Questions tagged [value-at-risk]
The value-at-risk tag has no usage guidance.
141
questions
0
votes
0answers
22 views
Correlation in GARCH model
I don't think I have ever come across the concept of stochastic correlation so I imagine it's not very widespread, but I had the idea to implement a Monte Carlo VaR model for a portfolio of stocks by ...
0
votes
1answer
37 views
How does delta-gamma VaR work in practice and when can it be preferable to Monte-Carlo VaR?
So I will start off by just stating my understanding of the two methods through some examples and lead that into my question. Hopefully it is correct but if not then perhaps the answer to my question ...
4
votes
1answer
143 views
Value at Risk for portfolio with different maturities
I am new to StackExchange and relatively new to quantitative finance.
I work at a commodity trading company and we have an extensive portfolio of futures and options on commodities (traded on the CME, ...
1
vote
0answers
34 views
Can value at risk be computed using downside deviation?
Value at risk is usually computed with a regular standard deviation. But can it be computed using downside deviation (semi-deviation) instead? Particularly if I want to consider a Var that includes ...
4
votes
1answer
209 views
99.97% Percentile VaR Approximation
I have been working with a group which references a 99.97% 10-day VaR figure.
They calculate this value via a 99% 1-day historical simulation over 500 days and then scale it under the assumption of a ...
0
votes
0answers
24 views
Interpretation of $\alpha$ (confidence level) in mean CVaR optimization
How are an investors risk preferences related to $\alpha \in (0,1)$ in a mean CVaR optimization?
Would a risk averse investor choose a higher value of $\alpha$, and if so why?
My understanding is, ...
1
vote
1answer
166 views
Analytical portfolio optimization for VaR under multivariate normality
Given a set of assets with returns following a multivariate normal distribution with a known mean vector and a known covariance matrix,
$$
r \sim N(\mu,\Sigma),
$$
I want to find optimal portfolio ...
1
vote
1answer
178 views
Absolute and Relative Value at Risk
Is it correct to calculate the VaR as 99% max between loss and profit. E.g. if 99% VaR on the loss side of the distribution is -100, and on the positive side of the distribution there is a value ...
2
votes
1answer
136 views
Stop-Loss strategies
Does anyone know some bibliography about the problems or limitations of using Stop-Loss strategies in a portfolio?
Let me explain better: for example you can have a portfolio of 30 stocks from ...
-1
votes
1answer
87 views
Backtesting a stock scoring model
I'm working on a simple stock scoring model consisiting of 3 factors:
1.market cap
2.liquidity of the stock
3.the value at risk
we defined 3 intervals for each factor and we assigned the ...
4
votes
1answer
151 views
Portfolio optimization w.r.t. value at risk: introductory or survey references
I am looking for references introducing the problem of portfolio optimization when the target characteristic is value at risk. A textbook treatment would be great. Surveys on the topic are also ...
2
votes
0answers
29 views
Estimator for Conditional value at risk (average value at risk)
I am following a book: Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi
I'm learning about average value at risk. ...
0
votes
1answer
56 views
How to calculate value at risk in accordance with Basel?
I would greatly appreciate if you could let me know whether Value at Risk should be calculated for net open position (foreign currency assets-foreign currency liabilities) or for foreign currency cash?...
1
vote
0answers
57 views
Block maxima estimation of Expected Shortfall
I want to calculate the expected shortfall of a return series with the block maxima (BM, link) method in Extreme Value Theory, however I can't seem to find out how this should be done. All papers I'...
0
votes
2answers
132 views
understanding Value-at-Risk correclty
The are several types how to calculate the VaR. I am focussing on the method of calculation the VaR in percentage.
$VaR=I*z*std*\sqrt{t}$
This gives the VaR in ā¬.
I have the z-value, the daily ...
3
votes
1answer
135 views
CVaR formulation
I am a research intern and I am working on a topic about a profit maximization of a risk-averse newsvendor by using Conditional Value-at-Risk.The problem is that I found different expressions of CVaR. ...
0
votes
2answers
53 views
From risk limits to pnl projection?
As a fresh risk manager, today I got an assignment to check whether our risk measurements / limits are setup properly (whether the limits are so tight that affect our p&l) . Better if I can ...
