WALL ST ROCKET SCIENTIST'S CRIB SHEET
(c)1987,1999,2006 Vasos-Peter John Panagiotopoulos II
ACCOUNTING:(CURR_ASSET=CASH+(ACCTS_RECVBL-BAD_DEBT)+INVTRY)
+PLANT_P_EQPT+ACCRU_INCOM_RECVBL+PREPAID_EXPC
=ASSETS=LIAB+EQTY
=ACCTS_PYBL+NOTE_PYBL+BOND_PYBL+TX_PYBL+UNEARN_INCOM+EQTY
NET_INCOM=SALE_REVNU-COST_GOODS_SOLD-SELL_GENL_ADM_EXPC
-INTRST_EXPC-DEPREC-TX-RENT
CASH_FLOW=(CASH_DUE_DEPREC=DEPREC_AMT)
+STOCK_SALES+GRANTS+BONDS-DEBT_PYMT-DIVIDEND-CAP_EXPDTR
DEPREC_AMT=PRICE*RATE*(1-RATE)^(YR-1)
QUICK_ACID_RATIO=(CASH+NET_RECVBL+MKTBL_SECURTS)/CURR_LIAB
CURRENT_RATIO=CURRENT_ASSETS/CURRENT_LIAB
ASSET_TURNOVER=NET_SALES/TOT_ASSET; WRK_CAP=CURR_ASSET-CURR_LIAB
INTRST_EARN_TIMES=(NET_INCOM+INTRST_EXPC+TX)/INTRST_EXPC
DEBT_EQUITY_RATIO=TOT_LIAB/EQTY should be around 2/3
COLLEXN_PERD=365/(ANN_CRED_SALES/AVG_ACCTS_RECVBL)
OPTCASH= CUBRT(.75 TRSXNCST * CFVAR^2 / i) + LOWLIM
ALTMAN_Z_SCORE(.GT.3 for no bankrupt)=(1.2*WORKG_CAPTL+SALES
+1.4*RETAIN_EARN+3.3*OPER_INCOM)/TOT_ASST
+.6*MKT_VAL_COMM_AND_PREF_STOCK
BREAK_EVEN_SALES=VAR_COST*QUANT+FIX_COST+BRKEVN_PROFIT=PRICE*QUANT
FINANCE: FUT_VAL/PRES_VAL=(1+INTRST)^NUM_PER
FUT_VAL_ANNUIT/ANNUIT_PMT =((1+INTRST)^NUM_PER -1)/INTRST
PRES_VAL_ANNUIT/ANNUIT_PMT=(1-(1+INTRST)^-NUM_PER)/INTRST
0=FUT_VAL+PRES_VAL*(1+INTRST)^NUM_PER
+PMT*(1+INTRST*TIME)*((1+INTRST)^NUM_PER -1)/INTRST
NPV=TIME_SUM(CASH_FLOW[TIME]/(1+INTRST)^TIME)
IRR:=IRR-NPV(IRR,CF)*IRR*.01/(NPV(IRR*1.01,CF)-NPV(IRR,CF))
ROE=1/P:E+GRO*RTN=NO_RISK_RTN+BETA*(MKT_RTN-NO_RISK_RTN)
FIRM_VALU=NPV(NET_INC_AFT_INTRST_&TX+DEPREC+TX_CRED+ACC_DEPREC
-CHG_INVST-CHG_WRK_CAP-DEBT)
WT_AVG_COST_CAPTL*(CAPTLSN=BONDS+STOCKS+ ...)=
(1-TX_RATE)*COST_DEBT*BONDS+COST_EQTY*STOCKS+...
