Newest questions tagged risk - Economics Stack Exchange most recent 30 from economics.stackexchange.com 2019-09-20T07:26:27Z https://economics.stackexchange.com/feeds/tag?tagnames=risk&sort=newest https://creativecommons.org/licenses/by-sa/4.0/rdf https://economics.stackexchange.com/q/30576 0 Corporate finance - capm beta estimation salad salad https://economics.stackexchange.com/users/24042 2019-08-19T17:29:33Z 2019-08-19T17:29:33Z <p>I want to solve the following problem as an exercise to test my understanding of the capm material:</p> <p>Assume that CAPM is valid. The market portfolio consists of 3 stocks such that <span class="math-container">$i = A, B, C$</span> with respective weights <span class="math-container">$0.12$</span>, <span class="math-container">$0.19$</span> and <span class="math-container">$0.69$</span>. The stocks’ expected returns, <span class="math-container">$E(R_i)$</span> are <span class="math-container">$16.2$</span>%, <span class="math-container">$24.6$</span>% and <span class="math-container">$22.8$</span>%, while the market portfolio’s standard deviation <span class="math-container">$\sigma_m = 15.2$</span>% and <span class="math-container">$r_f = 4$</span>%. We are also given <span class="math-container">$\sigma_{A, B} = 187$</span>, <span class="math-container">$\sigma_{A, C} = 145$</span>, <span class="math-container">$\sigma_{B, C} = 104$</span>.</p> <p>Questions:</p> <p>(i) Estimate the <span class="math-container">$\beta$</span> for all stocks. (ii) Calculate the variances <span class="math-container">$\sigma^{2}_{A}$</span>, <span class="math-container">$\sigma^{2}_{B}$</span> and <span class="math-container">$\sigma^{2}_{C}$</span>.</p> <p>For (i) I used the formula expected return = risk free rate + <span class="math-container">$\beta \cdot$</span> market return premium which for stock A would be <span class="math-container">$0.162 = 0.04 + 0.152 \cdot \beta \iff \beta = \frac{0.122}{0.152} = 0.8026$</span>. However, I am not sure if I am doing this the correct way and whether the market return premium is the same as the market portfolio's standard deviation (highly probably not).</p> <p>Any hints are appreciated. Also for solving (ii).</p> https://economics.stackexchange.com/q/30231 1 Assessing risk in a decision problem with repeated toss moritzthird https://economics.stackexchange.com/users/23747 2019-07-21T05:49:25Z 2019-07-21T07:46:35Z <p>The problem starts at time t0. At each time step, the participant can choose to opt out and claim a loser's reward Rl. At each time step, the participant has a probability p to win a winner's reward Rw, the participant is aware of p. Rewards decrease after each time step, at the same rate, and Rw > Rl always. After tn the 'game' is over and the participant claims Rl - the participant is aware of time tn.</p> <p>For example at t0 Rw = 100, Rl = 50, p = 0.05, reward decay rate is 1 each turn and the tn = 30. First participant wins at t10 and claims a reward of (100 - 10 * 1) = 90. Second participant opts out at t20 and claims a reward of (50 - 20 * 1) = 30. Third participant loses at t30 and claims (50 - 30 * 1) = 20.</p> <p>I'm interested in assessing the risk behavior of the second participant. I'm thinking that the second participant considers the remaining number of turns, probability p to win each turn, and average amount that the participant would win, and weights it against the current loser's reward at time t20. But I'm not sure this is the right way to consider the risk involved.</p> <p>I've read the early works by Kahneman and Tversky but this seems a bit more complex, I would appreciate any hints on where to find solutions in literature as well.</p> https://economics.stackexchange.com/q/30201 0 Risks Quantification (soft question) Egor Epishin https://economics.stackexchange.com/users/18583 2019-07-17T16:09:57Z 2019-07-17T16:09:57Z <p>Can anyone please recommend literature (books, papers, whatever) on the topic of risk quantification? By risk quantification I mean financial assessment of e.g. credit or market risk. </p> <p>Free sources welcomed.</p> https://economics.stackexchange.com/q/30012 0 Proof: Risk averse; Certainty Equivalent smaller than expected value user333444 https://economics.stackexchange.com/users/13313 2019-07-01T19:10:20Z 2019-07-01T19:42:48Z <p>I would like to show for a randomly distributed variable <span class="math-container">$x$</span> with CDF <span class="math-container">$F(\cdot)$</span> , given a Bernoulli utility function <span class="math-container">$u(x)$</span> the following property holds:</p> <p>The certainty equivalent, <span class="math-container">$CE(\cdot)$</span>, is smaller than the expected value, <span class="math-container">$\mathbb E(\cdot)$</span>, if and only if the decision maker is risk-averse. </p> <p><span class="math-container">$$CE(F,u) \leq \int_{-\infty}^{\infty} x dF(x) \quad \forall F(\cdot)$$</span> </p> <p>By Jensens Inequality for risk-averse agents we have: <span class="math-container">$$\int_{-\infty}^{\infty} u(x) f(x)dx \leq u(\int_{-\infty}^{\infty} x f(x) dx)$$</span></p> <p>I know that the CE is defined as: <span class="math-container">$u(CE) = \mathbb E(U(X)) = \int_{-\infty}^{\infty} f(x)u(x)\,dx$</span> </p> <p>Hence, </p> <p><span class="math-container">$$u(CE) \leq u(\int_{-\infty}^{\infty} x f(x) dx)$$</span> </p> <p>and</p> <p><span class="math-container">$$CE \leq \int_{-\infty}^{\infty} x f(x) dx$$</span></p> <p>Is it possible to kind of invert the u() function is we assume it is strictly increasing?