Browse
related articles
We often face not only financial constraints, but also shortages of information, time, and cognitive capacity. In many cases, we also face additional constraints on how we can employ available resources to achieve our goals (for example, limits to the maximum amount of funds that can be invested in one area, or the maximum acceptable probability of a result below some threshold).
Broadly, these are all asset allocation problems. We solve them every day using a variety of methodologies. Many of these are non-quantitative, such as dividing resources equally between options, using a rule of thumb that has worked in the past, or copying what others are doing. However, in cases where the stakes are high, the allocation problem is complicated, and/or our choice has to be justified to others, we often employ quantitative methodologies to help us identify, understand, and explain the potential consequences of different decision options. This article considers a typical asset allocation problem: how to allocate one's financial assets across a range of investment options in order to achieve a long-term goal, subject to a set of constraints.
Core challenge: Decision making under uncertainty
All investment asset allocation methodologies start with two core assumptions. First, that a range of different scenarios could occur in the future. Second, that investment alternatives are available whose performance will vary depending on the scenario that eventually develops. A critical issue is the extent to which a decision-maker believes it is possible to accurately predict future outcomes. Traditional finance theory, which is widely used in the investment management industry, assumes that both the full range of possible outcomes and their associated probabilities are known to the decision-maker. This is the classic problem of making decisions in the face of risk.
However, when you dig a bit deeper, you find that this approach is based on some questionable assumptions. The obvious question is: how can a decision-maker know the full range of possible future outcomes and their associated probabilities? One explanation is that they understand the workings of the process that produces future outcomes. In physical systems, and even in simple social systems, this may be true. But this is likely not to be the case when it comes to investment outcomes. Financial markets are complex adaptive systems, filled with positive feedback loops and nonlinear effects caused by the interaction of competing strategies (for example, value, momentum, and passive approaches) and underlying decisions made by people with imperfect information and limited cognitive capacities who are often pressed for time, affected by emotions, and subject to the influence of other people. An investor can never fully understand the way this system produces outcomes.
Even without such causal understanding, an investor could still believe that the range of possible future outcomes can be described mathematically, based on an analysis of past outcomes. For example, you could use historical data to construct a statistical distribution to describe the range of possible future outcomes, or devise a formula for projecting a time series into the future. The validity of both these approaches rests on two further assumptions. The first is that the historical data used to construct the distribution or time-series algorithm contain sufficient information to capture the full range of possible future outcomes.
Staff
