  Margin system for margin loans using cash and stock as collateral is
considered in this paper, which is the line of defence for brokers against risk
associated with margin trading. The conditional probability of negative return
is used as risk measure, and a recursive algorithm is proposed to realize this
measure under a Markov chain model. Optimal margin system is chosen from those
systems which satisfy the constraint of the risk measure. The resulted margin
system is able to adjust actively with respect to the changes of stock prices.
The margin system required by the Shanghai Stock Exchange is compared with the
proposed system, where 25,200 margin loans of 126 stocks listed on the SSE are
investigated. It is found that the number of margin calls under the proposed
margin system is significantly less than its counterpart under the required
system for the same level of risk, and the average costs of the loans are
similar under the two types of margin systems.
