 welcome and good morning to the second day of the ECB research conference and to the first session this morning entitled heterogeneity and press persistence in returns to wealth with a paper by Luigi Grisso and his co-authors. That title sounds pretty technical but actually if you look at the debates about income inequality, wealth distribution, intergenerational mobility, those are the topics that we've just very recently also seen in the being taken up in the German election where specifically questions were raised relating to aging population and the related tax distributions. We're very much looking forward to this. Luigi, your paper contributes to this wider debate by offering hard evidence. It's studying 20 years of population data retrieved from Norway's administrative tax records and we look forward to listening to your findings. But before you start let me just introduce the panelist. Luigi Grisso is a professor of Household Finance at the Inaudi Institute for Economics and Finance in Rome and fellow in the Center for Economic Policy Research. I won't go much further into this. You'll find the full CV in the conference brochure but what you won't find there is that Luigi was listed among the world's most influential scientific minds by Reuters both in 2014 and 2016. So I'm almost wondering what you were doing in 2015. But also what I wanted to do is really mention that back 10 years ago you helped design the ECB's Household Finance and Consumption Survey which is now well-designed, well-established and has been released for a second wave. So thank you very much for that as well. Chetil Storisleten will be the discussant of the paper and you are a professor of macroeconomics at the University of Oslo and member of the Northern Executive Board and Monetary Policy Committee. We look forward to your comments and on your what expertise and experience. But without further ado over to you Luigi. Very much. I think in 2015 I will be delisted. So that's my prediction. Don't pay too much attention to these citations indexes. Thanks for the introduction. So the paper I'm going to present is joint work with and David Malacrino and is about, you know, hinges on this debate about the sources of wealth inequality. You know, that's the trigger, the factors that can sort of contribute to provide an explanation for why assets are so much concentrated in a few ends. And the second feature is why we see relatively fast swings in assets concentration over time. Now this is a sort of popular feature from the US, from the United States and Zucca and is exactly documenting these two features of the wealth concentration. That is very highly concentrated. So, you know, the top 0.1% of the population, very few people, they control something like 20% of the wealth of a country. And the other feature is that, you know, at least in the US and according to these estimates, it has been climbing up and increasing almost doubling. The share has gone up by from 10% to 20% in a relatively short period of time. So, you know, the big questions in this debate are why we see so much concentration in asset ownership and what can potentially rationalize the fact that concentration can move within a relatively short period of time. More of these features are shown in papers, in other papers for France looking at, you know, very long periods of time by Tomas Piketty. Now, there has been a huge debate trying to rationalize the concentration in asset ownership. The problem is that, you know, the features that have been brought to the analysis in particular, you know, the idiosyncratic earnings across individuals, differences in saving rates across different segments of the population, heterogeneity in discount rates and persistent differences in ability to earn income, they don't seem to be able to rationalize the differences in asset concentration that we see. And essentially when they do is at the cost of some counterfactual assumption. So in order to, you know, to reproduce the amount of wealth inequality or wealth concentration that we see in the data, you need to make assumptions about the concentration of income that are off compared to the data. So for instance, in a calibration exercise by Kinder and Kruger, they show that they require the top 0.25% of the population to earn between 400 and 600 times the median. If you look at the data, the difference is big, but it's not as big as required is the order of 30 times. So 30 is big, but it's not as big as 500. Okay, so there's been a sort of swing in the literature trying to, you know, find the sources of heterogeneity that can potentially rationalize the thickness in the distribution of wealth. And the attention has been drifted from the labor market to the assets market. In particular, a couple of papers by Jesse Benabino and Alberto Bicin, you know, building on a long strain of statistical models. They show that if people differ persistently in returns on wealth, then you can reproduce the concentration in assets that you see in the data. They also require some persistence across generations. These individuals that are sons or daughters of fathers with above average returns in assets, they should also be, you know, able to earn higher returns. And another couple of papers, they show that if people, besides differing in persisting in their ability to generate returns out of assets, they also, you know, these returns are correlated with wealth, then you can explain fast transitions in the concentration of