</p> <p>I also thought about rearranging it to: </p> <p><span class="math-container">$$u(CE) = \int_{-\infty}^{\infty} f(x) dx * \int_{-\infty}^{\infty} u(x) dx$$</span></p> <p>but I fail to see how that helps.</p> <p>I thought perhaps showing that the risk premium is positive for risk-averse agents is equivalent but I could not get started either. </p> <p>I would be glad for a hint to work out the solution myself.</p> https://economics.stackexchange.com/q/29950 0 Why might firms be averse to idiosyncratic risk? user14513 https://economics.stackexchange.com/users/15079 2019-06-25T17:26:16Z 2019-06-25T17:26:16Z <p>Under the CAPM and other theories, a widely held corporation should be averse only to systematic risk, correlated with other investments in the economy, not idiosyncratic risk like a CEO dying or a fire which are special to the firm and which shareholders could diversify away. Yet there do exist a number of reasons why firms might be averse to idiosyncratic risk. I'm working on a paper on one of them,and I wonder whether economists ever think about it. I think it would come up in non-economists' minds, but I pretty quickly but I haven't seen it mentioned by economists. </p> <p>So I am curious as to what reasons people here think of for firms to be risk averse. Why would a firm require a higher return from a project, a policy, or a contract with more risk uncorrelated with other risks? I won't list even the four or so standard ones, because I am curious as to what might be mentioned.</p> https://economics.stackexchange.com/q/29896 0 How to interpret the (expected) exposure and CVA of an option or a single share Charlie Shuffler https://economics.stackexchange.com/users/23491 2019-06-20T20:54:53Z 2019-06-20T20:54:53Z <p>I have a quick (hopefully simple) question regarding the interpretation of the expected exposure of a call option and a single share. I've done some computations on the formula for the expected exposure and this yielded that the expected exposure of both the option and the share, are equal to their initial value, i.e. <span class="math-container">$EE(t)^{option}=V(t0)$</span> and <span class="math-container">$EE(t)^{stock}=S(t0)$</span>. I arrived at these results by using that both the discounted option value and the discounted stock value are martingales under the risk neutral measure. However, I'm reading mixed definitions on what just the term exposure actually is. Some say it is what you could lose on an investment, which would go well with my results, but others say it is what you could lose if things go bad, i.e. if you own a share worth 100 euros/dollars, then this is your exposure no matter what you purchased it for.</p> <p>Could anyone help me in clarifying what the concept of exposure/expected exposure means for these two objects? The concept is slightly easier to grasp for swaps, but for products as 'basic' as these, it seems to be harder to understand. The same holds for how to think about the CVA of a single share, which I also have a hard time wrapping my head around.</p> <p>Thanks in advance!</p> <p>Note: I also asked this question on quant.stackexchange but since it is rather theoretical I felt it could be a good fit here also.</p> https://economics.stackexchange.com/q/29646 0 How to calculate indentical cash flows? Sara Salvante https://economics.stackexchange.com/users/21642 2019-06-04T17:10:23Z 2019-06-04T17:10:23Z <p>So i have this question:</p> <p>Homemade leverage Companies A and B differ only in their capital structure. A is financed 30% debt and 70% equity; B is financed 10% debt and 90% equity. The debt of both companies is risk-free. Rosencrantz owns 1% of the common stock of A. What other investment package would produce identical cash flows for Rosencrantz?</p> <p>This is the answer on the answer sheet:</p> <p>The two firms ha ve equal value; let V represent the total value of the firm. Rosencrantz could buy 1% of Company B’s equity and borrow an amount equal to:</p> <p><strong>0.01 x (DA-DB)=0.002V</strong></p> <p>This investment requires a net cash outlay of <strong>0.007V</strong> and provides a net cash return of </p> <p><strong>(0.01 x profits)-(0.03 x rf x V)</strong> where rf is the risk free rate of interest on debt. Thus , the two investments are identical.</p> <p>I am having some problems understanding this answer. First of all , under what point would Rosencrantz buy 1% of company B's equity ? Couldn't he start with a different number? </p> <p>Secondly, why would he borrow an amount equal to 0.01 x (DA-DB)=0.02. Why is DB being subtracted from DA?</p> <p>Thirdly, why does this investment require a cash outlay of 0.007v and under what basis is the net cash return (0.01 x profits)-(0.03 x rf x V).</p> <p>I have some learning disabilities and this really does not make any sense to me. Could somebody please explain how to answer this question in a clearer/simpler way or explain the steps the answer sheet in a clearer manner so that all these number i am having issues with make sense?