1. Holding Period Return=(V1-V0+D1)/V02. Standardized Return=
(mean return-Target return)/standard deviation of returns3.
Expected Portfolio Return= E(Rp)= w1*E(R1)+w2*E(R2)+.....+wn*E(Rn)
for n assets portfolio4. Standard deviation of portfolio=
w1^2*sd1^2+w2^2*sd2^2+..........wn^2*sdn^2, sd=standard deviation5.
CAPM: E(Ri)= Rf+ Betai*[E(Rm)-Rf] where Betai=Cov(Ri,Rm)/var(Rm),
Rm is market return and Ri is security return6. Capital Market
Line(CML): E(Rp)= Rf+ [[E(Rm)-Rf] /SDm]SDp7. CAPM with taxes:
E(Ri)= Rf+
Betai*[E(Rm)-Rf]+taxfactor*[(divyield(i)-Rf)-Betai(divyield(m)-Rf)]
taxfactor that measures market tax rates, divyield(i) is dividend
yield of stock8. Multi Beta CAPM: E(Ri)= Rf+
Betai,m*[E(Rm)-Rf]+Betai,f1*[E(f1)-Rf]+Betai,f2*[E(f2)-Rf]+........
where Betai,m is sensitivity to market, Betai,f1 is sensitivity to
factor 1,....9. Treynor ratio= [E(Rp)-Rf]/Beta(p) p is subscript
for portfolio10. Sharpe ratio= [E(Rp)-Rf]/StdDev(p)11.Jensen's
alpha= E(Rp)-{Rf+ Betap*[E(Rm)-Rf]}12. Sortino
Ratio=[E(Rp)-Rmin]/sqrt(MSDmin) Rmin is benchmark and MSDmin is
standard deviation of portfolio returns below the Rmin13.APT Model:
Rn=Rf+ Xn,1*b1+ Xn,2*b2+ Xn,3*b3+ Xn,4*b4................+unwhere
Rn is the return for stock n; Xn,k is kth factor exposure for n; bk
is return for kth factor, un is the systematic risk14. Bayes
formula: P(A/B)=P(A&B)/P(B) A and b are
events15.Correlation(Ri,Rj)=
Covariance(Ri,Rj)/[stdDev(Ri)*stdDev(Rj)]16. z parameter for
ND(mean,stdDev)z= (observation-mean)/stdDev17. test of differences
between
means:t=[(mean(s1)-mean(s2))-(mean(p1)-mean(p2))]/sqrt[sp^2*(1/n1+1/n2)]where
sp^2= [(n1-1)*s1^2+(n2-1)*s2^2]/(n1+n2-1)s1 is standard deviation
of sample 1, s2 is standard deviation of sample 2s1,s2 are samples
1 and 2 while p1 and p2 are populations 1, and 218. chi-Square test
stat= (n-1)*s^2/stdDev^219.F test stat. = s1^2/s2^220.t stat.=
(sample mean- population mean)/(s/sqrt(n))21. Poisson distribution:
P(X=x)=lambda^x*exp(-lambda)/x! 22.adjusted R^2=
1-(n-1/n-k-1)*(1-R^2) where R^2 is the coefficient of
determination, k:no of independent variables 23. Geometric Brownian
motion= dSt= mean(t)*St*dt + stdDevt*St*dz where mean(t)*St*dt
=constant drift term and stdDevt*St*dz is volatile component24.
Binomial probability function= nCx p^x*(1-p)^n-x where n is no of
trials , x is the no of succeses and p is probability of success25.
dollar value of basis point= DV01= Price @YTM0- Price @ YTM126.
Hedge ratio= HR= DV01(per $ of initial position)/DV01(per $ of
hedging instrument)27.Duration of Bond= BV(y-)-BV(y+)/2*BV0*(total
change in y)28. Convexity of Bond=BV(y-)+BV(y+)-2BV0/2*BV0*(total
change in y)^229. percent price change in bond= duration effect+
convexity effect= [-duration*(total change in y)]
+[.5*convexity*(total change in y)^2]30. BSM option pricing model:
c=S0N(d1)-Xe^(-rT)*N(d2) where
d1=[ln(S0/X)+(rf+.5*stdDev^2)T]/stdDev*sqrt(T) and
d2=d1-stdDev*sqrt(T)31. continously compounded return=
ln(St/St-1)32. delta= dc/ds if the rate of change of call option
price w.r.t the change in underlying asset price that is stock
price32. gamma= d^2C/dS^2= rate of change of delta w.r.t the
underlying asset value33. theta= dC/dt is the rate of change of
option price w.r.t. the time34. vega= dC/d(volatility)= rate of
change of option price w.r.t the volatility of the underlying
asset35. rho= dC/dr is the rate of change of option price w.r.t the
interest rate
36. Taylor series:
f(x)=f(x0)+f'(x0)*(x-x0)+.5*f''(x0)(x-x0)^237. Expected Loss=
AE*LGD*PD where AE-Adjusted exposure, LGD: loss given default and
PD: probability of default38.Unexpected loss=
AE*sqrt[EDF*(volatility LGD)^2+LGD^2*(volatility EDF)^2] where EDF
is expected default frequency; AE=OS(outstanding)+alpha(COMu)39.
Hedge ratio= corr(S,F)*(stdDev of S/stdDev of F)40.beta(S,F)=
co-variance(S,F)/variance (S)41.No of contracts= beta of
portfolio*[portfolio value/value of future contract] after
adjustment to beta* No of contracts=(beta*-beta of
portfolio)*[portfolio value/value of future contract] 42. Forward
price, F0= S0* e^rT 43. Accrued interest= Coupon*[No of days from
last coupon to settlement day/No of days in coupon period]44.T Bill
Discount rate= (360/n)*(100-Y) 45. Cheaper to deliver bond= Qouted
Bond price- QFP*CF where QFP is quoted futures price and CF is the
conversion factor46. Duration based hedge ratio= N= -(P*Dp/F*Df)
where Dp is duration of bond and Df is the duration of futures used
to hedge the bond price movement47.Forward rate(T1,T2)=
(R2T2-R1T1)/T2-T148. Hedge effectiveness= 1-[var(S-F)/var(S)]
