The investment problem is predominantly concerned with the optimization of the risk-return tradeoff associated with portfolios. Specifically, an individual or institutional investor is to attempt to maximize the expected future return for the given amount of future risk taken. Equivalently, he/she is to minimize the amount of future risk taken for the desired amount of expected return.

This implication is rather intuitive and may beg the question: "If that's all you have to do, investing is simple, right?" Wrong. Such a conclusion would be wrong because the simple task of maximizing the expected return for the given amount of risk requires one to go through a mental exercise consisting of three phases, which are far from trivial. These phases are: (1) choosing the appropriate measures of expected return and risk, (2) correctly estimating the future (as opposed to measuring the past) values of risk and expected return for each asset or asset class, and (3) finding such combination of all available assets, which achieves the goal of minimum risk for the desired level of expected return. The importance of these three phases and their challenging aspects have been alluded to by several authors, including the Nobel Prize laureates Harry Markowitz and Bill Sharpe.

Another important question to consider is how frequently, if at all, and in response to what factors should the portfolio allocation be updated. Too frequent rebalancing may be not only costly, but also increase risk because it may not provide sufficient time to allow a particular portfolio achieve its full potential. On the other hand, too infrequent rebalancing may also be suboptimal and may result in a stale portfolio whose allocation to different asset classes, sectors, industries, and companies may be inappropriate to the current economic environment. What is the appropriate rebalancing regime in each particular case is a question that is far from simple.

Our primary focus is the top-down approach to portfolio allocation. This means the following:

• identifying the primary forces that drive the fundamental values of the different assets or asset classes that are of interest to our client;
• projecting the international and macro-economic factors that move markets, industries, sectors;
• using the projected fundamental factors to obtain the fundamental values of the various assets and asset classes;
• calculating the projected asset returns;
• given the client's situation, choosing the appropriate risk measures, e.g., volatility, semideviation, Value-at-Risk, tracking error, etc.;
• executing numerical algorithms that choose the amounts to be invested in each asset or asset class so as to achieve the lowest risk for the client's desired rate of return;
• given sufficient data, backtesting the strategy.