Overview
Many models in use today are rather blunt or simple tools which may not accurately capture the dynamics of the thing they are trying to model. Depending on what the source of the inaccuracy is, this may not necessarily be a bad thing. That is, the model may still be useful.
As an example, many banks will manage their portfolios such that the loss of the portfolio in the event of a 100 basis point move (1%) of the yield curve does not result in a loss above a pre-specified level. This example is sometimes criticized for being unrealistic. That is, there is never an instantaneous 100 basis point move the yield curve, rather, this type of move plays out over time.
Uses of Simple (not totally accurate) Models
- Rank Ordering - some models, particularly those that compute a probability, such as a VAlue at Risk (VAR) model are not terribly accurate in their probability forecasts, particulary in the tails. However, the model may be accurate in rank ordering the outcomes. That is, choosing a lower VAR will necessarily create a less risky situation than a higher VAR, even if it is impossible to measure the value at risk probabilities.
- Ensemble Modeling - while a simple model by itself may be too simplistic to use, it can be used as one of many models in an ensemble.
Example
The following example creates a simple scenario that demonstrates some of the principles. Suppose that an asset manager wants to manage their portfolio such that it stays within a certain risk limit. The manager determines that she can only hold 100 units of asset A (or short 100 units), or 100 units of asset B. She decides that her risk rule will be that
{% a+b = 100 %}
That is, the sum of the number of units of each asset should equal 100.
The investable universe can be plotted as follows.
(the number of unites of asset A is on the X axis and asset B is on the Y axis)
The manager has chosen this rule as a simplification, in actuality, because asset A is likely a diversifier to asset B, a combination of the two in a portfolio is likely to diversify away some of the risk, and so the managers simple linear rule is conservative. The actual investable universe should look something like
The inaccuracy of the model is somewhat irrelevant if the models diamond model fits within the actual risk universe, as in the following
That is, the manager is justified in using a simple model over the more complex model, if she has reason to believe that it still achieves her goal, in this case, keeping her within a certain level of risk.
When the linear model extends beyond the theoretical risk boundaries, as in the following, the manager may have some concerns about the usefulness of the model, unless she can argue that the probability of investing outside the theoretical universe is still small.