• Economics,  Math

    Portfolio Insurance and Black Monday, October 19, 1987

    On the thirtieth anniversary of Black Monday, the stock market crash of October 19th and 20th in 1987, there have been mentions of “portfolio insurance” having possibly exacerbated the crash.   Portfolio insurance, in principle, is exactly what you might expect it to be: if you own a stock, Stock A, you insure it with a put option on Stock A.  Your position becomes equivalent to a call option on Stock A until the put option expires, with the price of this position being the premium of the put option when you bought it. If you are managing a portfolio on behalf of clients, though, and you just need to…

  • Economics

    Value-added Tax and Sales Tax

    (This is mostly a summary of and heavily borrowed from https://en.wikipedia.org/wiki/Value-added_tax, archived). (The first three figures are taken from Wikipedia).   Comparing No Tax, Sales Tax, and VAT Imagine three companies in a value chain that produces and then sells a widget to a consumer. The raw materials producer sells raw materials to the manufacturer for $1.00, earning a gross margin (revenue – Cost Of Goods Sold, COGS) of $1.00. The manufacturer sells its product, the widget, to the retailer for $1.20, earning a gross margin of $0.20. The retailer sells the widget to a non-business consumer (for the customer to use and consume) for $1.50, earning a gross margin…

  • Math

    Testing MathJax-LaTeX

    emph https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference Default font size. Different font size. Bold text. bold text. italic text. Italic text. Underlined text. At first, we sample $$f(x)$$ in the \(N\) ($N$ is odd) equidistant points around \(x^*\): \[ f_k = f(x_k),\: x_k = x^*+kh,\: k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \] where \(h\) is some step. Then we interpolate points \((x_k,f_k)\) by polynomial \begin{equation} \label{eq:poly} \tag{1} P_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j} \end{equation} Its coefficients \(a_j\) are found as a solution of system of linear equations: \begin{equation} \label{eq:sys} \tag{asdf} \left\{ P_{N-1}(x_k) = f_k\right\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \end{equation} \begin{equation} \label{eq:sys2} \tag{asdf2} \{ P_{N-1}(x_k) = f_k\},\quad k=-\frac{N-1}{2},\dots,\frac{N-1}{2} \end{equation} Backslash left and right parentheses: \[ \left( \frac{1}{2} \right) \qquad ( \frac{1}{2} ) \\ ( \frac{1}{2} ) \] $$ 1…