Illustrative calculation of regulatory capital using an equity at risk methodology

For any firm, define

E(Rp_t+1) = E( D P_t+1 + Y_t+1 - C_t+1)

Where:

E(Rp_t+1) is the forecast value of earnings in time t+1 (assumed to be one year)
DP_t+1 is the change in the value of the firm's portfolio of assets in time t+1
Y_t+1 is the value of the firms new business revenues in time t+1, and
C_t+1 is the costs which the firm incurs in time t+1

where

RER = - ((Reg E(Rp_t+1)) - (Stress D P_t+1) - (Stress Y_t+1) - (Stress C_t+1))

Reg E(Rp_t+1)) is the lower of the previous year's earnings and the average of the preceding five years' revenues
Stress DP_t+1 = market risk stress loss + credit risk stress loss
Stress Y_t+1 = the difference between Yt/12 and the worst monthly business revenues in the previous 4 years * 12

Capital Firm A

Max (- ((1500-300-1,000-1,200 - 600)*4), (300+1,000+1,200+600))

= Max, 6,400, 3,100 = 6,400

Firm B (Lower risk)	Period1	Period 2	Period 3	Period 4	Period 5
Earnings	500	510	515	530	525
Business revenue	2,000	2,100	2,100	2,200	2,200
Lowest month					165
Costs	1,540	1,600	1,660	1,650	1,720
Portfolio change	40	10	75	(20)	45
Market risk					50
Credit risk					150

Capital Firm B

Max(-((516-50-150-220-188)*4), (50+150+220+188))

= Max, 368, 608 = 608