Risk in Finance is generally defined as the chance of a loss.  In order to quantify risk, one needs to use a precise statistical measure of dispersion of returns or events.  This measure is referred to as the standard deviation, often denoted by the Greek letter “Sigma” ( σ ).  The larger the range or spectrum of possible returns or outcomes, the larger the Sigma, and thus the larger the risk taken by the investor.

Most investors have been exposed to the ubiquitous Finance statement: “High risk, high return.”  This can lead one to believe that a risky strategy guarantees a high rate of return in the long run.  But this statement tends to be more valid ex-ante rather than ex-post (i.e. before the facts vs. after the facts).  Ex-ante, if one perceives an investment to be risky, one will indeed expect, demand or require a higher rate of return in order to agree to invest significant capital.  However, ex-post, if the investment did turn out to have incurred several large downward fluctuations, the overall return can easily end up being less than that of a safer or less volatile strategy.

Ideally, one should strive to maximize the targeted long-term average or expected return while simultaneously attempting to minimize the downside risk taken to achieve this return.  These two objectives can be combined into the Reward-to-Risk (Sharpe) Ratio as the expected or average return divided by the risk level.  In order to maintain portfolio efficiency, this ratio should be regularly maximized through active periodic rebalancing and re-optimizing.

A basic concept of diversification states that one should not put all of one’s eggs in one basket.  This very general principle is also known as “naïve diversification.”  However, how many eggs and in which baskets is a question that can only be answered by precise quantitative optimization tools. The answer yields a mean-variance efficient portfolio, i.e. a portfolio that contains the least amount of risk for the level of targeted average return.  This approach of maximizing the Sharpe ratio is made possible by the computationally-intensive use of statistics gauging the performance of each security, their volatility, and how they “correlate” with one another.

Mean-variance quantitative risk-reducing tools and individual security selection (or “stock picking”), although two radically different approaches appearing to be very philosophically different at first, can actually be combined to achieve a portfolio efficiency of even higher quality.

Thanks to the availability of actively-managed assets such as Mutual Funds, for instance, a quantitative mean-variance optimization scheme using those as inputs can strengthen a portfolio in two ways: through superior security selection at the fund manager’s level, and through optimal risk minimization given the targeted return.

This approach allows one to benefit from the “best of both worlds.”