Using historical data, the risk and return of products may be calculated. Accordingly, the portfolio (expected) return is simply the weighted (by fund allocation) average expected return of all the investments in the portfolio.
Portfolio risk (or standard deviation) is more complicated than a simple average of the standard deviation of the investments in the portfolio. It also involves the covariance between investments in the portfolio. Covariance being part of the equation essentially explains the risk of not diversifying – the higher the covariance between investments, the higher the risk, and the lower the covariance between investments, the lower the portfolio risk.
However, it should be understood that by plugging historical data into fairly straightforward formulas, portfolios with expected risk and return can be constructed. It follows that portfolios can be constructed to suit the different risk profiles of clients. For instance, a young entrepreneur seeking aggressive returns comparable to or higher than that of his business may target a high-risk, high-return portfolio. On the other hand, a wealthy and aged businessman seeking wealth preservation for his future generations might favour a low risk portfolio. Regardless of the preference for high or low risk, the portfolio should have an appropriate (optimum) level of reward for every unit of risk. This is known as the efficient frontier – which is essentially a set of portfolios that offer the highest possible (expected) return given the amount of risk taken. Intuitively, no portfolio should seek to be sub-optimal (not on the efficient frontier) following the logic that maximum possible returns are desirable.