# Rebalancing Portfolio

Suppose you initially have \$100 in stock and \$35 in T-bills so that total assets are \$135. Suppose also that the stock market index at time 0 was 124, and at time 1 is rose to 135. At time 2, the stock market had fallen back to 130. Assume that at time 0, you are at your optimal stock to toal assets ratio. Calculate the following: The amount of stock you should buy or sell at t=1 and t=2 under a constant mix strategy? Below is my calculation: Optimal ratio=100/135=74.07% Beginning of time1 stock value=(100/124)*135=108.87 At time 1: 74.07%=(108.87+x)/(35+108.87) -> x=-2.26 -> sell \$2.26 At time 2: beginning time2 balance=end time 1 balance adjusted for mkt movement=(108.87-2.26)130/135=102.66 74.07%=(102.66+x)/(102.66+35) ->x=-0.69 However, the back of schweser answer states differently: For time 2, total assets=143.87-(106.61-102.66)=139.92 where 143.87=108.87+35 106.61=108.87-2.26 Anyone can please explains schweser’s logic! and tell me why I am wrong. Thanks

singlesong80 Wrote: ------------------------------------------------------- > 74.07%=(102.66+x)/(102.66+35) Here’s where you went wrong. It’s (102.66 + 37.26), not +35, because now you have an extra 2.26 in T-bills from the stock that you sold at t=1. You should buy \$0.98 in stock accordingly.