Present Value (PV) and Future Value (FV

Annuities

Simple Interest: P * r * t

Compound Interest: A = P * (1 + r/m)^(m*t)

Continuous Compounding: A = P * e^(r*t)

Example: A ≈ 11,274.1 for a principal of 10,000 CNY at 6% annual interest over 2 years with continuous compounding

Single Period Return: R = (P1 - P0 + D) / P0

Geometric Average Return:(1+R_avg) = nth_root(Π(1+R_i))

Internal Rate of Return (IRR): NPV = Σ(C_t / (1+IRR)^t) - C0 = 0

Example IRR ≈ 9.7% for an investment of 1000 CNY with cash flows of 400 CNY over 3 years

Expected Return: E(R) = Σ p_i * R_i

Variance: σ^2 = Σ p_i * (R_i - E(R))^2

Standard Deviation: σ = √σ^2

Covariance: Cov(Rx,Ry) = E[(Rx-E(Rx))(Ry-E(Ry))]

Correlation Coefficient: ρ_xy = Cov(Rx,Ry)/(σ_x * σ_y)

Example: Diversifiable risk for Stocks A and B with correlation coefficient = -0.3

CAPM (Capital Asset Pricing Model)

APT (Arbitrage Pricing Theory)

Bond Price: P = Σ(C / (1+y)^t) + F / (1+y)^n

Yield to Maturity YTM: Solve for yield that equates price to present value

Duration: D = Σ t * PV(C_t) / P

Dividend Discount Model (DDM): P0 = D1 / (r - g)

Example: P0 = 33.33 for a dividend of 2 CNY/share, growth rate of 4%, and discount rate of 10%

Price-to-Earnings Ratio (PE Ratio): P = EPS * PE

Option Pricing (Black-Scholes) Model

Forward Contract Pricing: F0 = S0 * e^(rt)

Value at Risk (VaR): VaR_α = Z_α * σ_P * V

Expected Shortfall (ES)