How do short sale prohibitions cause the active portfolio alpha to fall and the allocation of long positions to fall? I would think that the allocations to long positions would increase?
I think it is because with short sales you can take advantage of the cash inflow (from shorting the negative alpha stocks) to buy a larger proportion of positive alpha stocks.
You can use the proceeds from short sales to buy more long positions. So if you have no short sales, that’s money that can’t be used to buy more stocks. Also, if alpha is lower then I would assume the allocation to the active portfolio would go down as well since there’s less reward for straying from the passive portfolio. (I’m just going by what I know here, I don’t know what the curriculum actually says… someone with the books might want to check me on this.)
Not positive on this but given a fixed amount to invest in the active portfolio and a select number of stocks to choose from, then by having a short sale prohibition you would not be able to take advantage of the stocks with negative alpha. Therefore, you are missing out on opportunities so the alpha for the whole active portfolio would be lower. Most likely this leads to a lower information ratio for the active portfolio which means the active portfolio will get a lower weighting when combined with the passive portfolio. So since the active portfolio consists of only long positions and you are now giving less weight to the active portfolio, the allocation to the long positions would fall. -J