Questions tagged [risk]

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

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36 views

Classical Ruin Theory - Lundberg Model

In classical risk/ ruin theory, I see this formula crop up in my notes but my lecturer didn't explain to me why/ when it's employed: $M_X(r) = \int_{-\infty}^{\infty} e^{rx} f(x) dx$ I understand ...
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29 views

Skewness and kurtosis measures when full distribution is not available

I have asked this question here, but did not get any answer. I was wondering if anybody knows a method of deriving skewness and kurtosis measures from different quantiles, mean, and/or variance. I do ...
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16 views

Portfolio construction with volume based bars

In the book Efficiently Inefficient, Lasse Pedersen interviews Myron Scholes: LHP: Why do spreads tend to widen during some periods of stress? MS: Well, capital becomes more scarce, both physical ...
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64 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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39 views

Mean Semivariance Optimization VS PMPT

Mean Semivariance optimization defines semivariance, variance only below the benchmark/required rate of return, as: $(1/T).\sum_{t=1}^{T} [Min(R_{it}-B,0)]^2$ where $B$ is the benchmark rate, $R_{i}$...
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29 views

How to calculate R for strategies with dynamic exit points

Calculating R is easy when trading a straight forward strategy which has its entry and exit points clear: ...
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52 views

One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$ S_t= 120 \, \text{with probability}\, 0.5 $$ $$ S_t= 60\, \text{with probability}\, 0.5 $$...
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To price Municipal Bonds and risks I want to know the percent of unfunded pension liabilities ($3.8T) to total state and local gov liabilities

Unfunded pension liabilities keep growing and this seems alarming to both pension holders but also Municipal Bond holders. I would like to know how large this problem is to better price Munis and ...
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Are Muni REVENUE bonds secured or can the local gov. use the revenues for other purposes not paying the bond holders if its going bankrupt? [closed]

Municipal bonds are of two kinds: GO (General Obligation) Bonds or Revenue Bonds. My question on Revenue Bonds is: are the revenues from the specific project secured or can the local government use ...
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21 views

American Option - Early exercise risk management

This is for American Option Book Management in real trading. Let`s suppose, American Option seller(Book manager) only do delta hedging, which means seller cannot do Vega hedging, American Option ...
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54 views

Using transaction data to predict default of the customer

I am trying to build a prediction model that utilize the huge transaction database of all the customers of a bank. My dataset currently looks like this: ...
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46 views

Options trade - statistically expected return calculation?

I am calculating expected return for composite option strategies based on event probabilities provided by the broker. For example, consider the following spread On the left hand side we see: maximal ...
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88 views

What does 5 year OIS actually mean?

I am aware that OIS is the new reference/risk-free rate for collateralized cashflows. OIS is by definition an overnight rate (annualized, I assume). So once I have constructed my OIS yield curve, what ...
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42 views

CRRA Utility Function Problem

"Assume an investor with total wealth of $100 that has a constant relative risk aversion (CRRA) utility function. The functional formula for the CRRA utility function is given as $\ U[W]=\frac{W^{1-θ}...
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90 views

Why is change in risk premium not a violation of the Efficient Markets Hypothesis?

A passage in my textbook is confusing me. It states that various market indicators (e.g. yield spreads between high/low grade bonds, earnings yields) lead to predictability in the security's risk ...
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62 views

Allow drift in weights in a risk benchmark?

I am tracking the risk of portfolios using a standard 2-asset benchmark (S&P500 / Agg bond) and I want to throw a flag if the risk of a portfolio goes outside of a certain range relative to that ...
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17 views

single period security market with two assets

Consider a single period security market with two assets. Assume the current prices are There are two states at time one and the payoff matrix is 1.Suppose the investor believes that each state has ...
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243 views

Which rate to use as a risk free rate in emerging markets?

By looking at Fama and Frenchs global Portfolios, they just use the USD-RF rate as the risk free rate, because they converted their Returns to US-Dollar. Im currently estimating Strategy Returns in ...
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85 views

How do I derive a blend of a 3Y future and 10Y future risk?

So I have a portfolio of Govt. bonds that I'm trying to hedge with futures. Let's take one of the bonds out of the portfolio as an example. In bloomberg, every bond and its future counterparts has a ...
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232 views

Absorption Ratio

I'm actually trying to implement Mark Kritzman's absorption ratio (Principal Components as a Measure of Systemic Risk by Kritzmam, Li, Page and Rigobon, 2010, SSRN 1633027) using Python, but I'm not ...
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111 views

Barra model: why standardize the fundamental risk factors?

The two main types of risk factors included in the famous Barra model are called the "fundamental factors", and "industry factors," and the thing that I do not understand is why are only the former ...
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Adjust the Capital Market Line For Margin Interest

Modern Portfolio Theory assumes unlimited borrowing and investing at the risk-free rate. Of course, this is not realistic; margin interest costs several multiples of the RFR, especially for portfolios ...
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85 views

Having only 2 Industry risk factors?

Is it possible to build a risk model that only has 2 industry risk factors? For example, if I wanted just Tobacco and Healthcare industries as risk factors can I do that? If I did that do I have to ...
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41 views

Put-call parity for equity share and debt share

Considering Merton's structural approach" for credit risk modeling, we arrive to prove that the pricing formules are $S_t=V_t\phi(d_{T,1})-Fe^{-r(T-t)}\phi(d_{T,2})$ for equity share and $F_t=FP_0(t,T)...
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52 views

Factor Loading with multiple exposures?