</p> <p>Thanks! I really appreciate it.</p> https://economics.stackexchange.com/q/27012 2 Why do riskier investments pay more? Woe https://economics.stackexchange.com/users/21207 2019-02-23T18:55:58Z 2019-02-24T04:43:28Z <p>I'm talking about bonds, stocks, and the sort.</p> <p>I understand that an individual investor that's planning to invest, say, 50% of his savings, may require a higher expected gain to go for a riskier investment.</p> <p>However, if risk can be diversified away, wouldn't people with enough money, even if they are risk averse, choose the investment opportunities with highest expected value and diversify among them? Wouldn't then any investment with higher-than-average expected value be flooded with money until they almost don't pay more?</p> <p>Is it that...</p> <ol> <li>most risky investment options are too correlated to allow for almost all of the excess risk to dissolve?</li> <li>risk premiums only happen in markets with limitted access or that don't work like the ideal 101 market in a relevant way?</li> <li>some other reason?</li> </ol> https://economics.stackexchange.com/q/26817 1 Why does it seem like the average cost threshold protocol has a possible gain but no chance of loss? PyRulez https://economics.stackexchange.com/users/5716 2019-02-09T20:51:43Z 2019-02-10T02:51:55Z <p>So, the average cost threshold protocol is a theoretical protocol for crowd funding club goods (it can also be used to crowd fund public goods, but I'll only focus on club goods in this post). It is explained <a href="http://blog.felixbreuer.net/2013/01/20/average-cost-threshold-protocol.html" rel="nofollow noreferrer">here</a>, but I'll give a brief summary.</p> <p>Let's say someone created a club good. As an example, I'll say the good is a ebook titled "Introduction to the Bean trade". The author decides to sell it using protocol.</p> <p>To do this, he comes up with some price <span class="math-container">$R$</span>. This is how much total revenue he wants to accrue by selling the book. He then announces to the public that he is selling his book using the average cost threshold protocol, and what value he assigned <span class="math-container">$R$</span>.</p> <p>Now, potential buyers announce how valuable they think the book is to them (they could lie, but as it turns out there is no incentive to do so). Let <span class="math-container">$V_i$</span> be the value consumer <span class="math-container">$i$</span> announced.</p> <p>Now, most likely using a computer, a price <span class="math-container">$P$</span> is calculated. This price <span class="math-container">$P$</span> must the minimum price such that <span class="math-container">$|B_p|P = R$</span>, where <span class="math-container">$B_p$</span> is the set of consumers such that <span class="math-container">$P \le V_i$</span>. If such a price does not exist, the protocol failed, and no products or money change hands. It can however be attempted again if wanted, and may succeed if there are more buyers or the buyers announce a higher value. (In an actual implementation, if no <span class="math-container">$P$</span> is found, you can just wait until more buyers show up, instead of requiring them all to announce it at the same time.)</p> <p>Finally, all customers in <span class="math-container">$B_p$</span> pay the author <span class="math-container">$P$</span> and the author gives each of them a copy of the ebook. The author has made his revenue <span class="math-container">$R$</span>, as intended, and the customers got a copy of the ebook in exchange for a price no greater than how much they valued it.</p> <p>The protocol is usually defined in such a way that more potential customers may announce prices, and previous potential customers who were not in <span class="math-container">$B_P$</span> may change their prices. If this causes the value of <span class="math-container">$P$</span> to change to <span class="math-container">$P'$</span>, new customers pay <span class="math-container">$P'$</span> to the author and previous customers are refunded <span class="math-container">$P - P'$</span>. However, for simplicity, I will say that protocol ends immediately after failing or a transaction being made.</p> <p>Anyways, now for the paradox. If a custom believes that the book has value <span class="math-container">$V_i$</span>, and they announce this price, then three things can happen:</p> <ul> <li>The protocol fails or <span class="math-container">$V_i &lt; P$</span>. They do not pay, nor do they get the book. Their net gain is <span class="math-container">$0$</span>.</li> <li>The protocol succeeds with <span class="math-container">$P = V_i$</span>. They pay <span class="math-container">$P$</span> and get the book of value <span class="math-container">$V_i$</span>. Their net gain is <span class="math-container">$0$</span>.</li> <li>The protocol succeeds with <span class="math-container">$P &gt; V_i$</span>. They pay <span class="math-container">$P$</span> and get the book of value <span class="math-container">$V_i$</span>. Their net gain is <span class="math-container">$V_i - P$</span>, which is positive.