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Questions tagged [risk]

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

39
votes
8answers
32k views

How does the “risk-neutral pricing framework” work?

I've struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
12
votes
12answers
119k views

How to calculate unsystematic risk?

We know that there are 2 types of risk which are systematic and unsystematic risk. Systematic risk can be estimate through the calculation of β in CAPM formula. But how can we estimate the ...
42
votes
4answers
16k views

What is the best way to “fix” a covariance matrix that is not positive semi-definite?

I have a sample covariance matrix of S&P 500 security returns where the smallest k-th eigenvalues are negative and quite small (reflecting noise and some high correlations in the matrix). I am ...
20
votes
3answers
9k views

What is a “coherent” risk measure?

What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in ...
18
votes
2answers
3k views

When should you build your own equity risk model?

Commercial risk models (e.g., Barra, Axioma, Barclays, Northfield) have evolved to a very high level of sophistication. However, all of these models attempt to solve a very broad set of problems. ...
13
votes
2answers
4k views

Equity Risk Model Using PCA

I'm trying to build a simple risk model for stocks using PCA. I've noticed that when my dimensions are larger than the number of observations (for example 1000 stocks but only 250 days of returns), ...
2
votes
1answer
648 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
45
votes
11answers
5k 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 ...
19
votes
1answer
2k views

Portfolio optimization with monte carlo sampling from predictive distribution

Let's say we have a predictive distribution of expected returns for N assets. The distribution is not normal. We can interpret the dispersion in the distribution as reflection of our uncertainty (or ...
26
votes
4answers
3k views

How are risk management practices applied to ML/AI-based automated trading systems

A potential issue with automated trading systems, that are based on Machine Learning (ML) and/or Artificial Intelligence (AI), is the difficulty of assessing the risk of a trade. An ML/AI algorithm ...
15
votes
2answers
2k views

What is the relationship between risk aversion and preference for skewness and kurtosis in portfolio optimization?

Is there any relationship between the risk aversion coefficient in an individual's utility function (commonly used in portfolio optimization) and the preference for higher moments such as skewness and ...
6
votes
2answers
540 views

Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...
18
votes
1answer
506 views

What approaches are there for stress testing a portfolio?

Wikipedia lists three of them: Extreme event: hypothesize the portfolio's return given the recurrence of a historical event. Current positions and risk exposures are combined with the historical ...
7
votes
5answers
971 views

Indicators and research for stress-based investment strategies

In reference to this paper: Can risk aversion indicators anticipate financial crises? and the investable UBS Risk Adjusted Dynamic Alpha Strategy: http://www.ibb.ubs.com/mc/strategyindices/ubsrada/...
12
votes
2answers
924 views

Minimizing Correlation

Is there a quantitative method in monitoring trades to reduce the possibility of correlated trades?
9
votes
1answer
4k views

Why using the swap curve as riskfree rate and no longer gov bonds?

I recently had an interview where I was asked what to use as risk-free rate. In all my textbooks it was always the US treasury yield curve. But they said no its now the "swap curve". Why is the swap ...
7
votes
3answers
846 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 ...
3
votes
1answer
1k views

Pre-trade evaluation and risk assessment of option trading strategies (in market practice)

When a trader gets conclusion of the volatility is being underestimated (via volatility cone or some other technology), actually there are multiple ways for his trading. (Let's assume the underlying ...
17
votes
3answers
4k views

Is Conditional Value-at-Risk (CVaR) coherent?

When the risk is defined by a discrete random variable, is CVaR a coherent risk measure? I stick to the following definition of CVaR: $$ CVaR_\alpha(R) = \min_v \quad \left\{ v + \frac{1}{1-\alpha} \...
3
votes
1answer
6k views

Drawdown calculation for strategies

I am developing a trading strategy for currencies. I am trying to find an indication for risk, something like Sharpe ratio or Sterling ration; for that, I thought of using the (maximum) drawdown ...
15
votes
2answers
14k views

Why using 3 months forward to hedge fx risk on a fund of funds portfolio?

In my previous job, a fund of funds, they used 3 months forward FX contracts (renewed every 3 months) to protect their portfolio against currency risk. If I do understand why forwards are useful for ...
7
votes
2answers
6k views

What is the significance of Relative Risk Aversion

I know that the relative risk aversion is defined as $$R(c) = cA(c)=\frac{-cu''(c)}{u'(c)}$$ where $u(c)$ denotes the utility curve as a function of wealth $c$. But I do not understand the intuition ...
10
votes
1answer
428 views

What distribution should I apply to estimate the likelihood of extreme returns?

Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns. Because the estimate will require extrapolation, I ...
3
votes
4answers
6k views

Which risk-free interest rate to use in Black-Scholes equation

Sorry but i'm new in quantitative finance. According to BS derivation the risk-free interest rate is the rate to wich the rate of a particular investment tends when the risk tends to zero. Suppose i ...
8
votes
2answers
4k views

Computing the Sharpe Ratio

The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are subject to estimation error. The main problem I have is ...
2
votes
1answer
143 views

Risk, required return and expected volatility - what is the relationship?

Return required from risk averse agents from risky investments are proportional to expected return variance. That is from the textbook, you take the portfolio with the highest return to standard ...
2
votes
3answers
1k views

Semi-variance/Downside Risk, what about the rest of the covariance matrix?

I just bumped into a rather interesting article from wikipedia : http://en.wikipedia.org/wiki/Downside_risk where they define the semi-variance also called Downside risk, which bascially only ...
1
vote
2answers
219 views

What knowledge should I have for a risk management and risk modeling job at a bank? [closed]

I have a masters degree in Econometrics and a undergraduate in Finance I am going soon to start an internship at a bank where I will evaluate risk models and possibly possibly create them aswell and I ...
1
vote
2answers
2k views

Risk contribution of part of a portfolio

Is it quantitatively sound to say that if I have assets $x, y,$ and $z$ in a portfolio, and that the total variance of the portfolio is defined as $\sigma_p ^2 = w_x^2\sigma_x^2 + w_y^2\sigma_y^2 +...
1
vote
1answer
69 views

Compute moments of aggregate loss using Monte Carlo

Spin-off from here. Richard referred to me an article that tells me how to get parameters of a translated gamma distribution to which I should consider fitting simulated aggregated loss values. The ...
0
votes
3answers
900 views

Parametric/Analytical VaR

Suppose I want to calculate VaR for a known distribution with mean $\mu$, variance $\sigma^2$ and $\alpha$-quantile as, $VaR_{\alpha}$ = $\mu + \sigma q_{\alpha}$. For a Gaussian distribution it is ...