Not sure if it’s a rounding problem. My calculation tells me I should sell stock at t=2.
which notes, what question?
Schweser Notes, Book5.
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, it 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-total-assets ratio (S/TA).
Calculate the following:
v. The amount of stock you should buy or sell at t = 2 (under a constant-mix strategy).
sell 4.03 $ stock - is what I am getting
100, 35 at T=0
108.87, 38.11 @ T=1
104.84, 36.71 @ T=2
are those numbers looking right?
per my calcs you need to buy stock at T2 to get back to the original equity allocation of 74.074%
Schweser’s answer is to buy $1.02.
after T1 your psotions are:
stock = 106.57
cash = 37.30
total = 143.87
after T2 (the market drops 3.7%)
the stock would be $102.62 and cash would still be $37.30 = $139.92
to get back to stock allocation of 74.1% you need to buy stock for $1.02
stock is now $1.02 + 102.62 = 103.65
103.65 / 139.93 = 74.1%
How did you get the 106.57?
135/124 = 1.0887 isn’t it?
you are wrong in that logic - got to work thru the numbers
t1 is 108.87 after stock goes up, but you are now overallocated to stock (75.6% vs target of 74.1%) so you must SELL stock of 2.30 to get back to target weight of 74.1%, so ending t1 values are stock 106.57 and cash 37.30
now in t2, market drops 3.7% so stock allocation goes down to 102.62 and cash remains 37.30
you are now UNDERweight to stocks and need to get back to 74.1% target
so you BUY stock for 1.02 and decrease cash by 1.02
new allocation is now stock 103.64 and cash 36.28 for total of 139.92
check = 103.64 / 139.92 = 74.1% alloc to stock = your target weight
I missed: cash = $37.30 after the rebalancing at t=1.
Thanks mcap , for working it out for us