thing that we seem to, this is a timely paper in our opinion and the reason is because we are dealing with drawdowns and it happens that we wrote it two years ago and we're thinking about what could have helped us and marco have mentioned a point he mentioned options he mentioned you can think of the credit default swap you can think of other mitigation strategies and there's an important point that we're really trying to emphasize in this paper is this is a limited study so only cross sections in equity market. And the cross-section only in the equity market can help you without having like a big drag on the returns. And Marco was mentioning one at a time, one at a time, one at a time. But generally what we do here is, in this slide at least, we're saying, okay, we don't know what other people portfolio are. Could be 60-40, could be a risk parity, could be other stuff, which I'm going to show you in the next slide. But largely we're thinking very simply, if we have added a smaller portion of our allocation to this long-short portfolios? Some people call it systematic, some people call it quantitative, but just imagine you have a department inside your team that actually can do long-short portfolio quantitative only in the equity market. Would that be helpful? And here we single out profitability and investment. And I see a question here that define what's profitability for Marlon, and it's probably a good time to even answer it. Profitability, we have, this is Marco mentioned in the beginning, there is around 75 strategies directly we implement. There are different ways to do profitability. In the appendix, we have around 13 different ways or 14 different ways, but think about it as usually some sort of a bit. I don't want to drag it too long, but it's something that shows that these firms on average are more profitable than others in terms of what they have in their balance sheet and income statement. And it's more fundamental analysis. We gave you exactly what they are. It's not one, but it's different ones for which we implemented so that we show that our result is robust to different ways of implementing profitability and this was a question just mentioned now by Alan but generally with this slide just so that I finish on time shows if we combine the 60-40 portfolio with anomalies like profitability and investment it will help you during recessions to give you a number a 60-40 in the entire unconditional portfolio will make a 5.4 percent returns. If you add profitability, it added around 1.3%, becomes 6.7%. Now, where that 6.7% really come from? As Marco was emphasizing, it come from helping you during bad times. So it's actually exactly what you need. Just think of today's, where to hide, where to invest. Everything's go down. There's a problem here, problem there. And then we think these types of strategies can help you during recession, but it's not a panacea. If profitability and investment help you during recessions, they may not be great during inflationary time. And that's why we say momentum can also be a good strategy to implement during inflationary time. It means really the outcome of this is you don't have to have one strategy that you're running. You have to have a bunch of strategies for which some help you during some different downfalls like recession, some help you during inflationary time, but on average, they provide a positive value for your portfolio. This is what we want to leave you thinking about is in your department, don't sleep on these systematic strategies in the equity market. They are liquid enough. They provide help during period of stress. And we define period of stress here as it be a recession and inflation of return. We go one step further in the next slide. In the next slide, we just ask ourselves, why not everybody have a 60-40 portfolio? Some people have a risk parity type portfolio. Some people have an equity portfolio plus fixed income plus commodities. Some people have an all equity portfolio, how would they even fare? And without getting to these violent plots, which explain in what they really mean, if you want to just take the takeaway, regardless what portfolio we consider, it seems that profitability and investment, especially profitability, and as Alan was asking in the chat, you can define it very different ways that has been in the literature. And you can actually see that at least from our result in sample for data from 1970s to today, it's not like we're singling out a period, that they provide an important help, both in sharp ratios and both in reducing the loss, which come actually from reducing the loss in bad times. It means the moral of the story is simple in this paper. We have developed a large set of anomalies. And if you can go to the next slide, really what we have really done, we just said, look, let's be serious about this. Let's develop them all. We look at the literature. There are hundreds and hundreds of them. We just single out the one that actually have robustness. We implemented them all to around 70-something strategies. We clustered them into five different categories, momentum strategies, profitability, investment, transaction, and other ones. And