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6

Note that $\beta$ is the coefficient of the portfolio regressed on the benchmark. That is \begin{align*} r_P = \alpha+\beta r_B + \varepsilon, \end{align*} where $\varepsilon$ is the residual. The standard deviation of the residual is called the residual risk. Specifically, \begin{align*} std(\varepsilon) &= \sqrt{var(r_P-\beta r_B-\alpha)}\\ ...

2

Even in calculating VAR, you have certain assumptions / constants / random numbers being used. Hence, even your VAR calculation is not 100% correct. So, you are estimating VAR and you hedge similar portion of risk, however your Estimations aren't 100% correct. This is Estimation Risk. Estimation risk is a generic term. It could be applied to models, VAR, ...

2

I assume that risk it measured here in volatility. Then a portfolio with 100*$w$ percent invested in A and 100*$(1-w)$ percent invested in B has the annual variance $$v = w^2 0.25^2 + 2* 0.5 w(1-w) 0.25*0.5 + (1-w)^20.5^2.$$ Searching for the portfolio with the samllest variance is equivalent to searching for the smallest volatility. To get the minimum ...

0

You are looking for the minimum variance portfolio of two assets, assuming "risk" translates into volatility (variance) here. So what you would do mathematically speaking is introducing a variable $w\in[0,1]$ which is the weight of stock A (say) in the portfolio, calculate the "risk" - which is the variance - of the portfolio $wA+(1-w)B$ and then solve for ...

0

The dominant IRS float tenor at longer maturities for EUR is 6m Euribor. So we assume that the EUR 3m leg of the xccy basis swap is constructed from a 6m IRS and therefore also 3s6s EUR basis. In the interbank world there will also be risk contributions from the EONIA or FedFund discounting, via OIS or again basis (3sOIS). These sensitivities are generally ...

1

From the Basel II accord: For corporate and bank exposures, the PD is the greater of the one-year PD associated with the internal borrower grade to which that exposure is assigned, or 0.03%. So it is 0.03%

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For a normal random variable $\xi$ with mean 0, then \begin{align*} P(\xi < 0) = P(\xi > 0) = 50\,\%. \end{align*} For a normal random variable $\eta$ with mean (i.e., realized mean return) $\mu=3\,\%$ and risk (i.e., standard deviation) $\sigma = 3\,\%$, then \begin{align*} P(\eta < 0) &= P\left(\frac{\eta - \mu}{\sigma} < \frac{ - ...

1

Financial markets & Corporate Strategy - Grinblatt & Titman The book is very intuitive, but as a consequence less comprehensive than ex. Options, Futures, and other Derivatives by Hull (which is seen as the basic foundation of everything quant in some parts of the industry.) A great entry level book to finance, and is publically avaliable here: ...

1

If I had to give only one title this would be it: FT Guide to Understanding Finance by J. Estrada (Second Edition published 2011) It explains all of the above concepts (and more) in a very accessible, yet mathematically correct manner. A sample can be found: Here The only thing is that it is not really short (the first part, i.e. up to p. 150, is ...

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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. They don't sum up to $\sigma$. contributions to volatility (Euler allocation) As $\sigma = \sigma^2/\sigma$ you can define risk contributions by  ...

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