WEBVTT
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Sorry you yeah I think you're muted.
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Yeah, we don't hear you. Okay, nice. Excellent. So, um, so for for the online participants. I was muted than they just said that today they're going to do an exercise in this session.
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So, some sorry you'll have to do, you know, a little bit of algebra and a little bit of work and just listening.
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Okay. So the plan is. We're going to do a very nice problem that is an economy with financial fictions. And the nice thing is there's going to be closed form solution so we will actually be able to, you know, do it together and get some satisfaction out
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of it. So I'm going to show you what the problem is.
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But if you have not listened to those, then I will review the, the key parts so that you can still follow along with the, with the exercise. So then I'll, I'll give you a little bit of time to actually read the problem.
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And then the problem will be divided into sub questions, and some of the questions will be, I'll give you a chance to think about it individually and it's going to be a multiple choice.
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And then there will be, I think, three parts where I'll put you into into groups and the online participants, you will be in the breakout rooms, and they'll give you a little bit of time to to work it out together so.
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So the basic idea is you know, I'll get you started with multiple choice. And then you know you can do those those spots on your own and I hope that the exercises in the just the right amount of difficulty for the amount of time that we have for this.
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Okay.
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So let me give you an adjust of the problem that we will be doing.
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Okay, great. So, um, so the problem is online, but these are the main components so this is going to be an economy where they're actually experts in house.
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So like the models that Marcus has talked about.
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And there's going to be a difference between experts in hospitals. So, both households and experts in in this model they will have the same predictive with you, Frank.
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So A is going to be equal to A underlying which which is going to make exercise manageable for us to do.
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So, whenever somebody manages capital, then they can invest, to build the capital capital depreciates at rates Delta. And there's going to be aggregate shocks, which are the same for for the whole economy.
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And there will be detail that they are idiosyncratic shocks.
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They are specific to the agent that's holding the cup.
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Okay.
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And
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you don't have to follow everything here because I'll give you a chance to Annette and the Princeton initiative program. This problem is actually written up so give you a chance to actually read it so don't worry if you don't follow every single detail.
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Um, so the difference between households and experts is that experts they are more efficient at managing this capital they either can diversify some of that you do some credit risk, or they face, let's do some practice.
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So for households. This is going to be the equation.
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And for experts that is going to be the equation.
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Okay.
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So, everybody is going to have a logarithmic utility.
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But with it with, there's going to be a twist that I'll tell you in the moment. So, the.
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There's going to be a discount rate row, and actually for expert there's going to be the expected this country because there's going to be some stochastic taste the Gothic this company.
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So this is the expected volatility of the household, they have logarithmic utility with this country through and experts, they have logarithmic utility but they have the state shocks okay so they take drugs, they have this drift.
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This is discounting, and they also have this this volatility so. So, because of this experts they have this preference for risk. Okay.
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And this is a way of building into the model, some interesting risk sharing between experts in households.
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So here the risk sharing between experts in households is not going to be guided by the skin in the game constraint there's, there is going to be. No.
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Well,
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the aggregate risk in this model is going to be fully tradable, meaning that,
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you know, if Marcus is an expert and, and I'm less productive, then we can write a contract, you know, on,
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on this aggregate risk, and there's going to be some, some price of risk in this market is going to be completely frictionless.
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But the constraints, however there's going to be a constraint on the sharing of b2c credit risk, which is, you know, very natural constraints that
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it is credit risk cannot be okay so however much capital an individual expert calls. Well, this idiosyncratic risk of of capital multiply by this parameter by that is going to be held by the x.
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So, this is, this is the setting, and we'll be want to understand the equilibrium in the setting so you want to understand
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as a function of a bigot socks. what are the dynamics.
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How much wealth will be in experts hands how much will be in households hands, how this this wealth.
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Sarah so the western US will change with shocks and also how capital will be reallocated between experts and also so we want to characterize this for the next.
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And in order to to do it so I'm going to review some of the key things that we should remember.
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So, um, when Marcus went through this sequence of steps to solve the model.
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There was very nice you know finance block, then there was this, you know law of motion of the state variable, the welfare of experts. Okay. Um, and, and so so what we will need to solve this model is we will need a little bit of asset pricing so this
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is the finance book.
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And on this slide the asset pricing, there is going to be the there is the price of risk. and there's also the.
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The Return of the, of the ass. Okay. And then we will also need the, the evolution of the bus distribution. And we will also need to talk about the allocation.
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So, I'm asset pricing, the main principle is that the stochastic discount factor, which is the discounted the marginal utility of a particular agent. And in this model, we're going to have experts and their marginal utility and we're also going to have
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a household, and there are more.
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So this the caustic discount factor has to price. Any acid, which is available for for this individual agents to invest in what does it mean pricing the asset.
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Well if we have a self financing trading strategy with value, a, um, it's the principle that a, times the discounted marginal utility, the gastric discount factor this is in March.
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And the condition that this is a Martin Gill, it's an optimization condition. Okay. So, if this is not a marketing deal that means that the agent is not optimizing so this is an optimization.
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If this is not the marketing gal than this individual can.
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So for example, if this is going up an expectation, then this individual should be consuming a little bit less than investing a little bit more wealth in the strategy and then this individual will be able to improve it.
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is Martin Gill from ethos formula is, is, is a condition like that. This is the drift of the product is the sum of the threats, plus the product of volatilities.
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Okay.
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Um, so, um, and, you know, in the online lectures, you know we can do this in different new Myers Okay, and there is a way to do it so.
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And then, if, if you have new Miranda why, then we can deflate the value of A by the numerator, and then he can take the SDF and multiply it by the new minor and then in this product.
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A is divided by yc is a multiplied by yn. And so this is this is the famous that and this is still a month. Okay. And this tells us you know we're just going to be the entity FM, and not anywhere.
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Okay. But, so okay so what does it mean a self financing trading strategy. Some of you may ask the question well so financing 2020 is basically you're receiving any dividends, you're reinvesting the divots and this is the return of this cottage.
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Now, if you had dividends, then this would also apply. Okay. In that case, we have to take this to be the sum of the capital gains rate, as well as the dividend yield so that the two together.
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And this formula tells us that
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the return and any expected return any asset.
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This is the negative of the risk free rate.
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And this is the negative of the the price of risk, so that they turn in any assets equals the risk free rate plus the risk of the asset, times the price.
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That's what it's okay. And for logarithmic utility. Well, we have that consumption is that proportion to wealth, which tells us that the volatility of consumption is equal to the volatility of books.
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Okay.
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And the personality but patience is that this.
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And for this specific problem you also have this you know fancier utility with Tay Sachs, and here the key is, what is the rate of discounting wrong. And then, also for this type of eternity consumption is going to be proportional to well.
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Okay.
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And so for algorithmic utility agent.
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We can
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we can use, not just consumption, but you can also use the wealth to to price, the assets, because of this relationship. And then, the price of risk is a minus.
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The, the volatility of marginal utility so if consumption to see marginal utility is one overseas or log is utility marginal utility is one oversee the derivative of the log in the volatility FC is sigma see than the volatility of one oversee is minus
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If the volatility FC is sigma see than the volatility of one oversee is minus sigma see so this is the volatility of Marshall eternity and minus the minus the volatility of Marco, is, is the price, which is, which is also equal to sigma.
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Right, so he has it, because the price of risk is minus the volatility of marginal utility.
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and the risk free rate is.
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minus the drift of the SDF, it's it's very easy to get confused about science so whenever you do the calculations, you know, always go to double check the science I always get the get the wrong thing.
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But but you know what the answer is supposed to be so that later on.
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What's the question you have a bush.
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on the negative sign. Okay, the negative sign in the diffusion coefficient that means when the aggregate Brownian motion goes up.
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So the whole economy expands and consumption, you know, possibly expense.
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If they're if this. If the volatility is negative, the net process in response is going down. Okay, so let's see so. So for example, when the economy expands and total consumption is, is going up.
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Then the marginal utility is one oversee the marginal utility is is going down so you enjoy and Marshall unit the presumption less in booms and you enjoy marginal utility consumption more.
