A regression model for valuation

this model can be used to test the investment opportunties. for another side to seek the relationship between market and book value of equity

statistical market value accouting model. the model relates the market value of firms' euqity(MVE) to its book value of equity (BVE)as follows:

MVE= a+b*BVE +e.

where a and b are estimated regression coefficients and e represents an approximation error or random distubrance term. the equation can be estimated over time or cross sectionally. it is easy to see that if a=0 and b=1, then marekt and book values of equity or net worth do not diverge, except for random disturbances that on average are expected to be zero.

going beyond the statistics of the model, the econmic interpretation of hidden capital is the important message. consider the intercept first, supporse that a firm is book-value insolvent (Asset-Liability is negative) but still trading in the market at a positve value,. since it is dead but still living, the only requirement is that a is positve.that is ,there is positive unbooked net asset value. some chinese stocks are traded in this situation, some time goverment guarantess also permits book-value insolvent.

when the slope coefficient equals one, b=1, and the intercept is constant, then when a is positive, a premium exists becuase on dollar change in book value results in more than more dollar change in the market vlaue. if a is negative and b=1, then a discount exists because a one dollar change in the book value results in less than a one dollar change in equity value. the discount is due to negative hidden capital.

what about situation in which  a=0 but b is not 1? when b is less than one, a one dollar change in book value results in less than one dollar change in market value, the discount suggest accouting overvaluation of changes in booked assets and booked liabilities relative to market valuations. when b is bigger than one, a premium exist and can be interpreted as a reward for the present value of future growth opportunities not captured by assets in place.