Formula Sheet

Formula Sheet for Test 2: FINA 465

Chapter 8

1) Change in interest rate in the ith bucket:

NIIi = (GAPi) Ri = (RSAi - RSLi) Ri

Chapter 9

2) The price of a bond is the present discounted value of all future cash flows.

P = Σnt=1 [CFt/(1+R)t]

3) The duration of any fixed-income security that pays interest annually is given by:

D = Σnt=1[CFt• t/(1+R)t] / Σnt=1 [CFt/(1+R)t] =>

D = Σnt=1[PVt • t] / Σnt=1 [PVt]

D = duration measured in years

CFt = cash flow received at the end of period t

n = last period in which cash-flow is received

R = is the annual yield or current level of interest rates in the market

PVt = present value of the cash flow from period t

4) The change in price for a small change in interest rate:

ΔP = -D[ΔR/(1+R)]P

5) The percentage change in price for a small change in interest rate:

ΔP/P = -D[ΔR/(1+R)]

6) Duration of assets:

DA = X1A D1A + X2A D2A + … + XnA DnA

Duration of liabilities:

DL = X1L D1L + X2L D2L + … + XmL DmL

Where XiA and XiL are the market value proportions of each asset or liability held in the respective portfolio and n (m) is the number of assets (liabilities) in the FI’s asset (liability) portfolio.

7) Leverage adjusted duration gap = DA - DLk , where k = L/A.

8) The effect of change in interest rates on the value of equity:

ΔE = -[DA - DLk] A [ΔR / (1+R)], where k = L/A.

Chapter 11

9) Promised return on a loan

(of + (BR + m))/(1-[b(1-rr)])

of = fees as a proportion

BR = base lending rate (e.g., prime)

m= risk premium

b = compensating balance requirement

rr = reserve requirement

10) Probability of Default in the Linear Model

PDi =

11) Altman’s Linear Discriminant Model

Z=1.2X1+ 1.4X2 +3.3X3 + 0.6X4 + 1.0X5

Z= inverse indicator of risk

X1 = Working capital/total assets; X2 = Retained earnings/total assets; X3 = EBIT/total assets; X4 = Market value equity/ book value LT debt; X5 = Sales/total assets....