0
votes
0answers
64 views
Approximation of portfolio VaR (after mapping) when Delta and Gamma both equal zero
As titled, I am having trouble estimating the VaR of a portfolio mapped as a function of a single risk factor $S$, in the form :
$$V(S) = S^3 - 30S^2 + 300S + 150$$
with current value $S = 10$.
$S$...
4
votes
2answers
1k views
How to add Risks-Not-In-VaR (RNIV) to VaR under Basel III
I am trying to generate/prove the magnitude of the over-conservativeness of the regulatory VaR (internal models) under Basel III against what a more accurate VaR would be.
However, I can't seem to ...
2
votes
1answer
143 views
PCA on a portfolio of spot and forward contracts
I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l.
...
0
votes
0answers
49 views
How can I manually calculate the VAR of a call and put portfolio?
How would I solve the following question? Im unsure how to estimate the stock price using MCS.
0
votes
1answer
178 views
Historical Simulation of Bond, Stock and Option Portfolio
If I have a portfolio consisting of
1-one stock of unit price equal to S,
2-one 9% coupon American bond with 20 years to maturity and a par value of $1000,
3-and one European call option on the ...
1
vote
0answers
31 views
How to measure specific risk charge?
IFRS requires banks to compute different risks including market risk based on Basel iii.
To do so, the capital requirement is defined as follows:
$$max(VaR_{tā1},m_c Ć VaR_{avg}) + SRC$$
$SRC$ is ...
2
votes
1answer
112 views
Modified Sharpe ratio
I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
1
vote
1answer
125 views
Prove Subadditivity - Entropic Value at Risk
Any insight in how to prove the following risk measure is subadditive?
$\rho_{1-\alpha}(X) = \inf_{z>0}\{z^{-1}\ln(\frac{E[e^{zX}]}{\alpha})\}$, with $\alpha \in ]0,1]$
I want to prove it is a ...
1
vote
0answers
60 views
Opposite of Value-at-Risk. Criteria for Optimization
I'm trying to optimize portfolio of undervalued and portfolio of overvalued stocks. I have simulated scenarios of stock returns, and based on them I would like to find optimal weights. One criteria is ...
1
vote
0answers
44 views
Risk Measure-identication
Let X be a variable with existing moment generating function $M_x(z)=E[e^{zX}]$.
Define the following risk measure: $\rho_{\alpha}(X)=inf_{z>0}(z^{-1}ln(\frac{M_x(z)}{1-\alpha}))$
Does anyone know ...
2
votes
2answers
594 views
1 day VaR vs 10 day VaR
Even while using historical simulation VaR, 1 day VaR is converted into 10 day VaR by multiplying 1 day VaR by Sqrt(10) for regulatory reporting purposes.
What are the underlying assumptions for ...
1
vote
0answers
100 views
Compute the VaR from NPV (Net present value)? [closed]
A client is evaluating an investment in
Indochina requiring an initial expenditure (period 0) of 10,000, and
which then in periods 1 and 2 gives a benefit V1 and V2. Assume
that the discount rate to ...
0
votes
2answers
90 views
Value-at-Risk theory papers
I am looking for some papers related to the value-at-risk theory. I would like to focus on mathematical aspects of VaR. I would like to read something about modern approaches to VaR (maybe using ...
2
votes
1answer
142 views
Historical VaR for shares in foreign currency
I'm currently studying John Hull's [1] example on historical value at risk for portfolio consisting of four stock indices.
In this example Hull converts the prices of the stock indices to the home ...
2
votes
1answer
238 views
The VaR of a portfolio with Student t returns
A portfolio consists of 300 stocks,150 of A and 150 of B, their annualized covariance matrix is as following:
$\begin{pmatrix}
0.09 & 0.018\\
0.018 & 0.04
\end{pmatrix}$
Thoese two stocks ...
1
vote
0answers
45 views
Does it make sense to subtract VaR from spot shocks?
I have a model to compute the Event Risk (in dollars) from a shock to the spot price of an asset. I also have the 10-day VaR PnL for the same assets returns. These two numbers are then aggregated to ...
3
votes
1answer
112 views
Value-at-Risk for a portfolio model with Gearing
My models:
Say I want to construct a portfolio so I maximize my expected return while keeping my risk (measured by Value-at-Risk) lower than my risk target.
$$\max \sum x_i \mu_i \\
VaR_{0.05} \leq \...
