Questions tagged [value-at-risk]
The value-at-risk tag has no usage guidance.
137
questions
4
votes
1answer
196 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
22 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
156 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
66 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
127 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
81 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
142 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
53 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
52 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
125 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 €.
I have the z-value, the daily ...
3
votes
1answer
131 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
53 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
710 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 ...
1
vote
1answer
115 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
46 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
153 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
28 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:
$$max(VaR_{t−1},m_c × VaR_{avg}) + SRC$$
$SRC$ is ...
2
votes
1answer
105 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
114 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
378 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
75 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
88 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
105 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
206 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
111 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
92 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
417 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
179 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
113 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
91 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
78 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
333 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
373 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:
∆(V) = Delta * ∆(X) + 0.5 * Gamma * ∆(X)²
where:
∆(V) = change in value of the asset in portfolio
∆(X) = ...
0
votes
2answers
99 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
145 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
56 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
72 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 Daníelsson, Jón, et al. "Fat tails, VaR and subadditivity." Journal of econometrics 172.2 (2013): 283-291 (...
0
votes
1answer
98 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
218 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?
0
votes
0answers
42 views
Does it make sense to simulate from the multidimensional GBM?
Suppose I have times series data on 3 assets and I do $N$ simulations (GBM) first for each of assets individually and then from a multidimensional GBM since their log-returns are correlated (I use ...
2
votes
1answer
249 views
Volatility scenario generation for value-at-risk
I have the following problem: For a single name plain vanilla equity option calculate 1y VaR for given confidence level.
Is there any state-of-the-art or current market practice known on how to ...
1
vote
1answer
243 views
Negative VaR equivalent Volatility (VEV) and its meaning?
Can a VaR equivalent Volatility (VEV) as defined by KID/PRIIPS law be negative and what does it mean if it has a negative value?
1
vote
1answer
49 views
What is the relationship of Value-at-Risk of a random variable $X$ and a constant $D$ $VaR_{\alpha}(min(X,D))$and $VaR_{\alpha}(X)$?
Suppose $X$ is a nonnegative random variable and $D$ is a constant, what is the relationship of $\text{VaR}_{\alpha}(min(X,D))$ and $VaR_{\alpha}(X)$? Here, $VaR$ stands for Value-at-Risk as,
$$
VaR_{\...
