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Questions tagged [risk-management]

The identification, assessment, and prioritization of risks, followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities.

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How to calculate impact on portfolio with various asset classes

I was given a portfolio consisting of equities, commodities and high-yield bonds and respective weights. I also have correlation data of different asset classes and standard deviation of each asset. ...
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36 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 ...
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42 views

Scenario Analysis - Real life application

Given a portfolio consists of Stock = usd 40, Bond = usd 40, commodity =usd 20. Also given the correlation between these assets. Scenario 1 : stock down by 30% When performing scenario analysis, do ...
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2answers
72 views

Portfolio volatility - Real life application

Given that a portfolio consists of Stock=USD 30, High-yield bonds(duration=5 years,spread duration=5 years) =USD 40 , Commodity = USD 30. I was given monthly data for MXWD Index for stock, CL1 Comdty ...
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1answer
36 views

how to simplify Inflation year-on-year option to Zero-coupon option

Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon ...
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2answers
126 views

Verifying two properties of the Clayton Copula

So I'm trying to verify the first two properties of a copula for the Clayton model. The first two properties being: $C(u_1,…,u_d)$ is non-decreasing in each component, $u_i$ The $i^{th}$ marginal ...
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2answers
69 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 ...
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2answers
136 views

How does one make money from CVA (Credit Valuation Adjustment)?

I am new to Quantitative Finance but have been doing a lot of reading on Counterparty Credit Risk. I understand the definition of CVA being: "the difference between the risk-free portfolio value ...
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Example of Coherent Risk measure with Compact Representation

Every coherent risk measure $\rho$ can be represented as $$ \rho(X)\triangleq \sup_{Q \in \mathcal{Q}} \mathbb{E}\left[ -X \right], $$ for a set of probability measures $\mathcal{Q}$ defined on the ...
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1answer
109 views

How to check if a portfolio has momentum bias

I am wondering what methodology exists to check if a fund/portfolio is having momentum bias or chasing the past performance, assuming you have their full returns and full portfolio holdings for past ...
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41 views

Risk mapping a zero-coupon bond portfolio

I'm trying to understand example 2.6 taken from McNeil and Embrechts "Quantitative Risk Management". The example consists of obtaining the risk mapping of a portfolio of $d$ zero-coupon bonds. The ...
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1answer
88 views

Co-variance of Portfolio A with Portfolio B

I'm trying to calculate the correlation between two separate portfolios. I've used A*COV(AB)*B to calculate the co-variance of each portfolio where: A = Array ...
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4answers
91 views

How to test the linearity assumption of a model?

Let's say I want to have a model that projects income over a stressed period. I have a marked-to-market component that shows the P&L of trading book positions during this stressed period. Along ...
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1answer
85 views

Retail Algorithmic Trading

Is it possible for the retail algo traders to take the same approach to risk management as the larger quant funds? is there a risk management budget imposed on the trader beyond that which they impose ...
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2answers
174 views

Kelly criterion for normally distributed returns

If the returns of my strategy are distributed like 𝒩[μ,σ], what is the optimal fraction of capital to invest in each single trade, as a function μ and σ? Help! PS. I know that normally distributed ...
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71 views

Full Revaluation vs Factor-based Model for risk management

I am looking for literature on comparison of these two approaches. It looks like many places are using some type of Factor-based Model (Barra, Axioma, Northfield, etc.) for risk management purposes. ...
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3answers
89 views

How to determine the optimal start capital for a strategy?

Suppose my strategy generates a stream of daily profits distributed like 𝒩[μ=1€, σ=10€]. Intuitively, if I trade with 10€ start capital: I could very well be ruined on the first day, if the first ...
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31 views

Reference: Journal on Risk Measures

I'm wondering, where can I find a list of the journals which specialize (partly) in publishing risk-measure related topics? If no such standard list exists, what are some top and mid-tier journals ...
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1answer
95 views

Which market developments are we likely to see within the next years?

I am working on an analysis to estimate financial risks, especially for pension funds. More specifically, I am trying to define some stress scenarios which could have an affect on the solvency of a ...
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1answer
93 views

Construct a butterfly interest rate portfolio to eliminate PCA exposures

I have data from 2012 to 2016 for interest rates whose term range from 2 month to 30 years, a total of 10 Principal components can be calculated. Then I want to construct a portfolio, $$WFLY = w_1 *5Y ...
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41 views

GARCH(1,1) and Value at Risk: Rolling window or non-overlapping samples

Currently studying on financial risk management. I want to test different methods of VaR estimation. I want to model volatility using a GARCH(1,1) model. My question is what should the size of the ...
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2answers
142 views

Position Sizing Algorithm for Multi Asset Portfolio

I'm currently working on a position sizing algorithm for my trading system. By combining fixed ratio money management and setting the stop loss based on the current ATR value I receive reasonable ...
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1answer
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When estimating P/L through greeks based on zero rate curves, does it contain time (theta) PNL?

Suppose on day 1 we calculate a delta wrt. a point on an interest curve of zero rates, we then let 1 day pass, recalculate the interest curve of zero rates with the same bonds (though now day 20 bond ...
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2answers
312 views

Hull White help needed

I've been trying to calibrate Hull-White 1 Factor & 2 Factor model using Caps but I've some major doubts about my methodology, and would really appreciate some help. I am using these formulas ...
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1answer
216 views

How is internal risk transfer different than moving from banking book to trading book?

