  An active margin system for margin loans is proposed for Chinese margin
lending market, which uses cash and randomly selected stock as collateral. The
conditional probability of negative return(CPNR) after a forced sale of
securities from under-margined account in a falling market is used to measure
the risk faced by the brokers, and the margin system is chosen under the
constraint of the risk measure. In order to calculate CPNR, a recursive
algorithm is proposed under a Markov chain model, which is constructed by
sample learning method. The resulted margin system is an active system, which
is able to adjust actively with respect to the changes of stock prices and the
changes of different collateral. The resulted margin system is applied to
30,000 margin loans of 150 stocks listed on Shanghai Stock Exchange. The
empirical results show the number of margin calls and the average costs of the
loans under the proposed margin system are less than their counterparts under
the system required by SSE and SZSE.
