Accounting
(British: Accountancy)
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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)
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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)
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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
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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.,
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- 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
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Different statements
- stautory accounts
- taxes?
- management reports (informal)
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cash is cash,
balance sheet is balance sheet
[For traders, all you care about is your MtM.]
income, equity: these are trickier issues
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Basic principle of accounting;
a linear relation, a conservation law.
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Inaccuracy of linear accrual:
(vs. exponential growth)
- conceptually easier (EZ to check too)
- can't arb difference
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One aspect / issue is *valuation*
(Equity valuation / credit analytics)
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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)?]