Questions tagged [risk]
The risk tag has no usage guidance.
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Logarithmic utility and zero consumption
I am working on a model that assumes expected utility maximisation with a vNM function $u$ that exhibits some standard properties:
$u'(w) > 0$ and $u''(w) < 0$ for all $w \geq 0$.
$\lim_{w \...
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Arrow-Pratt Theorem - More risk aversion leads to more balanced bundles
I have an economics question but it more so interested me mathematically; related to Arrow-Pratt theorem - risk aversion; hence I wanted to ask the following.
Given $p \in \mathbb{R^s}_{++}$ $\pi_s \...
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Reduction of compound lotteries seem to be incorrect?
Wikipedia reads:
I feel that this axiom is much stronger than the usual "axiom of reduction of compound lottery" that we talk about because the Axiom 4' sufficiently imply EU (with weak ...
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Single Crossing Property - Approach
I have the following problem, and want to learn how to proceed in a very precise and short manner to show the SSCP for $U(.)$ without the brute force approach. I wanted to ask for your help to find ...
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Degrees of Risk aversion and Expected utility [closed]
There are two agents with utility functions $g_1$ and $g_2$, where the agent with function $g_2$ has higher (absolute) risk-aversion. The agents face a lottery $((q,x_1),((1-q),x_2))$, i.e. agents ...
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The liquidity of bank's assets and bank's systemic risk
I would have the following question. May the liquidity of a bank's assets be non-linearly related to the bank's systemic risk? More specifically, more liquidity can increase systemic risk during ...
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What is the proper way to derive risk definitions from utility functions?
In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form
$\frac{\mu}{\sigma^2}$
with further weighting and normalization depending on the ...
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Comparing agent decision-making under risk-neutrality and risk-Aversion
I am working on the following question but have not been able to come up with a suitable way to proceed. The setup is as follows:
There is a technology (for example, a vaccine) which reduces the ...
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Clarifying question about utility theory and preferences
I am trying to solve this question about preferences and I got into an argument about it. I just want to make sure I am not overlooking something really simple.
What can you tell about the risk ...
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Effectiveness of liquidty regulation
I am writing to collect some thoughts regarding the best way to study the effectiveness of liquidity regulation (LCR and NSFR). To study the latter, I should avoid to collect actual banks' ratios, ...
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Bond syndicates and systemic risk
I'm looking at both bond syndicates (groups of banks underwriting bond issuance), and also the holders of those bonds (groups of investors that hold those bonds for some time, potentially selling them ...
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Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries
I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my ...
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Can FOSD-transitivity replace the transitivity in utility representation theorem?
Let $\succsim$ be a complete, non transitivity preference relation. I wonder if FOSD-transitivity implies transitivity.
The primitive is the space of lotteries $p_1,p_2,p_3,...$. We say the preference ...
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What is a very very famous example of structural estimation?
I took a behavioral econ class and learnt the "structural estimation" of risk-aversion parameter.
Later some friends told me that what I learnt is too simple when I was bragging about my ...
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interest rate risk vs duration risk?
Is there a difference between interest rate risk vs duration risk? I feel as though I have heard them used interchangeably but I don't know if there is any distinguishing factor between the two.
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Willingness to sell a lottery ticket vs. willingness to buy a lottery ticket
I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would ...
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Stocks and call option
I've been asked this question by my professor, but I'm not sure about the answer:
"A broker proposes you two type of investment: the first is buying 100 shares of the company X at the current ...
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example of risk neutral or risk loving utility function
i"m looking for an example of either risk loving or risk neutral utility function. what i mean is like for risk averse, we have the HARA utility function. is there a utility function that exhibit ...
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Covered interest rate parity: the forward contract is not risk free
Covered interest rate parity (CIRP or CIP) can be formulated as:
$$
(1+r_{f,Home})=\frac{S_0}{F_{0\rightarrow 1}} (1+r_{f,Foreign})
$$
where $r_f$ are risk-free rates in the home and foreign countries,...
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What was the original paper that showed that estimates of risk aversion from micro and macro are inconsistent?
One of the well known paradoxes in macroeconomics is that estimates of risk aversion from experimental micro data do not match the ones estimated from macro data.
I know there was an important paper ...
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Who insures the FDIC in case it fails?
I understand that the Federal Deposit Insurance Corporation (FDIC) failing is unlikely, but the probability of such a failure is still positive. In case the FDIC fails, who covers the customers' ...
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What is the difference between consumption smoothing and risk smoothing?
So there is a body of literature that talks about consumption smoothing (e.g. Rosenzweig & Stark 1989) and another body of literature that talks about risk smoothing in the context of insurance.
...
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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 $w_0=60000$, $...
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What are the difference between "settlement risk" and "counterparty risk"
From Lannquist,2020, p.6, the wholesale Central Bank Digital Currency (CBDC) could reduce settlement risk and counterparty risks.
I am wondering what is the intuitive difference between these two ...
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Bond Price expression
I've researching some mathematical finance and I've stumbled upon something I can't seems to find sources on. I'm probably overlooking something, but I hope someone can enlighten me and give me some ...
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Choice under uncertainty
I am practising past micro economics questions from the internet and I am not sure how to proceed with this question:
Imagine a situation where a risk averse agent has positive wealth(w) and may face ...
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$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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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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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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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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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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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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