wealth. I think the big merit of the literature is, you know, is this change in focus from the labor market to the asset market, from heterogeneity of returns to human capital to heterogeneity in returns to capital. The question is, you know, what is the evidence that can support this shift? How much heterogeneity we see in returns? How much persistent heterogeneity we see in returns? Is that true that, you know, individuals differ systematically in their ability to generate returns? Do they correlate across generations? Are they correlated with wealth and so on and so forth? So all, do the ingredients that are required in order to reproduce the inequality that we see are actually born in the data. So what I'm going to do is to sort of try to back these literature and provide, you know, measurement, to look at the properties of individual returns on wealth. And what I'm going to do, I'm going to use, as Christine was mentioning, population data for Norway. Using population data from this specific country, not because, you know, Norway is particularly representative of the world. In some sense it is, but many others it's not. But just because they have the data and the reason why there is very little evidence of returns is precisely because we lack information. So that is the only source of data that can allow, you know, an exercise of the source. And what we find is that there is a lot of heterogeneity in returns. There is persistence across individuals. So, you know, people tend to differ systematically, persistently, in their ability to produce returns. They are correlated with wealth and there is also persistence across generation and actually intramarital, too, in the sense that people tend to sort based also on returns, on the ability to generate returns on wealth. So, this is what I'm going to show you. I will first, you know, discuss the data because that is an important input in the exercise. Then show some stylized facts on the heterogeneity returns and the correlation with wealth. And then provide some modeling in order to see how much persistence is in these returns. Discuss a little bit some implications for the debate on inequality and other debates that matter for each, you know, these heterogeneity returns may matter and then conclude. So, the Norwegian data, the data I'm going to use, they cover 20 years of data. They cover the whole population, including, you know, the most poor and the most wealthy guy in Norway. And the Norwegian data are beautiful because, you know, besides paying taxes are beautiful when it's a statistical point of view. If you are an asset holder, probably they are less appealing. So, because besides, you know, paying income taxes in Norway, you have to pay a tax on wealth. And so, the tax records include both, you know, incomes and stocks. And they have to report details on all asset holdings, distinguished by broad source. For most assets, they are reported at market price. One exception is private businesses. That there is no market, so they have to report a sort of tax-based valuation. But, you know, the way it is reported is not too far from what conceptually would be a sort of market value for the business. I have no time to go through the details, but essentially there is a play between, you know, the business owners that has an incentive to under-report and the tax authority that has an incentive for the business owner to properly report the value of the business. All the assets, apart from the valuation of private businesses, are reported by third parties. So, if you have an account at the bank, is the bank that is directly reporting to the tax authority. So, there is no scope, you know, for manipulation on the side of the tax payer and very limited scope for tax evasion. So, there are a number of, you know, nice properties of this data. The first one is that measurement error is by definition limited. It's still there because there are gaps between what, you know, the administrative records measure and what ideally you would like to capture. There is no attrition except from the fact that people die and sometimes they move away. All individuals belong to the data and this is an important feature when you are interested in the case as we are. The panel is long and that matters because you are interested in persistence. So, if you want to measure, you know, a fixed effect as we are, so you need a relatively long panel. The data allow for identification of different generations because you can trace sense to their parents. There is a family ID. You can see also records before people marry. So, you know, the data fit very well, the needs to characterize the properties of these return. There is one problem which I think is relatively important but we are sort of dealing with it that in this version of the paper I do not have housing wealth. I'm going to, we are working on it and the next version will also include housing wealth and mortgages. And the reason is that we had only incomplete data on housing. So, the exercise is about returns on assets excluding wealth. How do we compute returns? Essentially, we have information on interest, dividends and realized capital gains. So, we take some of the things and divide by the stock of wealth at the beginning of the period. Now, this measure is fine if there are no trades during the period. These are additions or sales of assets. To correct for that, what we do, we simply scale the income by the mean holdings of assets between the beginning