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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....