Questions tagged [risk]
The possibility that a negative event (such as a loss) will happen.
589 questions
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Is GARCH (and or it's variations) actually used in risk-modelling for expected-shortfall?
I understand there are limitations and practicality issues with GARCH, but does any company actually use it in their risk-management system when calculating their expected-shortfalls? Even as a basis ...
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How to handle intraday risk when evaluating performance with PnL/VaR?
When evaluating a proprietary trader's performance at the end of the year, it's common to use the PnL/VaR ratio as a key metric. From what I understand, the VaR used as the denominator should ...
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Why would a pension fund use immunization?
According to wikipedia, https://en.wikipedia.org/wiki/Immunization_(finance), immunization (i.e. ensuring assets and liabilities are affected similarly by rate movements) is used by pension funds to '...
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Hedging benchmark issuance swaps
Suppose a corporate is issuing a fixed rate bond and swaps into floating by receiving fix on a swap (let’s say it’s a benchmark bond and thus has a significant dv01).
The bank paying fix in this swap ...
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VBO - Vega Break Out
Good morning, everyone,
I would need to understand what is meant by vega break out of options on underlyings having themselves an expiration.
The trader showed me a matrix with one dimension ...
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Transforming log-return expected shortfall to arithmetic-return expected shortfall
When deriving the Value at Risk (VaR) for log returns, one can easily transform the log-return VaR to an arithmetic-return VaR via $VaR_{arithmetic} = e^{VaR_{log}}-1$
However, how is the log-return ...
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Quanto pricing question, stuck on self financing strategy derivation
I'm a bit stuck on doing part 2, I'm not sure if I have done part 1 correctly...
\begin{align}
&\max \left( 0, X(T) \tilde{S}(T) - X(\theta) \tilde{S}(\theta) \right) \\
&\tilde{S}(T) = \tilde{...
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Resources for equity risk management industry best practices
Has anyone got any papers that can help me lower volatility of a market neutral equity portfolio?
I have a basic covariance variance matrix which is used to optimize the portfolio but I am wondering ...
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How do you map bond RepFlows into forward swap RepFlows?
RepFlows
Practically speaking, a RepFlow is a vectorised representation of the cash flows from investing in a cash instrument that can be used for modelling.
For example, an investment of £1 today (...
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Coin flip 5 heads in a row how much would you pay interview question
I was trying out interview questions in preparation for quant interview season and came across this question: Flip a coin 5 times in a row. If you get 5 Heads, you get 28 dollars. How much would you ...
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Computing statistical risk factors with SVD/PCA - do you center daily returns?
Imagine you have a matrix of returns (n assets, t days) and want to compute c statistical risk factors using PCA/SVD, so that you get (n, c) matrix of factor loadings and (c, t) matrix of factor ...
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PCA risk modelling
Been doing loads of reading about PCA, FA and SVD but still fail to understand the fundamentals of how PCA links with factor analysis in the context of risk modelling. Here is where I'm stuck:
Given a ...
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Scenario probability in portfolio optimization
I have few questions regarding linear programming formulation of expectile-based portfolio optimization. From this article on page 51 the LP algorithm is presented.
And the problems are that I don't ...
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Decompose portfolio in factor risk
I am reading the risk chapter of Grinold Active Portfolio Managment. I understand how to calculated specific and factor risk of my portfolio, what I don't understand is how to calculate how much risk ...
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Improving Portfolio Optimization on a Mean-Variance Basis
Is there a point to conduct research to improve mean-variance optimization (MVO)? Because I understand that most of the poor performance in MVO is a result of the estimation error in expected returns.
...
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Subpar Results of Historical Portfolio Optimization with Few Assets
Probably a simple question to the P-Quants here, but if you performed portfolio optimization using a historically calibrated covariance matrix (a rolling month of daily returns) with very few assets, ...
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Risk Aversion Coefficient Literature Rationale and Sources
I'm running a Black-Litterman model and for the Risk Aversion Coefficient I have two potential formulas.