and the end of the period. There are some issues, as I said, with the valuation of private businesses. There are alternatives to taking face value, the reported value, like, you know, imputing, using book-to-market ratios for listed companies. We don't do that and the reason is that it's very difficult to find a firm that is listed and that is very, very close, very similar to the one that you want to impute. So, what do we do? We take a more drastic approach and do the exercise, also dropping the private business owners. Capital gains, you know, usually we compute returns using capital gains on a cruel base rather than on realization. We do not observe it. So, for stocks, what do we do? We take the unrealized capital gains for the total economy and redistribute proportionate to stock holdings in the in the cross-section. That is one of the potential adjustments that we can again do. Okay, so this is a picture of the portfolio composition. So, the green line is sort of safe assets. As you can see, most of the population is heavily invested in safe assets. The share of risky assets is relatively contained. But as you move to the top of the wealth distribution, all you see is that individuals are heavily invested in risky assets, in particular in private businesses. That is the top of the wealth distribution, the very top. So, in the top one percent, in the top zero one percent, in the top zero point zero one percent, essentially there are the entrepreneurs. That is not particularly novel. It's a general feature of all countries, essentially. Maybe there is some, you know, in the kingdom, you can find the queen, the king, and so on. Now, this is the first fact. Returns are heterogeneous. So, if you look at, this is one particular year, 2013, look at the total sample. In the cross-section, the standard deviation of these returns on wealth is five percent. There is more heterogeneity when you look at risky assets older. So, the standard deviation on the cross-section, standard deviation is 24 percent. Now, this is not per se surprising in the sense that we know that, you know, if you invest more in equity, you're going to earn an equity premium, so your return on wealth will be higher. So, in a standard portfolio model, heterogeneity is all driven by differences in asset allocation, which in turn reflect the differences in risk tolerance across individuals. The problem is that this model, what we would predict is that if you look at, let's say, a regression of return on wealth on the share-investing risky assets, then controlling for that, there should be no difference because everyone is going to invest in the same, you know, well diversified market portfolio and faces the same return on the safe asset. Now, if you plot the standard deviation of the cross-sectional standard deviation of returns for each, you know, level of the share-risk assets, what you see is that there is heterogeneity always at all levels of the share-risk assets and more importantly, it is also increasing with the share. That is, the more people are invested in risky assets, the more heterogeneity they face in returns. Another way of seeing that is computing sharp ratios for the individuals and then looking at the distribution of these sharp ratios. One standard prediction of the standard Myrtle model is that sharp ratios should be the same across individuals. We see a lot of heterogeneity in the cross-section. The second fact is that returns tend to be correlated with wealth. They are strongly correlated wealth. So this, again, this is a particular cross-section, but the fact is true in all years, the degree of correlation varies from year to year. The same is true when you adjust for returns for risk and look at the sharp ratio. Sharp ratios are correlated with the wealth percentile. Now, we are interested in persistent heterogeneity. So there could be essentially two big reasons why people can differ persistently in returns to wealth. The first one is the one that I already mentioned, and that belongs to the classical portfolio theory. The fact that people differ in restorerance and so more restorer can reap higher equity premium, higher returns because they are more invested in stocks. Another possibility is that they differ in their capabilities. Like, for instance, they may be better at stock-picking, they may be better at timing the market, so trading. If you include pre-business owners, talent may matter and entrepreneurs may be good, they may be bad, and some are better than others. So recent literature has been emphasizing the importance of these second features, these second channels in explaining differences in returns on wealth. So in order to try to say something about this, what I do is to estimate a very simple panel-date model where the variable that we want to explain is the individual return on wealth and explain it with a bunch of observables and then residual. Observables are controls, for instance, for lack of wealth. You want to see whether, you know, size matters and whether having a lot of assets gives you some advantage in the investment market. Secondly, you want to control clearly for the portfolio composition, how much risk shares you have in your portfolio, how much private business wealth you have in your portfolio. Then you want to control for time effects, because returns may vary over the cycle. And finally, you want to control for features of the individual, like age. Age may matter because you learn how to do things