Questions tagged [risk]

The possibility that a negative event (such as a loss) will happen.

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34 views

To gamble or not to gamble! (solving a system of ODEs maybe?)

Assume we have some money. At every point in time $0\le t \le T$, we can take either action 1 that is to keep our money until $T$ say in a bank and have an expected return of $f(t)$ or take action 2 ...
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25 views

Market Risk - credit v. equity

I am requesting language for the use of derivatives in a portfolio. The goal is to allow the use of derivatives only in instances where the portfolio aggregate market risk exposure (post ...
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97 views

Attribute P&L to PCA vectors (swaps)

I have a daily US swaps data here for 2020 https://easyupload.io/yh4rnd . I have run PCA on standardized data and got PCA matrix (and basic statistics): I also have such hypothetical portfolio that ...
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64 views

Does VaR calculations consider my portfolio past

I am relatively new to trading and decided to become more quantitative about it. I have had a portfolio for about two years, where I changed my positions several times. I now learnt about VaR ...
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77 views

Calculation of Total Credit Risk Capital % but seeing lower capital percentage for higher risk band. Is there any correction required?

I am trying to calculate the Total Credit Risk capital % for my learning purpose as given below. Assuming adding 1 single loan with different pds. i have noticed one point in the table and have two ...
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43 views

pooling equilibrium

I was hoping for some help on how to answer a question about pooling equilibrium. Suppose a bank wants to give loans of 1 million dollars to people, but it cannot differentiate between high risk ...
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51 views

How is VaR calculated with mixed return-periods

For example, if you have a dataset of returns that are not daily or yearly, but span 24 days, 1 day, 5 days, 7 days, etc., how do you calculate or interpret the VaR of that? I've tried linearly ...
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90 views

How to set VaR and other Risk Limits

I have read a lot of literature on how to calculate VaR and it's advantages and disadvantages. But I am struggling to find anything on how to set a VaR limit. For example, say if I am a Risk Manager ...
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98 views

Why is it that returns at the efficient market hypothesis has to be risk-adjusted?

Let us assume the following situation: Average market return: $R_M = 8\%$ Risk-free rate: $R_F = 2\%$ Actual return of share A after one year: $R_{A} = 15\%$ Actual return of share B after one year: $...
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1answer
88 views

Can you still sum the weighted up betas to find portfolio up beta, or not?

The portfolio beta in the conventional sense is simply the sum of weighted beta coefficients for each holding in the portfolio. Is it the same for portfolio up and down beta, where I can simply take ...
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42 views

Difference between Risk minimization and local risk minimization

According to the survey paper "A Guided Tour through Quadratic Hedging Approaches" by Schweizer the risk function is defined by $$R_t(\phi)=E[(C_T(\phi)-C_t(\phi))^2|\mathcal{F}_t]$$ When ...
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Parallel Interest Rate Shocks (shock before boot strapping or after?)

I'm looking to create interest rate shocks (parallel (25/50/75 bps up/down), non parallel (steepener/flattener) on a fixed income portfolio. Should I be shocking the market instruments before ...
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48 views

Easy, but doubts - Annualize daily turnover

I am fairly certain I am correct but I just want to double-check on portfolio turnover calculation. I need to annualize the daily turnover rate. To calculate, the daily turnover, I am using the ...
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Reference request (Risk Management + Insurance Theory) [duplicate]

I have to study the following topics: Market and credit risk assessment models Technical risk assessment models: non-life and life Models for the valuation of bonds and for the determination of the ...
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112 views

Should I include zeros in downside beta calculation?

Downside beta is the beta coefficient for an asset and a benchmark restricting benchmark returns to be less than a given value. Let’s assume zero for simplicity. We have: If we have returns in period ...
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110 views

How do I estimate the factor sensitivity in a Vasicek Single Factor Model?

I understand the formula of an asset return for an obligor i is given by the following: $$A_i = \sqrt{w_i}*Z + \sqrt{1-w_i}*\epsilon_i $$ My question is - How do I calculate $w_i$? I have the PD, LGD ...
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47 views

Does the interval of a portfolio's returns affect Sharpe and Sortino? If so, what's the gold-standard interval?

