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EXISTENCE OF A NONNEGATIVE EQUILIBRIUM PRICE VECTOR IN THE MEAN‐VARIANCE CAPITAL MARKET
Author(s) -
Konno Hiroshi,
Shirakawa Hiroshi
Publication year - 1995
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1995.tb00066.x
Subject(s) - economics , market portfolio , portfolio , capital market line , econometrics , rate of return , weighted arithmetic mean , capital (architecture) , financial economics , mathematics , market depth , finance , statistics , stock market , history , paleontology , archaeology , horse , biology
We derive a necessary and sufficient condition for the existence of a nonnegative equilibrium price vector under which the total demand and supply of each asset balances in the standard mean‐variance capital market. Also, we give an explicit formula for such a price vector. This formula shows that the price of assets is an increasing function of p̄, the weighted average of the requested rate of return of individual investors, which tends to infinity as p̄ approaches the expected rate of return on the market portfolio. Further, we construct a macroeconomic index which gives information about the soundness of the capital market.