Questions tagged [risk]
The possibility that a negative event (such as a loss) will happen.
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Why does NPV correspond to "cash in our pockets now" for risky investments? [closed]
For a positive NPV project with risk free cash flows and assuming access to a competitive money market, it is trivial to show (by appropriately borrowing or lending at the risk-free rate) that the ...
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What is the correct procedure for discounting risky cash flows? [closed]
My apologies if this question is too basic/inappropriate for this venue. Please let me know if so.
I am currently reading Berk and Demarzo's Corporate Finance and am a bit confused about how risky ...
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Taking a set of normally distributed random variables as the sample space to fitting an exponential distribution
Disclaimer, this is my first question/interaction in this forum.
Let's assume I have random variables that are normally distributed. Then, say I take the observations that are greater than the mean, i....
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What is the meaning of the asset risk contribution in a long-short portfolio?
If I have a portfolio of weights $\mathbf{x}$ and the covariance matrix of asset returns $\Sigma$ then the volatility contribution per asset is given as standard $\mathbf{x}' \Sigma$. For a standard ...
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If investors are risk-neutral, should the (equity) risk premium be zero?
I looked up ChatGPT and they stated that the (equity) risk premium should be zero for a risk-neutral world. The definition of a risk-neutral investor is that one is indifferent between additional or ...
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If there was a way to back out implied volatility (IV) from a stock, would it be the same as the IV backed out from an option on that same stock?
I know that it is not possible to back out an IV for a stock, because the concept of IV is based on a model with underlying assumptions applied to pricing an option.
I was thinking of why IV is ...
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From parameter risk (sensitivities) to market risk (sensitivities)
In models where the underlying is not modeled directly - such as in the HJM framework or short rate models - how does one then compute the Greeks, i.e. sensitivites wrt. market variables.
As an ...
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Portfolio risk of correlated assets using Mahalanobis distance
I am trying to understand if there is an agreed methodology to measure the total risk in a portfolio of correlated assets.
I am taking a simple model of stock prices following geometric Brownian ...
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Value At Risk Modelling for electricity market with negative prices
I'm a bit at loss after trying to find papers regarding tail risk for electricity markets. There doesn't appear to be a whole lot of literature (or perhaps I haven't managed to find it) regarding ...
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Basis risk between future and a non-dividend paying stock
I am a bit confused about the definition of basis risk, and how it applies to a zero dividend stock.
A study manual that teaches me about that mentioned basis risk happens when there are mismatches in ...
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Can PCA be used to transform a ladder of interest rate risk?
The context
For traders/market makers on interest rate swaps desks, it is essential to have a model that transforms risk from its most complex representation (i.e. a ladder of every tenor) into a less ...
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Tricky question about returns [duplicate]
I have a list of monthly returns.
-10% -20% -70% -30% -15% -60%
The total end return is -94.859%. Because you calculate = 100 x (1+ -10%) x (1+ -20%) x ...
Now I ...
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CoVaR/dCoVaR modelling using bivariate DCC-GJR-GARCH
For the several weeks, I have been looking for a way to calculate and display the results of my DCC-GJR-GARCH model to picture a dynamic relationship between daily return of, let's say for example, ...
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Estimating risk premium with cross sectional regression
I am trying to estimate a carbon risk premium according to the Fama & MacBeth methodology using a cross-sectional regression approach.
Therefore, I regress the excess return in period t+1 on the ...
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Estimating Appropriate Risk Premiums without Comparable Project Data
Objective
I wish to estimate an approximate reasonable return (a) for a project, given its inherent risk and risk-free rate, and compare that to the anticipated project return (b).
Such that, all else ...
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Fama French Factor adjusted returns
I want to understand the extent to which portfolio performance can be explained by the three Fama French Factor model. I use the following approach:
Regress the portfolio's excess returns against the ...
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FRTB - Federal Reserve vs Basel
The federal reserve has released its proposed Market Risk rules for Basel III.
https://www.federalreserve.gov/newsevents/pressreleases/bcreg20230727a.htm
Is anyone aware of any resource that compares ...
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Standard Deviation and Monotonicity property
I just read that standard deviation is a coherent risk measure, and therefore it should satisfy the monotonicity property:
$X_1 \geq X_2 \implies \rho(X_1) \leq \rho(X_2)$ where $X_1,X_2$ are asset ...
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"fix" a sample covariance matrix which is not positive semidefinite by using daily returns instead of monthly
In the portfolio optimization problem at hand, one of the constraints is that the tracking error should not be greater than $\gamma$.
The constraint is therefore:
$(\textbf{x}-\textbf{w})^\mathrm{T}\...
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Risk Neutral Pricing - Why the Risk Free rate for Risky security (Intuition) [duplicate]
I am struggling with this concept of risk neutral probabilities.
My understanding of how a risk neutral pricing framework works is as follows: (discrete, binomial lattice for simplicity) I do not know ...
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Risk of bond calculation
I am studying a course and I am a bit confused on how to find the a bonds $\sigma$. My course mentions the following:
Once calculated the expected returns on the bond $\mathrm{E}(r_d)$, we can
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Intuition behind risk-return realation (Mark Joshi's concepts 1.2) [closed]
In Mark Joshi's "The concepts and practice of mathematical finance" section 1.2, it is given an intuitive motivation behind "high risk high returns" claim. It goes as follows:
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If I know the Price, DV01, and Duration of a Fixed Income instrument, is their approximation for the Convexity?
As the title says, I am looking to see if there is a good approximation for the convexity of a Fixed Income instrument. Say I know all the parameters of the instrument, can the Convexity be written as ...
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High-frequency risk management methodologies
In a high-frequency environment, such as a proprietary trading firm or market making firm, the primary goal of the risk management team would be to limit potential losses, but how is that done in this ...
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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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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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