I'm currently creating a backtesting script and I've got to the point of calculating risk metrics. It seems like the interval (daily, weekly, or monthly) I use for returns heavily changes the ...
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89 views

Practical implications of Andy Lo paper on Sharpe ratio using quarterly returns?

I am hoping to determine the practical implications of the Andy Lo paper criticizing the use of a scaling factor in converting periodic Sharpe ratio to annualized Sharpe ratio. I am particularly ...
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130 views

IRS - sensitivity to estimation (projection, coupon) curve and discounting curve

The mark to market of an interest swap that is close to zero (e.g., at the swap's inception) has more sensitivity to which curve - the estimation (projection, coupon) curve or the discount curve? And ...
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335 views

Quarterly Survival rate given there is a Quarterly Probability of Default

I am trying to calculate the Quarterly Marginal PD. I have calculated it as given in the below image but I am thinking about whether the Survival rate calculation is making sense or not. The ...
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Ruin theory with infinite-mean Pareto-distributed claims: how to characterize the ruin time and the reserve prior to ruin

Consider the Cramér–Lundberg model $$\hspace{8em}R(t)=u+c\,t-\sum_{j=1}^{N(t)}V_{j}\,,\hspace{8em}(1)$$ where $c$ and $u$ are positive constants, $N(t)$ is a Poisson process with a rate $\lambda$ (in ...
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84 views

Optimal active risk

Can someone help me prove the statement or share a link of the proof - "The optimal amount of active risk is the level of active risk that maximizes the portfolio’s Sharpe ratio. This optimal ...
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124 views

Question in convex arbitrage [closed]

In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance, $$ C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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64 views

Risk sensitivities of equity TRS

If we go short on an equity TRS (as in we sell the swap and pay the equity returns). Is it correct to say that we are: -Short spot -Long borrow cost -Long interest rate (the rate benchmark of the ...
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77 views

Why is the interest rate risk secondary for a vanilla equity option?

Consider the vanilla payout: $Max(S(T)-K,0)$ priced under the RN measure as: $E[e^{-rt}Max(S(T)-K,0)]$ which under no dividend/borrow assumption equals $E[e^{-rt}Max(S(0)e^{rt}X(T)-K,0)]$ for $X$ ...
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56 views

Identity of recent books on stock market & risk

Apologies if this seems out of place, but a couple years ago I read several popular books written in the last decade by a single author who was trying to disabuse readers of several fallacies ...
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How to find percentage of FX exposure hedged through financial statements

I am analyzing a company's annual report, and wish to find the percentage of FX exposure they have already hedged. I have the following information: The net FX exposure for 4 different years The ...
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1answer
37 views

Price of a floating coupon bond with issuer credit risk and recovery rate

I need help. I have an assignment for an exam where i have to compute the price of a portfolio composed by floating coupon bonds taking into account the issuer credit risk and the recovery rate in ...
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1answer
665 views

Quick rule of thumb for DV01 and CS01 calculations

If someone tells me there is a IRS and a CDS both with 10M notional and 5y maturity, is there a reliable quick calculation that I could easily do mentally to approximately calculate their ...
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82 views

Why is infimum chosen to define value at risk as opposed to the minimum?

I believe that the VaR is defined as the infimum of the generalized inverse of the CDF of the loss function (something like that, please correct accordingly): $$\text{VaR}(\alpha)=\inf\{x: F_L(x)\geq \...
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36 views

Where can I get historical updates to equity risk models (e.g. Barra)?

In risk models (such as Barra), new factors are added over time, and the model structures are also changed over time. I hope to get as much information on historical changes as possible. Apart from ...
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122 views

Non financial risk management

I am looking for some discussion papers, research insights on the Digital risk for fintech companies, bank etc. what they should. consider when offering their services (banking, lending etc.) ...
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157 views

Dependence between Credit Default Risk and Credit Spread Risk

I am trying to understand the difference and similarities between Credit Spread Risk and Credit Default Risk. Here is brief (and not all too precise) definition. Credit Spread Risk: Losses due to ...
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36 views

How to use CAPM model to calculate expected value of portfolio?