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Right, right, yes yes yes they're there, they're invested in this so that's why there is a. So the question was about the minus sign here. And
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when the foot for the type for the types of risks that you consume more when, when there is a positive shock. It means that your marginal utility goes down when there's positive song so they're, they're inversely related.
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great question.
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Um, so Okay, so now the excess return over the recipe rate and the risk they're very much cheese. Okay. and then if we talk about the.
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How did this wealth distribution is evolving, or if you talk about the allocation of assets than, then those are going to make. Okay. So if we talk about the evolution of wealth distribution, then
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it's convenient to write the law of motion of wealth as the risk free rate. Plus, the risk.
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multiplied by by the Brownian motion and plus the bright servers in here. Okay.
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So, and minus the consumption rate and I think I should have put dt. So, they need to hear, which I forgot what.
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And this equation tells us that.
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Well, the more risk a particular class of agents is taking the more risk premium they're going to her. Okay.
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And then this is going to have implications, or
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for the law of motion of wealth shares. So, if we are inserted, for example, in the wealth of experts, divided by total wealth, then
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we can,
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we can take this equation and look at it in the numerator of total wealth in the economy.
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Or we can use it as formula for ratio. So this is the wealth of experts, and then be divided by the law of motion of the total wealth in which we can also write it right in the same way, and get the law of motion of the welfare.
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So, the point of this slide is that we can express the law of motion of any wealth process as a function of the risk free rate and the price of risk and the amount of risk taking.
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And then if you use the same principle for every type of agent that there is an economy, then from that. It's very straightforward and very convenient to get the locomotion of wealth FX.
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Okay.
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Yeah, that's that's an excellent question so we can think about this.
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So, the question is how it is, is going to to enter into this equation. So we can think about this as a vector of a brownie and socks. Okay.
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Okay. So, and then this is also going to be event, so that the individual is going to be exposed to several different shocks and then the particular model that that we are going to do there is going to be any Jason Quranic shock for each individual agent and
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and also, you know, aggregates.
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And then we have to deal with z as a vector and we have to deal with the price risk is effective so each component is going to be a price of a particular Brownian shock, and this is this is how we generalize this.
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Um, so Okay, and then another thing that we have to solve for is so okay so this economy is going to be hit by shocks and the wealth distribution is going to change.
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And as a function of the wealth distribution right now, there's going to be at every single moment of time some type of an allergy.
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So something else which we also have to determine is this allocation.
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And so here's something which is a very convenient way for thinking about allocation to think about the price taking plan. So it's a planner, who is going to allocate every single asset to the agent who gets the highest risk adjusted return from this.
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Okay, so this is an economy with financial friction, so different agents could have different prices.
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And in this particular economy, because the aggregate risk can be traded, everybody is going to have the same price of a good rest, but they're going to have different price of idiosyncratic.
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And now, well, who is going to hold this capital. Well, whoever gets the highest risk adjusted return that an expected return that this particular agent can earn, given his or her productivity risk adjusted meaning that minus the you know the price of
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risk of this particular agent. Well, you know that particular agent is going to hold the cup.
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And if you have an interior solution so how schools, because some of the capital and experts the whole the rest of the rest of the capital means that the marginal unit of capital which could be held by equally, a household, or an expert.
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It has to
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earn an equal risk adjusted return when held by household.
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So, so these are the principles that, that we will have to use. So, from asset pricing the fact that they as df prices assets. So the SPF explains the excess return have any assets over the risk the acid.
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The fact that the SDF can be connected with the risk taking, of individual agents will have to use that into account.
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Okay, and then we'll have to use this principle to to write down the how wealth of individual agents evil, and you'll have to use this to
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also determine the allocation.
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Okay.
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Now, um, Any, any questions.
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Okay.
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Now, here's the problem that that you're going to do.
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And
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there are seven questions.
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One and two are multiple choice if you're going to do all together.
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And then three is, you know, a little bit of algebra and output you into into groups to do those in groups, sorry, one and so multiple choice, three is in groups, then four and five and multiple choice sixes in groups, and then seven is the most ambitious
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one is, is, is, is also.
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Okay.
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So at this point, let me give you a chance to to do two things. The first of all go to the Princeton initiative online program, and download the, the problem and you can spend, you know, like seven minutes to read it on your own.
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And then so, is we are going to
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do the multiple choice questions through online zoom poll. Okay, so we have the zoom link, you know, go, go to zoom on your phone and and log in and, you know, no video you know have have yourself muted because otherwise get in and get some
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feedback and.
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And then, and then for the polls you know I'll ask you to make a choice. A B C D or E.
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So, let me give you like five minutes to prepare.
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And then you will get started.
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If it tries to make you do
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it three times.
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You have trouble logging in.
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Sure.
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Thanks 19 2021. Yes, yes.
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Okay.
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Okay, there's, make sure you mute.
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the polling right
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yep yep so you can you can mute yourself, you don't have to, you know, you can turn the camera off, just, you know, when it when asked what are the poll so that, you know, so that they can see the aggregate numbers from from people you know for here and
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people who are, you know, are far away.
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Okay so Shall we get started. Okay.
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So,
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let me
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think. So if somebody is not muted then we might be might get feedback. feedback to make sure that you're all muted.
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You still have some feedback but no it's not as Mark knows better Okay, great.
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So, so in this in this
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setting, what is the friction.
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So the fiction is
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the sharing, etc and kind of correct. Right.
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Okay that's that's the friction that there's no friction with respect to aggregate risk but there is friction with respect to idiosyncratic risk.
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Okay, So aggregate risk, you know, can be can be traded. And because of that, that's what determines the allocation of aggregate.
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So just the two words.
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It's the words
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the shocks right, it's the expert states drugs, they're going to determine the delegation of aggregators.
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And what determines the allocation of cup.
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Also towards
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anything characters, right.
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So, so I'm not going to you know cold call your or put you on the spot but they just wanted to ask this question so everybody is is on the same page. Okay, so let's go through these questions, one by one, and let's talk about,
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Click here.
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Hand here but it's nothing with
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okay yeah so that's a great question how because that's going to be.
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Yes, now I'm able for some reason I'm able to do.
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We have magical powers.
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The equation and secondly.
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I can change the size okay so how the shocks. So, so here's a slide about, about the taste. So, can blog utility consumption is proportional to wealth, even, even when they're these drugs consumption is proportional to wealth.
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And that means that we can price assets from consumption volatility, or we can price assets, equivalency from wealth volatility of both the experts and of the sign Okay, we can we can price assets.
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Yeah. Be careful.
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We can price assets from consumption volatility or from a wonderful today popsicles.
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Okay.
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And what about experts Well, our consumption is proportional to wealth. But if you look at the utility. Okay. And they'd be looking at the, the marginal utility so the marginal utility.
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If you talk about the marginal utility. Okay, the dense rocks, they will enter the marshal details. Okay. And because of this, we have the price assets, through, through this right so the volatility of this is going to be what we know, the volatility
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the ratio is the difference in volatility so you can figure out what this is consumption is proportional to wealth. And from that, we can get the price of risk for for experts that is going to be adjusted appropriately, by the volatility that takes.
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So, so that's going to be the difference that the for for the households is just the volatility of wealth, but for the experts is adjusted for
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for that they socks.
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Okay, so.
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So that's what we have to do and this is, this is actually the first question, which is given. So the first question suppose that we take the price of risk is given.
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And this is, if you take on a good risk you earn a risk premium. And how much do you earn, it's given by by this, this variable.
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Okay. So given this, how much risk will household, choose to take on so this, this should be a question, you should be able to answer if somebody wakes you up at three o'clock in the morning.
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And the second question is, is a little bit trickier. What about for experts What is this, What is it, how much risk.
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Will the experts, choose to take on, given that they have the state's drugs and given. Also, the risk.
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Okay.
00:37:17.000 --> 00:37:29.000
Okay. And there are five possible answers and I believe that this is this is anonymous. This, I got you know I believe this should be this should be set up anonymously.
00:37:29.000 --> 00:37:31.000
So let's, let's do a poll.