over time to catch a life cycle effect. The unobservable component will decompose it into a fixed effect, a feature of the individual, and then a residual. Now, the residual I'm not going to talk about it. I'm interested in the fixed effect. What we document is that the residual, essentially, is purely white noise and there is no persistence in that. Okay? Now, these are some regressions. The first one, there are no fixed effects. It's simple or ordinary squares, but that's to get a sense of the correlation. So, what you see is that the risk share matters. So, people that are invested more in stocks, they earn higher returns on wealth. The more so if they have a high share in private equity. So, there is a private equity premium in these data. There is no puzzle. Private businesses, they earn higher monetary returns. Then there are a couple of demographics that seem to be correlated. So, boys seem to make somewhat lower returns, but the effect is super tiny. So, we can, you know, pin down the coefficient because we have millions of observations, but the effect is 2.8 basis points. Education matters and, you know, drives up returns, particularly if you have an economic and business type of training. And the effects are not trivial. So, ten years of education are correlated, you know, with, I think, is 34 basis points in returns on wealth. With an extra kick of 10 basis points, if you have an economics degree, which is good news for us. Now, look at overall, these controls can explain 8% of the variation in the data. Now, if you add the fixed effects to the regression, so it's the third column, the explanatory power goes up substantially. So, you can explain 23% of the variation in the data. So, this saying that, you know, there is an individual component that explains a substantial portion of the heterogeneity, even when you account for differences in asset allocation and so on, risk taking across individuals. And actually, this individual component seems to, in terms of explanatory power, to be predominant. Now, this is the distribution of the fixed effects. It's sort of interesting to look at the shape. So, it's skewed to the right. It's not normal. There is a lot of kurtosis. So, there seems to be that, you know, some individuals that persistently can earn very high returns on wealth. And then you can see easily how this can contribute, you know, to drifting in wealth accumulation and wealth inequality over time. We get the same features as this one, if you use, you know, different measures, robustness of various sorts and so on. So, that is a robust thing. The other thing that I want to do is to use the model in order to decompose the correlation between returns and wealth between, you know, the observables and the fixed effect. How much of this correlation is due to the observables and how much is due to this individual persistent component? Essentially, the bottom line is that overall, the observables cannot explain the positive correlation in between average returns on wealth and the level of wealth, which you can see is a sort of convex at the very top of the distribution. But there is one component of the observable, which is the risk share that matters, particularly at the top. So, at the very top, the risk share can explain two thirds of the correlation in between returns and wealth that you see, you know, above, let's say, the 85th percentile. So, it's saying that, you know, at the very top, compensation for risk-taking matters a lot in terms of, you know, explaining the correlation. All the rest of the correlation in the residual distribution is essentially explained by the fixed effect. At the very top, a third is explained by this permanent individual component. Okay? That is the kind of the composition. Now, let me tell you about intergenerational correlation. We can, since we have measured this individual component for all individuals, and we can trace back fathers and sons, we can look at intergenerational correlation. I want to contrast the intergenerational correlation in returns with the intergenerational correlation in assets. Now, this is the wealth of the father on the horizontal axis, and the wealth of the son on the vertical axis. Now, this is no novelty. It has been widely documented that the two are strongly correlated. What you see is that at the very top, the persistence is even much, much stronger. So, essentially, you know, the son of Bill Gates is going to be as almost as wealthy as Bill Gates. So, you will receive a lot of transfers from the father. If you look at the correlation in returns, there is correlation. The slope is much flatter. It's kind of, you know, the slope coefficient is 0.08. And most interesting is concave at the very top. There is a lot of mean reversion at the very top of the returns, which means that the son of Bill Gates, he will receive a lot of assets, but will not be as good as the father in terms of generating returns out of wealth. So, assets can be easily transmitted. Ability to generate returns much less so. And that is important in terms of, you know, intergenerational mobility. Yeah. Finally, can these features, can this number sort of explain the wealth concentration that we see in the data? We haven't done that exercise, essentially what you need to do is to take all these moments, all these features of, and properties of the returns, build a life cycle model, an overlap in generation model, stick in all these features, and then see what happens. Okay. That has