Shiryaev-Zhou index - a noble approach to benchmarking and analysis of real estate stocks

Real estate markets and real estate stocks are interrelated and are important not only to the investors, but also to the academics. Real estate stocks are, in a sense, good measures of performance of the physical real estate market. The objective of this paper is to provide a preliminary study on gauging the performances of real estate stocks in Hong Kong using the Shiryaev-Zhou index. Evidence shows that the Shiryaev-Zhou index can gauge a real estate stock's performance, good or bad, according to the sign of the Shiryaev-Zhou index. Thus a trading strategy can be formulated as follows: buy a stock if its Shiryaev-Zhou index changes from negative to positive, then hold it until its Shiryaev-Zhou index turns negative, when it is time to sell the stock. We examine the Shiryaev-Zhou indices of the real estate stocks in Hong Kong, and from this we deduce the latest best selling dates of the stocks during the period of our study. The Shiryaev-Zhou index could be an indicator of whether the market is bullish or bearish and consequently tells an investor to hold a stock or not, and it naturally leads to an optimal selling strategy that maximize the average ratio of the selling price to the maximum stock price when the underlying coefficients are assumed to be constant over a definite period of time.