# Underestimating economic capital?

#### afterworkguinness

##### Active Member
When calculating economic capital, how can we underestimate risk by ignoring the diversification benefits? I can see how we can overestimate by ignoring the correlation between the risk types (credit, market, operational), but I don't see how we can underestimate.

From the notes:

Since individual risk components are typically estimated without much regard to the
interactions between risks (e.g., between market and credit risk), aggregation
methodologies used may underestimate overall risk even if “no diversification”
assumptions are used.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @afterworkguinness

It's a good question because, after all, the syllabus faults VaR for a lack of sub-additivity, where sub-additivity insists that total portfolio risk should not be greater than the sum of its component risks. The apparent violation, which you note, refers (maybe?) to the Range of Practices in Economic Capital Frameworks. Jorion (see below) also mentions it. Jorion's point includes that idea that additional risks (e.g., via reputational risk) can be created in the portfolio; this is tantamount to something like, the portfolio includes risk (A) and (B), but if risk (A) and (B) occur, then risk (C) is introduced as an "emergent feature" of the system. The Basel Committee is more specific, they cite a paper which shows the mathematical justification using the classic example of market risk and credit risk: adding them is classically conservative by implicitly assuming perfect correlation, but this might forget a "malign interaction" between market and credit risk. If market and credit risks (or any risks) can be separated into different sub-portfolios, then adding them cannot understate the portfolio risk. (Separability is the mathematical key). However, if there is an malign interaction between market and credit risk, then adding them can understate risk. Verbally, this amounts to the dynamic where, in the tails where adverse outcomes occur, credit defaults can actually exacerbate market exposure ... this would have the effect of a correlation that seems greater than 1.0 due to an interaction term. I hope that helps!

From Range of practices and issues in economic capital frameworks, Basel Committee (i.e., likely the source of our note. Emphasis mine):
"IV. Risk Aggregation: In the context of risk aggregation across different portfolios or business units, some of the assumptions that underpin the above logic may fail to hold. One issue is purely technical and relates to the choice of VaR as a metric because it can fail to satisfy the subadditivity property. That is, it is possible for the VaR of a pooled portfolio to be higher than the sum of the VaR of the individual constituent portfolios. A more important reason why aggregate risk may be larger than the sum of its components is independent of the choice of metric (ie it applies to metrics other than VaR) and relates to the economic underpinnings of the portfolios that are pooled. The logic outlined above assumes that covariance (a linear measure of dependence) fully captures and summarises the dependencies across risks. While this may be a reasonable approximation in many cases, there are instances where the risk interactions are such that the resulting combination may represent higher, not lower, risk. For example, measuring separately the market and credit risk components in a portfolio of foreign currency denominated loans can underestimate risk, since probabilities of obligor default will also be affected by fluctuation in the exchange rate, giving rise to a compounding effect. Similar types of “wrong-way” interactions could occur in the context of portfolio positions that may be simultaneously affected by directional market moves and the failure of counterparties to a hedging position. From a more “macro” perspective, asset price volatility often interacts with the risk appetite of market participants and feeds back to market liquidity leading to a magnification of risk rather than diversification"

And just to complement this: from the FRM Handbook, 27.1.3. Risk Aggregation (emphasis mine):
"In practice, most banks that now report VAR estimates for market, credit, and operational risk often simply add up the three risk measures to get an estimate of the bank's total risk. As an example, JPMorgan estimated that its economic capital was $50 billion,$15 billion, and $9 billion for credit, market, and operational risk, respectively, which sum to$74 billion. This simple summation, however, generally overstates the risk because it assumes that the worst loss will occur simultaneously across the three risk types [Footnote 2]. Footnote 2: This is not necessarily the case, however. VAR may not be subadditive, as shown in Chapter 15. In practice, other types of risk, which are much harder to measure, can conspire to create more risk for the total entity than the sum of the individual risks. For very large institutions, liquidity is an example. As Long-Term Capital Management (LTCM) has shown, the potential loss from liquidating a $100 billion position is greater than the sum of losses from liquidating 10 positions of$10 billion separately. In addition, reputational risk can cause problems to one unit to spread and affect funding costs for the entire firm.

#### afterworkguinness

##### Active Member
Appreciate the very detailed answer! I'll look it over and digest it and post back if I have further questions.