P1.T1: Chapter 1 - Economic Captial (EC)

[carloscm]

Hi everyone,

Economic Capital (EC) was introduced in Chapter 1 as risk capital being used to absorb Unexpected Loss (UL) and is express as multiple of UL. <Page 4>

However, when taken into account in relation to RAROC, it was said that EC is a risk measure that includes both UL and Expected Loss (EL).

I'm a bit confused how these are linked together, could anyone give me some hints please?

Regards,
Carlos

 

[Torsleno]

Hello,

My understanding when studying this part was the following:
Expected Loss (EL) is predictable, but doesn't capture the part of risk arising from uncertainty. Unexpected Loss (UL) tries to address that and can be defined as the volatility of the Expected Loss (hence why you need EL to get to EC).
I see EL as the 'starting point' that is needed: you do need to make assumptions in order to derive an Unexpected Loss (as the name implies, quantifying something unexpected is challenging if not impossible; that is why the final UL number is not very accurate).

Hope that helps and happy to read anyone's take on the matter!

 

[David Harper CFA FRM]

I agree with you @Torsleno and that's helpful!

@carloscm Here is the page 4 snippet (new emphasis mine):

"The definitions of value-at-risk (VaR) and economic capital (EC) depend on the definition of unexpected loss (UL)

• VaR is the worst expected loss associated with some confidence level (typically 95% or 99%) over some horizon (e.g., one day, three months, one year). VaR requires a confidence level and a time horizon, such that many VaRs are possible.
  
  For example, we might say that our options position has a one-day VaR of $1.0 million at the 99.0% confidence level, meaning that our risk analysis shows that there is only a 1.0% probability of a loss that is greater than $1.0 million on any given trading day.
• Economic capital is the risk capital employed by the firm to absorb unexpected losses (UL) such that we can typically define economic capital as a multiple of UL, even if the multiple is simply 1.0." -- page 4

And I think maybe this is the other reference:

Risk-adjusted return on capital (RAROC)

Most practitioners are at least familiar with risk metrics such as value or risk (VaR) or even expected shortfall (ES). Additionally, financial analysts are proficient in return-type metrics such as return on equity (ROE) or earning per share (EPS). Similarly, most systems are able to analyze profitability by group or product line. But a more sophisticated approach is to link risk and reward (aka, return) into a single measure, such as risk-adjusted return on capital (RAROC). In its general form, RAROC is given by:

After-tax net risk-adjusted expected return ÷ Economic capital (EC)

In this way, economic capital is a fully loaded measure of risk that includes both expected loss (EL) and unexpected loss (UL). RAROC is theoretically superior to older methods (e.g., IRR or NPV) because it explicates the risk of the project (although NPV can attempt to do this via
calibration of the discount rate). If the RAROC exceeds the cost of equity, the project is desirable.

However, there are two disadvantages of RAROC: lack of a uniform (or regulatory) definition and implementation difficulty. Says GARP about RAROC, “There are many variants on the RAROC formula, applied across many different industries and institutions. Their level of sophistication varies but all have the same purpose: to adjust performance for risk … There are many practical difficulties in applying RAROC, including its dependence on the underlying risk calculations. Managers of business divisions often dispute the validity of RAROC numbers, sometimes for self-interested reasons.” [footnote 6: "Education, Pearson. Foundations of Risk Management. Pearson Learning Solutions, 2020. VitalBook file.]

The sentence of ours, "economic capital is a fully loaded measure of risk that includes both expected loss (EL) and unexpected loss (UL)", is not good. The numerator in RAROC subtracts EL and, in this way, is described as "risk-adjusted". But RAROC's numerator excludes EL and, consistently, the denominator of EC is the difference between the total worst expected loss (aka, the quantile) and the EL. As a super simple example, if a credit portfolio of $1,000 has PD = 1.0%, then the EL = $10 and if the 99.0% loss quantile is $800, then $800 = $10 + UL of $790. I'm being silly simple but RAROC's numerator would subtract the EL of $10 and the EC denominator would be $790 not then entire $800. I hope that's helpful,

 

[Torsleno]

As always, a much more accurate and detailed answer from @David Harper CFA FRM !

 

[carloscm]

@David Harper CFA FRM - Definitely very helpful to illustrate with numbers here.
@Torsleno - Thanks for helping as well.