1) Rebalancing strategies Suppose you initially have $100 in stock and $35 in T-
ID: 2729853 • Letter: 1
Question
1) 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)
Explanation / Answer
1) optimal S/TA ratio = current S/TA ratio = 100/135 = 0.7407
2) Stock holding at T1= 100 + (11/124*100)% of 100 =$108.87
3) Stocj holding at T2 = $108.87 - (5/135*100)% of 108.87 = $104.84
4) Optimum stock holding at T1 = {100/135*(108.87+35)} = $106.56
Therefore we have to sell $(108.87-106.56) i.e. $2.31 worth of stock.
Assuming T bills do not generate any return
5) Optimum stock holding at T2 = {100/135*(104.84+35)}= $103.58
Therefore we have to sell $(104.84-103.58) i.e., $ 1.26 worth of stock.
Assuming T bills do not generate any return
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