Quantitative Methods

For continuous compounding, EAR = $e^{rt}-1$

PVperpetuity = $\frac{PMT}{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$y$}\right.}}$

Time Weighted Rate of Return (TWROR) = $\left[\left(1+r_1\right)\left(1+r_2\right)....{\left(1+r_n\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}-1\right]$
$Where, \left(1+r_1\right)=HPR$

$Samplw mean \left(\overline{X}\right)$ = $\frac{\sum _{i=1}^N{X}_i}{n}$
when n is sample size

Harmonic mean (HM) = $\frac{N}{\sum _{i=1}^N\frac{1}{xi}} (average \cos t of shares purchase over time)$
AM > GM > HM (dollar cost averaging uses investing same amount every time period in a share;

Coefficient of variation (CV) = $\frac{\sigma }{\mu }\times 100 OR \left(\frac{S_x}{x}\times 100\right)$

Negative skewness = Mean < Median < Mode

Expected value E(x) = $Weighted average of all possible outcomes \sum PX$

$Cov(R_A,R_B)$ = $\sum P\left(S\right) x [R_A-E(R_A\left)\right][R_B-E(R_B\left)\right]$

$Correlation(R_i,R_j)$ = $\frac{Cov(R_i,R_j)}{{}_{{\sigma }_{R_i}\times {\sigma }_{R_j}}}$

$Cov\left(R_A{R}_A\right)$ = $Variance R_A or {\sigma }_{R_A}^2$

90% confidence internal = $\overline{x}-2.58s to \overline{x}+2.58s$

If threshold level = Risk free rate of return
$i.e. R_{min}=R_f, SFR = Share\text{'}s Ratio$

Testing of equality of variance (F distribution) = $F statistic=\frac{S_1^2}{S_2^2}$

Geometric mean return = $\sqrt[n]{(1+R\_1 )\times (1+R\_2 )\times (1+R\_3 )\dots \times (1+R\_n)}-1$

$Samplevariance:{\sigma }^2$ = $\frac{\sum {(x-x¯)}^2}{n-1}$