00:37:31.000 --> 00:37:35.000
I'm going to launch the poll.
00:37:35.000 --> 00:37:39.000
Okay.
00:37:39.000 --> 00:37:44.000
And that's real life not launching.
00:37:44.000 --> 00:37:46.000
There's an empty window.
00:37:46.000 --> 00:38:07.000
Whole.
00:38:07.000 --> 00:38:31.000
And then she window.
00:38:31.000 --> 00:39:01.000
This is what's coming up.
00:39:03.000 --> 00:39:33.000
Well.
00:39:40.000 --> 00:39:50.000
was working before me Is it possible, restart the last one we just like,
00:39:50.000 --> 00:39:57.000
Okay.
00:39:57.000 --> 00:40:27.000
this is the video. Yeah.
00:40:33.000 --> 00:40:43.000
without ending anything, you know, if you see close it should check.
00:40:43.000 --> 00:40:51.000
I mean I'm also hard tonight.
00:40:51.000 --> 00:40:56.000
Because it possibly also.
00:40:56.000 --> 00:41:07.000
Maybe
00:41:07.000 --> 00:41:14.000
it's possible that you know if you do the fall or the pole.
00:41:14.000 --> 00:41:18.000
Yeah Now everything is super, super.
00:41:18.000 --> 00:41:28.000
God doesn't work.
00:41:28.000 --> 00:41:51.000
Okay.
00:41:51.000 --> 00:42:18.000
I tried to look for my laptop tomorrow.
00:42:18.000 --> 00:42:32.000
Yeah. Now for some reason I don't
00:42:32.000 --> 00:42:35.000
kingdom.
00:42:35.000 --> 00:43:05.000
Yeah.
00:43:07.000 --> 00:43:19.000
Oh yeah.
00:43:19.000 --> 00:43:21.000
What is this factor.
00:43:21.000 --> 00:43:24.000
So the
00:43:24.000 --> 00:43:34.000
drift,
00:43:34.000 --> 00:43:59.000
or the poor, the poor has started. Okay.
00:43:59.000 --> 00:44:10.000
And this is this is being projected to be projected ok so the.
00:44:10.000 --> 00:44:15.000
Okay.
00:44:15.000 --> 00:44:36.000
Yes, that's what the choices are.
00:44:36.000 --> 00:44:39.000
I'm
00:44:39.000 --> 00:44:48.000
standing you
00:44:48.000 --> 00:45:05.000
know i think that would be, this would be a good right.
00:45:05.000 --> 00:45:10.000
14 people so far have responded here
00:45:10.000 --> 00:45:15.000
much time do we have to answer.
00:45:15.000 --> 00:45:18.000
How much time do we have to answer.
00:45:18.000 --> 00:45:20.000
Justin around.
00:45:20.000 --> 00:45:45.000
Well, I'm gonna wait until like 80% participation. If so, maybe one more one more minute.
00:45:45.000 --> 00:45:48.000
25 people come answered.
00:45:48.000 --> 00:45:59.000
So, this is anonymous so make make a wild guess, you know this is this is like one of those tests that, you know, you could still get full credit.
00:45:59.000 --> 00:46:01.000
Keep
00:46:01.000 --> 00:46:09.000
going on as long as long as you know you think about that, like a good educated that choice.
00:46:09.000 --> 00:46:11.000
Okay.
00:46:11.000 --> 00:46:14.000
31 people have answered.
00:46:14.000 --> 00:46:16.000
Okay.
00:46:16.000 --> 00:46:21.000
All right. So,
00:46:21.000 --> 00:46:25.000
So let me end the poll and.
00:46:25.000 --> 00:46:31.000
Okay, going one last chance, going twice.
00:46:31.000 --> 00:46:42.000
Okay, and sold okay okay and again now 46 people have entered so let me share the results.
00:46:42.000 --> 00:46:49.000
Okay. And so, so you can see the results and your devices. Right. Okay.
00:46:49.000 --> 00:47:05.000
So, I have to say that, you know, you are, you know, good educated guesses so let's actually work it out to figure out you know what the what the true answer is, I believe in C or D balancer let's figure figure it out.
00:47:05.000 --> 00:47:07.000
Okay, so.
00:47:07.000 --> 00:47:11.000
So this question is, um,
00:47:11.000 --> 00:47:16.000
I was wondering by why you know I cannot think clearly.
00:47:16.000 --> 00:47:22.000
Okay so, um, so this is a question about the sharing of aggregate threats. Right.
00:47:22.000 --> 00:47:36.000
And they get aggregate the risk is going to be shared based on the, on the faith songs. So, however much capital people hold so you'll see you know Kappa the experts capital capital set.
00:47:36.000 --> 00:47:41.000
So that should not affect the.
00:47:41.000 --> 00:47:46.000
How much aggregates people hold in this model because they can get through it can be traded.
00:47:46.000 --> 00:47:53.000
And so, and so therefore, the,
00:47:53.000 --> 00:48:09.000
the correct answer should be it should be theology and, and for households, well, how much risk, they will choose to take on. Well, I, the volatility of wealth has to be equal to the price of breeze.
00:48:09.000 --> 00:48:13.000
That's the rule for for like breath in the kitchen.
00:48:13.000 --> 00:48:29.000
And now let's see how this for for experts, so for for experts. Here is what we saw. So this is the emotional needs, and therefore the volatility of marginal utility is sigma theta minus sigma.
00:48:29.000 --> 00:48:36.000
See, right, and sigma C is also equal to sigma.
00:48:36.000 --> 00:48:48.000
And this is mindless This is the price of. So this is minus boxing. Okay, so, so therefore, this is equal to minus.
00:48:48.000 --> 00:49:07.000
So, therefore, we are trying to figure out how much race. The experts will choose to take on right so we are trying to figure out that sigma and so we take sigma, and to one side, and we get sigma n equals two sigma theta plus birthing.
00:49:07.000 --> 00:49:11.000
So, the experts, they have a taste for this risk.
00:49:11.000 --> 00:49:33.000
And in addition, there is a there is the bicycle. So this is how much they choose to take on, and therefore the correct answer here is C. Right. So those of you who have big C, which is a nearly half of you, this is the this is the correct tense.
00:49:33.000 --> 00:49:35.000
Okay.
00:49:35.000 --> 00:49:41.000
So hopefully this will work more smoothly now so let's see.
00:49:41.000 --> 00:49:47.000
Okay, so this is a guest this is a guest explanation here and the flight also.
00:49:47.000 --> 00:49:57.000
So now the question to is, you have a question right
00:49:57.000 --> 00:50:12.000
so that's that's that's that's a really good question right. Okay, so, um, so any, let's take a look at what a says so this is the share of capital and experts for this is their wealth.
00:50:12.000 --> 00:50:14.000
Right.
00:50:14.000 --> 00:50:20.000
And it'd be had to, and this is the risk of.
00:50:20.000 --> 00:50:24.000
Okay. Yes.
00:50:24.000 --> 00:50:27.000
Right, so right here right.
00:50:27.000 --> 00:50:41.000
Um, and so if we had that skin in the game constraint. And, however, capital experts held this determines their.
00:50:41.000 --> 00:50:48.000
The aggregate risk that they would hold. In that case, This will be the correct answer for how much risk.
00:50:48.000 --> 00:50:53.000
Okay. and this will be the correct answer how much risk the hospitals.
00:50:53.000 --> 00:50:55.000
So this would be correct.
00:50:55.000 --> 00:50:58.000
If,
00:50:58.000 --> 00:51:12.000
if there is a friction and the sharing of aggregate risk there is an extreme friction, and assuming that however here. People can write site contracts to say aggregate separately so it doesn't have to be connected to the amount of capital that they hold.
00:51:12.000 --> 00:51:30.000
And so because of that reason, you know, this is, this is not this is not right so it's good that you asked this question because, because a would be the correct answer in a different model, right, and b is, is also,
00:51:30.000 --> 00:51:41.000
but also be a correct answer if sigma Q is equal to zero. And in fact, in this model because it is equal to a lower bar.
