Exercises in Advanced Risk and Portfolio Management: [mu,sigma_square]=LognMomentsToParameters(e,v) - File Exchange

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Highlights from
Exercises in Advanced Risk and Portfolio Management

BlackScholesCall(spot,K,r,vol... Black-Scholes price of a European call
BlackScholesCall(spot,K,r,vol... Black-Scholes price of a European call
ChoiceOptimal(Market,Investor...
ComRets2Prices(Exp_Comp_Rets,... this function computes the mean-variance inputs for stocks
Cost(Allocation,Market,Invest...
D=Delta(Time_to_Maturity,Stoc...
DecisionBestPerfomer(Market,I... % find index of best performer
Dy2Prices(Exp_DY,Cov_DY,Times... this function computes the mean-variance inputs for zero-coupon bonds
Dy2Prices(Exp_DY,Cov_DY,Times... this function computes the mean-variance inputs for zero-coupon bonds
Dy2Prices(Exp_DY,Cov_DY,Times... this function computes the mean-variance inputs for zero-coupon bonds
E=TwoDimEllipsoid(Location,Sq... this function computes the location-dispersion ellipsoid
EfficientFrontier(NumPortf, E... This function returns the NumPortf x 1 vector expected returns,
EfficientFrontier(NumPortf, E... This function returns the NumPortf x 1 vector expected returns,
EfficientFrontier(NumPortf, E... This function returns the NumPortf x 1 vector expected returns,
EfficientFrontierQP(NumPortf,... this function computes the mean-variance efficient frontier by quadratic programming
EfficientFrontierQPRets(NumPo... This function returns the NumPortf x 1 vector expected returns,
EfficientFrontierQPRetsBench(... This function returns the NumPortf x 1 vector expected returns,
EntropyProg(p,A,b,Aeq,beq) This function computes the entropy-pooling change of measure, see
FlexM(returns,demean,eps,df) PURPOSE: estimate FlexM multivariate GARCH model
G_Hat_a(X)
G_Hat_b(X)
G_Hat_c(X)
G_Hat_d(X) we use var(X,1,2) instead of var(X,0,2) to obtain the true sample estimator, which is slightly biased
G_Hat_e(X)
Goodness(Who,M)
IIDAnalysis(Data) this function performs simple invariance (i.i.d.) tests on a time series
IIDAnalysis(Dates,Data) this function performs simple invariance (i.i.d.) tests on a time series
K=Solve4Strike(Strike,Time_to...
MleRecursionForTFast(x,Nu,Tol... this function computes recursively the ML estimators of location and scatter
NormalCopulaPDF(u,Mu,Sigma)
PlotDistributions(X,p,p_)
PlotFrontier(Portfolios)
PlotFrontier(Portfolios, vol) This function plots the efficient frontier in the plane of portfolio
PlotFrontier(Portfolios, vol) This function plots the efficient frontier in the plane of portfolio
PlotNIWMarginals(Mu_Simul,Inv... this function plots numerically and analytically the marginal pdf of
Q=QuantileMixture(p,a,m_Y,s_Y... this function computes the quantile of a mixture distirbution by linear interpolation/extrapolation of the cdf
RobustEfficientFrontier(Targe...
RunAnalysis(Dates,Data,Label) this function performs simple invariance tests with generic time series
Satisfaction(Allocation,Marke...
TCopulaPDF(u,nu,Mu,Sigma)
TwoDimEllipsoid(Location,Squa... this function computes the location-dispersion ellipsoid
TwoDimEllipsoid(Location,Squa... this function computes the location-dispersion ellipsoid
TwoDimEllipsoid(Location,Squa... this function computes the location-dispersion ellipsoid
X=GenerateUniform(J,N) this function generates a uniform sample on the unit hypersphere
X=JumpDiffusionMerton(m,s,l,a... simulate number of jumps;
X=MvnRnd(M,S,J) % this function generates normal simulations whose sample moments match the population moments
X=MvnRnd(M,S,J) % this function generates normal simulations whose sample moments match the population moments
X=MvnRnd(M,S,J) % this function generates normal simulations whose sample moments match the population moments
XXX=minfro(A); function XXX=minfro(A);