2
votes
0answers
103 views
Methods for calculating Expected shortfall
Let B1, B2 be two defaultable zero-coupon bonds maturing in 1 year, each
with a face value of $100. Assume:
each bond is priced at 90 dollars
each bond has a 4% probability to default within 1 year
...
4
votes
1answer
569 views
How do I compute Value at Risk of a European call option?
Consider a European call option on a non-dividend paying stock, where the
option has strike K = 100 and expiry T = 0.25, i.e. the option expires 3
months from now. The option is on a single share. The ...
2
votes
0answers
42 views
VaR of ARCH model
Consider the following:
$r_t = \theta r_{t-1}+u_t$
$u_t=\sigma_t\epsilon_t$
$\sigma^2_t=\omega+\alpha u^2_{t-1}$
$-1<\theta<1,\omega>0,\alpha \in(0,1)$
What is the 99% 2-day VaR of a ...
1
vote
1answer
241 views
Value-at-risk and Equity delta
How to validate value-at-risk calculation on an equity portfolio using equity sensitivities? I don't have trouble doing that for rates instruments or options but I don't know which underlying risk ...
1
vote
0answers
123 views
Monte Carlo VAR with differente asset classes
I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
0
votes
1answer
108 views
Scenario generation for Value at risk: How to interpret the scenarios
This is a a simple and rather pratical approach and not theoretical. Let's assumes I have generated 250 scenarios for a given fixed portfolio. Hence we assume that the asset returns can result in 250 ...
1
vote
1answer
82 views
Computing Montecarlo VaR for a single asset
I'm trying to understand the procedure to compute the Value-at-Risk for a single asset by implementing the Montecarlo technique.
Here it follows the procedure step-by-step in 5 points:
selecting the ...
0
votes
1answer
359 views
Variance-Covariance VaR: how to get the volatility?
Because the variance-covariance VaR assumes that the returns are normally distributed, in theory it is easy to get VaR by simply finding the mean and the volatility (standard deviation) of the ...
0
votes
1answer
437 views
Delta-Gamma VaR question on inputs (do I need only one delta or the delta for the past 500 days?)
When calculating a VaR using the Delta-Gamma approach, I am supposed to use this formula:
ā(V) = Delta * ā(X) + 0.5 * Gamma * ā(X)Ā²
where:
ā(V) = change in value of the asset in portfolio
ā(X) = ...
0
votes
2answers
111 views
Procedures to follow when VaR model fails backtest
I was wondering what the correct procedure is to follow when a VaR model fails a backtest (either conditional coverage and/or independence tests)?
Assuming I am restricted to using a historical VaR ...
2
votes
2answers
167 views
How to prove the following relation of Conditional Value-at-Risk and Value-at-Risk?
How to prove the following relation of Conditional Value-at-Risk $\text{CVaR}_{\alpha}(X)$ and Value-at-Risk $\text{VaR}_{\alpha}(X)$,
\begin{equation}
\text{CVaR}_{\alpha}(X) = \text{VaR}_{\alpha}(X)+...
2
votes
0answers
57 views
Pricing default risk in cryptos
I'm looking to figure out how to price "insurance" against a counter-party defaulting in an OTC cryptocurrency transaction. I think the first measure would be to calculate VaR? I'm planning on ...
1
vote
1answer
76 views
Value at Risk for normal r.v. with shock (regimes)
I am struggling to understand how was this simple Value-at-Risk calculated. It's Example 1 in DanĆelsson, JĆ³n, et al. "Fat tails, VaR and subadditivity." Journal of econometrics 172.2 (2013): 283-291 (...
0
votes
1answer
100 views
How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?
How to calculate $\frac{\partial\ \text{CVaR}_{\alpha}(\min(X,d))}{\partial d}$ and $\frac{\partial\ \text{VaR}_{\alpha}(\min(X,d))}{\partial d}$?
Here, $\text{CVaR}$ is short for Conditional Value-...
2
votes
1answer
239 views
How to compute a single Value-at-Risk (a single quantile) of portfolio returns taking into account correlation between individual returns?
Introduction
My goal is to retrieve a single Value-at-Risk (VaR) of a N(0, H) random variable $X$ at the $\alpha \in (0,1)$ confidence level where H is a known d-dimensional positive definite matrix ...
1
vote
0answers
30 views
Hedger's utility function associated with minimizing value at risk
What must be the general shape of a hedger's utility function if the hedger is minimizing value at risk?
What is a simple example of such a utility function?
