# Computing Buy-and-hold abnormal returns (BHARs) $= \prod_{t=\tau_1}^{\tau_2}(1+R_{i,t}) - \prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$

I am doing an event study and wanted to know if was going about this correctly$$\text{BHAR}_{i(\tau_1,\tau_2)}\quad=\quad\prod_{t=\tau_1}^{\tau_2}(1+R_{i,t})~-~\prod_{t=\tau_1}^{\tau_2}(1+R_{m,t})$$

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

Then if I want to calculate the 4-day $\text{BHAR}$ from the 2015-02-01 to 2015-06-01, would it simply be: $$\begin{array}{cr} & (1.9950)_{\text{Day0}} \times (1.0098)_{\text{Day1}} \times (1.00975)_{\text{Day2}} \times (1.01445)_{\text{Day3}} \times (0.9952)_{\text{Day4}} \\ - & (1.0049)_{\text{Day0}} \times (1.0039)_{\text{Day1}} \times (0.9990)_{\text{Day2}} \times (1.00593)_{\text{Day3}} \times (1.00491)_{\text{Day4}} \end{array}?$$

• First row: If price goes from 100 to 101, $(1+R_{i,t})$ is 1.01000 not 1.99503 – noob2 Oct 21 '16 at 17:31
• Oh, yes - I multiplied by 100 by accident - is the rest fine? – elbarto Oct 21 '16 at 18:10
• My point is I believe the daily returns used in BHAR are simple returns, not logarithmic returns. Can anyone confirm? – noob2 Oct 21 '16 at 18:25
• I have received confirmation that it is indeed simple returns that are used for BHARs, not Log returns. Thank you :) – elbarto Oct 22 '16 at 1:42