been done by Ben-Abi Bezin and Lou in a calibration exercise for the US. Now, what we find is that, you know, in our data, we find that there is weak intergenerational correlation and there is a correlation between these returns and wealth, which can be characterized by this equation here with, you know, putting the return on the left-hand side and the wealth percentile on the right-hand side, the slope is 0.03, let's say. Now, the exercise by Ben-Abi Bezin, what they do, they calibrate the model and then estimate the properties of the return in such a way that they replicate the distribution, the concentration and the distribution of wealth in the US. What they find is that the mean return of 3.4 percent, which is close to our 3.2 percent, weak intergenerational correlation, like in our data, and then, you know, the correlation between the individual return and the wealth is, you know, the slope is 0.01, which is flatter than our, but it's in the ballpark. It's similar to what we get. Now, it's a different country, so you cannot extrapolate all that much. But this is saying that these features can generate, essentially. In a standard life cycle model, it can generate a very concentrated wealth distribution. And by the way, the wealth distribution in Norway, the concentration at the top is similar to the concentration in the US, despite all the redistribution in income and so on. There is, it is flat, there is no trend, but it doesn't seem in the order of magnitude. Now, a couple of, I have no time to discuss this stuff, but, you know, heterogeneity returns as a number of implications for other debates, some related to the wealth inequality debate, but others that are sort of somewhat different, like, for instance, it matters for the type of optimal taxation, whether you want to tax the returns or whether you want to tax the stock. Clearly, you know, if there is an individual component that is driven by ability, you want to tax the stock rather than the return. It matters for asset pricing. So there is a big debate in asset pricing that has been actually trying to, you know, explain equity premium, looking at heterogeneity in cross-sectional heterogeneity in rates of growth or consumption, reflecting uninsurable income shocks. Now, if you have heterogeneity in returns, also that matters for asset pricing is an extra, is an extra, is an extra kick. So can speak also to that, to that literature. So to conclude, I think we document that, you know, individuals differ systematically in their ability to produce returns from a given amount of assets. So there is persistence across individuals. There is also persistence across generations. And potentially, these heterogeneity that we are documenting can sort of provide a rational, provide an explanation for the concentration in assets. I think the, besides, you know, this feature, I think what I take from this literature is the importance of focusing on differences in ability across individuals in producing returns out of their savings and, you know, moving a little bit away from explaining the return on schooling in terms of return on, you know, labor earnings and looking at how, you know, people learn how to invest their money. In terms of explaining, you know, how much assets they can have at retirement, the two are probably of similar, of similar importance. Thank you very much, Luigi. It's good to discuss a paper where I'm actually a data point. So we're going to, so I have to say I really enjoyed reading this paper. I learned a lot. And I think I appreciate, certainly, this line of research. So the aim here is to measure individual specific rates of return. Later, I'll talk more about why, why they won't do that. But imagine you want to do that. Obviously, you have to think about whether that return is scalable or not. Also, something I'll get back to. So they use Norwegian Register data, which has data on the universe of people. And in terms of financial assets, they're reported by third parties. Except, of course, if you have those money brought. And they report annually, the data they use now are annual observations of the value of financial, market value of financial assets plus interest evidence and realized gains. Then they also use the assessed tax value of private loan firms. Something they don't use yet. But I think we'll improve the paper a lot once they get it. My understanding is that they're in the process of getting this data is to get, you get the data on the universe of transactions of listed financial assets. That's amazing, isn't it? But that they will be able to get. And also, to use the assessed housing values, which I think would be nice. All right. So they focus on financial assets, ignoring the biggest assets that people hold, namely homes and the associated mortgage. So they ignore that. So there are a number of, before we start looking at the results, it's important to think through the sources of mismatchments. So first, at the moment, they look, there could be changes in the portfolio holdings during the year. They only look at the portfolios on December 31st. They could be, they only measure realized gains. So if people systematically, for example, realize gains and don't realize losses, that is going to show up. That's going to affect the measurements. There is some, there are issues about how to evaluate private equity. And I think all these things can be, certainly the first three ones, changes in portfolio during the year, once they have this