</li> </ul> <p>The problem is that the net gain is always positive. I was under the impression that there are no guaranteed gains in economics. If there was, everyone would be using this all the time until people ran out of ideas for club goods.</p> <p>Here are some potential explanations I thought of, but I have an issue with each one:</p> <ul> <li>If the protocol fails, the author eats the price of the book. A small modification can be made to fix this, however. Have the customers announce their prices before he writes, so he can determine if <span class="math-container">$P$</span> will exist. The only risk to him then is if he fails to complete the book. This risk can probably be factored into <span class="math-container">$R$</span>. So the author would have a risk, but he would still probably take it (since he has to take it to write the book anyways, regardless of how he sells it), and the customers still have no risk.</li> <li>The author created value when he wrote the book, so of course the average gain will be positive. However, even when creating value guaranteed gains should not exist, since otherwise everyone would create value that way.</li> <li>The customers announce a price higher than their true <span class="math-container">$V_i$</span> for some reason, which makes incurring a loss a possibility. However, the possibility still remains that they <em>could have</em> gotten a guaranteed gain, so the paradox remains.</li> <li>The value of the book turns out to be less than the customer anticipated. For example, maybe the bean trade goes into decline. However, it should be possible to hedge something like this out. The customer can also require the author to publish a set of standards the book will meet before they announce a price, and make the payment contingent on the book meeting those standards. The customer can also announce a value that is a conservative estimate of the book's value.</li> <li>The customer incurs an opportunity cost by locking up their funds. This will not be recouped if they are not in <span class="math-container">$B_P$</span>. This can be resolved by making sure it is quickly determined what <span class="math-container">$P$</span> is after the values are announced, if it exists. This way the customer only needs to lock up their funds if they are in <span class="math-container">$B_P$</span>. When they announce their value, they can deduct the expected opportunity cost from it.</li> </ul> <p>So, what is going on? What does it seem like this protocol results in a possibility of a gain without a possibility of a loss?</p> https://economics.stackexchange.com/q/26430 4 Transformation of random variables and second order stochastic dominance user20775 https://economics.stackexchange.com/users/20775 2019-01-15T04:04:05Z 2019-09-17T19:02:40Z <p>Suppose <span class="math-container">$X$</span> and <span class="math-container">$Y$</span> are two random variables where <span class="math-container">$X$</span> has SOSD (second order stochastic dominance) over <span class="math-container">$Y$</span>. Let <span class="math-container">$g(\cdot)$</span> be a monotonic function and <span class="math-container">$X' = g(X)$</span> and <span class="math-container">$Y' = g(Y)$</span>. </p> <p>Under what conditions of <span class="math-container">$g(\cdot)$</span> <span class="math-container">$X'$</span> has SOSD over <span class="math-container">$Y'$</span>? I know that if <span class="math-container">$g$</span> is linear, SOSD property is reserved. Is there any sufficient and necessary conditions of <span class="math-container">$g$</span> that assures SOSD property?</p> https://economics.stackexchange.com/q/25883 4 Can I recreate an experiment on Allais paradox using student grades as payoffs? Zhang_anlan https://economics.stackexchange.com/users/19566 2018-12-04T14:03:28Z 2019-02-03T09:02:50Z <p>For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money.</p> <p>Is this reformulation of the Allais paradox conceptually right or not?</p> <p><em>Problem 1.1:<br> Consider the following scenario:<br> A.1 – you can get an B+ with probability 100%<br> B.1 – you can get A with probability 10% or get B+ with probability 89% or not passing the exam with probability 1%.<br> +<br> A.2 – you can get B+ with probability 11% or not passing the exam with probability 89%,<br> B</em>.2 – you can get A with probability 10% or not pass the exam with probability 90%.*</p> <p>Then I will modify the problem to see if for higher stakes student's preferences change.</p> <p>Edit: If we consider that not passing the exam gives utility = 0, (as in the Allais paradox we have the same case because it corresponds to receiving 0$) the graph of the utility function, assuming constant marginal utility of grades would look like this: <a href="https://i.stack.imgur.com/G0sdT.