Financial Reporting requirements often demand that estimates of value are made for illiquid assets or instruments (e.g. private equity, property, some types of bonds, and other bespoke instruments). Valuations conducted in such contexts (whether done internally or by external experts), are often “smoothed”. This generally understates volatility (and risk), resulting in a potential over-allocation of assets to such asset classes.
An example of volatility smoothing is where even if the prices of similar publicly-traded assets has changed significantly (such as suffering a major decline), most estimates for similar classes of illiquid assets will typically be based on a smaller adjustment. This results from the interaction of a lack of complete information, human behaviour, and incentives of most valuers (whether external or internal) [For example, it is easier to argue for a “conservative” approach] . Often, the true underlying changes in value are only truly fully reflected at the time of an open-market transaction. (Such changes may occasionally be reflected in other work only if very detailed work has been done, sufficient to overcome the implicit bias that results for the above reasons; however, such in-depth analysis is usually too cumbersome to be performed for quarterly financial reporting, for example).
In fact, the true behaviour between underlying (“true”) volatility and the volatility derived from smoothed appraisal processes is quite subtle. However, it is fairly easy to explore with Monte Carlo Simulation. In our studies , we have found that volatility will typically be understated by appraisal values, but for low-risk assets it may in fact be overstated (this gives a “double-whammy” to the overallocation to assets that are actually higher risk). In our experiments, we considered three generic models for measure the volatility of asset prices that follow a lognormal random walk:
- A standard multi-period random walk (whose mean and volatility are known and assumed).
- A standard one period random walk in which the beginning and ending asset prices are as in step 1
- A multi-period random walk in which the beginning and ending asset prices are as in Model 1, but the price changes in the interim periods are smoothed according to a variable smoothing factor. With no smoothing, this model reverts to Model 1, however when there is smoothing, it does not revert to Model 2, since there are interim asset prices which are smoothed.
For Model 3, the effects on measured volatility of various smoothing factors is interesting. For underlying processes which have high volatility, the smoothed values will have lower volatility. However, for processes with low volatility, the measured volatility of the “smoothed” process may be higher, since the resetting (a bit like marking-to-market) of the price in the last period of the multi-period model gives a volatility jump, whereas the underlying process has developed more smoothly.
We intend to do more work and research in this area (but would prefer to avoid it causing another financial crisis, if possible 😊)