The Expected return The expected value of the stock price is E(ST) The expected continuously compounded return on the stock is E(m=u-o/2(the geometric average) u is the the arithmetic average of the returns Note that E[n(ssl is not equal to InE(ST) In[E(STI-In So+u T, EIn(ST) =In So+(u-0/2)T Options, Futures, and Other Derivatives, 4th edition@ 2000 by John C. Hull Tang Yincai, C 2003, Shanghai Normal University11.7 Options, Futures, and Other Derivatives, 4th edition © 2000 by John C. Hull Tang Yincai, © 2003, Shanghai Normal University The Expected Return ➢ The expected value of the stock price is E(ST )=S0e mT ➢ The expected continuously compounded return on the stock is E(h)=m – 2 /2 (the geometric average) ➢ m is the the arithmetic average of the returns ➢ Note that E[ln(ST )] is not equal to ln[E(ST )] ln[E(ST )]=ln S0+m T, E[ln(ST )] =ln S0+(m-2 /2)T