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/G0sdT.jpg" alt="utility"></a></p> https://economics.stackexchange.com/q/24720 1 Can aggregate risk to the economy be insured, and how? Scott https://economics.stackexchange.com/users/14072 2018-09-27T21:09:16Z 2018-12-31T00:26:17Z <p>There has been a lot of discussion for a while now over how the short market on Tesla is quite crowded. This got me thinking of what possible benefits the short market bestows upon the economy as a whole. </p> <p>Specifically, supposing some hypothetical company <span class="math-container">$C$</span> (that isn't Tesla), that has random payoff at time <span class="math-container">$t$</span> of <span class="math-container">$P_t(x)$</span> where <span class="math-container">$x$</span> is the investment. Supposing that <span class="math-container">$P_t$</span> is 'risky' (e.g. <span class="math-container">$p(P_t(x) = x) = 1$</span> is 'non risky', and <span class="math-container">$p(P_t(x) = 2.5x) = 0.5; p(P_t(x) = 0) = 0.5$</span> is 'risky'). </p> <p>I can vaguely imagine that a mixture of investors and shorters would somehow even out the expected risk for the economy as a whole. Does this intuition hold in reality? If so, what is the mechanism and reasoning here?</p> <p>I can see at least one avenue by which aggregate risk to the economy can be insured under the right circumstances. Suppose that we have the "risky" business <span class="math-container">$C$</span> as defined above. Ceate another business <span class="math-container">$C_2$</span> with the same payout, but which succeeds or fails exactly when <span class="math-container">$C$</span> fails or succeeds, respectively. If we invest <span class="math-container">$x/2$</span> into each company, the payout at time <span class="math-container">$t$</span> is exactly <span class="math-container">$1.25x$</span> with probability 1. Thus, <span class="math-container">$C_2$</span> "evens out" the risk of <span class="math-container">$C$</span>, and vice versa. </p> <p>Do short positions also fill this role? Does anything else?</p> https://economics.stackexchange.com/q/24475 2 Mean vs. variance - which is dominant? Lafayote https://economics.stackexchange.com/users/19402 2018-09-11T19:46:28Z 2018-09-13T00:47:32Z <p>I am currently trying to gain some basic understanding of the mean-variance tradeoff. However, since I do not have an economic education background, I am struggling with some issues. Currently I am wondering which of the two is the key driver for decision-making. Let's say I have option A with a low variance and a low expected value, and option B with a moderate variance and a moderate expected value - which of the two would people choose? Are we more attracted by increasing profit or by relatively lower risks? Or is there no general principle and it depends on individual preferences?</p> <p>I appreciate any input on that! Thank you in advance.</p> https://economics.stackexchange.com/q/23826 2 Construct utility function for a risk-averse agent Anna https://economics.stackexchange.com/users/18865 2018-07-19T19:56:31Z 2018-07-20T00:28:52Z <p>I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent$i$who has an ideal point$x$in a policy space$X = [0,1]$. There is a policy (option) given by$a \in X$. Can we construct the agent$i$'s utility function as a distance between his ideal point and$a$as$u_i (a) = -(x - a)^\gamma$, where$\gamma &gt; 0$represents$i$'s attitude towards risk, such as$\gamma &gt; 1$means$i$is risk-averse and$\gamma &lt; 1$means that$i$is risk-seeking? </p> https://economics.stackexchange.com/q/22489 5 Why is everyone suggested to specialize their education? Mario https://economics.stackexchange.com/users/18601 2018-06-18T11:22:57Z 2018-06-20T23:19:55Z <p>Why is so common to suggest university students to specialize in order to get a better paid job?</p> <p>This goes completely against the principle of diversification of investments, in order to decrease risk by spreading it over a portfolio.</p> <p>Instead, students are driven towards specialization, investing their most valuable asset, time, in a single high risk endeavor. Specialization might be good for society as a whole, but can have disastrous consequences for the individual.</p> https://economics.stackexchange.com/q/22477 3 When does gambling reduce risk? afreelunch https://economics.stackexchange.com/users/17900 2018-06-16T18:54:48Z 2018-06-29T16:44:39Z <p>Suppose that you face risk. It is obvious that taking gambles whose outcomes are negatively correlated with the outcomes of your other gambles can reduce your overall risk ('hedging'). My question, however, concerns <strong>uncorrelated</strong> gambles - can these reduce your overall risk, and if so when?</p> <p><strong>Edit</strong>: to be clear, I am asking about when you can reducing your risk by taking <strong>additional</strong> uncorrelated gambles, not simply by replacing some gambles in your portfolio with others.</p> https://economics.stackexchange.com/q/21539 0 Value of Statistical Life and Risk Jan https://economics.stackexchange.com/users/16657 2018-04-18T00:46:15Z 2018-04-18T01:20:02Z <p>I have been reading a paper by <a href="http://journals.sagepub.com/doi/abs/10.1177/0022343311418265" rel="nofollow noreferrer">Bove &amp; Elia</a> (2011), where they quote a definition of the value of statistical life from <a href="https://www.ncbi.nlm.nih.gov/pubmed/19100640" rel="nofollow noreferrer">Bellavance, Dionne &amp; Lebeau</a> (2009). I have tried making my peace with the necessity of this concept, but I have been rather confused by the used definition. It says that the value of a statistical life is a function of the willingness to pay to reduce the risk of death and the risk of death itself. However, the risk of death reduces the value of a statistical life. Why would it do that? Is it a weight as in an NPV calculation, where the risk of default reduces the expected cash flow?