you can see the appendix have details of how do you construct them. And we have shown the exhibit counter-cyclical, meaning when things go bad, they seem to do good. And what is bad? We defined bad different ways. We defined bad with drawdowns. We defined it with NBR recession, inflationary time, a drawdown with those portfolios, and it seems to be a very robust result, that they improve our Sharpe ratio of the portfolio by reducing the losses in bad times. Paper is published. I would be happy if you guys read it, have a question, share with us. We're excited about this work. We started it around a year and a half ago, and I hope it's going to be helpful to your portfolio. Thank you. So we'll turn it over now to Stefano at State of Wisconsin Investment Board. Thank you. So let me start, before I even talk about the research that we've done at SWIB, let me just talk about three separate points. First is the use of leverage in achieving higher returns. Secondly, I want to address how pension plans manage their monies internally and how effective that may be. And then thirdly, I'll talk about, as an introduction, the value of defensive strategies that have already been highlighted by Marco and his co-authors. Let's talk first about leveraging. So as many of you may know, SWIB has for many years levered its policy portfolio. The concept is quite simple. Let's just say I'm sitting on a 60-40. I want more return. How can I get more return? Well, I can take more risk. Well, that's one way. Another way is I can say, well, let me reshuffle my portfolio. Let me reduce risk. Let me take a little less equity. But now I can use leverage. And if I use leverage, I can achieve a higher return with the same level of risk that I started from. So one strategy was get more return, get more risk. The other strategy is reshuffle the portfolio, lever up and get more return, but the same level of risk, right? And that's finance 101 in terms of conceptually what one can do in terms of what has to be done to implement that. That's a completely different story. And that's really a hard work. I have had the fortune of joining after all this hard work was done. So all I'm trying to do is build with my team a few little bells and whistles around this great concept. Now, let's talk a little bit more about how pension plans manage their funds internally. And I'm not saying that it's true of SWIB or any of the pension plans that are being represented here today, but it is commonly referenced as the delegated investment management style in the literature. Bill Sharpe referenced it years ago. And essentially, it says the following. I've got an equity manager that manages the... Let's just very overly simplify. I've got an equity manager that manages the equity book. I've got a fixed income manager that manages the fixed income book. Put them together, I get my portfolio. Now, let's think about what the equity manager will want to do and to do for the fixed income manager. The equity manager is benchmarked against, for the sake of argument, MSCI world. They will want to, of course, get some exposure to value because value in the long run will give them some extra return. The fixed income manager in the same fashion will want to take some credit exposure because that will get them a boost in return relative to their benchmark. Nothing wrong with that. Nothing wrong at all. But neither one of them will have an incentive to have defensive strategies. Why not? Well, let's just take the simplest one in the equity book. Take a thing like MinVol. MinVol's strategies have a beta of 0.65, 0.7. If you have a component of your strategy that has a low beta and the market it roars, you're going to underperform. So there is very little reason for you to buy low-risk portfolios. And by the way, the value and credit are highly correlated. So from a fund perspective, you have extra risk that you might want to diversify. So you've got too much risk from value and credit and too little defensive strategy. And that's just the nature of the structure. Nothing wrong with it. The structure is very effective in many different ways. From a management perspective, it's a charm, right? In terms of accountabilities. But from a risk angle perspective, there are some question marks. I've talked about, and Marco and his team have talked about defensive strategy. What is the value of defensive strategy? So let me give you a hypothetical example, right? And the hypothetical example is I have a global equity portfolio, and I'm going to put on top of that global equity portfolio, an overlay. So I'm sitting on a hundred bucks of equities, and I'm going to put on top of that something that is defensive. And I'll tell you what that something is very shortly. And I'm going to construct that something such that it has a return of zero. But because it's defensive, when the equity market takes, it gives me a positive return. And when the equity market roars, it gives me a negative return. Net-net, it has a return of zero. Formally speaking, it has a correlation of, call it, minus 0.6 with the global equity market. Now, if you're trying to accumulate wealth, and many of our clients are, what is the impact