Martin Vesely
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Positive definite matrix $A$ is defined as $x^TAx > 0$ for all vectors $x$. Since a term $w^T\Sigma w$ in Markowitz (and other models as well) expresses variance in returns, it is a measure of ...

You can use Lagrangian only with equal type constaints. There are inqualities in your problem, namely $w \ge 0$ and $w \le 1$. Hence Lagrange method cannot be employed here. According to tags you ...

A correlation and a dependence cannot be interchanged. The dependence is more general term that two radnom variables are somehow linked. The correlation concerns linear dependence only. So, in your ...

In continuous compounding, a nominal (or an index value) in time $t$ is given by formula $$N_t = N_0\mathrm{e}^{rt},$$ where $r$ is return (or interest) rate per annum. Based on the equation ...

You are right that if you use binary dummy variables for $n$ possible values of some feature (the country in your case) you need only $n-1$ variables because the last (or first) country is indicated ...

Your confusion is probably caused by these two facts: In theory, a surprise is descirbed by a random variable with so-called standard normal distribution having standard variation equal to zero. This ...

For example VaR, one of most widely used measure, is not coherent measure because it does not satisfy always sub-additivity property. However, under asumption of a normal distribution, VaR is sub-...

Concerning the hedging, you can use so-called catastrophe bonds. They are often issued by insurers and reinsurers, development banks and I can imagine issue by a pharma company. Funds raised from ...

Sometimes it is easier to work with continuos compounding in some models, especialy when you compound interest daily. Moreover, it can come from history when it was more difficult to calculate higher ...

There were many attempts to switch from normal distribution to some other which can describe a market more accurate, i.e. distribution with fat-tails (e.g. Cauchy distribution or broader familly of so-...

I tried to apply an entropy to time series of daily P/L on equity portfolios (developed markets). I found out that there is a strong correlation among entropy and other risk measures such as ...

Just to add, you did not mention which kind of momement. These calculated by formula in ir7 are called general moments. However, there are also: Central moments defined as $E[X-EX]^k$ Standardized ...

It does not matter whether you measure covariance of two portfolios or two securities, the formula is the same. Simply instead of returns and expected values for securities, put those for portfolios.

In finance, mainly linear algebra is very useful and necessary to know. Algebra in general is not necessary but I would recommend learning at least basics. It would improve your logical reasoning and ...

You can use high performance provided by database servers for calculations with huge amount of data, however, SQL is a logical language aimed mainly on searching in database. It is not intended for ...

C/C++ are low level languages in comparison with Python. Moreover, Python is scripting language. By nature, scripting languages are slow becuase they have to be interpreted. As there is a requirement ...

There is a lot of prepayment models for MBS, mostly every big bank has its own proprietary model. But the prepayment model can take into account many variables than only interest rate. A probability ...

You can measure inflation by so-called GDP deflator. The inflation for year $y$ is given by formula $$\pi_y = \frac{\text{GDP}_{nominal}}{\text{GDP}_{real}}.$$ The advantage of deflator in ...

BID/ASK spread always means difference between ASK and BID price. On Bloomberg, the spread is calculated for each price source. There is no averaging. The same is true for any other kind of spread (e....

You are right that many models are based on normal distribution or log-normal distribution which are connected. It seems that there is three reasons (of course, maybe more) for using normal ...

Usually both principal and par value refer to payment from a bond on its maturity. Sometimes term nominal is used for this as well. There can a little difference, however. Principal is used for a ...

See here list of articles and sources I have been interested in. They concern Monte Carlo method, derivative pricing and TSP. And here is a link to on-line course on basics of a quantum computing. I ...

You can use histogram in Excel. Either on Insert tab, where you choose Add graph and then histogram (in Excel 2016 and higher), or go to tab Data and Analytics tools (add-ins is needed for that) and ...

Firstly, a Poisson distribution is discrete one, so you can get CDF by sumation instead of integration. See here how CDF looks like. Secondly, 95 % VaR is a opposite value to 5 % quantile of the ...

If only US citizens can invest on US markets, total market capitalization has to be less than total wealth of society because finance investments are only part of total wealth. When you borrow money ...

Firstly, there is no possibility for a human to digest data used in algorithic trading. By definition, the algo trading is done by computer software (algorithms), there is no room for human ...

It seems that issuer of these notes took a position in options and it has gains only when the value of index is between 24 % and 27 %. Issued notes are probably used for funding some investment ...