Questions tagged [risk]

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

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Marginal Risk Contribution under Factor structure

Given the factor structure below with K factors, the return for N assets is given by (under matrix notation): $R =\alpha + \beta F + \epsilon$ where $F$ is matrix of K factor returns and $\beta$ is ...
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Swaption risk bucketing

In the IR swaption market, we have 24Expire10Tenor instruments(like a 2410 Matrix). Now I have the Vega number for each instrument, and I want to reduce the matrix size with the same total vega risk. ...
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For mean-variance portfolio optimization, shouldn't all the allocations sum to 1?

Reading a paper by Black and Litterman, I'm having trouble understanding the set of valid allocations in which we're trying to optimize expected returns. In Table III, the authors show two portfolios ...
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What does a portfolio risk of 20% mean?

From the book Active Portfolio Management there is a use of lingo I don't understand. Take this quote from pg. 100 "Why are institutional money managers willing to accept the benchmark portfolio ...
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The option is "purer" in its risk---what is meant by this?

In the book "The Concepts and Practice of Mathematical Finance" author M. Joshi writes on page 12 the following: "From the point of view of risk, we can regard an option as an attempt ...
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Simple (?) question about expected bond returns

Newbie here. I should say upfront that I'm not a quant, just someone trying to broaden his knowledge of fixed income investing. I apologise in advance if I'm mangling some terminology. Imagine a ...
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What is Leverage?

What would you consider leverage? I know this may sound like a basic question but I have spoken with several industry professionals with a significant amount of experience and all of them have a ...
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Help with simple derivation of probability of credit default

I'm going over a chapter in Hull's Options, Futures, and Other Derivatives and am stuck on how the probability of default is derived. Here's the image of the derivation. I can follow all of it except ...
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Introductory Books to Network Theory

Can anyone please suggest a good introductory book to Network Theory which is the area of mathematics that is widely used for systemic risk and contagion modeling in finance. If the book contains some ...
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Risk premium of insurance risk

I recently came across an equation in a paper. In short, suppose that $I(t)$ denotes a longevity index at time $t$. An informative indicator that is useful in the absence of any information about the ...
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Pareto comparison of return distributions

In making a choice among financial strategies, each of which has some estimated return distribution, some strategies will clearly be better than others. But many times, the choice is a question of ...
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Does tail risk disappear in the long horizon in any rolling over strategy with shorter frequency?

Say I am investing to gain weekly yields ${y_{i}}$ for over a year, gaining the overall yield: $\prod_{n=1}^{52} (1+y_i) -1$ The most dominant term in the above product is the sum of all yields, which ...
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Square root specification of parameters in factor models

The following formulation is from Vasicek and refers to the cond. probability of the loss of a loan (equ. 3 in the reference): $$p(Y)=\Phi\left(\frac{\Phi^{-1}(p)-\sqrt{\rho}\,Y}{\sqrt{1-\rho}}\right)....
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efficient frontiers are equal

I created 3 different efficient frontiers with 3 different risk factors(sharpe ratio, ulcer performance index and serenity ratio) and I wanted to find both MSR and GMV(and their equivalent for the ...
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How to compute the combined probability of loss for 2 time series (consisting of historical stock prices)?

May I please ask the community's support with the following problem? I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily ...
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How can I show convexity of this risk function?

I have the following risk function: $\mathbf{Risk}(x):=\mathbb{E}[R(x)]+\delta\mathbb{E}[|R(x)-\mathbb{E}[R(x)]|]$ where $R(x)$ is the portfolio return and $\delta$ is any positive scalar. My textbook ...
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Are risk neutral probabilities (for the arbitrage theorem) the same no matter what betting strategy is chosen?

I am learning the basics of risk neutral probability and arbitrage theorem. The arbitrage thm states that given a series of bets $r_{1}, ..., r_{n}$ either there is arbitrage, or there exists a ...
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Is Aumann-Serrano risk measure coherent?

Is the Aumann-Serrano risk measure (Robert J. Aumann, and Roberto Serrano: An Economic Index of Riskiness, JPE, Vol. 116 No. 5, October 2008. <link>) coherent? And why yes or no?
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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2 answers
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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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