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

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42 views

How is possible to relate volatility with risk?

I read that equallying voliatility with risk is one of the hardest critics on Quantitative Finance and that this is -indeed- the fundamental base of Quant. This question is analogous considering that ...
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1answer
46 views

Non-contractual accounts behavioural study

I need to carry a non-contractual accounts behavoiural study for a bank. The objective is to estimate core/non core ratios and then bucket and ftp them. Any recipe where to start? I have 3yrs of ...
2
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1answer
95 views

ES not elicitable

Expected Shortfall is not elicitable as some papers have pointed out. That simply means that there is no scoring function that elicits ES. My question is, does this imply that Expected Shortfall ...
3
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1answer
121 views

Mathematical Derivation of Residual Risk

I understand the difference between Excess, Residual and Active Returns. I also understand what Active Risk; defined as: $\sigma_{r_P-r_B}$ (i.e. standard deviation of the difference in returns ...
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1answer
26 views

Why is the Risk Free Rate 1 over Contingent Claim Prices?

Reading Asset Pricing by John Cochrane (2005), in his second chapter he defines the risk free rate as: Rf = 1 / sum [pc(s)] Where pc(s) are state contingent claims, where s is the state of nature ...
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2answers
879 views

ex ante tracking error correlation between funds

I have two portfolio's called Comb & Global. They both have the same investable universe lets says 3000 stocks & are measured against the same benchmark. So it is possible that both funds hold ...
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0answers
20 views

Estimate the risk of swaptions

I would like to model OTM Swaptions. I can use some implementation of the Bachelier model (not B76 due to negative rates) and implied volatilities from Bloomberg. For 10Y X 10Y (10 years option ...
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1answer
36 views

What is Estimation Risk - VAR Backtest

Simple Question. Can someone explain please: What is Estimation Risk in Value at Risk Backtesting
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2answers
61 views

How to Calculate Minimun total Risk?

Is it possible to calculate Minimum Total Risk mathematically for below problem. ...
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1answer
26 views

Factor sensitivities for EURUSD swap

Trying to understand various risk factors for a EURUSD swap. While I understand why a EURUSD swap would have USD LIBOR, EURIBOR, EURUSD currency as risk factors, why is it that it would also have EUR ...
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1answer
94 views

Minimum PD under Basel II retail asset?

I have been told that under Basel II the minimum PD that one can assign to any portfolio/segment classified under the retail asset class is 0.33%. But Google searches return nothing and I can't seem ...
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0answers
52 views

subadditivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. $VaR(X)+VaR(Y) \le VaR(X+Y)$ But for elliptical distributions subadditivity is true. Questions: (1) Which ...
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1answer
31 views

Calculating ex ante returns & probability of a negative return over some horizon

One way to go on about this is to parametrically calculate the returns, i.e. hold the exposure constant and backtest against the factor changes over that horizon. This is not forward looking per se ...
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43 views

Coherent Risk Measures and VaR

I am working on a problem that is worded exactly as follows: Consider the functions $\rho_{1}$ and $\rho_{2}$, defined on the space of random variables with finite expected value in the following way ...
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0answers
30 views

Adding negative EV position to portfolio for diversification?

Say I have a portfolio of expected return $10%$ and volatility $20%%. If I have another asset that is either one of: Negatively correlated Positively correlated Uncorrelated With negative expected ...
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2answers
164 views

Where to find good notations to teach investment portfolio maths?

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a ...
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1answer
44 views

How to determine portion of portfolio's risks from components?

Say I have a portfolio of 3 stocks $A,B,C$ with $\mu_A = 5%$, $\mu_B = 10%$, $\mu_C = 15%$ and volatility $\sigma_A = 10%$, $\sigma_B = 15%$, and $\sigma_C = 25%$. Let us also say that correlations ...
4
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3answers
557 views

Why should there be an equity risk premium?

After years of mathematical finance I am still not satisfied with the idea of a risk premium in the case of stocks. I agree that (often) there is a premium for long dated bonds, illiquid bonds or ...
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1answer
207 views

how can we know the residual return will be uncorrelated with the market return

I was reading that if we know a portfolios beta we can break the excess return on that portfolio into a market component and a residual component. ...
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0answers
31 views

calculating long short portfolios currency exposure

I have calculated the currency exposures of a long short portfolio simply by summing the weights of each stock. However I was told that I need to incorporate the dollar borrowing (short dollars), I ...
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3answers
81 views

Are smart beta and risk parity the same?

So from what I have been reading online, smart beta ETFs aim to use a different type of weighting (instead of by market cap as traditional ETFs like SPY do to track an index) to achieve positive ...
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1answer
41 views

given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
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4answers
186 views

Bond portfolio hedging against currency risk

How do I hedge a bond portfolio against currency risk? Ideally I'm looking for books or other references on this topic.
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1answer
66 views

What are the some good measures of risk for options?

I've seen a number of measures of risk in my reading: Sharpe, Sortino, Calmar, etc. In CAPM there is Beta, and I've seen papers discussing how to modify CAPM for asymmetry. There is Value at Risk and ...
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4answers
623 views

Could we have prevented the World Economic Crisis in 2008?