[BLMu,BLSigma]=BLmFormulas(Mu...
[E_EM, S_EM, Y, CountLoop]=EM... this function implements the Expectation-Maximization (EM) algorithm to recover
[Expected_Value,Covariance,St...
[M,S]=Log2Lin(Mu,Sigma)
[Mu,Sigma,InvSigma,VecIndex]=... this function generates a multivariate i.i.d. sample of lenght J from the
[Mu,Th,Sig]=FitOU(Y,tau) this function fits a multivariate OU process at estimation step tau
[Who, Num, G]=AcceptByS(OutOf...
[Who, Num, G]=Naive(OutOfWho,...
[Who, Num, G]=RejectByS(OutOf...
[Who, g]=ExactNChooseK(OutOfW...
[X,F]=GenerateInvariants(mu_x...
[ga,mu]=SummStats(X,N) compute central moments
[mu,sigma_square]=LognMoments...
[q,qerr,hf,hferr]=garch1f4(x,... function [q,qerr,hf,hferr]=garch1f3(x)
[x_Hor,f_Hor,F_Hor]=Projectio... this function performs the horizon projection of a t-distributed invariant
f=fparam(x,th)
h=TwoDimEllipsoid(Location,Sq... this function computes the location-dispersion ellipsoid
h=pHist(X,p,nBins)
interpne(V,Xi,nodelist,method) interpne: Interpolates and extrapolates using n-linear interpolation (tensor product linear)
interpne(V,Xi,nodelist,method) interpne: Interpolates and extrapolates using n-linear interpolation (tensor product linear)
ka=Raw2Cumul(mu_)
mu=Raw2Central(mu_) code to map raw moments into central moments
mu=Raw2Central(mu_) code to map raw moments into central moments
mu_=Central2Raw(mu) code to map central moments into raw moments
mu_=Central2Raw(mu) code to map central moments into raw moments
mu_=Cumul2Raw(ka)
q=garch2f8(y,c1,a1,b1,y1,h1,c...
q=qparam(p,th)
xx=newton(M,i,b,m,aii,n,rho);
PlotEvaluationGeneric.m
S_AnalyzeLognormalCorrelation...
S_AnalyzeNIWPriorPosterior.m
S_AnalyzeNormalCorrelation.m
S_AutocorrelatedProcess.m
S_BLmBasic.m
S_BivariateSample.m
S_BondProjectionPricingNormal...
S_BondProjectionPricingT.m
S_BondResidualModel.m
S_BuyNHold.m
S_CPPI.m
S_CallsProjectionPricing.m
S_CornishFisher.m
S_CorrelationPriorUniform.m
S_DerivativesInvariants.m
S_DisplayCopulaPDF.m
S_DisplayJumpDiffusionMerton.m
S_DisplayNormalCopulaCDF.m
S_DisplayNormalCopulaPDF.m
S_EMexampleHighYield.m
S_ESContributionsFacts.m
S_ESContributionsT.m
S_EVT.m
S_EigenvalueDispersion.m
S_EllipticalNDim.m
S_EntropyView.m
S_EquitiesInvariants.m
S_EquityProjectionPricing.m
S_EstimateMomentsComboEvaluat...
S_EstimateQuantileEvaluation.m
S_EvaluationGeneric.m
S_FXCopulaMarginal.m
S_FactorAnalysisNotOK.m
S_FactorResidualCorrelation.m
S_FitSwapToT.m
S_FixedIncomeInvariants.m
S_FoDHedgeOptions.m
S_FoDHorizonEffect.m
S_FullCodependence.m
S_GenerateMixtureSample.m
S_InvestorsObjective.m
S_LinVsLogReturn.m
S_LognormalSample.m
S_MLEbasics.m
S_MVBenchmark.m
S_MVCalls.m
S_MVCallsRobust.m
S_MVHorizon.m
S_MVOptimization.m
S_MaxMinVariance.m
S_MultiVarSqrRootRule.m
S_NonAnalytical.m
S_NormalSample.m
S_OptionReplication.m
S_OrderStatisticsPDFLogn.m
S_OrderStatisticsPDFStudentT.m
S_PasturMarchenko.m
S_ProjSummStats.m
S_ProjectNPriceMvGARCH.m
S_ResidualAnalysisTheory.m
S_SelectionHeuristicsFoD.m
S_SemiCircular.m
S_ShrinkageEstimators.m
S_StatArbSwaps.m
S_StudentTSample.m
S_SwapPCA2Dim.m
S_TStatApprox.m
S_Toeplitz.m
S_UtlityMax.m
S_VaRContributionsUniform.m
S_VolatilityClustering.m
S_Wishart.m
S_WishartCorrelation.m
S_WishartLocationDispersion.m
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from Exercises in Advanced Risk and Portfolio Management by Attilio Meucci
text and comments on solutions available at http://symmys.com/node/170

[mu,sigma_square]=LognMomentsToParameters(e,v)

function [mu,sigma_square]=LognMomentsToParameters(e,v)

% this function inverts the formulas (1.98)-(1.99) in the book 
% "Risk and Asset Allocation" - Springer.

sigma_square=log(1+v/(e^2));
mu=log(e)-sigma_square/2;

Highlights from Exercises in Advanced Risk and Portfolio Management

Highlights from
Exercises in Advanced Risk and Portfolio Management