</p> https://economics.stackexchange.com/q/21207 1 How to estimate market risk using only publicly available data? PAS https://economics.stackexchange.com/users/16436 2018-03-26T11:50:20Z 2018-03-28T07:09:30Z <p>How can I calculate market risk for the US Stock Market (NYSE or NASDAQ) using only freely accessible data? I'm only interested in the market risk of the whole economy not of different industries, companies or sub-sectors. </p> <p>Somebody suggested to me to download market index data and construct the volatility as a measure of market risk. But I can't find a proper explanation how I do this.</p> <p>Thank you. </p> <p>p.s. Is the following procedure correct?:</p> <p>I get data US Stock market (for example <a href="https://fred.stlouisfed.org/series/SP500" rel="nofollow noreferrer">https://fred.stlouisfed.org/series/SP500</a>) calculate the growth rate and in the last step I compute the variance of the growth rate to get the market risk?</p> https://economics.stackexchange.com/q/21009 1 What were the liquidity requirements prior to Basel III? S. Scheibenpflug https://economics.stackexchange.com/users/16573 2018-03-13T13:45:25Z 2018-03-13T13:45:25Z <p>I am investigating the impact of enforcing the Basel III liquidity requirements with a focus on the LCR. I have found some information about regulations in fore prior to Basel III in Sweden and Germany. However, it would be very interesting to know if there were any European countries where there were <strong>no</strong> or <strong>very little</strong> liquidity requirements prior to Basel III.</p> <p>Do you know of any such examples?</p> <p>Many thanks!</p> https://economics.stackexchange.com/q/18847 2 Why does Mascolell define second-order stochastic dominance as such? Megadeth https://economics.stackexchange.com/users/11843 2017-10-20T19:21:48Z 2017-10-20T21:19:49Z <p>Is not Mascolell's definition in his microeconomic theory of the second-order stochastic dominance narrower? He defines for distribution functions with the same mean only. Although he gives some motivation for doing this, somehow I do not get his motivation.</p> https://economics.stackexchange.com/q/17772 7 References for particular definitions of risk and uncertainty Richard Hardy https://economics.stackexchange.com/users/4230 2017-08-10T11:53:28Z 2018-06-18T13:02:17Z <p>I have some doubts about risk vs. uncertainty. I have read the thread <a href="https://economics.stackexchange.com/questions/14761/what-is-the-difference-between-risk-uncertainty-and-ambiguity">"What is the difference between risk, uncertainty and ambiguity"</a> and have skimmed through Knight's <a href="https://mises.org/sites/default/files/Risk,%20Uncertainty,%20and%20Profit_4.pdf" rel="nofollow noreferrer">"Risk, Uncertainty, and Profit"</a> Chapter VII (starting on p. 197). It seems there exist alternative definitions of these concepts, which is a bit confusing. </p> <p>I have a particular example that implicitly defines risk and uncertainty. I would like to know if these implicit definitions are in line with any of the established ones.</p> <p><strong>Example:</strong> In a lottery, the probability to win is$p$and the probability to lose is$1-p$. If I know$p$and participate in the lottery, I am facing <em>risk</em>. If I do not know$p$and participate in the lottery, I am facing <em>uncertainty</em>.</p> <p>Does this match any existing definitions of risk vs. uncertainty?<br> Could I also get a reference to an academic paper or a textbook?</p> <hr> <p><strong>Edit 1:</strong> User 123 notes correctly that there seems to be risk in both cases (whether I know the probabilities or not, I am still participating in the lottery which by itself is a source of risk). Hence, the term <em>uncertainty</em> seems to incorporate risk + the lack of knowledge of the probabilities. This may suggest the terms <em>risk</em> and <em>uncertainty</em> are not mutually exclusive; when we call something <em>uncertain</em>, it might also include an element of risk; but when we identify something as <em>risky</em>, we must know the probabilities, thus it is not <em>uncertain</em>. Yeah, it is convoluted...</p> <p><strong>Edit 2:</strong> Quoting Knight via <a href="https://en.wikipedia.org/wiki/Knightian_uncertainty" rel="nofollow noreferrer">Wikipedia</a>, <em>a measurable uncertainty, or 'risk' proper, as we shall use the term...</em>. Thus it is enough that the probability be measurable in the above example and is does not have to be known precisely. So I understand that the implicit definitions in the example above are not in line with the Knightian ones.</p> https://economics.stackexchange.com/q/17048 0 Swaps and systemic risk user13479 https://economics.stackexchange.com/users/13479 2017-06-05T12:20:04Z 2017-06-05T18:31:08Z <p>I understand the systemic risk that can be associated with the trading of credit default swaps, but is it the same with interest rate swaps? What was the "default rate" on interest rate swaps during the 2007-2008 crisis compared to CDS for instance?