of adding this zero return asset or strategy? Over time, what that asset does is it reduces the volatility of the global equity exposure. By reducing that volatility, it gives us extra returns. It's called the diversification premium, formally speaking. More intuitively, the way I think about it is, with this new defensive strategy, what I'm doing is I'm protecting my capital. And if I'm protecting my capital, I can compound more into the future. Take a 30-year horizon. what is the difference in terminal wealth of a ma and pa that invested in these two strategies. A ma and pa start with $100, and 30 years later, they have about $1,000 if they're just in the global equity portfolio. If they're in the global equity portfolio plus this defensive strategy that has a return of zero, they have $1,300. What does that mean? It means that their annuity when they retire is 30% higher. Now, the diversification premium is small. It's not as big in terms of return. It's nowhere near the returns of hedge funds. So this is the so-called unglamorous strategy, but it has a significant impact on the well-being of retirees. 30% more of what you can eat when you retire is a significant number. And we should care about that number. We have been doing research actually for the last 10 years on this very issue. So let's get a bit more formal on this topic. What was that magical defensive strategy? That magical defensive strategy was actually what we call a factor premium. That factor premium tends to be called quality. Water factor premia, some people call them anomalies, whatever it may be, they are essentially strategies that have been well documented in the academic literature and that have risk and return properties that are slightly different from those of traditional assets like equities or bonds. Actually, they fall somewhere in between. They have a little less return than equities and a little more return than bonds for a volatility that sits somewhere in the middle. Unfortunately, the investment profession has used those factor premia or whatever you may call them, strategies, as return generators. They're called ARP strategies and have had their consequences for those who've invested in. But if you go back in the literature, if you go back to the grandfathers of factor investing, you will find subtle references that say, these factors are hedging tools. What do I mean by hedging tool? I have my core portfolio, and I'm going to put on top of it a bunch of factor premium. Excuse the informality of my language, but this is how I often think. I'm going to put a bunch of these factors and I'm going to change the risk and return pattern of my underlying portfolio. If I want more risk, I can take more risk. I'll buy those factor premium that give me lots of kickers. If I want less risk, I'll buy those factor premium that have less that will reduce my risk. So if I've told you that the defensive property is an interesting property that can benefit a ma and pa, you can now understand why we decided to do a research study, which has now been published in the Financial Analyst Journal. And there's a whole series of studies that support that work over time. But your main emphasis has been, can we use a defensive strategy? Can we create a defensive strategy that has benefits out of sample, in other words, as if you were predicting the effectiveness of the strategy through time for our pension plan participants. What we did was we used a data set that has been put together by a firm, AQR. It looks at equities, bonds, equities fixed income, currencies and commodities. It has a number of factor premia that are not as, in terms of detail, clearly not as detailed as the work that Marco and his colleagues have done, but that still are fairly representative of that universe of phenomena. And we find that there are some of these factor premia, as Marco and Dean have found, that are highly defensive or highly counter-cyclical and some that are highly pro-cyclical. So if you want lots of excitement, you can buy those. Go ahead and have fun. And what we do is we create a portfolio that has a long exposure to the stuff that is counter-cyclical, that's defensive. And then we sell the stuff that is pro-cyclical, the stuff that is going to give you lots of excitement. That's a way of reducing the excitement, so to speak. You sell it. So what do we find? And then we do this formally, analytically. We do this in a way that we go back through time. And by the way, this is a data set that goes from 1931 to present. So we actually run this strategy for about 90 years. And what do we find? The starting point is a 60-40. And the starting point of the 60-40 has a volatility of, let's see, 11.5%. If we apply this strategy, which again, the counter cyclical is longer defensive and is short, the cyclical, we're able to reduce the volatility to 10%. That's not with kind of cheating or anything like that. We kind of roll through time. We kind of say, we're sitting there in 1931 and we had some information, the information that was available to me in 1931, what portfolio would I have constructed? And then we roll through time just like that, all through the 90 years, right? Been