00:51:41.000 --> 00:51:51.000
You can, you know you can already figured out that few is going to be constant. And because Q is going to be consonant sigma Q is going to be equal to zero.
00:51:51.000 --> 00:52:06.000
And therefore, you know, a and b, you know, would be would be equally correct right. So, so it would be correct under a different set of assumptions, but under our assumptions, I see is the is the right.
00:52:06.000 --> 00:52:13.000
So, so that's about the sharing of aggregate.
00:52:13.000 --> 00:52:25.000
Now let's talk about the idiosyncratic risk, so it is you can Aquarius will determine how much capital is held by entrepreneurs.
00:52:25.000 --> 00:52:38.000
So, the question is given, copper, what are the prices of etc characteristic of entrepreneurs, and households this should be underlined.
00:52:38.000 --> 00:52:49.000
And um, and full house was this is that is underlined. And remember that
00:52:49.000 --> 00:52:57.000
the price of EDC pedicurist is the idiosyncratic volatility of wealth for a lot of utility.
00:52:57.000 --> 00:53:12.000
And remember that it is increase the stigma Tilda for expert for hospitals, and this five times sigma to the full house, so for for experts, it's, it's, multiplied by coefficient fine.
00:53:12.000 --> 00:53:15.000
Okay, so let's do this.
00:53:15.000 --> 00:53:24.000
This question to and let me launch the poll and think about, about this question.
00:53:24.000 --> 00:53:36.000
So.
00:53:36.000 --> 00:53:42.000
okay, so the ball has started and once they have.
00:53:42.000 --> 00:53:49.000
Once most of you have answered.
00:53:49.000 --> 00:54:12.000
I'm sharing the wrong screen again.
00:54:12.000 --> 00:54:21.000
Okay.
00:54:21.000 --> 00:54:36.000
Still,
00:54:36.000 --> 00:54:57.000
and now the question where's my poor.
00:54:57.000 --> 00:55:02.000
Oh, maybe if I click on ok ok
00:55:02.000 --> 00:55:08.000
ok no.
00:55:08.000 --> 00:55:11.000
Okay, let me give
00:55:11.000 --> 00:55:13.000
10 more seconds.
00:55:13.000 --> 00:55:24.000
Because I think most of you have already answered.
00:55:24.000 --> 00:55:28.000
Going once,
00:55:28.000 --> 00:55:32.000
going twice last chance.
00:55:32.000 --> 00:55:37.000
And let me end the poll, and share the results. Okay.
00:55:37.000 --> 00:55:40.000
And
00:55:40.000 --> 00:55:53.000
I was told that, that some of you could see the right answer and zoom I'm not sure events by you, you have all answered correctly, you know, hopefully you have figured it out, but you know the correct answers.
00:55:53.000 --> 00:56:01.000
But anyways, let me discuss, you know why the correct answer is B because what's important is, is actually that, right.
00:56:01.000 --> 00:56:04.000
So,
00:56:04.000 --> 00:56:14.000
so the price of a decent product risk for low utility is this radical risk exposure
00:56:14.000 --> 00:56:17.000
of experts and.
00:56:17.000 --> 00:56:32.000
Okay. And what is the it is radical risk exposure so depends on how much capital default, it depends on the net worth so this ratio for experts Kappa over ew should be expected right.
00:56:32.000 --> 00:56:37.000
And it has to be multiplied by idiosyncratic risk per unit cost, right.
00:56:37.000 --> 00:56:55.000
Right. So, so it's not bad, because because experts, they have a coefficient, by any this guy Chris. So this is this is correct for experts in four households, it should be one minus cup of wine man is either and to have the fight to be because of that
00:56:55.000 --> 00:56:56.000
is the right. Right.
00:56:56.000 --> 00:57:06.000
Okay, and now this is going to be important for us, for determining the allocation of capital, which is the next question. Okay.
00:57:06.000 --> 00:57:15.000
Because Because think about the allocation of capital so what's going to happen is
00:57:15.000 --> 00:57:20.000
the capital earns the same.
00:57:20.000 --> 00:57:29.000
The same expected return for both experts and for house. Right, but has different etc.
00:57:29.000 --> 00:57:42.000
So it has to be the case that if you take the different categories of capital that experts again, when they called it, and if you take the it is compared to the Socratic risk of capital when households hold it.
00:57:42.000 --> 00:57:52.000
And if you multiply by the price of risk for experts and by the price of risk for hospitals, the nose has to be the same for Marshall unit.
00:57:52.000 --> 00:58:05.000
So that's the equation that you have to set up in order to determine the cup so let me, let me stop sharing and show you the next question that you're going to do.
00:58:05.000 --> 00:58:16.000
Okay. So, question three is going to be a question that you know I will ask you to talk to,
00:58:16.000 --> 00:58:34.000
to your partner or you know if there are five of you sitting, you know, for example in. In, then you know you can have a group of two and three. So, you know, work it out, talk to each other and the question is to determine copper as a function of either
00:58:34.000 --> 00:58:38.000
a quote, and there's going to be a closed form solution for the allocation of capital.
00:58:38.000 --> 00:58:39.000
Right.
00:58:39.000 --> 00:58:47.000
So what I'm going to do next is I'm going to give you. Let's say think five minutes to to work this out.
00:58:47.000 --> 00:58:57.000
And for the island participants I have set up breakout rooms, I'm going to put you into breakout. Okay.
00:58:57.000 --> 00:59:07.000
So, let me see breakout rooms. Hopefully there to set up breakout rooms.
00:59:07.000 --> 00:59:15.000
I have my.
00:59:15.000 --> 00:59:21.000
Okay, so let's, let's do this I'm going to create three breakout rooms.
00:59:21.000 --> 00:59:30.000
And if you're here you don't join the breakout room and. And for those of you who are online. You can join the breakout room and work with each other.
00:59:30.000 --> 01:00:00.000
Okay.
01:00:29.000 --> 01:00:34.000
We'll be
01:00:34.000 --> 01:00:42.000
right
01:00:42.000 --> 01:01:12.000
back.
01:03:46.000 --> 01:03:57.000
So let me just ask by show of hands I'm not gonna call bull Don't worry if you have gotten the answer you think that you're close to getting the end.
01:03:57.000 --> 01:03:59.000
give you a bit more time.
01:03:59.000 --> 01:04:02.000
Okay.
01:04:02.000 --> 01:04:32.000
So I'm going to walk around in case you want me to take a look at something, you have any questions.
01:09:51.000 --> 01:10:07.000
Okay so, so maybe let's, let's talk about it so was anybody able to get the final expression that you're willing to share Yes,
01:10:07.000 --> 01:10:12.000
minimum
01:10:12.000 --> 01:10:19.000
minimum.
01:10:19.000 --> 01:10:36.000
Oh I see, I see so you got you actually got two regions right you got you got two regions I see, I'm right right right right right you you would get two regions under, under slightly different assumptions right so so this is this is actually this is actually
01:10:36.000 --> 01:10:43.000
what what you would get but I think under this specific assumptions. I think it's, it's one one region right.
01:10:43.000 --> 01:10:46.000
But let me.
01:10:46.000 --> 01:10:50.000
Anybody got one region.
01:10:50.000 --> 01:10:52.000
Yes.
01:10:52.000 --> 01:11:07.000
Okay.
01:11:07.000 --> 01:11:14.000
is this is this correct.
01:11:14.000 --> 01:11:20.000
Oh, equal to the entire divided by either plus one minus eight to 10 spies quick.
01:11:20.000 --> 01:11:36.000
Okay. Right, right, right. Okay, so Okay so, so this is the correct answer so let me, let me explain. Thank you and, and also and also thank you yeah this is this is this is closed or
01:11:36.000 --> 01:11:40.000
not that now Okay, okay, right.
01:11:40.000 --> 01:11:48.000
So, so let's, let's talk about it. So, um, so I guess I can do two ways I can do it in this way and they can sort of like do it through through short.
01:11:48.000 --> 01:11:54.000
Right. So doing it through as far as to say that, okay.
01:11:54.000 --> 01:12:05.000
You know, this is what you're maximizing right by the expected return is the same for experts in households because. is equal to a lower bar so it was different from a lower budget and you would have to take this into account separately.
