Questions tagged [risk]

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Risk Premium for Prospect Theory-like value function

I am curious how to calculate the following risk premium for a utility function that is not linear in $w$. What i'm asking is the following: Consider an agent with utility function $u$, initial wealth ...
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Is Epstein-Zin utility a generalization of dynamic expected utility (DEU)?

Epstein-Zin (EZ) utility is the solution to: DEU is relatively simple: $\sum_t \delta ^t\mathbb E[u(c_t)]$. Is DEU a special case of EZ? How are those two models compared? Since EZ is a solution of a ...
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Consumption CAPM and compounded risk free rate [closed]

I am studying consumption CAPM and trying to prove, assuming lognormal consumption growth one can show that the continuously compounded risk-free rate is:
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Most utility functions under risk and uncertainty generalizes expected utility. What is deadly wrong if a model does not include EU as special case?

Why do people generalize EU instead of making an entirely new model, or create a model that is neither a special case nor an extension of EU? To my knowledge, most utility functions under risk and ...
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Finding the risk attitude parameter in a CPT Risk Elicitation Model

I'm working with this article by Bauermeister et al. that compares the risk attitude parameters found using two different risk elicitation models. The models each use a series of gambling options to ...
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Why does Central Bank Digital Currency affect commercial banks' retail deposits?

Lannquist,2020, p.6 said that Retail CBDC Can challenge commercial banks’ market power over retail deposits, pressuring banks to increase interest rates and offer better financial services to ...
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Negative certainty equivalent

Let us consider an agent of initial wealth $w_0$ whose utility function is $u(x)=\sqrt{x}$. This individual faces a risk of loss $Z$ which occurs with probability $p$. It is assumed that $w_0=60000$, $...
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What are the difference between "settlement risk" and "counterparty risk"

From Lannquist,2020, p.6, the wholesale Central Bank Digital Currency (CBDC) could reduce settlement risk and counterparty risks. I am wondering what is the intuitive difference between these two ...
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Hazard X population density

Not quite able to calculate risk ... I know the hazard across a given geographic region (probability an intensity threshold will be exceeded in a given window of time) and I know the population ...
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1 answer
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Bond Price expression

I've researching some mathematical finance and I've stumbled upon something I can't seems to find sources on. I'm probably overlooking something, but I hope someone can enlighten me and give me some ...
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Combined Buffer Requirements Basel III

Let's take this example: A bank is required to maintain minimal capital requirements according to Basel III as follows: CET1 - 4.5% Tier1 - 6% Tier1 + Tier2 - 8% In addition it has to apply these ...
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Choice under uncertainty

I am practising past micro economics questions from the internet and I am not sure how to proceed with this question: Imagine a situation where a risk averse agent has positive wealth(w) and may face ...
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$E[F_T] = F_0$ implies $p = \frac{1-d}{u-d}$? or is implied by?

From Ch 12 in Hull's OFOD, we compute the risk-neutral probabilities for a futures contract: Later in Ch 17, futures options are valued, and we have the same result: In relation to Chapter 16 and 17,...
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Are passive asset management strategies increasing the volatility of big cap stocks?

Over the last decade, more money has been allocated using passive asset management strategies. A good part of the latter relies on ETFs that are replicating indices that are mainly comprised of big-...
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Proof that $U(\sum_{n=1}^{N}{p_nL_n})=\sum_{n}^{N}{p_nU(L_n)}$

I understand the expected value of a lottery is $\sum_n^N{p_nL_n}$ where there are $N$ possible outcomes, each with a probability $p_n$ with $n=1,...,N$ and $\sum_{n}p_n=1$ (that's rather trivial I ...
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Bertrand game with delivery risk and side payments

Consider three agents $A_i$, who engage in a Bertrand game. All agents have perfect knowledge on all parameters and the distribution $F()$. $A_1$ moves first and selects price $0\leq p_1\in \mathbb{R}...
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Second order stochastic dominance

I have two very basic questions about second order stochastic dominance (SOSD): Am I right in thinking that this is only a partial order, i.e. you can find a pair of lotteries such that neither SOSD ...
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Does the Fed/SEC have tools to address shock-propagation from correlation of fund flows?

Premise In 2017, passively invested assets totaled 37% of mutual funds and ETFs; by 2021 this number is closer to 50% if not more. After the market downturn in (March) 2020, the Fed updated their ...
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2 votes
1 answer
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How to interpret risk premium

I do not understand the notion risk premium. Let us suppose that John goes to the city by car, but he is thinking about not paying for the parking. If he is caught in the act he must pay the fine. How ...
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Can we model risk with only probability?