Sum((1+r)^-t)=integral(exp(-rt))=(1-(1+r)^-n)/r=(1-exp(-rn))/r
Gordon Sum(DIVDD*(1+g)^n/(1+r)^n)=DIVDD/(r-g)
BETA=slope of return vs mkt=COVAR(INVST,MKT)/VAR(MKT)
OLD_PRIC=(DIVDD+PRIC)/(1+RTN)=DIVDD/(RTN-GRO)=PERPET_PMT/RTN
YIELD_TO_MAT=2*(NOM_INTRST+DISCT(or -PREM)/YRS)/(PV+MAT_VAL)
CAPM_EXPEC_RTN=RISKFREE-BETA(MKT_EXPEC-RISKFREE)
Duratn=d ln P / d Y Cvxty= d d ln P / d Y d Y
Fwd[n,t]= (((1+yld[n+t])^(n+t))/((1+yld[n])^n))^(1/t)-1
OPT_CASH_LEV=SQRT(2*FIX_TRANSXN_COST*TOT_REQD_PERD_CASH/INTRST)
NPV_LESSOR=-COST_ASSET+SUM((LEAS_PMT*(1-TX)+TX*DEPREC)/(1+WACC)^TIME)
OPM PDE: 0=.5*(CALL_VALU DIFF STOCK_PRIC DIFF STOCK_PRIC)
*(RTN_STDEV*STOCK_PRIC)^2
+(CALL_VALU DIFF TIM)
+RISKFREE_RATE
*(STOCK_PRIC*(CALL_VALU DIFF STOCK_PRIC)-CALL_VALU)
CALL_VALU=0 wherever STOCK_PRIC=0
END TIME CONDITION: CALL_VALU=MAX(STOCK_PRIC-CALL_PURCH_PRIC,0)
ECONOMICS: GNP=(MONEY_SPLY/PRICES)*EXP(CONST*(INTRST=RL_INTRST+INFLN_EXPEC))
=(COMSUMP_INTCEPT+INVEST_INTCEPT+GOVT_SPEND_INTCEPT
+EXPORT_INTCEPT-IMPORT_INTCEPT
-CONSUMP_SLOP*(BUSN_SAVG_INTCEPT+TAX_INTCEPT-TRANSF_INTCEPT))
/(1-CONSUMP_SLOP-INVEST_SLOP
+CONSUMP_SLOP*(BUSN_SAVG_SLOP+TAX_SLOP+TRANSF_SLOP)
+GOVT_SPEND_SLOP+IMPORT_SLOP) ..slopes abs val & vs GNP..
BOSKIN_POSTWAR_LOG_CONSUMP=-3.85+.62*LOG_DISP_PRIV_INCOM
+.007*LOG_DISP_PRIV_INCOM[time-1]+.72*LOG_WEALTH[time-1]
-.003*LOG_UNEMPL_RATE-2.08*RL_AFT_TX_RTN+.007*EXPEC_INFLN
FRIEDMAN CONSUMP_PERM/GNP_PERM= fct of: +RL_INTRST,-AGE,-LIF_EXPEC,
+RATE_TIM_PREF, +NONSLAVE_WEALTH/GNP_PERM ..PERM+TEMP=ACT..
PRODXN_FCT=d*(a*CAPITAL^((e-1)/e)+b*LABOR^((e-1)/e))^(c*e/(e-1))
e=SUBSTN_ELAST;a+b=1;ELAST=LN(QUANT) DIFF LN(PRICE) = d%q/d%p
optpric=margcost/(1+1/elast)
COBBDOUGLAS(e=1)=d*(CAPITAL^(c*a)+LABOR^(1-c*a)) ..d=TECH..