</p> https://economics.stackexchange.com/q/16773 1 Are risk-costs a form of external costs? visionInc https://economics.stackexchange.com/users/10913 2017-05-13T21:32:14Z 2017-05-14T02:14:33Z <p>An example to make to question more clear: With the use of nuclear power plants come several risk-costs (the risk of a nuclear disaster). These costs aren't included in the energy price and there is nobody who pays for it. So are they considered as external costs? </p> https://economics.stackexchange.com/q/16426 2 Inc Linear Transformation of Bernoulli Utility Frank Swanton https://economics.stackexchange.com/users/8560 2017-04-23T13:16:50Z 2017-04-23T17:37:24Z <p>According to MWG Proposition 6.B.2, it illustrates that the expected utility form is preserved only by increasing linear transformation. </p> <p>What is the significance of this proposition?</p> <p>The part I find challenging in connecting the dots is when right after the proof of this proposition, the authors claim that this proposition allows us to interpret meaning in differences of utilities. How are these two exactly connected?</p> https://economics.stackexchange.com/q/16424 1 Consequentialist View of Risk Frank Swanton https://economics.stackexchange.com/users/8560 2017-04-23T12:31:51Z 2017-05-05T21:25:12Z <p>In MWG, the authors introduce the consequentialist view of risk by assuming for any risky alternative, only the reduced lottery over final outcome matters to decision maker. </p> <p>From philosophical view, how reasonable and unreasonable is this assumption? Can you provide examples where this assumption is in fact reasonable while it isn't?</p> https://economics.stackexchange.com/q/16274 1 How a utility function which is both DARA and CRRA can be explained? user12883 https://economics.stackexchange.com/users/0 2017-04-14T12:05:11Z 2017-04-14T18:01:43Z <p>I'm studying risk aversion and I cannot make a intuitive explain about the utility function which is DARA and CRRA.</p> <p>for instance, let's say,$\ln W$, where$W$stands for one's wealth.</p> <p>by the definition of absolute risk aversion, its ABA is${1}/{W}$and it is CRRA since its relative risk aversion is$1$. </p> <p>then here's the start of my confusion. </p> <p>first, consider a fair gambling, and two guys who have same utility function as$\ln W$. By DARA, the one who is richer would not feel much riskier than the poor. So he would not spend as much as the poor guy do for making fix his income, for example by contracting insurance(it means the richer would pay less insurance fee for hedging his risk than the poor guy.</p> <p>second, what about the aspect of RRA(relative risk aversion)? It is constant. I understood this as,, that the rich man and the poor man's spending in their insurance fee does not depend on their wealth(specifically, does not vary when their wealth increases or decreases) let's say for some risk they would like to pay 3% of their wealth to avoid the certain risk. Then, from here, it is clear that the 3% of wealth of rich man is bigger than the poor man. </p> <p>In other words, It looks that the rich man would pay much more money for insurance than the poor man when we see the aspect of RRA. However, DARA says that it is not the case. For me, this does not makes sense. And with a common sense, if a person who is willing to avoid risk would feel less risky when he becomes rich. So DARA looks fine. But the situation with CRRA looks contradiction about one's utility (function). </p> <p>The question should have been shorter..sorry about that. Please leave me a hint to solve this confusion. Thanks. </p> https://economics.stackexchange.com/q/15476 2 Certainty Equivalents and Risk Premiums in Expected Utility Theory for Asymmetric Distributions BjoSch https://economics.stackexchange.com/users/12134 2017-02-16T15:33:55Z 2017-02-17T21:31:06Z <p>I want to calculte risk-premiums in order to assess how much risk-averse customers would be willing to pay for an insurance against an uncertain loss modeled by a random variable$X$. How would a risk-premium be calculated, if$X$does not follow a normal distribution? My reading of the literature is as follows: </p> <p>1) Expected utility theory: Assumes CARA (CRRA) like utility functions with well behaved properties that are more or less agreed to model the behavior of rational risk-averse decision makers by satisfying certain axioms. The risk-aversion of decision makers can be modelled by Arrow-Pratt with$\alpha=R(X)=-\frac{u''(x)}{u'(x)}$. Using Arrow Pratt, one can calculate a risk-premium$\pi$if$X$is normally distributed such that$\pi(X)=\frac{\alpha}{2}\sigma^2(X)$which derives from the formula of the certainty equivalent. </p> <p>2) Downside risk measures from finance: Since losses (or returns) may not be normally distributed, finance has developed other measures to capture the concept of risk. One of these measures is the semi-variance as a special case of lower partial moments, which is very similar to the idea of mean-variance principle as outlined above:$SV=E((max[0,E(X)-X])^2)$. </p> <p>Now the problem is as follows: </p> <p>Aiming to calculate a risk-premium I can either follow utility theory. If$X$is normally distributed we get a well contained formula to calculate the risk-premium$\pi(X)$. If not, then what? Would the certainty equivalent be calculated based on numerical integrat? If so, how would this look like for an arbitrary distribution of$X$?