Asset allocation investigates the optimal division of a portfolio among different asset classes. Standard theory involves the optimal mix of risky stocks, bonds, and cash together with various subdivisions of these asset classes. Underlying this is the insight that diversification allows for achieving a balance between risk and return: by using different types of investment, losses may be limited and returns are made less volatile without losing too much potential gain. These insights are made precise using the benchmark theory of mathematical finance, the Black-Scholes-Merton theory, based on Brownian motion as the driving noise process for risky asset prices. Here, the distributions of financial returns of the risky assets.