How do I decompose portfolio exposures when assets may have exposure to a few of my risk factors? For instance I have some sector and state specific risk factors. If I have a bond with exposure to ...
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46 views

Poisson distribution and counting process

Let $\begin{Bmatrix} N_t \end{Bmatrix}_{(t\in[0,T])}:=\mathbb{I}_{(\tau \leq T)}:=k, \forall t \in [\tau_{k}\leq \tau_{k+1})\sim \mathrm{Po}(\lambda_{t}:=\int_{0}^{t}\lambda_{s}ds<+\infty)$ a ...
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Definitions of bubbles

In Financial Bubbles: Mechanisms and Diagnostics, Sornette and Cauwels define the concept of "bubble": More technically, during a bubble phase, the price follows a faster-than-exponential power law ...
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2answers
124 views

understanding Value-at-Risk correclty

The are several types how to calculate the VaR. I am focussing on the method of calculation the VaR in percentage. $VaR=I*z*std*\sqrt{t}$ This gives the VaR in €. I have the z-value, the daily ...
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58 views

Wave Method and Implied Duration

I am pricing an MBS under three different rate scenarios: a base case, +5bps and -5bps I compute partial durations on the base case using the wave method (P. Hagan: Calculating Delta Risks and Hedges ...
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1answer
122 views

How to interpret the (expected) exposure and CVA of an option or a single share

I have a quick (hopefully simple) question regarding the interpretation of the expected exposure of a call option and a single share. I've done some computations on the formula for the expected ...
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39 views

Choquet integral risk measure

I have one question that cannot fully understand why. What is the definition of the Choquet integral risk measure?
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93 views

what are the underlying transactions for SOFR?

Recently I am reading about SOFR (Secured Overnight Financing Rate), which is projected to replace LIBOR to be the reference for risk-free rate in the market. But I still don't understand or imagine ...
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46 views

What 10 year bond data to use when making a risk/return scatter plot?

I am making a risk/return scatter plot (seen below) (from this site): What data must be used for bonds (e.g. 3 month or 10 year US bonds)? I thought you would use this data, but if you take the years ...
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115 views

PCA on a portfolio of spot and forward contracts

I have a portfolio of spot and FX forwards on various currencies all based to AUD. I need to able to quantify how the changes in amount, tilt and curvature of the AUD curve would impact my p/l. ...
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1answer
74 views

Averaging Correlation Matrices based on different Periodicity

Averaging correlation matrices based on different models, but the same data, is commonly done. If the correlation matrices are derived from return series, is it proper/common to also average the ...
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2answers
127 views

Financial Statement Analysis [closed]

So i have just completed a beginners course on understanding financial statements. As part of the final assignment, we are supposed to pick a real company, study its financial statements and conclude ...
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84 views

Why are thousand-ish-factor vendor risk models not extremely overfit and inaccurate?

Many vendor risk models have many hundreds, or even thousands of factors (many of which are highly correlated with each other). Underlying all these risk models is some sort of covariance matrix in ...
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71 views

Risk-aversion parameters estimation in utility functions

Are there any "typical" risk-aversion parameters for power utility function and exponential utility function? Once I've seen an articel, in which author stated that for extremely risky person gamma in ...
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1answer
80 views

Bregman Mean of a Distribution

In a paper (link), author writes, given that $\gamma:R\rightarrow \bar{R}$ is a convex function, $dom_{\gamma}:=\{x\in R:\gamma(x)<+\infty\}$ is a non-empty open set and $\gamma$ a closed proper ...
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Philosophy of Financial Risk [closed]

Do you think that there exists a framework on that you can build risk measures? What are the necessary and desirable properties of a risk measure? (necessary means compulsory and desirable means more ...
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1answer
82 views

Modified Sharpe ratio

I would like to model different type of investors, hence I need to find some kind of utility functions to optimize. Apart from very abstract exponential utility function, I couldn't find any proper ...
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1answer
114 views

Prove Subadditivity - Entropic Value at Risk

Any insight in how to prove the following risk measure is subadditive? $\rho_{1-\alpha}(X) = \inf_{z>0}\{z^{-1}\ln(\frac{E[e^{zX}]}{\alpha})\}$, with $\alpha \in ]0,1]$ I want to prove it is a ...
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1answer
78 views

Backtesting model results, but backtesting output sampled at different frequency than model output

So, I'm trying to backtest a model that computes P&L. This model pulls sensitivities on a weekly basis and applies market shocks to these sensitivities to project quarterly P&L. I want to ...
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98 views

What is the purest way to get exposure to Jump risk premia, is there a jump swap

So to get exposure to Variance risk premia one could use variance swaps, is there a equivalent security for jumps. Hedging against jump but not diffusion risk could allow one to take targeted exposure ...
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1answer
83 views

Should one calculate CVA even when exposure is negative?

I have an example, where two companies have the bilateral nature of derivative contract. Companies have exchanged collateral a number of times, so at a certain point in time each sides holds some ...
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3answers
522 views

What does Volatility Smile tell? [closed]

Could you please share your opinions about Volatility Smile? What does it tell us when it gets more convex or when its level changes over time or any other change on it. Any paper/work/blog ...
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2answers
51 views

Annualisation of Downside Deviation

Is it possible to annualise the downside deviation? If so, on the basis of what theory? The downside deviation (DD) of a series of daily returns is computed according to the formula: $\text{DD} = \...
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1answer
148 views

Risk-return ratio using ML default probability

I have access to a very large bond database (>20m rows) where 50% of the set are matured bonds for which a dummy variable identifies whether the bond defaulted or not. The remaining 50% are 'live' ...
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123 views

What is a counterparty risk trading desk

Can someone explains what does the above mentioned desk do? What are their responsibilities and how do they manage them, where do they fit into the rest of the organization?
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55 views

Quantitative model for investing in ETFs [closed]

I want to build a model for asset allocation of my own personal pension in ETFs across four main asset classes: equity, bonds, commodity and property. I am familiar with Python and the basics of risk ...