transaction data, they can do that. The measure realized gains, same Proviso. Also, since they look over a long period of time, perhaps the issue of realized gains is less of an issue. And then when it comes to private equity evaluation, that is, that obviously is an inherent problem, but that, that will always be hard. However, as it turns out, the main conclusions hold up to just throwing all of them out. So that's interesting. The last issue there, that they're ignoring residential housing and mortgage debt, I think that's, that's a much, that's an issue that has much more potential bearing on the results. I'll get back to that. Okay, so why, so closely held firms are systematically undervalued. Why? Well, because the value essentially is going to be the tax, the book value of, of the firm. And if there is systematic survival bias, the firms that survive have more goodwill. So therefore, they tend to be undervalued. And then you see those, that value only when the, when the, when the firm is sold. But it could well be that they look over a 20-year period, but it could well be that people hold private equity for 20 years. Okay, so the main findings, so with, with those measurements provisos in mind, the main findings are five. First, they find a large dispersion in the persistent rate of return on wealth. Second, they find that the wealth rich in terms of explaining, in terms of stuff that explain that rate of return, the main, the main systematic factor is wealth. So the wealth rich have persistently higher rates of return. The, the surprising of the standard covariates that we, we always, and whatever we do when you put education, it does a lot of stuff in, in labor economics. Not here. Since they, since they look at the whole population, everything is significant. But, but the effects are minor. When you look at the short ratios, however, the effects are very large. I'll get back to that when thinking about how to interpret these findings. Okay, they also find a lot of intergenerational persistence, which I think is very interesting. And they also find that there is no private equity in person, which is good, I think, for many reasons. Anyway, here is, here is a dispersion of the sharp ratios. So sharp ratio, let me remind you, is you look at the excess return of the, of the, of the, of this individual, minus the risk rate, and scale it by the volatility of that risk return. So it's, it's, it's the excess, it's a way of doing, a simple way of doing risk adjustments. I think they should do something else, but I'll get back to that. A simple risk adjustment. And the finding is an amazing dispersion in the sharp ratios. With, so, so, what could that be? Could be luck. Simply that there is just, people do crazy stuff. And, and therefore you get a big dispersion. So it would be nice to look at some time-serious evidence. I'm going to do that in a second. Could be skill. As a simple model, I think we have in mind is some entrepreneurial skill. It could be that you get a great idea in the shower, build Facebook. That's going to give you a huge return. It's not the scalable investment, by the way. If they, if Zuckerberg doubles the labor and capital in Facebook, that does not double the value of the company. But, but still, it could be, it could be, that would be an a version of skill. It could be investmentability. That you basically, these people, some people, which have higher alpha. That's, to some extent, scalable. Or it could be that some people just make more mistakes. Other people make less mistakes. Okay. Time series evidence. So let's write down the simplest possible model. Actually, I would write down a different model, but we'll get back to that. The simplest model, it just has the rate of return is equal to, the real-est rate of return is equal to some, some regression on observables, plus some an unobservable, individual specific unobservable thing. And then they model the unobservable stuff as a fixed-effects plus error term epsilon. Whether epsilon could in principle be, have some persistence. Let's look at, so, so the luck would be epsilon. That would not be so interesting. But imagine that there was a lot of dispersion in F, in a fixed-effect over, this is a over 20 year period. Here is the dispersion of that. And that's a huge dispersion. That's a huge dispersion. So these are percentage points on the X-axis. So, yeah, if we, so that's fact one, big dispersion in, in returns. Let's look at, let's try to break that down on some observables. Start with wealth. So what they do is that they split the population in 100 bins. And within each percentiles, in each percentile they look at the median return of the people in that percentile. And they find an amazing regularity. Basically the wealth rich, they have a higher average rate of return. So about more than two, the top percentile, or the 90th percentile has two percentage points, more than two percentage points, higher average rate of return annually than the 10th percentile. Let's break that down on safe assets and risky assets. It's about the same. Sorry, if you look at the right one is the safe assets. The difference in return is about the same. For risky, and for risky assets, the bottom half don't have many risky assets. So it cannot be calculated. The slope is basically, the slope is similar. So just think about this, just think about before we go on. Let's just think about the numbers. Look at that, look at the safe assets. Is it reasonable that the 90th