01:12:05.000 --> 01:12:16.000
Okay, so it's about the cost and the cost of risk of the marshal the unit of capital for experts in the four households has to be the same.
01:12:16.000 --> 01:12:27.000
So sorry you. Sorry, I think, can you somehow cold the people from the breakout rooms because I think those online, have not returned.
01:12:27.000 --> 01:12:57.000
Okay, okay. Right.
01:13:25.000 --> 01:13:36.000
I don't see the meeting controls again I'm sorry.
01:13:36.000 --> 01:13:52.000
The controls the, keep switching windows with the controls.
01:13:52.000 --> 01:14:18.000
know I'm saying right.
01:14:18.000 --> 01:14:32.000
You can close this window right.
01:14:32.000 --> 01:14:36.000
Okay.
01:14:36.000 --> 01:15:06.000
Is there a way to think it through here.
01:15:30.000 --> 01:15:36.000
Because
01:15:36.000 --> 01:15:58.000
we can pull the video again.
01:15:58.000 --> 01:16:07.000
Just pull it out and leave it out.
01:16:07.000 --> 01:16:30.000
Sit back to you.
01:16:30.000 --> 01:17:00.000
sharing.
01:17:11.000 --> 01:17:26.000
Okay, so let me start from the beginning. So what I said is, let me answer this question and I can do it in two ways I can do it in a, in a fast way, or I can do it, you know in a in the full arc way so to do it in a fast way.
01:17:26.000 --> 01:17:30.000
And of course, you probably want to hear the pathway first is.
01:17:30.000 --> 01:17:41.000
Notice that the return doesn't depend on who is holding the capital only the cost of risk, depends on who is called the capital and the risk is typically is.
01:17:41.000 --> 01:17:49.000
And they believe that this is the risk of my children per household and Phi Sigma to the four experts.
01:17:49.000 --> 01:17:54.000
And for letting me be a bicycle Matilda.
01:17:54.000 --> 01:18:11.000
Yeah. And then the price of risk is a. That was the answer to question two. Okay, so here. You said correctly that the answer is correct. So the price of risk for households in one one minus.
01:18:11.000 --> 01:18:27.000
divided by one minus e cig Matilda, and the price of risk for for experts is copper divided by either times by sequencing, so a month playing two things.
01:18:27.000 --> 01:18:37.000
This is the month of risk that the capital has been helping experts. This is the price of this, and this is the amount of rest of the capital Hell has been held by households.
01:18:37.000 --> 01:18:43.000
And this is this is the price. Right. So, I'm
01:18:43.000 --> 01:18:46.000
for Mario topical these have to be the same.
01:18:46.000 --> 01:19:04.000
Okay, these have to be the same. And, and then after that, after you said this, then sigma cancels out from both sides, and you can rearrange things a little bit it's a linear equation for copper and once you solve for copper you get this.
01:19:04.000 --> 01:19:20.000
So this is, this is, you know, you think about it the right way it's very quick to, to figure this up. Okay. And if you do it in a more full out with a price taking center planner right and I'm going to raise this a little bit so that you know this is
01:19:20.000 --> 01:19:29.000
not visible for the online audience. So then you maximize the expected return which is a minus yoga.
01:19:29.000 --> 01:19:40.000
So, we just a minus yoga divided by cube. This is the capital gains rate plus by a viewer con minus delta.
01:19:40.000 --> 01:19:43.000
And this is the same for for experts in house.
01:19:43.000 --> 01:20:00.000
And this word different for experts impossible, than this, and I would, I would have to replace it by a linear combination of couple things, eight plus one minus kappa things, a lower bar right but in this case this is this is actually the same for experts
01:20:00.000 --> 01:20:16.000
in house. So I maximize the expected return minus the cost of race, and what is the cost of race, well the cost of risk is that is that whole expression, because they have to say that, well actually it's funny it's like it's taking the.
01:20:16.000 --> 01:20:21.000
So I have this amount of risk.
01:20:21.000 --> 01:20:23.000
Kappa Phi Sigma Tilda.
01:20:23.000 --> 01:20:29.000
That is held by experts and their price of risk is capital bring Eva.
01:20:29.000 --> 01:20:44.000
Phi Sigma to them on and then I have one minus Kappa Sigma Tilda. This is how much risk is held by of sorts.
01:20:44.000 --> 01:20:51.000
And then multiplied by one minus copper over one minus, either by sigma to them.
01:20:51.000 --> 01:20:52.000
Okay.
01:20:52.000 --> 01:21:07.000
Um, and so, so this is, this is, this is what we have to maximize with respect to copper. And while we could also maximize this with respect to your time with, you know, but.
01:21:07.000 --> 01:21:15.000
So if I make some changes with respect to your otter then this is also about the efficient use of capital, you know, it's maximising.
01:21:15.000 --> 01:21:28.000
Its that but if you take the first order condition and the first order condition that we get is going to be exactly this expression. Okay, so these are two, two ways of getting the allocation of capital, and this is the funny.
01:21:28.000 --> 01:21:44.000
And now let me talk a little bit about the Economic Education behind this formula for not visible online. So the economic intuition behind this formula is that, um, well, this is increasing in EDA, right.
01:21:44.000 --> 01:22:00.000
Um, and if i is equal to one. So, if experts in households are equally, you know, have faith equally the same credit risk, then this is just equal to eat, because everybody is going to hold capital proportionately to their wealth.
01:22:00.000 --> 01:22:01.000
Right.
01:22:01.000 --> 01:22:18.000
But because five is less than the one. This is actually going to reduce the denominator and make the cup of bigger right so then copy is going to look something like, I'm changing this so that it's visible but unlike here.
01:22:18.000 --> 01:22:31.000
So then, for this is the thing. This is that you've got your vertical axis but this formula is going to be, you know, some technical expression expression like that.
01:22:31.000 --> 01:22:38.000
How much capital expert. So this is, this is question three.
01:22:38.000 --> 01:22:41.000
Okay.
01:22:41.000 --> 01:22:46.000
And then, Um, and then this is about daily.
01:22:46.000 --> 01:22:57.000
And to characterize the glue Bram, we have to figure out the allocation for every single Eva. And we also have to figure out how either is going to move in response to the shops.
01:22:57.000 --> 01:23:02.000
And in order to figure out how either is going to move. Well, we have to.
01:23:02.000 --> 01:23:08.000
So, so okay so in question one.
01:23:08.000 --> 01:23:13.000
We have figured out the,
01:23:13.000 --> 01:23:19.000
the aggregate the risk exposure of experts and households.
01:23:19.000 --> 01:23:30.000
And from this aggregate risk exposure, we can figure out what is going to be the volatility of, of, eat. Okay. And then,
01:23:30.000 --> 01:23:42.000
you know, this question also tells us something about the price of aggregate risk. Question two tells us about the price of the different categories because you're so used to determine the allocation of capital.
01:23:42.000 --> 01:23:48.000
So those piece, two pieces of information we can use them to get the.
01:23:48.000 --> 01:24:03.000
The locomotion of EDA experts wealth and. And now to answer this question I broke it into two parts. The first part is the law of motion of experts wealth.
01:24:03.000 --> 01:24:07.000
And the second part is
01:24:07.000 --> 01:24:15.000
the law of motion of thought. And then we can use either formula to get
01:24:15.000 --> 01:24:30.000
the law of motion of experts buff. Okay, so So question for is a multiple choice question now the question is what, which one of these expressions, gives the law of motion of experts.
01:24:30.000 --> 01:24:38.000
And from a part a, you know, the aggregate volatility of experts wealth.
01:24:38.000 --> 01:24:59.000
And then you also have to figure out what is going to be the premium over the risk free rate and what is going to be the, the rate of consumption. So, so let me launch a poll and
01:24:59.000 --> 01:25:02.000
ask you.
01:25:02.000 --> 01:25:32.000
What is, what is the right answer for question for.
01:25:37.000 --> 01:26:07.000
So far, for answers, of which three are correct. And in one is incorrect.
01:27:12.000 --> 01:27:42.000
Let me give you 15 more seconds.
