Research On Measuring Of Stock Loan-to-value Ratio

Pricing of stock loan-to-value ratio is very important for securities companies to balance risks and benefits in stock pledge business.On one hand,although the high stock loan-to-value ratio can attract more investors(mortgagors)and extend the scale of business,it increases the risk positions of the pledgee.It means that stock loans tend to be beyond the reasonable scope and it is difficult for pledgee to match risk and return.One the other hand,although the low stock loan-to-value ratio can make sure the safety of stock loans,it will weaken the market appeal of pledgee and compress the scale of business.It also means that its earnings will be narrowed with the smaller risk and difficult to get reasonable income,which is adverse to the development of the stock pledge business.At present,the most widely used pricing model of stock loan-to-value ratio in theory and practice is based on the VaR(Value at Risk).In other words,stock loan-to-value ratio is calculated simply based on the volatility in the existing research and practice.Although the pricing method is easy to operate,it in fact fails to consider the risks after the pledgor default,such as liquidity risk and leverage risk.In addition,the existing research ignores the effect of diversification on pricing of stock loan-to-value ratio.For the pledgee,regardless of a single stock is pledged by pledgor or a portfolio,the risk of pledgee’s overall stock pledge business also should not be the weighted average of single pledgor.Aiming at the shortcomings of the existing research,stock loan-to-value ratio is studied from three aspects in the paper:(i)Build the pricing model of stock loan-to-value ratio considering the liquidity risk and different risk preference of the pledgee.(ii)Introduce leverage risk into pricing of stock loan-to-value ratio,and use Monte Carlo method to evaluate and compare the result of pricing.(iii)Refer to the theory of portfolio investment and risk control method,and give the pricing of stock loan-to-value ratio under the view of diversification and the risk contribution of pledgor.The main conclusions are as follows:(Ⅰ)Stock loan-to-value ratio is overestimated significantly if only consider the volatility risk only;If consider liquidity risk additionally,stock loan-to-value ratio is the lowest when the pledgee takes passive liquidation strategy;Correspondly,if the pledgee takes positive liquidation strategy,stock loan-to-value ratio is positively related to the degree of pledgee’s risk preference,that is,the stock loan-to-value ratio under the situation of linear strategy is lower than the situation of upward convex quadratic function strategy,which is higher than the situation of downward convex quadratic function strategy.(Ⅱ)Stock loan-to-value ratio is significantly affected by leverage and liquidity shock.Compared with the traditional model which is based on forecasting volatility only,the stock loan-to-value ratio according to pricing model put forward in the paper is significantly lower than the former.In addition,when introducing leverage risk into pricing of haircut dynamically,a special case of pledging stock,the paper also proves the conclusion.Leverage risk plays the most significant effect on haircut.Only the pricing of haircut considering leverage risk can cover the downside risk of the underlying stock during the crisis.(Ⅲ)In the pricing method under the view that pledgors are to be seen as a portfolio,the paper utilizes two method(Copula-GARCH and ES)to measure the risk contribution of pledgor.The comparative analysis results show that loan-to-value ratio pricing will be overestimated if not considering the influence of pledgor risk.The main innovations are as follows:(i)it fully depicts the liquidity risk of stock pledge business which is reflected in the pricing of stock loan-to-value ration.Specifically,the market impact of the pledgee is characterized,and it is established as a key factor to influence the pricing.Then analyze the behavior of pledgee to prevent liquidity risk,in other words,different liquidation strategy.The pricing method of stock loan-to-value ratio considering volatility and liquidity risk is benefit to pledgee with different risk preference.(ii)on the basis of liquidity risk,the paper innovatively consideres the influence of leverage on stock loan-to-value ratio,and further improve the pricing method.By considering the fact of leverage and cross shareholding,when facing liquidity risk caused by pledgor default,this paper analyzes the positive feedback effect resulted from portfolio rebalancing of leveraged investors.Thus we build a optimized pricing model considering volatility risk,liquidity risk and leverage risk,which helps the pledgee to set loan-to-value ratio reasonably and flexibly under different market conditions.(iii)extend the problem of single stock pledge to the perspective of a portfolio of pledgor and construct the pricing model,which is more practical.The pricing method takes full account of diversification effect,and accord with risk contribution of the pledgor,which will help pledgee to balanace between the overall risk and benefit in stock pledge business.The paper analyzes the source of risk in the stock pledge business,and systematically studies pricing of stock loan-to-value ratio.It not only enrich the theory of pricing method of stock loan-to-value ratio,but also is instructive to practices in stock pledge business.