percentile has two percentage points higher rate of return than the 10th percentile? Well remember, it's not the 10th percentile in net worth. Is it simple in financial assets? No, get back to me. I have some stocks and pension wealth, but that's not counted here. Then I have a house and I have a huge debt. So my investment in a house is about 200 percent of my net worth. So I have, I'm one of those at the bottom there I guess. When it comes to, when it comes to, because I don't have that much financial wealth, I have a checking account that that I use as a buffer and then I have a mortgage, which is like a, which is the standard mortgage in Norway as it's like a credit line. So I can move money in and out. So I do, I live an SS life. So that means I have a low return because the return is the return of that checking account. But my parents, they are in their upper, I don't know, 80, perhaps, 70, 80 in terms of financial assets. They have a lot of money in, they have a lot of money in safe assets, but they, when they're invested in, you know, these accounts where you're buying the money for, I don't know, five years or something like that. Those with an upward slope in yield curve, they're obviously going to get higher returns. So it's not that surprising, I think. So I think the magnitude there makes sense. And in the rate of return, return, yeah. Here's something that don't make sense. This is the sharp ratio. Now we've written a sharp ratio for the, for the 5% that. So the medium here has a sharp ratio of what? I'm eyeballing 0.35 or something like that. But, but this is the me across people. Obviously, that, that means that the vast majority of, of financial wealth is going to be, get the sharp ratio of, I don't know, 0.6 or something like that, on average, evaluated. But with the, with the sharp ratio on the Norwegian Stock Exchange is 0.25. In this period, that doesn't make any sense. So they've, so I, I don't know. I think that the, the empirical sharp ratio should be lower. So not that, not that the red is for people who loan the financial assets. So the simple portfolio management model in, in, in finance says, oh, you can, with, with efficient markets, you can get the sharp ratio. If CAPM is true, you can get the sharp ratio of the market. You just invest in the market portfolio. But you can also get less, is, but you cannot get more. You can operate inside of the frontier, but just to crazy stuff. So, so it's easy to explain why the poor have a low sharp ratio. But it's hard to explain why the rich have so much higher sharp, okay. Oops. Let me just say something about the regression results. Gender education, it all has really tiny effects on, on the ratio of three basis points per year education on average return. That's small. But what is, what is large is the effect on the sharp ratios. So that suggests, that suggests that in terms of the efficient market portfolio says, oh, you can, you can get higher sharp ratio on the market. You can, you can operate inside of the frontier. That seems consistent with this, that perhaps the higher educated work, the higher educated people, they operate on the frontier. But as people do crazy stuff by randomizing, you can get a low sharp ratio of your real inter-directional return. Here is the model they should run, which just, they should just do calculate the Jensen's Alpha, for example. Controlling for the exposure to the, to the to the market portfolio. And, and perhaps scale that with that alpha with the amount of the diversifiable risk since I'm in the last minute let me skip to the last point and say they focus on the ability of the to explain wealth and equality. So I think that's interesting from a positive point of view but from a normative point of view why do we care about the wealth and equality we care about could be if we care about we care about return at your native for like a misallocation point of view could be if if some people are really efficient but they don't have enough if you could allocate fund to the best investors and the best investors have investments that are scalable then we could improve output that's like the ultimate right-wing view of the world it's the best thing we can do is to let the rich keep their money unless of course that those returns them from from some kind of monopoly rents. Alternatively which is a view I think I believe a bit more in from a from a welfare point of view the the poor somehow miss out on high returns so so here they get a low sharp ratio perhaps because they do crazy stuff in that case the government could invest for them that's what pension systems one interpretation of the pension systems is about that so I think this paper is left I you think of it as a left-wing ultimately left-wing paper let me just say one last word about stabilization policies close to my heart so obviously what do we do with the monetary policy we want to the key thing one key challenge we believe in is if we if we move the interest rates that through the Euler equation say we can move consumption now that hinges on the idea that we can actually affect the rates of return that people have we do affect the rate return obviously to the to the mortgage to the extent that people have flexible interest rate mortgages but I think it will be useful to quantify exactly whose rate of return are factored by a multiple that's something you could do all right thank you thank you very much and we can now open the floor to questions let me start over here