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Yes, investors want to earn more than risk free but do they always get it? Or does the risk premium just fill the gap - sometimes positive sometimes negative? … Sometimes stocks are just falling and there is risk and no premium. What do you think? …

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 …

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 …

Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS reg …

First, I am quite sure that this is a typo and it should be $$ 0 < VaR_1 < VaR_0 $$ then $$ -VaR_0 < -VaR_1 $$ and the plot is correct. Second, the put strategy does not change only the expected pro …

I assume that you calculate ECL in the context of IFRS9 -correct? market practice often follows the following approach: estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your lifet …

Looking at sharpe-ratio in an ex-post way you only divide average return (above risk free) by volatility. Volatlity can have many patterns. A draw-down is something path dependent. …

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 …

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? …

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 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). …

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. …

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 …

You can do the following: For each $i$ in $1$ to number of Mont-Carlo runs $K$ simulate the number of losses $N_i$ simulate $N_i$ many loss-sizes $X_{i,1},\ldots,X_{i,N_i}$ calculate $L_i = \sum_{j= …