The banking book risk and the economic value of equity

Question 1

Modified Duration Formula

Answer 1

MD=D/(1+i_A)

Question 2

Duration GAP Formula

Answer 2

ΔMVE=-(MD_A-LEV* MD_L) * MVA * Δi or
ΔMVE=-DG * MVA * Δi

Question 3

Duration formula

Answer 3

Weighted Average of the maturity of each cash flow in years weighted by PV of each cash flow divided by the total PV of the security

Question 4

Duration Gap: Problems and Limits

Answer 4

• Duration (and duration gap) changes every instant, when interest rates change, or simply because of time
• Immunization policies based on duration gap should be updated continuously
• Duration (and duration gap) is based on a linear approximation
• Impact not estimated precisely
• The model assumes uniform interest rate changes (Di) of assets and liabilities int. rates

Question 5

What is the beta duration gap formula?

Answer 5

ΔMV_B=-(MD_Aβ_A-LMD_Lβ_L)MV_A*Δi

Question 6

What is the duration gap and convexity gap formula?

Answer 6

ΔMV_E=-(MD_A-LMD_L)ΔiMV_A+(MC_A-LMC_L)((Δi)²/2)MV_A

Question 7

What problem does the clumping model solve?

Answer 7

Duration Gap assumes a uniform change of interest rates for different maturities, clumping solves that

Question 8

How does clumping work?

Answer 8

• The model is built upon the zero-coupon curve (both the repricing gap and the duration gap model were focused on the yield curve)
• The model works through the mapping of single cash flows on a predetermined number of nodes (or maturities) of the term structure

Question 9

How does bootstrapping work?

Answer 9

1. From prices of zcb we extract the corresponding r_t
2. We use these zero-coupon rates to estimate the present value of the first four cash flows (coupons) of the 4.5% coupon paying bond
3. Find the rate that equates the present value of 102.5 to the residual value of the bond which has not been explained by the PV of the four coupons

Question 10

How to map cash flows?

Answer 10

Building a new security, identical to the real cash flow in terms of market value and riskiness (modified duration)

Question 11

How to choose the number and the position of the nodes?

Answer 11

• Changes in ST interest rate are more frequent and larger than changes in LT interest rates
• The relationship between volatility and maturity of interest rates is negative
• Usually cash flows with short maturities are more frequent that cash flows with long maturities
  Bottom Line: It’s better to have a larger number of nodes in the ST part of the curve
• The choice of node is also influence by the availability of hedging instruments

Question 12

How to map step-by-step

Answer 12

1. Figure out the Market Value and the Modified Duration of the real Cash Flow
2. Figure out the Modified Duration of the fake cash flows according to the nodes
3. MV_n = MV_t((MD_t-MD_n+1)/(MD_n-MD_n+1))
   MV_n+1 = MV_t((MD_n-MD_t)/(MD_n-MD_n+1))
   Where t is the real cash flow, n is the earlier node and n+1 is the later node

For the last step we essentially take the weighted average of the modified duration for MVn by taking the period from the real cash flow to the end of the period between the nodes over the full period, and MVn+1 by taking the period from between the early node and the real timing and dividing by the the full period

Question 13

What is the Basel Committee Approach of 2004

Answer 13

• Banks are required to allocate their assets and liabilities to 14 different maturity bands
• For each maturity bucket, the net position is computed (difference assets and liabilities)
• The net position for each maturity bucket is weighted by a risk coefficient espressing the potential change in value
• A uniform Δi= 2% change of interest rates is assumed
  ΔNP_i=-NP_iMD_iΔi_i
• Total risk is computed as the sum of all these ΔNPi

Question 14

Basel Committed Aprroach 2016 scenarios

Answer 14

(i) parallel shock up
(ii) parallel shock down
(iii) steepener shock (short rates down and long rates up)
(iv) flattener shock (short rates up and long rates down)
(v) short rates shock up, and
(vi) short rates shock down