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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88 views

Risk measurement of multicallable bonds

Assume you have bought a multicallable bond where the issuer has the right to redeem the notional at various dates, e.g. a $10$ yr maturity, $5$% coupon yearly and each year one call date. Next, ...
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57 views

How to calculate contributions to the granularity adjustment

In the Basel pillar 2 framework a granularity adjustment is introduced. While the capital requirements in pillar 1 do not take concetrations into account, this is meant to be covered with this ...
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How to model run-off ratio for non-defined maturity deposit?

I'm trying to model run off ratios for different deposit products as well as how long it takes to lose all deposits, would anyone please suggest any methodology? In addition, would I be able to define ...
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32 views

Implications of modeling operational risks without frequency distribution

When modeling operational risk, the Loss Distribution Approach (LDA) is widely used. Usually, we model the loss frequency distribution and the loss severity distribution and then aggregate both to ...
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53 views

Exercise on Delta-Neutal-Hedging

Suppose you have three positions in the following assets in euros: long on 10.000 calls (maturity T = 3 months, strike= 0.55, Delta (1 call) =0.533), short on 210000 calls (maturity T = 3 months, ...
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71 views

Resources for Bayesian methods

I will be joining a risk management firm in a few months, and I was wondering if some of you could help we with resources on certain methods. Some of the things that I would be called upon to work on ...
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60 views

Optimal withdrawal rate based on alpha and drawdown

My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to avoid risk of ...
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294 views

Deep Reinforcement Learning in Quant Finance?

I've been struggling to find engaging papers on the application of deep reinforcement learning in quantitative risk analysis, portfolio management, algorithmic trading and/or options pricing. What are ...
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25 views

What is the shadow cost of capital for a bank?

With regard to banks RWAs (risk weighted assets), what does it mean a trade leads to a positive shadow cost of capital?
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70 views

how do we use portfolio optimization to hedge an existing portfolio?

I am working on a risk management project and want to create a custom hedge portfolio to add on to an existing portfolio. I am wondering how do we treat the existing portfolio in the optimization ...
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40 views

Extreme value theory in QRM: Lemma 5.16 from Quantitative Risk Management: Concepts, Techniques and Tools

From the slides: https://raw.githubusercontent.com/qrmtutorial/qrm/master/slides/qrm_05.pdf Lemma 5.16 Assume, for some $u$, $F_u(x) = G_{\xi, \beta}$ for $0 \leq x < x_F - u$. Then $F_v(x) = G_{\...
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58 views

VAR interpretation

I definitely struggle to understand the following interpretation of VAR (value at risk) provided by Jorion $$VAR(c)=E[X]−Q(X,c)$$ where $X$ is a random variable, $E[X]$ its expected value, $Q(X,c)$ ...
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How to set a portfolio turnover ratio threshold according to volatility?

With the various crises affecting the financial markets, here a pandemic, this ratio skyrockets almost every time, which limits its interpretability. We know that the ratio increased during the ...
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How to link market risk and the transition to the new risk-free rates?

I'm a market risk analyst intern and I've the opportunity to do a project related to it. So I would like to move towards SOFR and €ster transitions, I have seen quite a lot of documentation on this ...
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164 views

The best “risk measure” for an investor who does not want to lose any of his seed money

Question There is an investor who is afraid of losing any of his seed money (initial investment). Variance of investment returns is not a problem to him. He is willing to take variance as long as he ...
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1answer
117 views

Code (Python or R) references for operational risk models (AMA/COM)

I have to build an operational risk model and to be compliant with Basell II and III regulations I thought of using AMA (Advanced measurement approach) or COM (change of measurement). We have no ...
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1answer
168 views

Core Deposits when modelling Non-Maturity Deposits according to IRRBB

When modeling Non-maturity deposits (NMDs) the Basel Committee suggests the following (see 31.109 of the guidelines): Banks should distinguish between the stable and the non-stable parts of each NMD ...
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70 views

Counterparty Risk [duplicate]

I am looking for some good text books for Counterparty risk management and measurement with many working examples. Could you please suggest few such books. Thanks for your help.
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50 views

A simple question about VaR estimation

"A 99% VaR using 1,000 (simulation) replications should be expected to have only 10 observations in the left tail, which is not a large number. The VaR estimate is derived from the 10th and 11th ...
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75 views

Looking for non-GAUSS Code for Thiery Roncalli's book on Risk Parity and Budgeting

I am going through the book 'Introduction to Risk Parity and Budgeting' by Thierry Roncalli (2013). The author provides software for the various concepts illustrated in the book, but it is all done in ...
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1answer
76 views

Option proofing: Analytical solution for option math

How do I prove the following equation: P(X=100)≤(P(X=110)-P(X=90))/2 I am not sure how to start and whether it involves using the Black-Sholes formula or not (something like this: https://www.youtube....
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54 views

Good ways to select best decision among N decisions, each with a profit/loss distribution? [closed]

I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but ...
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1answer
102 views

Interest rate swap performance attribution

I have learned some attribution models such as Campisi. It decomposes the return of bond into treasury return, spread return, and coupon return. It works like: $$r = y\times dt - D \times dy_\text{...
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146 views

CVar optimization algorithms

An alternative measure of losses to Var, with more attractive properties, is Conditional Value-at-risk or CVar which is also called Mean Excess Loss, Mean Shortfall, or Tail Var. CVar is a more ...
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105 views

What put options would the Universa Tail Fund have bought?

