Block Q · Financial mathematics basics
‹ Financial markets handbook: overview
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Six calculation concepts carry almost all of capital market practice; whoever masters them can derive every metric instead of believing it.
195 · Compound interest, present value & future value
Definition: Future value = K x (1+r)^n; present value = future payment / (1+r)^n; discounting is the inverse of compounding.
Use: The basis of EVERY valuation (bond, DCF, annuity).
Interpretation: The rule of 72 as mental arithmetic: 72/return ~ years to doubling.
Typical mistake: Linear thinking; compounding works exponentially, above all toward the end of long periods.
See also: 196 · IRR; money-weighted vs. time-weighted return · 197 · Annuities & amortization schedules
196 · IRR; money-weighted vs. time-weighted return
Definition: IRR = the rate that sets the present value of all payments to zero (money-weighted, MWR); time-weighted (TWR) eliminates payment flows and measures the manager's performance.
Use: TWR for manager/fund comparison; MWR/IRR for one's own wealth development and private equity.
Interpretation: A large contribution before a weak phase pushes MWR below TWR; the two numbers tell different stories.
Typical mistake: Comparing PE IRRs with the TWR of liquid investments.
See also: 198 · Return calculation (discrete vs. continuous) · 112 · Sharpe ratio
197 · Annuities & amortization schedules
Definition: A constant periodic payment of interest + principal; the annuity formula links loan amount, rate, term, installment.
Use: Financings, withdrawal plans ("how long does the wealth last at withdrawal X?").
Interpretation: In annuities the interest share falls, the principal share rises; the remaining debt declines slowly at first.
Typical mistake: Computing withdrawal plans without inflation-adjusting the withdrawal.
198 · Return calculation (discrete vs. continuous)
Definition: Discrete return = P1/P0 - 1; continuous (log) return = ln(P1/P0); log returns are additive over time.
Use: Statistics/models use log returns; reporting uses discrete ones.
Interpretation: -50% + 100% = 0% only in the log world; in discrete terms it takes +100% to offset -50% ("volatility drag").
Typical mistake: Presenting the arithmetic mean of discrete returns as the achieved return; compute geometrically.
See also: 196 · IRR; money-weighted vs. time-weighted return · 110 · Volatility (historical/implied)
199 · Yield curve bootstrapping (basic idea)
Definition: Deriving the zero coupon curve (spot rates) step by step from coupon bonds/swaps; from it discount factors and forward rates.
Use: Consistent valuation of all cashflows; understanding where "the" curve in YAS/SWPM comes from.
Interpretation: Forward rates are an arithmetic consequence of the curve; not a forecast (see Blocks E/F).
Typical mistake: Equating the yield curve (YTM) with the spot curve.
200 · Option pricing theory basics (Black-Scholes, put-call parity)
Definition: Black-Scholes prices options via replication (hedge portfolio); drivers: strike, spot, time, rate, VOL; put-call parity links call, put, spot and the present value of the strike.
Use: A fair-value feel for all option structures (certificates!); vega/theta intuition.
Interpretation: Direction is NOT priced in; what is traded is volatility; parity violations = arbitrage or data errors.
Typical mistake: Calling options "cheap" because the premium is small; what matters is implied vol vs. expectation.
See also: 61 · Options (call/put, basics) · 110 · Volatility (historical/implied)