01:27:42.000 --> 01:27:45.000
Okay, I'm going last chance.
01:27:45.000 --> 01:27:55.000
Going once, going twice, and going three times.
01:27:55.000 --> 01:28:01.000
Okay, and now let me end the poll and share the results.
01:28:01.000 --> 01:28:03.000
Okay.
01:28:03.000 --> 01:28:11.000
So, so then I guess you can see the results in a new devices.
01:28:11.000 --> 01:28:17.000
And most of you have answered be okay so let's, let's figure out which we can. Correct.
01:28:17.000 --> 01:28:19.000
Correct. Okay.
01:28:19.000 --> 01:28:31.000
So, I'm so the law of motion of experts, so their aggregate report is a question we have already answered.
01:28:31.000 --> 01:28:40.000
In, in part, in question one and.
01:28:40.000 --> 01:28:42.000
And that was the.
01:28:42.000 --> 01:28:51.000
So that was the main perhaps a.
01:28:51.000 --> 01:29:09.000
So, that it's, it's, it's the it's, it's in the parts, A, B and C is the correct aggregate the risk exposure of x. So from from question one we know that question D Israel.
01:29:09.000 --> 01:29:15.000
Now you have to search among questions. A B and.
01:29:15.000 --> 01:29:29.000
And what do we have to make sure we have to now look at the drift, and the drift has to have the risk free rate, it has to have the aggregate risk opinion.
01:29:29.000 --> 01:29:37.000
It has to have the EDC categories premium. It has to have the consumption has to have those three parts all correct.
01:29:37.000 --> 01:29:48.000
And if you notice, in part, either the missing consumption. So there's this factor also from that you know that is wrong.
01:29:48.000 --> 01:29:58.000
So because of that, you're only looking between, A, B and C, and it comes down to choosing the right risk being. Okay.
01:29:58.000 --> 01:30:08.000
So, there is either synthetic risk premium and aggregate risk premium and B and C they're only different with respect to aggregate risk.
01:30:08.000 --> 01:30:14.000
And the biggest risk premium is equal to.
01:30:14.000 --> 01:30:22.000
The price of risk, which is by sigma times the risk exposure, which is what multiplies dz.
01:30:22.000 --> 01:30:39.000
And from that, you see that the is the correct expression, right. So be is the correct expression and, you know, and there's also Ed Socratic Chris premium so let me just explain why he disagrees premium there is correct.
01:30:39.000 --> 01:30:57.000
So, so this is the derivation, that we just did.
01:30:57.000 --> 01:31:00.000
The basic of experts.
01:31:00.000 --> 01:31:05.000
And this is also the,
01:31:05.000 --> 01:31:09.000
the amount of idiosyncratic risk that experts.
01:31:09.000 --> 01:31:23.000
So, we have to take the amount of EDC pedicurist that experts hope and multiply by itself, but the price of risk of experts in order to get the term. And that's why that's that's the term that that.
01:31:23.000 --> 01:31:49.000
So the correct answer is B.
01:31:49.000 --> 01:31:52.000
Come.
01:31:52.000 --> 01:31:57.000
Figuring out all the
01:31:57.000 --> 01:32:00.000
glitches, let's see.
01:32:00.000 --> 01:32:20.000
Okay, so now we have the next question which is question five, which is now what we have to do is we have to take the expression from the previous slide for experts, and you have to take the expression for four households.
01:32:20.000 --> 01:32:27.000
And this question is asking about the law of motion of total work.
01:32:27.000 --> 01:32:34.000
And here there are
01:32:34.000 --> 01:32:38.000
five possible choices.
01:32:38.000 --> 01:32:43.000
And let me ask which one you think is is correct.
01:32:43.000 --> 01:33:13.000
And the just a little bit of a hint. It's possible that more than one of them is correct.
01:35:53.000 --> 01:36:09.000
Okay, so I'm going to end the poll soon but before I end the poll those of you who have not answered yet that we just say a couple of things. So, if you look at these expressions right I'm already going to give give away a part of bands, right.
01:36:09.000 --> 01:36:23.000
So, you know, be here is correct, right, because b is well if you just take the Q times k just eat those formula applied straightforward, it gives you be so.
01:36:23.000 --> 01:36:34.000
So from that we know be correct, but then there can be other answers which are which are also potentially correct, right, and the trickiest one is. See, right.
01:36:34.000 --> 01:36:40.000
And the trick to see is that well, it's a completely different expression.
01:36:40.000 --> 01:37:00.000
So the question is, is it the same as as be or is it different, and well the logic behind see is that well it's written in the same way that the road the locomotion of em, take the risk free rate subtract consumption rate and add the risk premia, the
01:37:00.000 --> 01:37:12.000
weighted average risk premia of experts in household. And the question will is this right, or, or is this is this not right. So, and in that, that's the question right.
01:37:12.000 --> 01:37:35.000
So, so let me, let me give you five more seconds to make your final choice we haven't answered yet so I see that 30 to 46 people have answered.
01:37:35.000 --> 01:37:37.000
Ok.
01:37:37.000 --> 01:37:41.000
Okay, I think.
01:37:41.000 --> 01:37:42.000
All right.
01:37:42.000 --> 01:37:46.000
Going once,
01:37:46.000 --> 01:37:51.000
going twice.
01:37:51.000 --> 01:37:54.000
And.
01:37:54.000 --> 01:38:08.000
Okay, let me end the poll and share the results. Okay, so you can see on your devices that most of you have answered that. So, I have to say that but about this question, whatever, whatever you answered.
01:38:08.000 --> 01:38:23.000
I know that you have some knowledge, because, because, you know, all of the answers, but what is that what is the correct answer so most of you have answered the D or E, and the correct answer is D in fact all of the, all of the all of these expressions
01:38:23.000 --> 01:38:32.000
that correct right. Okay. All of these expressions are correct. So let's, let's take a look at these expressions to see what what's going
01:38:32.000 --> 01:38:46.000
to stop sharing the poll results and then hopefully I can do the point is the point that came back on. All right, so, um, so be is correct because Eb is just, it was formed.
01:38:46.000 --> 01:38:47.000
Okay.
01:38:47.000 --> 01:39:09.000
And then A is, well, this part is the capital gains rate plus the dividend yield, and this part is also the dividend yield because by market clearing condition for a logarithmic utility, the dividend yield is, is the consumption rate, and people can zero
01:39:09.000 --> 01:39:14.000
times there well so this is, this is, this is, this is correct. Right.
01:39:14.000 --> 01:39:28.000
Okay so, so a is also correct. So, most of you have answered the D or E and NB is included in books. Now it. Now it comes down to see. Right. So the question is, well, you see correct or is he not correct.
01:39:28.000 --> 01:39:43.000
And let me, let me take a look at the previous expression. So, so, from the previous slide, we have the,
01:39:43.000 --> 01:39:51.000
the volatility of em, the ability of experts well, is
01:39:51.000 --> 01:40:07.000
the price of risk plus sigma, sigma See, this is, this is the volatility of the experts and the volatility is just that because the household even.
01:40:07.000 --> 01:40:15.000
Now, if I take this and multiply by Eva, plus one minus Eva, and multiply by, by that.
01:40:15.000 --> 01:40:27.000
Then this whole thing is going to be the photo, because I just took the portfolio we have all the work of experts in house.
01:40:27.000 --> 01:40:34.000
And, and this is going to be what this is going to be
01:40:34.000 --> 01:40:36.000
sigma,
01:40:36.000 --> 01:40:54.000
sigma theta times even. Plus, the price of words, right. So, so this is going to be this, this expression. Right, right. So, at least we know that this part is correct, even though this looks very different but this part is is correct and in fact that
01:40:54.000 --> 01:40:57.000
these are the sea.
01:40:57.000 --> 01:41:04.000
And then over here. What we need to have is we need to have the,
01:41:04.000 --> 01:41:19.000
the total aggregate the risk, times the price of risk on. And then the weighted average of Ed Socratic risk of experts in households and and the price of it is in progress.
