复利终值:
\( F = P \times (1 + i)^n = P \times (F/P, i, n) \)
复利现值:
\( P = F \times (1 + i)^{-n} = F \times (P/F, i, n) \)
预付年金现值:
\( P = A \times (P/A, i, n) \times (1 + i) \)
递延年金现值:
\( P = A \times (P/A, i, n) \times (P/F, i, m) \)
永续年金现值:
\( P = A / i \)
递延年金终值:
\( F = A \times (F/A, i, n) \)
实际利率(多次计息):
\( i = \left(1 + \frac{r}{m}\right)^m - 1 \)
实际利率(通货膨胀):
\( \text{实际利率} = \frac{1 + \text{名义利率}}{1 + \text{通货膨胀率}} - 1 \)
预期收益率:
\( E(R) = \sum_{i=1}^{n} (P_i \times R_i) \)
期望值:
\( \overline{E} = \sum_{i=1}^{n} X_i \times P_i \)
方差:
\( \sigma^2 = \sum_{i=1}^{n} (X_i - \overline{E})^2 \times P_i \)
标准差:
\( \sigma = \sqrt{\sum_{i=1}^{n} (X_i - \overline{E})^2 \times P_i} \)
标准差率:
\( V = \frac{\sigma}{\overline{E}} \times 100\% \)
两项资产组合方差:
\( \sigma_P^2 = W_1^2 \sigma_1^2 + W_2^2 \sigma_2^2 + 2 W_1 W_2 \rho_{1,2} \sigma_1 \sigma_2 \)
组合β系数:
\( \beta_P = \sum_{i=1}^{n} (\beta_i \times W_i) \)
资本资产定价模型:
\( R = R_f + \beta \times (R_m - R_f) \)
高低点法(单位变动成本):
\( b = \frac{\text{最高点业务量成本} - \text{最低点业务量成本}}{\text{最高点业务量} - \text{最低点业务量}} \)
固定成本总额:
\( a = \text{最高点业务量成本} - b \times \text{最高点业务量} \)
总成本模型:
\( \text{总成本} = \text{固定成本总额} + \text{变动成本总额} = a + b \times \text{业务量} \)