Reading the FRTB paper, I'm not clear on what an internal risk transfer is. To me, it sounds like moving an asset from the banking book to the trading book or vice versa.
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1answer
192 views

Risk management tools for long term Gamma/Vega sellers subject to margin calls

TL;DR: if you're a retail investor and you systematically sell long-term vertical spreads while staying Delta-neutral, your main risk comes from Vega and the Gamma of opening gaps that can throw you ...
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2answers
91 views

How to calculate the multi-asset class portfolio vega?

I am viewing a risk report of a hedge fund and the portfolio vega seems to be a plain summation of the vegas of the different asset classes the fund invests in (i.e. Equity, Credit etc) As far as I ...
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1answer
94 views

Klein and Chow Orthogonal Transformation - Lowdin Orthogonalization

I've doing research on the orthogonal transformation in Orthogonalized Equity Risk Premia and Systematic Risk Decomposition They borrow a mathematical technique called symmetric orthogonalization ...
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0answers
54 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 ...
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0answers
60 views

Statistical methods to compare two financial series data

I have two financial series data, x and x', where x' was formed form ...
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1answer
43 views

Risk attribution model without weights data

I was just wondering if there are risk attribution model that does not require the asset weights data. It appears that most risk attribution models do require asset weight data. I am looking for model ...
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0answers
42 views

Calculating daily underlying move from options volatility?

My broker has provided a risk report that shows our options book shocked at various standard deviation moves of the underlying. Their report has the future at $66.64, ATM Vol at 23.74% with 2 days ...
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59 views

Constrained Optimization for performance attribution

I am trying to perform constrained opmitization for portfolio performance attribution analysis. Specifically, I am trying to determine the impact of sectors performance on the S&P 500 index. Min ...
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104 views

Backtest Portfolio Analysis

I actually finished an algorithm that i can use to extract all the trades for each stock (each file for each stock). Essentially, i run this code on Excel where there are the input about one stock, ...
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124 views

How to compute the portfolio risk when weights are negative?

In QMiF (p. 239) , the variance of a portfolio is defined as: V(R) = w'Vw = w'DCDw = x'Cx Does this formula hold if the weights are negative (i.e., short)? For example, if I have a 5x5 covariance ...
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1answer
667 views

Absorption ratio by Mark Kritzman

In Principal Components as a measure of systemic risk, the author Mark Kritzman defines absorption ratio (AR) as the fraction of the total variance of a set of asset returns explained or absorbed by a ...
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57 views

CreditGrades model calibration and initial values

Currently doing a project on structural models, and I want to apply the CreditGrades model. My question is what values are the parameters going to take, in order to update the implied probability of ...
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1answer
94 views

Calculating Flat Price Risk for Physical Commodity Trades

I've been reading Craig Pirrongs Economics of Trading Firms published by Trafigura: https://www.trafigura.com/media/1364/economics-commodity-trading-firms.pdf Very informative read. The point I have ...
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47 views

Jump diffusion model and Firm probability of default

I want to examine whether corporate events affect firm's probability of default. My initial thought was a jump diffusion model, although in the literature, the only work I found, involved CDS market ...
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1answer
107 views

Using option pricing methods to model real asset liquidity

Liquidity risk (in the sense of asset exit risk) is warranted on investments that may not be easily divested at the going market or fair-value price. I am looking at a portfolio of private assets ...
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2answers
270 views

Risk Parity / Equal Risk Contribution with Tail Risk Measures

Risk Parity or (synonymous) Equal Risk Contribution is an approach to portfolio construction which could work in theory with a broad class of risk measures. Yet, all references I have found so far ...
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0answers
35 views

z-score of an active return with a no-volatility benchmark

I don't know how to approach the problem I am having. Basically, the statement I am trying to make is: the fund's return is X standard distribution away from the mean. Normally, for a single fund, ...
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24 views

Altman Z-Scoring and unknown variables [closed]

Assume we have the known Altman Z-Scoring model $Z= 0.012X_1 + 0.014X_2 + 0.033X_3 + 0.006X_4 + 0.999X_5$ But the variables $X_i ,i=1,2,3,4,5$ are unknown. Is it statistically correct to make an ...
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0answers
18 views

DCCfit speed up formula

I am estimating the covariance matrix by using GARCH DCC model with function dccfit from package rmgarch. My code is something like: library(rugarch) library(rmgarch) ...
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37 views

Cramer-Lundberg: Adjustment coefficient does not exist

The question is about Ruin theory and the Cramer-Lundberg model. I am wondering if there is an example of distribution where the MGF is finite, but the adjustment coefficient does not exist. Can you ...
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1answer
92 views

Using Normal Distribution to forecast active return

I wanted advice on how to go about forecasting active return via a standard normal distribution, The asset is a security with annual volatility of 6%. The benchmark is a 5% annual return with 0% ...
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1answer
84 views

Value-at-Risk and dividend payments

How should dividends be considered when computing Value-at-Risk for a stock portfolio using Historic data. To simplify let's consider a very simple portfolio of one long position on a stock. My VaR ...
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1answer
860 views

Semivariance calculation (downside deviation)

what is the accurate formula for semivariance? I see two versions up to now: this version which considers as N (denominator) all the numbers over/under the mean-or any other number. This is the ...
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48 views

How can I find what Loss Given Default to use

I want to come up with the appropriate loss given default for a commodity derivative in my CVA calculation. would anyone know where I can find this information?
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1answer
84 views

Where can I find free security and derivative pricing software?

I am looking for a free derivative valuation software that can compute value and sensitivities. It should be easy and straightforward to use, e.g., I can get results by supplying market data and trade ...