Computación Comprar y mantener rendimientos anormales (BHARs) $= \prod_{t=\tau_1}^{\tau_2}(1+R_{i,t}) - \prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$

Question

Estoy haciendo un caso de estudio y quería saber si iba acerca de este correctamente $$\text{BHAR}_{i(\tau_1,\tau_2)}\quad=\quad\prod_{t=\tau_1}^{\tau_2}(1+R_{i,t})~-~\prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$$

$$\begin{array}{|c|c|c|c|c|} \hline \textbf{Date} & \begin{array}{c} \text{Price of} \\ \text{Stock}~i \end{array} & \text{LOG RET} & 1+R_{i,t} & 1+R_{m,t} \\ \hline \text{2015-01-01} & 100 & \text{--} & \text{--} & \text{--} \\ \text{2015-02-01} & 101 & \phantom{-}0.99503 & 1.99503 & 1.004987\phantom{0} \\ \text{2015-03-01} & 102 & \fantasma{-}0.00985 & 1.00985 & 1.0039722 \\ \text{2015-04-01} & 103 & \fantasma{-}0.00975 & 1.00975 & 0.9990084 \\ \text{2015-05-01} & 104 & \phantom{-}0.01445 & 1.01445 & 1.005934\phantom{0} \\ \text{2015-06-01} & 104 & -0.0047\phantom{0} & 0.99520 & 1.00491\phantom{00} \\ \hline \end{array}$$

Entonces, si quiero calcular la 4-día $\text{BHAR}$ a partir de 2015-02-01 a 2015-06-01, podría simplemente ser: $$\begin{array}{cr} & (1.9950)_{\text{Day0}} \times (1.0098)_{\text{Day1}} \times (1.00975)_{\text{Day2}} \times (1.01445)_{\text{Day3}} \times (0.9952)_{\text{Day4}} \\ - & (1.0049)_{\text{Day0}} \times (1.0039)_{\text{Day1}} \times (0.9990)_{\text{Day2}} \times (1.00593)_{\text{Day3}} \times (1.00491)_{\text{Day4}} \end{array}?$$

Answer 1

Resumiendo el debate en los comentarios: BHAR son calculadas usando simples regresa, no logarítmica devuelve.