The first is the standard formula which I believe is used in the original Black-Litterman ...
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When optimizing a portfolio for risk parity, can any portfolio weights turn negative?
As the title reads, when performing risk parity optimization (equal risk contribution amongst all assets to the portfolio volatility), is it possible for weights to turn negative?
I understand that in ...
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PCA and OLS regression to transform to interest rate risk? [duplicate]
I’ve been working on different interest rate risk transformation methods for swaps and was interested in implementing PCA & OLS regression. I’m looking to bucket my exposure in all tenors to ...
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JP Morgan CreditMetrics
I am trying to apply CreditMetrics on a 2 bond portfolio. As far as I know, this model returns the expected recovery rate and the volatility between those 2 bonds, so my question is how I calculate ...
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Cubic Spline Interpolation partial derivative to the point
Still didn't figure out this, so looking for some help, kindly apppreciated.
By this blog https://blog.timodenk.com/cubic-spline-interpolation/index.html, the piecewise cubic spline interpolation is ...
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How is option pricing related to the correlation between implied volatlity and the underlying?
The correlation between the index returns (e.g SPX) and its changes in option-impled volatility (e.g. VIX), is strong, stable and negative (the implied volatility feedback effect). To me at least, it ...
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Calculating marginal risk contribution of FX for foreign asset portfolio
I am a European investor investing in US equities. My US equities portfolio returns in EUR can be broken down into (1) equities returns in USD terms, and (2) USDEUR spot currency returns.
Using the ...
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constrains of return distribution and risk return trade off
Suppose we have a portfolio $V$, we are only allowed to invest in one stock $S$, its price movement follows the geometric brownian motion, i.e. $dS=S(\mu dt+\sigma dW)$. We are allowed to choose ...
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Why should investors be compensated for accepting systematic risk? [closed]
Investors should be compensated for accepting systematic risk, as it cannot be diversified.
Why do the investors need to be compensated for accepting systematic risk? Because no one can avoid it and ...
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On measurements of ambiguity and their shortcomings
Ambiguity in quant finance is defined as the uncertainty in the probabilities of the return distribution, whereas risk is defined as the uncertainty in the returns of the asset.
There are various ...
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Potential Future Exposure for vanilla swap
I need to calculate the PFE for vanilla swap. I wonder if it makes sense to simulate the MC scenarios with a 1-factor Hull white model. In my opinion, this model only allows parallel curve ...
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Taking a set of normally distributed random variables as the sample space to fitting an exponential distribution
Disclaimer, this is my first question/interaction in this forum.
Let's assume I have random variables that are normally distributed. Then, say I take the observations that are greater than the mean, i....
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What is the meaning of the asset risk contribution in a long-short portfolio?
If I have a portfolio of weights $\mathbf{x}$ and the covariance matrix of asset returns $\Sigma$ then the volatility contribution per asset is given as standard $\mathbf{x}' \Sigma$. For a standard ...
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If investors are risk-neutral, should the (equity) risk premium be zero?
I looked up ChatGPT and they stated that the (equity) risk premium should be zero for a risk-neutral world. The definition of a risk-neutral investor is that one is indifferent between additional or ...
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If there was a way to back out implied volatility (IV) from a stock, would it be the same as the IV backed out from an option on that same stock?
I know that it is not possible to back out an IV for a stock, because the concept of IV is based on a model with underlying assumptions applied to pricing an option.
I was thinking of why IV is ...
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From parameter risk (sensitivities) to market risk (sensitivities)
In models where the underlying is not modeled directly - such as in the HJM framework or short rate models - how does one then compute the Greeks, i.e. sensitivites wrt. market variables.
As an ...
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Portfolio risk of correlated assets using Mahalanobis distance
I am trying to understand if there is an agreed methodology to measure the total risk in a portfolio of correlated assets.
I am taking a simple model of stock prices following geometric Brownian ...
