Question: Rebalancing strategies:

Suppose you initially have $100 in stock and $35 in T-bills creating a portfolio with total assets of $135. Suppose the stock market index initially at time 0 was 124 and at time 1 rose to 135. At time 2, the stock market has fallen back to 130. Assume that at time 0 you are at your optimal mix of Stock to Total Assets (S/TA). Also make the assumption that $100 of stock in the portfolio moves % wise the same as the market index. Calculate the following:

i) Your optimal S/TA ratio

ii) Your stock holdings at time 1 (under buy and hold)

iii) Your stock holdings at time 2 (under buy and hold)

iv) The amount of stock you should buy or sell at t=1 (under a constant mix strategy)

v) The amount of stock you should buy or sell at t= 2 (under a constant mix strategy)