Formulas Flashcards
CPPI Strategy with Futures
F(t)= [(Alpha / Futures Return) + Beta] x [Optimal Weight - Current Weight]
Equity in Merton Model
E(t) =
A(t) x N(d) -
Ke(-rt) x N (d - sigma(A) sqrt(tau))
D in BSM
d =
[ln (A(t) / k)
+ (r+1/2 x sigma^2)tau ] /
[sigma x sqrt(tau)]
Reduced Form D(0)
D(0) = e(-rt) x
[RR x K x (1 - e(-lamda x t)
+ K x e(-lambda x t)]
Altman’s Z-Score
Z = (1.2 × X1) + (1.4 × X2) + (3.3 × X3) + (0.6 × X4) + (1 × X5)
X1: working capital/total assets. (Liquidity)
X2: retained earnings/total assets. (Profitability)
X3: earnings before interest and taxes/total assets. (Productivity)
X4: market value of equity/book value of total liabilities. (Insolvency)
X5: sales/total assets. (Turnover)
Expected utility with risk aversion and growing liabilities
E(u) =
[V(A) x R]
-
(lambda/2 x sigma^2)
x
[(V(A)xR) - (L x G)]
V= value of the invested assets
L= present value of the liabilities
G = estimated growth rate for the liabilities
Mean-variance optimization with growing liabilities
w
1/lambda
x
[E(R-R0)]/sigma^2
+
L x (delta/sigma^2)
ROE
ROE = (ROA x L) - [r x (L-1)]
P(t,true)
P(t,true) =
P(t-1,reported)
+
(1/alpha)
x
[P(t,reported) - P(t-1, reported)]
Delta Beta Exposure
Beta(new) =
Beta (portfolio) +
Beta(futures) x (futures size / portfolio size)
Up Multiplier
U = e(sigma x sqrt( delta t))
Cointegrated Stock Prices
Ln(pt) - [a x Ln(st)] = constant
Vega
v = SN’(d) sqrt(t)
p = put or call option value
σ = underlying asset volatility
S = underlying asset price
N’(d) = probability density function for the normal distribution at d
T = time to expiration of the option
Gamma
g = N’(d) / (S x sigma x sqrt(t))
Theta
theta = - SN’(D) x (sigma /2 )x sqrt(T)
