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I strongly recommend not assesing risk using the risk neutral measure. Doesn't this already sound like a contradiction (risk and risk-neutral)? … Coming up with an expected value different from zero you risk to mix up your "trading idea" with your risk measure - which is in my mind not a good thing to do. …

You can do 2 things: incremental risk: Calculate the volatility with the asset and with the asset replaced by cash. … The difference gives you the (non-linear) incremental risk contribution of the asset. …

I assume that risk it measured here in volatility. … Thus we should invest all our wealth in stock A and the minimal risk is 25%. If the volatolity of B were smaller it could reduce risk to invest in B. …

As a risk manager I often have to tell portfolio managers to reduce risk (e.g. due to VaR limits or exposure limits). … What do you tell risk takers in order to tame their risk appetite? Where do you reference to in order to underpin your opinion? …

as vanguard2k points out the prolem is dealt with e.g. in Scaling portfolio volatility and calculating risk contributions in the presence of serial cross-correlations and references therein. … But in my mind using daily data (and handling the effects described above) is superior in ex-ante risk analysis and portfolio optimization (more reactive, more data points). …

Thierry Roncalli adresses the issue of expected returns in risk parity in Introducing Expected Returns into Risk Parity Portfolios: A New Framework for Tactical and Strategic Asset Allocation. …

It is unclear to me what you ask. You have the covariance matrix and today's weights - then you get an ex-ante TE. Why do you need ex-ante correlation? Ex-ante means that weights are fixed and you tak …

There are two things: First: You have one stock of $B$ (worth \$30) and the calculation tells you to short 1.14 stocks of $A$. Of course you can only short whole stocks. So you would have to decide w …

Let's start with one observation: Take a random variable of the form $X=\mu + \sigma Z$ for some real $\mu$ and $\sigma>0$ then $$ P[X \le x] = P[X-\mu \le x - \mu] = P[\frac{X-\mu}{\sigma} \le \frac …

Translation invariance of a risk measure $\rho$ is defined as $$ \rho(X+k) = \rho(X)-k, $$ where $X$ is a random variable such that $\rho(X)$ exists and $k$ is a constant. … The meaning is that if I add an amount $k$ to my risky positions then the risk is reduced by this amount. …

The next question is what the aim of your risk measures is. … portfolio B or my portfolio is riskier or less risky if I add/remove a tiny position in stock S then I would say: Variance is (of course) as fine as standard deviation (volatility); a Gaussian Value-at-Risk …

There are several aspects: The holding period that you want to measure: Usually, you want to calculate VaR for a specified holding period. For USCITS funds it is e.g. 20 days for bank pillar 2 regulat …

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 matur …

We define a convex risk measure as $$ \rho( \lambda X_1 + (1-\lambda) X_2) \le \lambda \rho( X_1 ) + (1-\lambda) \rho(X_2), $$ for $\lambda \in(0,1) $. … Thus a coherent risk measure is convex. The reverse is not true in general. …

The VaR of level $\alpha$ a loss random variable (the bigger the worse) is the quantity $q$ such that the loss is bigger with probability $1-\alpha$. Thus we need a $q$ such that $$ P[L>q] = 1-\alp …