Questions tagged [risk]
The possibility that a negative event (such as a loss) will happen.
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Derivation of optimal portfolio weights using Risk Budgeting approach
In Thierry Roncalli's book Introduction to Risk Parity and Budgeting (2013), he gives an example of particular solutions to the Risk Budgeting portfolio such as for the $n=2$ asset case.
The risk ...
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How to construct a forward exposure portfolio with bonds?
I was asked in an interview to get an exposure to 5Y5Y forward rate using bonds alone. Essentially it is short 5Y bond and long 10Y bond, and I needed to compute the relative weights. Regarding risk:
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Alternative form of mean-variance optimization that uses standard deviation
I'm curious about an exercise found in Optimization Methods in Finance. Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm ...
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Maximizing Mean+Variance in a Portfolio
Mean-Variance optimization trades off expected returns with portfolio variance. The idea is that excess variance is not desirable.
But what if you weren't averse to high variance and you wanted to ...
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How can I correctly assess the risk of real estate debt fund? [closed]
I'm trying to assess the attractiveness of real estate debt funds. I'm very surprised when I look at the investment performance of many of those funds. Many of them have no negative returns, and can ...
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Conceptual problem with risk neutrality-What is a 'risk-neutral world', exactly?
I have persistent, deep problems with the concept of 'risk-neutrality'. To make it more precise, let's look at the following explanation taken from a book:
"In a world where investors are risk ...
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Cohort-based model vs. population-based model for mortality
A cohort-based model groups individuals with at least one common characteristic over a period of time through a state-transition process. A population-based model reflects as much information as ...
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Minimizing variance of a long short equity portfolio in practice
I understand the finance 101 explanation of how to minimize variance of a long-short portfolio using a covariance matrix. I also know that it doesn't really work because the covariance matrix is ...
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How to annualize sharpe ratio using quarterly data?
Say I have quarterly returns data for a stock. I am currently calculating rolling Sharpe ratios using an eight-quarter forward window. So for example, say I have quarterly returns data starting in ...
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FX Risk Reversal - RHS/LHS - Strike adjustments
I was wondering why ppl use the wordings being „rhs/LHS“ right hand side / left hand side when having an risk reversal for example Long EUR Call / USD Put and Short EUR Put / USD Call. Do they refer ...
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Relationship between Sharpe Ratio and Investment Horizon in a theoretical IID return world
In his paper, "The Statistics of Sharpe Ratio", Andrew Lo writes
"hence, the ratio will increase as the square root of q, making a
longer horizon investment seem more attractive. This ...
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Does a portfolio on efficient frontier also lie on CML(capital market line)?
I am trying to solve this question:
Assume that CAPM is true. The risk-free rate is 3%, the expected return on the market portfolio is 10% and the standard deviation of the return on the market ...
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Question on effective days of an exponentially weighted moving average model
I have been reading the book "RiskMetrics —Technical Document" by Longerstaey (J.P.Morgan) and Spencer (Reuters) (4th Edition, 1996). I am wondering what the effective days of the ...
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All I need to know about FRTB
I know the basics of FRTB (Fundamental Review of the Trading Book) but I can see that most of the risk management books have maximum a chapter dedicated to FRTB and are relatively old so don't reflect ...
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How to calculate the portfolio risk and return if daily share prices, volume held on that day is given for all assets?
The problem is with the changing volume of assets which changes the weights. I want to use the formula for portfolio risk but cannot figure out the weights. Should taking average weight of an asset ...
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Where to find dissertations in risk management
I'm looking for open databases of master's dissertations/theses in risk management & quantitative finance written by risk practitioners.
The goal is to find current research topics or problems in ...
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Why do rating grades have different PD ranges?
The following shows link how to map a PD to a S&P rating:
S&P Rating
PD range [%]
AAA
[0-0.05)
AA
[0.05-0.09)
A
[0.09-0.23)
BBB
[0.23-1.16)
BB
[1.16-5.44)
B
[5.44-4.21)
CCC
[14.21-)
I ...
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Value at Risk on equity options, what is the right approach on historical simulations
Questions on Historical VaR for options, how do you actually do this.
how you would evaluate Value-at-Risk for an equity option that has been recently listed on the exchange. The obvious is that you ...
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Why do companies trade options?
Companies buy options to reduce the variability in future cash flows.
Institutional investors invest in portfolios to maximize return for a fixed amount of risk. If an investor owns stock in company A ...
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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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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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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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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 ...
user36180
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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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