01:41:19.000 --> 01:41:27.000
So this part is correct because this is just the, the risk, times the price of risk. Okay.
01:41:27.000 --> 01:41:33.000
and these parts is what we do here is we take
01:41:33.000 --> 01:41:39.000
this expression for
01:41:39.000 --> 01:41:45.000
for experts and the multiplied by the by the weight.
01:41:45.000 --> 01:41:52.000
Eva. So here's, here's what would be happy for etc. So, we're experts.
01:41:52.000 --> 01:42:06.000
They earn copper over in the spread by square sigma squared, and you take that and multiply by eight, because that's their portfolio Wait, and this is, this is the risk disinvited risk premium that they are.
01:42:06.000 --> 01:42:19.000
And then one minus Eva is a portfolio weight on hospitals well, and they helped them by by an equivalent expression, which is going to be one square divided by one minus.
01:42:19.000 --> 01:42:20.000
square.
01:42:20.000 --> 01:42:32.000
and there's no fight, just right. So they Socratic risk premium has to be this term and let's just make sure that to check the decision, and this is this is really the right expression.
01:42:32.000 --> 01:42:38.000
Okay. So, so in fact it turns out that this expression is correct.
01:42:38.000 --> 01:42:55.000
So all of them, all of them are right. Okay, so, so that's question five, and why did we need to do questions four and five is because EDA equals m divided by q times.
01:42:55.000 --> 01:43:05.000
Okay. And then you can use either formula for the ratio to get the law of motion of either, so we had the law of motion of and then we have the lowest most acute anxiety.
01:43:05.000 --> 01:43:09.000
And so here we have the law of motion of n.
01:43:09.000 --> 01:43:21.000
And the question is what, which one of these expressions that was most convenient to use for for the local Muslim students K a b or c.
01:43:21.000 --> 01:43:32.000
We should use it right. Exactly. So all of them are correct. And you could use any one of them, but if you use C then either expressed in the same way in terms of the risk and the risk premia.
01:43:32.000 --> 01:43:35.000
So here we are going to get a lot of cancellations right.
01:43:35.000 --> 01:43:50.000
So, and that's question six for question six is to take the expression for the locomotion of and, and also take to take the expression for the locomotion of up to the last, and then to get the expression for the low voiceprint of Eva.
01:43:50.000 --> 01:43:57.000
As you know, I'm
01:43:57.000 --> 01:44:01.000
using this formula for the ratio.
01:44:01.000 --> 01:44:11.000
So, so at this point, let's maybe take you know five minutes and they give you a chance to the traffic driver. And after that, I'll show you and then we'll finish GoPro.
01:44:11.000 --> 01:44:13.000
Sounds good.
01:44:13.000 --> 01:44:20.000
Okay, so let's uh let's do that. And let me see if I can
01:44:20.000 --> 01:44:27.000
reopen the breakout room so that you get how are you guys doing. I'm like, Okay.
01:44:27.000 --> 01:44:38.000
Sorry for sorry it's a little bit tricky with the, with the hybrid still, still getting getting the hang of how to do it.
01:44:38.000 --> 01:44:40.000
Yes.
01:44:40.000 --> 01:45:10.000
So anyways, let me let me open all the rooms and give you a chance to work on this together.
01:45:17.000 --> 01:45:47.000
to make sure I remember to bring back this.
01:46:01.000 --> 01:46:12.000
We're.
01:46:12.000 --> 01:46:24.000
live on the launch before.
01:46:24.000 --> 01:46:54.000
Yeah.
01:47:09.000 --> 01:47:33.000
Any question, you know.
01:47:33.000 --> 01:47:49.000
nicely arranged right and we take this, the difference, you know, these parts are going to cancel out, you can see that already away and then Miss parts and you know similar cancellations, there may be some cancellations can we get the actual getting
01:47:49.000 --> 01:47:50.000
close expression for complex will be like this and
01:47:50.000 --> 01:48:02.000
for commerce will be like this and possibly you know we're not quite, quite nicely possible going to
01:48:02.000 --> 01:48:05.000
be very tractable.
01:48:05.000 --> 01:48:35.000
I have to say that, you know, the research can be really frustrating business and when you know when you get an expression that's like comes out.
01:56:11.000 --> 01:56:41.000
Su.
01:57:01.000 --> 01:57:15.000
Okay, so now that everybody is back let's discuss this. Okay, so let me just ask the question if anybody, of you were able to get the some type of a final expression and I'm going to ask you you know what the expression is because you know it's too.
01:57:15.000 --> 01:57:17.000
It's too long.
01:57:17.000 --> 01:57:22.000
Anyways, but, you know, raise your hand if you think.
01:57:22.000 --> 01:57:33.000
So, some, some of you, yeah so that that's good so some of you, some of you were able to get it so that's, that's awesome. So let's talk about, um, let's see.
01:57:33.000 --> 01:57:37.000
Did anybody raise their hand no okay.
01:57:37.000 --> 01:57:41.000
Oh, Okay, I Andre.
01:57:41.000 --> 01:57:43.000
Do you want. Yes, yes, I'm here.
01:57:43.000 --> 01:57:45.000
Yes.
01:57:45.000 --> 01:57:51.000
You you raise your hand so let me ask you, what you have to raise my hand.
01:57:51.000 --> 01:57:54.000
Oh, I see it. Sorry, I that happened.
01:57:54.000 --> 01:57:59.000
Okay, okay, okay. Right, right. Okay, great, great Sorry about that. Oh, sorry.
01:57:59.000 --> 01:58:02.000
I thought you have either the Have some.
01:58:02.000 --> 01:58:18.000
Alright, so let's uh let's, let's talk about it so first of all let's figure out the, the volatility of this, of this, of this ratio. So the volatility of this feature is the difference in both.
01:58:18.000 --> 01:58:36.000
And if you just subtract them it's going to be one minus Epoch Times, sigma thing. So, we're going to have a CMX whether it's visible so the battlefield determines going to be one minus, either time sigma theta.
01:58:36.000 --> 01:58:41.000
These. Right, that's going to be a part of this part of expression.
01:58:41.000 --> 01:58:46.000
And then we also have
01:58:46.000 --> 01:58:55.000
the drift. And in the drift term VC like very nice cancellation at the risk free rate is going to cancel out because it's the same for everybody. Okay.
01:58:55.000 --> 01:59:03.000
And then we have a drift term from these two terms, and you also have a drift term.
01:59:03.000 --> 01:59:07.000
So from these two terms, they're going to enter the difference in the drift here.
01:59:07.000 --> 01:59:21.000
And then from the volatilities you also have this this other term. Right. So this volatility chairman is going to be sigma why, which is in the denominator so that's that's sigma way right here.
01:59:21.000 --> 01:59:38.000
multiplied by the difference in the volatility of y in the volatility of x. So, this is the volatility of why this is the volatility of excellence can be either minus one times sigma i think that's that's going to be just.
01:59:38.000 --> 01:59:44.000
So that part is going to be this, this, this, either jump from the volatilities.
01:59:44.000 --> 02:00:00.000
And then from here. We are also going to be able to get something so I'm just taking the difference if it's if
02:00:00.000 --> 02:00:04.000
it's a.
02:00:04.000 --> 02:00:16.000
So you see that you have the price of race, but sigma, that multiplies both of those expressions times difference, one minus either sigma. So the.
02:00:16.000 --> 02:00:33.000
Okay. So, so we have those two. So, they will enter that, and then be, you're also going to have some terms from the DC categories. And here's specifically what we have is, so this is clear.
02:00:33.000 --> 02:00:42.000
And here you can do a little bit of a simplification. Okay. And we know that
02:00:42.000 --> 02:00:47.000
the because of because of the condition that they used for question city.
02:00:47.000 --> 02:00:48.000
Okay.
02:00:48.000 --> 02:01:07.000
That, that this without the square is the same as that, without the square, okay, if you take the weighted average was weights carbon one minute Scapa, then it's just going to be just a couple of divided by either thanks bye square sigma.
02:01:07.000 --> 02:01:18.000
So, so that's going to be there. And so then, if you take the difference in the draft. This is going to be worth and there's the drift of n minus would enter the gate.