Sorry for the confusion! I am adding an example to see if it helps: For example, consider a gamble A, with payoffs {a,b,c,d}, whose probability of each payoff being realized is equal (so 25% each); ...
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1 answer
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In Barro's (2009) Rare Disaster Model in AER: How to derive equation (5)

In Barro (2009) http://piketty.pse.ens.fr/files/Barro2009.pdf My question is reference to equation #5, whereby Barro is deriving the reciprocal of the market value 1/v, and I am trying to derive this ...
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Risk with unknown probability distribution of the outcomes

From Wikipedia: "Risk aversion comes from a situation where a probability can be assigned to each possible outcome of a situation and it is defined by the preference between a risky alternative ...
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Negative Risk Free Rate Sharpe Ratio

currently I am writing my Master-Thesis about SRI-Fonds. For analysing Sharpe Ratios from different Fonds I need to use the risk free rate (e.g. Euribor 3M). Unfortunately I can‘t find anything about ...
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1 vote
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Cashflow Risk vs Discount Risk

I'm studying financial economics/asset pricing and I often hear the terms cashflow risk and discount risk but I'm not sure what they mean? The Campbell/Shiller (1988) decomposition includes cashflows (...
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How is an interest swap collateralized

I am trying to understand what it means for an interest swap to be collateralized. If for example, I am paying fixed to a bank and receive floating in return. Who is giving collateral to whom? and how ...
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Term for risk AND ambiguity

This question is related to References for particular definitions of risk and uncertainty, which offers an excellent description of risk and uncertainty. Just as a recap: Knight (1921) described risk ...
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What are the differences between hedging with swaps, options or futures?

For instance if a bank wants to hedge against interest rate risk, it could use interest rate swaps, or options or futures contract. Or in any other example, when a manager is hedging against risks. ...
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1 answer
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CDO and Nonpositive Equity Questions

I have two questions about statements made in this video: https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/bank-bailout/v/bailout-2-book-value At 6:25, the video ...
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1 answer
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Job Search and the Investment Problem [closed]

I don't know what to take as the cost of accepting the job. Kindly guide me through deciding how to frame the equation.
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Solution to the Aiyagari model: why a sparse capital grid?

When solving a model à la Aiyagari, why is it needed to have more points close to zero? I would be grateful if you could point me out some reference on how to implement the sparse grid. In ...
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Could anyone here be able to explain gambling addiction and its debt with Microeconomics theory?

I am a research master student in Cognitive and Clinical Neuroscience, with the specialization/track Neuroeconomics and have to come up with a master thesis subject soon. I was thinking about gambling ...
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Is there some definition about risk sharing?

I was searching for a definition of risk sharing and I have found the following: $\underline{Definition:}$ Risk Sharing — also known as "risk distribution," risk sharing means that the premiums and ...
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3 votes
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Why is the risk premium always positive for risk averse individuals?

I think this has to do with the definition of concavity and the fact that a risk averse person has a concave utility function, but I'm not sure how that helps.
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2 votes
1 answer
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How to calculate CRRA bounds from Holt and Laury (2002) type lottery?

Lottery is between: Option A: a certain choice of £5 Option B: £10 with probability 0.1 and £1 with probability 0.9 The probability of receiving £10 increases in each subsequent choice. How do I ...
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1 vote
1 answer
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Why charge higher interest rates to poorer customers?

Consumer loans/credit charge different rates depending on the individual's risk. In particular, it charges more to poorer individuals. Whilst this seems to make sense from a risk perspective, there ...
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Does Medicaid or Medicare represent a higher risk to the Federal Government Solvency and Debt going forward?

I'm trying to understand not only which program is expected to be larger in terms of costs, but which one has the least capacity to adjust (reduce benefits if revenues for the program fall).
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How is the utility function with constant relative risk-aversion obtained?

In this slide, it says that constant relative risk-Aversion utility function have this form. $u(x) = \frac{1}{1-b} x^{1-b}$ for $b≠1$ $u(x) = In(x)$ for $b=1$ When I tried to derive the utility ...
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Assessing risk in a decision problem with repeated toss

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 ...
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0 votes
1 answer
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Proof: Risk averse; Certainty Equivalent smaller than expected value

I would like to show for a randomly distributed variable $x$ with CDF $F(\cdot)$ , given a Bernoulli utility function $u(x)$ the following property holds: The certainty equivalent, $CE(\cdot)$, is ...
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2 votes
1 answer
125 views

Why do riskier investments pay more?

I'm talking about bonds, stocks, and the sort. 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 ...
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Why does it seem like the average cost threshold protocol has a possible gain but no chance of loss?

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 ...
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3 votes
1 answer
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Transformation of random variables and second order stochastic dominance

Suppose $X$ and $Y$ are two random variables where $X$ has SOSD (second order stochastic dominance) over $Y$. Let $g(\cdot)$ be a monotonic function and $X' = g(X)$ and $Y' = g(Y)$. Under what ...
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4 votes
3 answers
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Can I recreate an experiment on Allais paradox using student grades as payoffs?

For a project in experimental economics, I thought of doing something related to expected utility theory/prospect theory, but using grades instead of money. Is this reformulation of the Allais ...
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Can aggregate risk to the economy be insured, and how?

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 ...
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2 votes
3 answers
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Mean vs. variance - which is dominant?

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 ...
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2 votes
1 answer
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Construct utility function for a risk-averse agent

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) ...
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5 answers
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Why is everyone suggested to specialize their education?

Why is so common to suggest university students to specialize in order to get a better paid job? This goes completely against the principle of diversification of investments, in order to decrease ...
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3 votes
2 answers
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When does gambling reduce risk?

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, ...
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0 votes
1 answer
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Value of Statistical Life and Risk

I have been reading a paper by Bove & Elia (2011), where they quote a definition of the value of statistical life from Bellavance, Dionne & Lebeau (2009). I have tried making my peace with the ...
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1 vote
1 answer
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How to estimate market risk using only publicly available data?

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, ...
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