According to this Bloomberg article, Universa was up 3,600% in March 2020, by hedging with extremely out-of-the-money puts: https://www.bloomberg.com/news/articles/2020-04-08/taleb-advised-universa-...
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1answer
151 views

How to derive the expected loss from the credit risk of a bond?

I am trying to work out a formula to derive the expected loss from the credit risk of a bond. My idea is to tie the credit risk to credit valuation adjustment and derive the expected loss from there, ...
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48 views

Can I say VAR is a prediction report?

We use Algorithmics RiskWatch where portfolios are analyzed by VaR over scenarios. Can I say that they are predictions reports? or descriptions reports?
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26 views

lot size formula for cfd and forex based on risk percentage

I have a question regarding the calculation of the lot size for cfd and forex instruments when we have a risk amount as a percentage of the balance. So how to compute the lot size to trade knowing the ...
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1answer
103 views

PnL due to model recalibration and its relationship with hedging error

Consider the case where at t=0, I calibrate my model to the market, but at t=1 my model is no longer able to recover the price in the market, so it needs recalibration. Say I have delta hedged my ...
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2answers
41 views

Calculating the allocation of a fund given two correlated variables

Imagine this hypothetical situation: I have a time series of cumulative performance of a fund and two time series of equities that are highly correlated to them. I know that that this fund ONLY ...
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3answers
1k views

Which is riskier: a call option or the underlying?

From Joshi's Quant Interview Questions and Answers: What is riskier: a call option or the underlying? (Consider a one day time horizon and compute which has bigger Delta as a fraction of value). I ...
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Credit Migration: Risk [duplicate]

Hi I am given two tables of two tables showing data about fictional corporate business partners and relevant credit risk data – ID, rating, probability of default (PD, defined by rating), loss given ...
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1answer
126 views

What is the intuition of CAPM model with Intercept at 0?

I only have a very general theory-based knowledge on Jensen's Alpha. I'm very curious about Capital Asset Pricing Model with intercept at 0. May I know what is the intuition behind this? What does it ...
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2answers
153 views

How does a pricing model 'understand' the cost of hedging?

Suppose I am pricing a multi asset at the expiry payoff. Theoretically I define their joint distributions in the risk neutral measure, and price using expectation. However, how do I know that the ...
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52 views

Pricing/Hedging a yield curve spread option (YCS)

I have 2 perspectives as to what model to use for a YCS option: It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it. To hedge the vega, I will need ...
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2answers
92 views

Definition of drawdown

Say I am considering the entire time horizon, is max drawdown what I've drawn in blue, or what's in purple? Likewise, how about the current drawdown for the period in black (in practice, I am asked ...
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1answer
69 views

What are the differences between hedging with swaps, options or futures? [closed]

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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2answers
104 views

Why do (life) insurance companies face equity risk?

I am currently reading through a study published by the Institute and Faculty of Actuaries on hedging practices within the insurance industry. Within the executive summary, under 'Key Risks', it is ...
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1answer
625 views

Simple strategies for tail risk hedging that retail investors can use

Universa Investments run by Mark Spitznagel popularized the idea of portfolio insurance (also known as tail hedge) protecting the investor against severe market declines (tail risks). By using this ...
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2answers
110 views

What is the best way to hedge a position with negative interest rate?

Suppose we have a following situation: $1).$ Company A takes a loan from Bank A at a floating interest rate. $2).$ In order to offset the payments at floating interest rate, Company A enters into an ...
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1answer
77 views

CRRA Ultility, simple question

for CRRA, does increasing gamma leads to increase in risk-aversion? Looking at the curve, I think increasing gamma leads to less in risk-aversion (since the risk preimum is less). But in terms of ...
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1answer
37 views

Properties of risk aversion

What are some common properties for risk aversion? I know the basic definition of the risk premium, absolute risk adversion, relative absolute risk adversion. Besides the basic definition, what are ...
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1answer
269 views

Variance attribution calculation from a covariance matrix

Say I have a portfolio with two assets with weights $(x, y)$, and the covariance matrix of the two asset is $((a, r)(r, b))$. Then the total portfolio variance would be $x^2a+2xyr+y^2b$. It is easy to ...
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1answer
96 views

Risk Neutral Pricing, a quick question [closed]

I am a newbie. The risk neutral pricing has the following formulation: $$P=\frac{\hat{E(d)}}{R}$$, But the discounted expected value has the formulation of: $$P=\frac{E(d)}{R}$$. The text book ...
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1answer
42 views

Minimum Variance Hedge Ratio and Risk Capital Relation

So I understand that the minimum variance hedge ratio minimizes the second moment of the portfolios. My question is how is it related to the size of the risk capital (which is calculated as the Value ...
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2answers
445 views

Book recommendation

I am currently a student of a "normal" Finance program and would like to know some more things about quantitative finance in general and especially risk management. When we derived formulas, such as ...
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149 views

What to do if certain parameters are not market observable?

Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best ...
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1answer
79 views

Time varying weights in a portfolio

As I have seen in my portfolio theory class, we define the weights of some assets and quantify the risk and return of the whole portfolio. In this setup, the weights do not change in time. What if the ...
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32 views

Equivalent constructions of risk budgeted portfolios?

When building an ERC portfolio given covariance $S$, I am familiar with the approach in optimalPortfolio. It takes the risks of a given weight vector $(w_i * (S w)_i)$, divides it by total risk to get ...
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2answers
270 views

Ways most financial institutions measure risk

Does most financial institutions measure risks in terms of https://en.wikipedia.org/wiki/Coherent_risk_measure? Or are they using other/newer theoretical tools?

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