There is an expression - "Too big to fall." - which means that if a bank or a financial institution manages a sufficient part of the financial assets than the state can't afford that this bank or ...
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0answers
41 views

Bayesian analysis in R: Probability of default, low default portfolios

I want to apply the knowledge of this paper (Bayesian estimation of probabilities of default for low default portfolios, by Dirk Tasche) in R, but I can't find the right bayesian package and functions ...
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1answer
46 views

Bilateral Counterparty risk

Why do counterparty risk pricing adjustments need be considered in a bilateral counterparty risk perspective? Thanks
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3answers
107 views

What assets other than bonds are risk free?

I saw a question the other day that said Assume you have only two assets to build a portfolio. Name and explain three scenarios under which a completely risk-free portfolio can be formed? I ...
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3answers
176 views

Why are investors risk-averse?

In CAPM, we assume people are risk-averse and people get compensated for the systematic risk they suffer. The assumption that most people are risk-averse makes sense, but why are the rational ...
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1answer
35 views

Calculate total risk [closed]

I have a question regarding how the risk is calculated, if I have only the returns. I think the risk premium (rp) is just the average of the returns and the sharpe ratio is the risk premium divided by ...
4
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1answer
83 views

How does RAROC identify capital requirements?

I've read that RAROC is used to set economic capital requirements for different products, projects, business lines etc. Is it just a matter of solving for the required economic capital level to ...
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0answers
92 views

Non-parametric estimator - CVAR / Expected shortfall

Is the estimation of the CVAR using known non-parametric methods (histogram , kernels) is different than the estimation of any other R.V.? If the answer is yes, then I am interested to know whether ...
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3answers
146 views

Appropriate measure of risk if return are not normally distributed

Normally standard deviation of an assets is used as an proxy for the risk in the financial market. In reality distribution of return is more peaked at the center and higher mass in the tail as ...
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0answers
12 views

Standardized and Advanced IRB together

Is it possible to use Standardized approach and AIRB together for the same asset class? For example sovereigns see a risk weight of 0% if AAA, but in AIRB they might not be seeing 0 weight. Is it ok ...
3
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2answers
268 views

Dollar-Neutral Strategy

Here is an excerpt from E. Chan's book Quantitative Trading, However, if the strategy is a long-short dollar-neutral strategy (i.e., the portfolio holds long and short positions with equal ...
3
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1answer
112 views

Spectral and distortion risk measures

Is there any difference between the spectral and distortion risk measure? Or is it just a different name for the same kind of risk measure?
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3answers
1k views

How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...
3
votes
2answers
107 views

Mathematical definitioln of Potential Future Exposure

I have come across a risk measure called "Potential Future Exposure" and I have not really understood the meaning of it. Knowing that this has to do with counterparty credit risk, I read different ...
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9answers
3k views

Lévy alpha-stable distribution and modelling of stock prices.

Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions ...
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1answer
115 views

Is Value-at-Risk translation invariant?

Let: $X=V_1-V_0R_0$ where $R_0$ is the interest rate. Then, is it so that this risk measure is Translation Invariant as: $\textit{VaR}_{\alpha}(X)=\textit{VaR}_{\alpha}(V_1-V_0R_0)=V_0+\textit{VaR}_{\...
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1answer
57 views

What are “risk” or “risk numbers?”

I work in finance but do not have any formal education in the subject (I do have a PhD, but not in finance). I've picked up a lot of the jargon but there's one thing that I haven't figured out, and it ...
2
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1answer
77 views

Option analysis

Assume zero dividend and that the strike price for a European call option on a stock at a fixed maturity T and strike price K is given by C(K).Suppose that $C(K)=e^{-k}$ for all $K\geq 0$ ,then, I ...
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1answer
132 views

Calculate VaR for a liabilty taking a exponential distribution?

An insurance company faces the liability loss off $L = \begin{cases} 0, & \mbox{with probability } 0.75 \\ Z, & \mbox{with probability } 0.25\end{cases}$ where $Z\sim Exp(\mu)$. I want to ...
0
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1answer
44 views

Convex risk measure and a coherent risk measure?

A coherent risk measure is: $\rho(\lambda X_1+(1-\lambda X_2))$ How can it be shown that everey convex risk measure is indeed a coherent risk measure? I assume that it is enough to show that a ...
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2answers
100 views

Futures Parameters for Value at Risk

I am new to risk management. I am calculating the VaR for a portfolio of futures contracts, long and shorts. I calculated it using the historical, parametric, and ...
16
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1answer
524 views

performance of historical VaR parameters

An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over ...
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1answer
297 views

Difference between Risk avoidance and Risk transfer

I was hoping some could explain the two terms namely, risk avoidance and risk transfer. Also, can a risk be avoided by transferring it?
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2answers
78 views

Finding Credit Risk Population Data

Are there any free or relatively cheap sources of aggregate data on credit risk for specific geographic regions, ages, and so on?
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2answers
85 views

Meaning of conservative in risk management?

I believe this question is best asked here, as it pertains to risk, rather than English SE. What is the meaning of conservative in the context of risk management? In general, conservative would mean ...
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2answers
49 views

What risks is an exchange exposed to?

Putting aside operational/reputational/business risks for a minute, a financial institution is concerned with the risk of losing money on their positions. What about an exchange ? I can only think of ...