Let's assume that vector $(R_1, R_2, R_3)$ has multivariate normal distribution $N(\mu, \Sigma)$ where $\mu = (2, 6, 4)$ and $$\Sigma^{-1} = \begin{bmatrix} 2 & 2 & 2\\ 2 & 4 & 4 \\ 2 &...
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1answer
390 views

Realized Variance (realized volatility)

I'm confused about realized variance. I roughly know the theory around Ito Calculus and quadratic variation and integrated volatility so I understand what realized variance measures (even though as ...
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25 views

Capital Charge or Capital add on for Concentration risk using Model-free measure standardised HHI (Herfindahl Hirschman Index)

I am looking to calculate the Capital Charge or Capital Add on for Concentration risk using standardised approach using HHI Below is the HHI index calculation What is procedure to calculate the ...
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82 views

Sharpe ratio differs from Tradingview

I tried to backtest a simple strategy on TradingView, it made 6 trades with these results: Now I want to calculate Sharpe ratio using definition provided by TradingView. So, my daily returns(...
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64 views

Interest rate risk calculation for Banking book

There is a detailed discussions on the Interest rate risk for Banking book. For Floating rate bond, this states like below - such positions generate cash flows that are not predictable past the next ...
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1answer
84 views

Joint probability of default

Had a couple of questions from Jorion's FRM book (5th edition, page 438, Table 18.2 shown below). The book has a very stylized example as shown in the table below. The example shows how to calculate ...
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Estimate of loan risk due to change in income

Disclaimer: despite working at a bank, my background is in data science and not in quantitative finance. I'm very likely to miss certain technical terms of the domain and if that's the case, I'd ...
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31 views

Statistical Inference of Variance Risk Premia

Good afternoon, I am currently following Carr and Wu (2009) to compute variance risk premia from options written as (RV-EV)*100 for the payoff of a long var swap position. Now I want to see whether my ...
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What happens if my risk factor caught by statistical risk model using PCA turns out to be totally different from other PM's risk factor? [closed]

In order to explain systematic risk we use risk factors and I've learned that since they try to explain 'systematic' risk, risk factors are relatively well-known. However, what happens if the risk ...
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216 views

Deriving the risk-aversion coefficient

By considering the parametrised formulation of the mean-variance criterion by Markowitz, the risk aversion coefficient $\lambda$ can be derived as follow. As suggested by Arrow and Pratt, given the ...
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94 views

What are some advanced methods for bond risk transformations?

Consider a portfolio of bonds within a given yield curve (e.g. Gilt curve), consisting of positions in every bond in the curve. I'm looking for ways to transform the risk of the portfolio into ...
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118 views

Equivalence of Standard Deviation and Variance as a risk measure - WRONG?

In Modern Portfolio Theory, I often see that people seem to view Standard Deviation and Variance as equivalent. Example from Markowitz himself: "Thus far I have used the standard deviation ...
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77 views

VaR and Expected Shorfall estimations with negative shape parameter of a GPD (Extreme Value Theory )

So im trying to replicate an code from the Quantative Risk Management Book (https://github.com/qrmtutorial/qrm/blob/master/code/09_Market_Risk/09_Standard_methods_for_market_risk.R). But when i try a ...
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39 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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140 views

Does "risk premium" imply a difference in expected value?

I'm trying to understand the term "risk premium". I keep seeing statements like this (from Investopedia) "A risk premium is the investment return an asset is expected to yield in excess ...
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806 views

Knightian uncertainty versus Black Swan event

I struggle to understand the difference between Knightian uncertainty versus Black Swan event. If I understand at least the basic premises, both views say that uncertainty is different from risk, and ...
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1answer
101 views

Estimating delta of VX futures to S&P 500

I'm trying to think about the right way to estimate the delta of a VX contract to the S&P 500. VX futures are on the VIX index, which is a basket of S&P 500 options. By extension, VX and ES (E-...

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