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Value At Risk Modelling for electricity market with negative prices
I'm a bit at loss after trying to find papers regarding tail risk for electricity markets. There doesn't appear to be a whole lot of literature (or perhaps I haven't managed to find it) regarding ...
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Basis risk between future and a non-dividend paying stock
I am a bit confused about the definition of basis risk, and how it applies to a zero dividend stock.
A study manual that teaches me about that mentioned basis risk happens when there are mismatches in ...
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Can PCA be used to transform a ladder of interest rate risk?
The context
For traders/market makers on interest rate swaps desks, it is essential to have a model that transforms risk from its most complex representation (i.e. a ladder of every tenor) into a less ...
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Tricky question about returns [duplicate]
I have a list of monthly returns.
-10% -20% -70% -30% -15% -60%
The total end return is -94.859%. Because you calculate = 100 x (1+ -10%) x (1+ -20%) x ...
Now I ...
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Estimating risk premium with cross sectional regression
I am trying to estimate a carbon risk premium according to the Fama & MacBeth methodology using a cross-sectional regression approach.
Therefore, I regress the excess return in period t+1 on the ...
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Fama French Factor adjusted returns
I want to understand the extent to which portfolio performance can be explained by the three Fama French Factor model. I use the following approach:
Regress the portfolio's excess returns against the ...
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FRTB - Federal Reserve vs Basel
The federal reserve has released its proposed Market Risk rules for Basel III.
https://www.federalreserve.gov/newsevents/pressreleases/bcreg20230727a.htm
Is anyone aware of any resource that compares ...
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Standard Deviation and Monotonicity property
I just read that standard deviation is a coherent risk measure, and therefore it should satisfy the monotonicity property:
$X_1 \geq X_2 \implies \rho(X_1) \leq \rho(X_2)$ where $X_1,X_2$ are asset ...
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"fix" a sample covariance matrix which is not positive semidefinite by using daily returns instead of monthly
In the portfolio optimization problem at hand, one of the constraints is that the tracking error should not be greater than $\gamma$.
The constraint is therefore:
$(\textbf{x}-\textbf{w})^\mathrm{T}\...
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Risk of bond calculation
I am studying a course and I am a bit confused on how to find the a bonds $\sigma$. My course mentions the following:
Once calculated the expected returns on the bond $\mathrm{E}(r_d)$, we can
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Intuition behind risk-return realation (Mark Joshi's concepts 1.2) [closed]
In Mark Joshi's "The concepts and practice of mathematical finance" section 1.2, it is given an intuitive motivation behind "high risk high returns" claim. It goes as follows:
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If I know the Price, DV01, and Duration of a Fixed Income instrument, is their approximation for the Convexity?
As the title says, I am looking to see if there is a good approximation for the convexity of a Fixed Income instrument. Say I know all the parameters of the instrument, can the Convexity be written as ...
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High-frequency risk management methodologies
In a high-frequency environment, such as a proprietary trading firm or market making firm, the primary goal of the risk management team would be to limit potential losses, but how is that done in this ...
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Derivation of optimal portfolio weights using Risk Budgeting approach
In Thierry Roncalli's book Introduction to Risk Parity and Budgeting (2013), he gives an example of particular solutions to the Risk Budgeting portfolio such as for the $n=2$ asset case.
The risk ...
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How to construct a forward exposure portfolio with bonds?
I was asked in an interview to get an exposure to 5Y5Y forward rate using bonds alone. Essentially it is short 5Y bond and long 10Y bond, and I needed to compute the relative weights. Regarding risk:
...
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Alternative form of mean-variance optimization that uses standard deviation
I'm curious about an exercise found in Optimization Methods in Finance. Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm ...
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Maximizing Mean+Variance in a Portfolio
Mean-Variance optimization trades off expected returns with portfolio variance. The idea is that excess variance is not desirable.
But what if you weren't averse to high variance and you wanted to ...
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