a phenomenal piece of work. And we find, as I said, that out of sample, you could have actually implemented the strategy. So now you've reduced risk. Again, you are going to get the benefit of the diversification premium. Yes, that's great. But wait a minute, your board told you that they were willing to tolerate 11.5% of risk, and now you've reduced risk to 10%. And basically, actually, by reducing risk to 10%, you make some money, actually. It doesn't cost you anything. It actually makes you money. Not going to worry about the fact that it makes you money. Let's leave that alone. It makes you about 50 bits a year. but that's you know that's not bad either but let's just say it gives you a return of zero but you've reduced risk what are you going to do well you've got a risk budget the risk budget says 11 and a half and you've gone down to 10 you can fill it you can fill it in so many different ways and so we show in the paper what you could do in all the different ways the one way is i can increase by, I can lever up my policy portfolio. And I can lever it up by about as much as call it 20% and get back to my 11.5% that I started with. 20% of 60-40 returns over the last 90 years, that's a pretty good deal. Another way I could do this is I could say, well, I've got my equity manager that has a certain exposure to equities. I've got my fixed income manager that has a certain exposure to bonds and bond premia. Can I build a completion portfolio that is going to complement what these two managers have built around the 60-40? so you build that you slightly tweak that risk reducing portfolio and again you get some higher returns oh that's nice and finally you could say well if you really like hedge funds i got one and a half percent of my risk budget i can fill it up with some hedge funds and if they're returning some positive numbers hold the power in fact what we show is that basically you could get an extra boost of about, on average, about 2% from having reduced risk and then going back to where you started before. 2% is not a small number. It's certainly not as glamorous or Hollywood-y like as what our hedge fund managers do. And by the way, I was a hedge fund manager, so I'm not taking fun of them. I'm taking fun of myself in a way. Again, it's just to put this in perspective of the long run, 2% is a big number. Even the diversification premium of 25 to 50 pips is a big number, right? We just can't ignore it. And this is the start for us of a journey of thinking about, as I mentioned earlier on, what we did at SWIB was we changed the composition of the portfolio, the asset class composition of the portfolio. but you can just as effectively change the factor exposures of your policy portfolio to then potentially lever it up and get some extra returns but this is all work in progress it's just research but hopefully it's something that will have future curiosity thank you thank you stefano there was a question that came in while you were speaking that i will just pass along, and then I'll turn it over to the rest of the group if there's further questions, either for you, Stefano, or for the folks from Hoop. The question was that you mentioned the data set that goes back to the 1930s and that this effort reduces volatility by one to two percent. With recent developments of technology and accessibility to that technology and the embrace of factor investing by a large number of firms and individuals, has this impact decreased in recent years? And if so, would you have a sense of how much? We've done, I don't know, about five different variations of that study. And when I say five, there are two vendors of factor premium services that aggregate investment bank products, Moment Games, and we've gone to them and they cover something like each one, something like 4,500 strategies around the globe. We've gone to both. We've used their benchmarks for value, momentum, yada, yada, yada. And we've replicated the study and we actually get a bigger risk reduction than what is in the paper. And we have restricted ourselves to live investment strategies, right? So the research paper is based on paper portfolio strategies that have been published by AQR. These are live strategies. Now, the sample period is shorter, but it's the last, call it 10 years. And then we've gone to a number of investment managers who manufacture these products, and they have replicated our research with their data sets and have found it consistent in every direction. Orders of magnitude, what they're doing, stability, so on and so forth. And it's pretty excruciating analysis, but we found that it's gotten a lot of comfort. clearly, again, it's work in progress. There's lots and lots of issues with this. That's where we're at. Thank you, Stefano. Thanks for listening to another episode of Peer Connections by GPFA. We hope you found the information shared in this podcast interesting and beneficial. And as always, please feel free to reach out to GPFA with ideas or interests for future episodes. And if you liked what you heard today, don't forget to subscribe wherever you get your podcasts. Now for the Disclaimer. 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