</p> <p>On the other hand, I could follow a down-side risk measure approach: Given that I use semi-variance as a concept to measure risk, how could you account for the risk-aversion of customer in order to derive a risk-premium? I would just weight the semi variance with a factor$\tau^{~}SV$(with$\tau$being some kind of a proxy for risk-aversion) this wouldn't do the trick, would it? Essentially it would probabily not satisfy the expected utility axioms such as CARA or CRRA do correct?</p> <p>How to approach this problem then? Are there any alternative strategies that I have overlooked?</p> <p>**Addition after update </p> <p>Now I have also found this <a href="https://economics.stackexchange.com/questions/9032/risk-premium-in-the-expected-utility-theory">post</a> on the matter which would give a solution to my problem - as far as I understand - since it allows$X$to have a non-zero expected value? This is due to the fact that the taylor approximation is - as it says - only an approximation of the risk premium with regard to various moments of the given distribution$X$. This also explains why the risk-premium can be correctly calculated for the normal distribution which is completely defined trough first and second moment.</p> <p>This brings me to my last question: Considering the risk premium for non-zero expected values this would according to the post listed above also be approximated by the formula$\pi \approx \frac{1}{2}R(w)\sigma^{2}_X\$? And the approxmation error for non-normal distributions is then depending on the question how well first and second moment capture the true nature of a distribution?</p> https://economics.stackexchange.com/q/15280 3 VaR and rating for commercial banks FabIO https://economics.stackexchange.com/users/10160 2017-02-01T09:58:20Z 2017-03-31T15:31:58Z <p>I would like to know if there exist a database where Value at risk of commercial banks are.</p> <p>Beyond that if there is a connection between the rating from agency (as S&amp;P, Fitch etc..) and the VaR of banks. And where I can find references of that.</p> https://economics.stackexchange.com/q/14799 7 Do stock markets price in existential risk (i.e. global nuclear war)? Justas https://economics.stackexchange.com/users/11566 2016-12-23T21:13:03Z 2017-04-14T13:54:38Z <blockquote> <p>Question Moved from Money StackExchange: <a href="https://money.stackexchange.com/questions/74002/do-stock-markets-price-in-existential-risk-i-e-global-nuclear-war">https://money.stackexchange.com/questions/74002/do-stock-markets-price-in-existential-risk-i-e-global-nuclear-war</a></p> </blockquote> <p><strong>Q: Do stock markets price in existential risk?</strong></p> <p>The <a href="https://en.wikipedia.org/wiki/Cuban_Missile_Crisis" rel="nofollow noreferrer">Cuban Missile Crisis</a> in November 1962 is an example of coming to the brink of global nuclear war, and while the markets were down until its resolution, the index price did not seem to reflect anything resembling "imminent end of the world". </p> <p><a href="https://i.stack.imgur.com/wx3TU.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/wx3TU.png" alt="Dow Jones Stock Market Cuban Missile Crisis"></a></p> <p>More recently, <a href="http://tass.com/defense/921420" rel="nofollow noreferrer">Putin's declaration to escalate nuclear weapon systems development</a>, <a href="http://www.nytimes.com/interactive/2016/12/22/world/americas/trump-nuclear-tweet.html" rel="nofollow noreferrer">Trump's comments on expanding nuclear capabilities</a>, and <a href="http://www.independent.co.uk/news/world/americas/donald-trump-nuclear-expansion-tweet-noam-chomsky-weapons-arsenal-twitter-a7491921.html" rel="nofollow noreferrer">Noam Chomsky declaring the exchange "very frightening"</a> suggests that we're in a period of elevated nuclear war risk.</p> <p>However, the US stock markets are at their historical highs. How can this be resolved? I can think of two possibilities:</p> <ol> <li><strong>Markets accurately reflect the risk.</strong> Cuban crisis was a real, but small risk, thus the market dip. Today, the risk is nearly zero, thus the markets are not down.</li> <li><strong>Markets ignore existential risk.</strong> Rational investors expect a return on investment, but if the investors believe an event would kill them and their estate, the loss due to that event is irrelevant. Thus the risk of existential, planet destroying events, does not correlate with the stock market prices.</li> </ol> <p>Is this true, can stock market price be trusted to reliably reflect existential risk?</p> https://economics.stackexchange.com/q/13039 0 Is there a good mechanism to incentivize leveraged firms to take less risks? Fix.B. https://economics.stackexchange.com/users/7593 2016-08-13T04:05:29Z 2016-08-18T15:58:12Z <p>It seems that there are some circumstances, say when the government foresees a financial crisis, where it would like firms to hedge, take less riesk etc. However, leveraged agents benefit from risk, and so they don;t benefit from risk eduction expenses. </p> <p>Is there some theory or idea, out ther eon how to design a mechanism that incetivizes firms to reduce their riskiness? Maybe subsidize financial hedging? Maybe tax profits very progressively/convexly?</p>