Tariffs. A radical foreign policy agenda. Often unpredictable but highly consequential domestic policy announcements. The most common adjective used to describe the new administration’s actions is “unprecedented”. For risk managers, this new environment presents a challenge.
Historical Value-at-Risk (HVaR), most commonly used to measure potential losses to portfolios in normal market conditions, is determined entirely by specified windows of returns, typically – 1Y, 3Y, 5Y or more. Markets right now feel anything but normal – throwing the statistical basis of HVaR into question in the current context. So, how can risk managers adapt to unprecedented times?
Exponential weighting
The first thing we can do is to adjust our HVaR calculation to utilize more recent data to better capture the “temperature” of the market.
Longer windows will capture a fuller set of returns, but the effect of such is diminished by utilizing a larger sample. In addition, the historically remote returns may be considered as not reflective of current market conditions.
On the other hand, short windows of returns are more current, but the smaller sample size implies greater statistical error. However, with exponential weighting, we can utilize the fuller set but achieve better focus on the present. This technique is commonly used in volatility estimation but works equally well in the calculation of HVaR. Figure 1 displays S&P 500 daily returns for the past three years, and Figure 2 shows the resulting HVaR (99%) results for various choices of the “half-life”. For example, a half-life of 0.25 means that a return from .25 years ago has half the weighting of a current return.
Figure 1
In Figure 1 above, the returns to the right are the most recent ones.
Figure 2
As the half-life increases, the HVaR approaches the original unweighted number of 3.3%. Half-lives of 2.0 years or less reduce the impact of the obvious volatility in the earliest period, 1.0 year or less, (which by itself would yield an HVaR of 3.63%).
Factoring this exponential weighting is an important first step in adapting HVaR to unprecedented market conditions. However, risk managers must consider the broader historical market context to identify potential blind spots and stitch real-life historic shocks into their VaR analysis:
- Take a step back: The worst one-day loss over the past three years is -4.2%, which means that the HVaR will still be less than 4.2%, no matter what statistical adjustment we employ. Our 3-year sample of returns simply cannot capture the potential losses that may occur, given the various financial and geopolitical impacts of the Trump2 administration.
- Stitch VaR: There is no requirement that returns be consecutive. Stitch VaR simply batches together returns from non-overlapping periods, stepping over intermediate periods. For example, if one wishes to include the 2008 Financial Crisis, one can use the past three years of daily data and augment it with returns from that period. This way, even though the market may have been quiet in recent times, you can still spice it up. Without using stitch VaR, one would have to use the past seventeen years of history in order to include 2008, which means its effect would be greatly diminished, being only 1/17th of the total number. Figure 3, “The Hurricane” displays the returns from that period – the fall of 2007 through spring of 2009.
Figure 3
So, even though we are in unprecedented times, this period can serve as a proxy for what could happen. The question is, how powerful is the hurricane?
- Putting it all together: We can use the hurricane metaphor to describe our approach. In Southern Florida, hurricanes are fact of life, and during hurricane season daily updates are provided on any current storms – their wind speed, size, etc – as well as a probability cone of where landfall may occur. It’s truly risk management.
Now suppose we utilize the past three years of daily data and add the hurricane – the financial crisis – about 1.5 years in duration, and calculate stitch VaR. Then we are implicitly assuming that the probability that we are in the hurricane period is 1.5/4.5 = 33%
But we can also make this an explicit input. Figure 4 displays the resulting VaR for various probability assumptions. We have assumed a half-life of 0.25 for the three-year period, although this has limited effect on the level of VAR obtained.
Figure 4
Calculating the calamitous
In unprecedented times, there is no mathematical or statistical algorithm that can provide an accurate determination of HVaR. It’s simply not in the tea leaves of recent historical returns. However, we can use calamitous events from the distant past to fill out our range of possibilities and bring them into the calculation.
However, this requires an assessment of the likelihood that such an event may occur. Have tariffs been imposed, and upon what and whom? What is the inflation rate, and the expected inflation rate, and how has it changed? Most firms have departments that focus on such data, and it is time to bring their expertise into your risk management.
Note: I recently moved to Key West.
