Dynamic Risk Management: Optimal Investment with Risk Constraints

When choosing an investment strategy, investors select assets that are likely to meet their particular return goals while managing the likelihood or sever-ity of returns falling short of these goals. Assessing the right trade-off between return and risk therefore requires the following: Target outcome: The investor’s goals should be clear. This may be expressed in terms of a benchmark or a return target, for example. Ideally these goals will be embedded in the wider situation facing the investor — the investor’s asset allocation is likely only one of several levers that can be adjusted to meet these goals. These goals then help determine the average return required of the investor’s assets. Risk tolerance: A judgement of the extent to which the investor is prepared to tolerate the return falling short of this target return. In the simplest situation, this could be expressed as an aversion to volatility, although more explicitly focusing on the probability or severity of poor returns may be more appropriate. With these in place, an investor will then seek to carry out a form of optimization — finding a strategy which gives as good a trade-off as possible between the average return and the variability relative to this average. In carrying out this optimization, further choices have to be made: What time horizon is relevant for the investor? What instruments are available in the investment universe? Is the strategy static or is it able to evolve dynamically in response to events?