MARG_PRDXVTY_A=PRODXN_FCT DIFF A;INTRST=MARG_PRDXVTY_CAPITAL
LEARNSPEED=A * UNITS ^-(IncrPrdxvty); SALESGRO=SUM(aTANH(t+b))
MATHEMATICS:udv=d(uv)-vdu; (n+1)b(a+bx)^n dx=d((a+bx)^(n+1))
2cdx(+-c^2-+x^2)=d ln( (x+-c)/(c-+x) )
a exp(ax) dx=d exp(ax);axa exp(ax)dx=d((ax-1)exp(ax))
-a sin ax dx=d cos ax; a cos ax dx=d sin ax
InfSum a^n = 1/(1-a;e^a=suninf(a^k/k!);sum-to-n-1 a^n=(1-a^n)/(1-a)
sin^2=.5(1-2cos2p); cos^2=.5(1+cos 2 p); sin(-p)=-sin(p);
sin(pi/2 +- p)= cos p; sin(pi+-p)=-+sin; sin(3pi/2 +-p)=-cos;
sin(2kpi+-p)=+-sin;cos(2k pi +-p)=+-sin; cos p = cos -p;
cos(pi/2+-p)=-+sin; cos(pi+-p)=-cos;cos(3pi/2+-p)=+-sin
sin=sqrt(1-cos^2); cos=sqrt(1-sin^2); lHospital lim f/g=lim f'/g'
Convexity=-Concavity=Hessian (pos/neg def) = second deriv
1.96|95% 2.58|99% 3.29|99.9% 3.89|99.99%
f(k-1,n-k)= r^2/(k-1)/( (1-r^2)/(n-k)) t(n-k) = beta /sigbeta
sigsq=sum(x-mu)^2 / (n-1) (lost 1 deg frdm to mu)
centrlimthm mu^k(mu) ~ N(mu,sig/( sqrt(n) ^k)
SLOP=(n*SUM(x*y)-SUM(x)*SUM(y))/(n*SUM(x^2)-SUM(x)^2)
INTCEPT=AVG(y)-SLOP*AVG(x);ABS(t-STAT).LT.2;DURB_W=2+-.5;R-SQ near 1
VAR=E((X-E(X))^2)=E(X^2)-(E(X))^2; COV=E(XY)-(EX)(EY)
CRAMERRAO H=-E[ln PDF DIFF theta DIFF theta]=E[ln PDF DIFF theta]^2=A
HETSCHED F TEST [sumsq top,bottom 5/12 var] ok:psi=1,OLS else GLS:
SLOP=(X[transp]psi^-1 X) X[transp] psi^-1 Y sigsq[ij]=/=sigsq[ji]
EXP_SMOOTH(y)=a*y_OLD+(1-a)y_OLD_SMOOTHED, ar(1)=ma(inf)
moment[k]=E[(x-mu)^k] momgen[k](t)=E[exp(tk)] dW=W*sqrt(step)
ITO dY[k]={g[k;t]dt+g[k;i,j]dX[j]dX[j]/2=0mtgl}+g[k;i]dX[i]
df=mu*dt+sigma*dw dtdt=dtdw=0 dw[i]dw[j]=rho[ij]dt dw=sigma*sqrt(dt)
FeynKac dx[i]=b[i]du+y[i,j]dw[j];g=E(h(T)):g[;t]+b[i]g[,i]+y[i,k]y[k,j]g[,i,j]=0
NUMERICAL INTEGRAL(ydx,x1,x3)=(y(x1)+4*y(x2)+y(x3))*(x3-x1)/6
METHODS: INTERPOL(x;known x[i],y[i])=SUM(j=1 to n: PROD(i=1 to n,never j:
(x-x[i])*y[j]/(x[j]-x[i]) ) )
RANDOM WALK: x[n+1]:=(x[n]*4782969) mod max;
REGULA FALSI: x0:=((x2:=x1)-(x1:=x0))*f(x1)/(f(x1)-f(x2))+x1;
RUNGE KUTTA 4: Y[n+1]:=Y[n]+k1/6+k2/3+k3/3+k4/4;
k1:=DELTA_X*Y_DIFF_X(x[n] ,y[n] );
k2:=DELTA_X*Y_DIFF_X(x[n]+DELTA_X/2,y[n]+k1/2);
k3:=DELTA_X*Y_DIFF_X(x[n]+DELTA_X/2,y[n]+k2/2);
k4:=DELTA_X*Y_DIFF_X(x[n]+DELTA_X ,y[n]+k3 );
FINITE DIFF: 2 U[J]:=U[J+1]+U[J-1]
U DIFF X DIFF X:=(U[J+1]-2U[J]+U[J-1])/((X[J]-X[J-1])^2)
U DIFF T:=(U[N+1]-U[N])/(T[N+1]-T[N])
SPENCER ANSELMO:
X[I]:=X[I]-INV(LAGR1*(FCT[K] DIFF X[I])*WT[K,L]*(FCT[J] DIFF X[L])
+LAGR2*MAGNIF[I,J])
*(FCT[J] DIFF X[M])*WT[M,N]*FCT[N]
..find X for opt F..WT may be ident..MAGNIF incr as chg shrink..
KUHNTUCKER dLAGRGOBJFCT/dx .LE. 0 dLAGRGOBJFCT/dLAGRGMULT .GE. 0
KALMAN d ln P = d[expect] h (R[transp]R)^-1 (dZ-h[expect]dt)