02:01:18.000 --> 02:01:29.000
And that's going to be that. So, so these terms are all are basically going to be there. So this is, this is the challenging. And that's going to be the drift.
02:01:29.000 --> 02:01:43.000
And after that, we just need to go ahead and do some simplification. And once you do the simplification, then this whole term is going to cancel out with this part of it multiplies the breath the breath, very very nice to see we'll just have that.
02:01:43.000 --> 02:01:56.000
And here, they're also going to be some simple vacation simply plug in this this copper. And in the end, um, here's the final expression that be a good.
02:01:56.000 --> 02:01:57.000
Okay.
02:01:57.000 --> 02:02:10.000
And so let me give some, some intuition about this final expression. So in this final expression this is the drift and it's beautiful because you were able to get it in close for for this specific exercise.
02:02:10.000 --> 02:02:17.000
And here, this is the EDC kind of Chris parameter and this whole part is positive.
02:02:17.000 --> 02:02:23.000
So there is a positive portion of the drift, which is driven by the idiosyncratic.
02:02:23.000 --> 02:02:42.000
So, so that means that because experts are better at managing etc credit Chris, then household, they're going to earn something in and have some, some profit from managing the city some categories, adding a positive drift to
02:02:42.000 --> 02:02:43.000
to this Express.
02:02:43.000 --> 02:02:57.000
And then this part is negative. So, the experts they have things, strong, so they have the want to expose themselves to aggregate risk, and they pay two households for exposing themselves to aggregate.
02:02:57.000 --> 02:03:07.000
And because they paid the households, then the households will earn some risk premium and that in the experts that will have to pay so this is this is negative portion.
02:03:07.000 --> 02:03:11.000
So there is what's the positive portion and the negative.
02:03:11.000 --> 02:03:13.000
And then there are some bullets.
02:03:13.000 --> 02:03:22.000
And then something else is if you look at this expression. Then, In fact,
02:03:22.000 --> 02:03:26.000
you can you can calculate.
02:03:26.000 --> 02:03:38.000
Well, it actually depends on the, on the relative parameters, but you can calculate what is going to be the stochastic status state. You know under, under certain parameters.
02:03:38.000 --> 02:03:46.000
Okay. And something else which is also very nice about this expression is, if you want there as part seven which you can do at home.
02:03:46.000 --> 02:03:55.000
Part Seven is you can actually get for this specific problem,
02:03:55.000 --> 02:04:09.000
the stationary distribution, up to a constant. And you can also get a condition under which the stationary distribution exists so that's going to be a parameter restriction, and you can get you can get the condition.
02:04:09.000 --> 02:04:28.000
So this is a this is a very nice problem in which, you know, you can you can get them closed form and actually in this specific setting, you can add some twists and still get things in closed form, as long as you open the market for the aggregate risk
02:04:28.000 --> 02:04:41.000
so opening the market for the aggregator ESCA allows you to, you know tractable a characterize exactly how much was experts are exposed to know my house was are exposed to and then get things very very next.
02:04:41.000 --> 02:04:48.000
So, So that's the problem. Any questions.
02:04:48.000 --> 02:04:52.000
Yeah.
02:04:52.000 --> 02:04:56.000
The price of risks, depends on a day. Yeah.
02:04:56.000 --> 02:04:58.000
So with the.
02:04:58.000 --> 02:05:00.000
Right.
02:05:00.000 --> 02:05:17.000
Okay, so maybe, maybe let's maybe let's, let's do.
02:05:17.000 --> 02:05:19.000
Yeah, right, right, right.
02:05:19.000 --> 02:05:29.000
Well, we could still be but still derive it right so so perhaps let's like the right. So, so we have that funnel with the sigma.
02:05:29.000 --> 02:05:33.000
Total with equals entertains.
02:05:33.000 --> 02:05:37.000
The.
02:05:37.000 --> 02:05:46.000
This is the risk exposure of experts, plus one minus Peter and the risk exposure of households is just the practical.
02:05:46.000 --> 02:05:55.000
Okay. And then, this expression equals okay so this is the price of risk was ether time stigma.
02:05:55.000 --> 02:05:57.000
Right.
02:05:57.000 --> 02:06:12.000
Um, and then by lift up, you can still see it, and then from here I can get that the price of risk, equals two sigma minus into time sigma theta for.
02:06:12.000 --> 02:06:33.000
So let's say dropped out but but you could do right with the six.
02:06:33.000 --> 02:06:43.000
Right, exactly. So you could just you could just you could just, you could just put it in so it dropped out and me know.
02:06:43.000 --> 02:06:51.000
But, but you know you could you could, if you're interested in it you could feel the right. And then, if you're interested in the risk free rate.
02:06:51.000 --> 02:06:55.000
You could also. Let's see.
02:06:55.000 --> 02:07:10.000
Yeah, you would you would take the, the expression for the total return on capital and if you figure out what Q is then you you you will be able to figure out the total return on capital so it's a constant.
02:07:10.000 --> 02:07:22.000
That doesn't depend on either. And you subtract from that the, the price of risk, you know, which which has given here so we can also get the risk free rate in closed form.
02:07:22.000 --> 02:07:30.000
Yeah, basically, can you.
02:07:30.000 --> 02:07:34.000
Can I ask a question uni. Yes.
02:07:34.000 --> 02:07:39.000
Actually, not an algebra question is more intuitive.
02:07:39.000 --> 02:07:55.000
In this equation about the dynamics of it, we have the Brownian motion. We know that Brownian motion can be any positive number, a very large example, and it's very large, it could go bigger than one.
02:07:55.000 --> 02:08:00.000
What is the economic intuition in those cases
02:08:00.000 --> 02:08:11.000
that that would be bigger than the one sorry the bigger than one for example because well sure cannot be economically cannot bigger than the bigger than one.
02:08:11.000 --> 02:08:14.000
Yeah.
02:08:14.000 --> 02:08:20.000
So, what what is bigger than the one I couldn't, I couldn't couldn't Sure.
02:08:20.000 --> 02:08:39.000
I Oh I see, I see okay okay okay no that's that's that's a good question. So here a welfare cannot be cannot become bigger than the one, because what you see is that enough.
02:08:39.000 --> 02:08:50.000
Then, let's get my point so if either becomes equal to one, then this goes to zero so the volatility goes to zero. And the drift, when I plug in either equal to one, is also zero.
02:08:50.000 --> 02:09:02.000
So once either event can hit one, which which, which is a big if you know if if if it can happen. It can happen. It just gets stuck.
02:09:02.000 --> 02:09:07.000
So, so it can never it can never become bigger than one, for sure. So the wealth.
02:09:07.000 --> 02:09:12.000
The wealth stays in this model in the interval between zero and one.
02:09:12.000 --> 02:09:17.000
And, you know, just
02:09:17.000 --> 02:09:25.000
a little bit of a property so if you actually explore the slow motion of eat that. Then there's going to be a parameter range.
02:09:25.000 --> 02:09:30.000
So the ratio of
02:09:30.000 --> 02:09:38.000
sigma, sigma state that has to be in the in the right range, given phi.
02:09:38.000 --> 02:09:53.000
If, if that ratio is a net range then there's going to be a stationary distribution and otherwise it could be that, you know, either experts eventually, you know, overtake the economy or the households eventually overtake the economy depending on the
02:09:53.000 --> 02:09:58.000
parameters.
02:09:58.000 --> 02:10:00.000
So.
02:10:00.000 --> 02:10:00.000
Okay. Okay. Thank you.
02:10:00.000 --> 02:10:30.000
Okay. Okay. Thank you.
02:10:57.000 --> 02:11:04.000
They stop the recording controls.
02:11:04.000 --> 02:11:16.000
I guess we just end the meeting right.
02:11:16.000 --> 02:11:21.000
We already put it out
02:11:21.000 --> 02:11:42.000
there with all of the training like this time. Yeah.
02:11:42.000 --> 02:11:55.000
Have to share.
02:11:55.000 --> 02:12:02.000
So why don't we located
02:12:02.000 --> 02:12:18.000
right on.