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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49 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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119 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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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
69 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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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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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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50 views

Risk budgeting (i.e. Risk parity) optimization algorithms

This new risk-based investment style puts diversification at the heart of the investment process and corresponding strategies share the property that they don’t use any performance forecasts as inputs ...
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1answer
71 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
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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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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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31 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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139 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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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
84 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
61 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
68 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
166 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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81 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
62 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
31 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
116 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
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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
38 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
282 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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71 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
48 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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31 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
262 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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Distribution of risk factors with mean-reversion properties

I'm trying to figure out a way to determine if a given change in a risk factor, such as a volatility node on a surface, or a basis spread on a curve or an FX rate etc. as well as equity prices can be ...
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1answer
95 views

How to model/price the risk of Covid-19 and other pandemics

How would you model and price the risk of Covid-19 pandemic? These large cost low probability events with very little history seems to pose a particular challenge when quantitatively modeling and ...
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2answers
88 views

Quantitative risk management for energy markets

I'm currently preparing an exam about energy markets. The knowledge of notions of quantitative risk management accounts for the 50% of the total exam. During my university education, though, I didn't ...
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1answer
59 views

Value at Risk (VaR): Normal distribution with gamma distributed volatility

If I was to do a 99% VaR calculation on a portfolio with normally distributed returns $\mathcal{N} (\mu,\sigma)$, the 99% VaR would be $\mu - 2.33\sigma$. Instead of having a constant volatility, let'...
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59 views

Why is VaR metric still used?

It is well know that VaR is not subaddtive measure which means that condition $$ \text{VaR}(X+Y) \leq \text{VaR}(X) + \text{VaR}(Y), $$ where $X$ and $Y$ are portfolios, is not satisfied. As a ...
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Where could I find code to compute Potential Future Exposure

Ideally code in SAS, R, Python or Matlab for calculations involving counterparties holding positions in energy markets on multiple price curves, with a Monte-Carlo methodology or a simpified ...
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1answer
62 views

Optimize risk return of portfolio

I have gathered stock prices from 15 companies over a year. I calculated the averages, yearly volatilizes, and the correlation matrix. I was asked to find the optimum weight for each stock with a ...
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25 views

conditional or unconditional probability in the calculation of LGD

lifetime LGD is calculated by the way of a term structure of PD. But this PD at the end are calculated using conditional or unconditional PD? I have found a Lot of different And confusing definition ...
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FRTB Spearman correlation coefficient definition

I am just writing my thesis and would like to understand the spearman correlation coefficient definition within the FRTB. Somehow it is not clear from the definition. The reason what I don't ...
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1answer
64 views

Jensen’s inequality in Convexity adjustment premium

I'm preparing for my FRM II test in May. Could someone help to explain where does the 0.0823 come from? 😥
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1answer
51 views

Highest asset allocation contribution to the fund’s performance

I am preparing for 2020 May FRM II test and will appreciate any explanation for this question: In terms of asset allocation contribution, why is real estate made the highest asset allocation ...
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2answers
94 views

Outperform the market with a Beta lower than 1, is it possible? [closed]

I have a portfolio which seems to have outperformed the benchmark for the past 2 years however the risk system I use advises that using recent past data (lookback period of 2 years) the Beta to this ...
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Intuition behind the Carr and Wu (2014) static hedging for ordinary options

Let $(S_t)_{t \geq 0}$ be the price of an underlying asset, $r$ be the risk-free rate of return, $q$ the dividend yield, $C_t(K,T)$ is the price of a call option written on $S_t$ at time $t$ with ...
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58 views

Hedging Strategy for European Call Option (Single period Binomial Model)

I am hoping to gain some insight to an exercise from my undergraduate Mathematics of Finance class. (This is my first course ever in finance, so bear with me.) The exercise is: Consider a single ...
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1answer
102 views

What is the SDE of this equation? [closed]

I am new and struggling to understand how to solve this using Ito lemma. Can someone please explain it to me: $$dS_t=-\frac{1}{2}\sigma^2 S_t dW_t$$ what is the solution with explanation please
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62 views

What is Variance of delta of brownian motion [closed]

I am new to this. If variance of Brownian motion b is t, what is the variance of db? db is delta of b
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1answer
136 views

Calculate duration of zero coupon bond

I am currently studying interest rate risk management, and i can't seem to get the derivation right, and I would like to do all of the steps, to be sure that I understand what is going on. Let Pz (t, ...
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1answer
185 views

Credit VaR Formula

in Chapter 23 of Hull's Options, Futures, and Derivatives he has an example (i.e. example 23.4) which shows how the Credit VaR formula is applied. The answer in the formula is 0.128. I can't seem to ...
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3answers
90 views

Calculate uncertainty of option expiring ITM

I know it is pretty straightforward to determine the probability that an option will expire OTM -- basically a 0.10 delta call will have a 10% probability of being ITM at expiration (see this question)...
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1answer
57 views

How to calculate R for strategies with dynamic exit points

Calculating risk-reward ratio R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
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91 views

Portfolio and Risk Management: Total Return Index vs Price Index

For portfolio construction and risk management purposes, when one should use Total Return based Index instead of Price Index? I am looking for pros and cons of using either Total Return and/or Price ...

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