Accounting (British: Accountancy) ---------------------------------------------- Mathematical lessons I learned: - mathematically equivalent equations admit different interpretations Assets - Liabilities = Equity vs. Assets = Liabilities + Equity (and EGs of other computations) - linear relations are conservation laws! - importance of non-commutativity of difference operators (path dependence & all that) ---------------------------------------------- Quips ------------------------ Cash is cash, but the naming of cash is accounting. Accounting is linear; finance is non-linear. Principles / accountant mind ---------------- - naming naming intermediate results y = mx :: change in output should be from change in input, times some ratio/slope EG of meta-applications (convergence of national standards: naming different levels of conformance) - attribution It's not ok to make money w/o explaining where it comes from! Breaking up changes in value. - prefer adding to subtracting: Assets - Liabilities = Equity ...is instead stated as: Assets = Liabilities + Equity - principles & details Like law, it has some principles (pseudo-universal), and a mass of details. AFAICT, it's more codified than law (less judgement/interpretation/precedent) --------------------------------------------------------- Value? - Some is simply pedantry (rectification of names) - Some is strategic (esp. return on capital etc.) - precision, analysis, and rigor are familiar from computers, math, science --------------------------------------------------------- Non-linearity - derivatives blow accountants' minds Rather, they're non-linear and hence don't fit the mold. - EG of x*y (as mentioned in email) Note that x*y is linear *in each variable*, so still sorta fits mold. - Why cumulate income: overall income is just overall change in balance sheet etc., --------------------------------------------------------- - step functions and delta functions Balance sheet is functions, generally locally constant (hence step functions); cash and income are delta functions (pure point measures); dBS = cash & income; \int cash and income = BS P&L statement --------------------------------------------------------- Different statements - stautory accounts - taxes? - management reports (informal) --------------------------------------------------------- cash is cash, balance sheet is balance sheet [For traders, all you care about is your MtM.] income, equity: these are trickier issues --------------------------------------------------------- Basic principle of accounting; a linear relation, a conservation law. --------------------------------------------------------- Inaccuracy of linear accrual: (vs. exponential growth) - conceptually easier (EZ to check too) - can't arb difference --------------------------------------------------------- One aspect / issue is *valuation* (Equity valuation / credit analytics) --------------------------------------------------------- EGs: - VaR for business units, overall VaR; the difference from the sum is called "diversification benefit" [though with VaR for catastrophes, this could instead be a (debit)?]