[Returnanalytics-commits] r2152 - pkg/PerformanceAnalytics/sandbox/Meucci/R
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Fri Jul 13 11:29:10 CEST 2012
Author: mkshah
Date: 2012-07-13 11:29:10 +0200 (Fri, 13 Jul 2012)
New Revision: 2152
Removed:
pkg/PerformanceAnalytics/sandbox/Meucci/R/ButterflyTrading.R
Log:
Deleting ButterflyTrading.R since all the functions have been moved to the demo script demo/ButterflyTrading.R
Deleted: pkg/PerformanceAnalytics/sandbox/Meucci/R/ButterflyTrading.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/ButterflyTrading.R 2012-07-13 09:28:02 UTC (rev 2151)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/ButterflyTrading.R 2012-07-13 09:29:10 UTC (rev 2152)
@@ -1,291 +0,0 @@
-# TODO: plot efficient frontier in R
-
-PlotFrontier = function( e , s , w )
-{
- # subplot(2,1,1)
- plot( s , e )
- # grid on
- # set(gca,'xlim',[min(s) max(s)])
- #
- # subplot(2,1,2)
-
- xx = nrow( w ) ; N = ncol( w )
- Data = apply( w , 1 , cumsum ) #TODO: Check. Take cumulative sum of *rows*. Try sapply?
-
- for ( n in 1:N )
- {
- x = cbind( min(s) , s , max(s) )
- y = cbind( 0 , Data[ , N-n+1 ] , 0 )
- # hold on
- #h = fill( x , y , cbind( .9 , .9 , .9) - mod( n , 3 ) %*% cbind( .2 , .2 , .2) )
- }
-
- #set(gca,'xlim',[min(s) max(s)],'ylim',[0 max(max(Data))])
- #xlabel('portfolio # (risk propensity)')
- #ylabel('portfolio composition')
-}
-
-ViewCurveSlope = function( X , p )
-{
- # view 3 (expectations and binding constraints): slope of the yield curve will increase by 5 bp
-
- J = nrow( X ) ; K = ncol( X )
-
- # constrain probabilities to sum to one...
- Aeq = ones( 1 , J )
- beq = 1
-
- # ...constrain the expectation...
- V = X[ , 14 ] - X[ , 13 ]
- v = .0005
-
- Aeq = rbind( Aeq , t(V) )
-
- beq = rbind( beq , v )
-
- A = b = emptyMatrix
-
- # ...compute posterior probabilities
- p_ = EntropyProg( p , A , b , Aeq ,beq )$p_
- return( p_ )
-}
-
-ViewRealizedVol = function( X , p )
-{
- # view 2 (relative inequality view on median): bullish on realized volatility of MSFT (i.e. absolute log-change in the underlying).
- # This is the variable such that, if larger than a threshold, a long position in the butterfly turns into a profit (e.g. Rachev 2003)
- # we issue a relative statement on the media comparing it with the third quintile implied by the reference market model
-
- library( matlab )
- J = nrow( X ) ; K = ncol( X )
-
- # constrain probabilities to sum to one...
- Aeq = ones( 1 , J )
- beq = 1
-
- # ...constrain the median...
- V = abs( X[ , 1 ] ) # absolute value of the log of changes in MSFT close prices (definition of realized volatility)
-
- V_Sort = sort( V , decreasing = FALSE ) # sorting of the abs value of log changes in prices from smallest to largest
- I_Sort = order( V )
-
- F = cumsum( p[ I_Sort ] ) # represents the cumulative sum of probabilities from ~0 to 1
-
- I_Reference = max( matlab:::find( F <= 3/5 ) ) # finds the (max) index corresponding to element with value <= 3/5 along the empirical cumulative density function for the abs log-changes in price
- V_Reference = V_Sort[ I_Reference ] # returns the corresponding abs log of change in price at the 3/5 of the cumulative density function
-
- I_Select = find( V <= V_Reference ) # finds all indices with value of abs log-change in price less than the reference value
-
- a = zeros( 1 , J )
- a[ I_Select ] = 1 # select those cases where the abs log-change in price is less than the 3/5 of the empirical cumulative density...
-
- A = a
- b = .5 # ... and assign the probability of these cases occuring as 50%. This moves the media of the distribution
-
- # ...compute posterior probabilities
- p_ = EntropyProg( p , A , b , Aeq , beq )$p_
-
- return( p_ )
-}
-
-ViewImpliedVol = function( X , p )
-{
- # View 1 (inequality view): bearish on on 2m-6m implied volaility spread for Google
-
- J = nrow( X ) ; K = ncol( X )
-
- # constrain probabilities to sum to one...
- Aeq = ones( 1 , J )
- beq = 1
-
- # ...constrain the expectation...
- V = X[ , 12 ] - X[ , 11 ] # GOOG_vol_182 (6m implied vol) - GOOG_vol_91 (2m implied vol)
- m = mean( V )
- s = std( V )
-
- A = t( V )
- b = m - s
-
- # ...compute posterior probabilities
- p_ = EntropyProg( p , A , b , Aeq , beq )$p_
-
- return( p_ )
-}
-
-ComputeCVaR = function( Units , Scenarios , Conf )
-{
- PnL = Scenarios %*% Units
- Sort_PnL = PnL[ order( PnL , decreasing = FALSE ) ]
-
- J = length( PnL )
- Cut = round( J %*% ( 1 - Conf ) , 0 )
-
- CVaR = -mean( Sort_PnL[ 1:Cut ] )
-
- return( CVaR )
-}
-
-LongShortMeanCVaRFrontier = function( PnL , Probs , Butterflies , Options )
-{
- library( matlab )
- library( quadprog )
- library( limSolve )
-
- # setup constraints
- J = nrow(PnL); N = ncol(PnL)
- P_0s = matrix( , nrow = 1 , ncol = 0 )
- D_s = matrix( , nrow = 1 , ncol = 0 )
- emptyMatrix = matrix( nrow = 0 , ncol = 0 )
-
- for ( n in 1:N )
- {
- P_0s = cbind( P_0s , Butterflies[[n]]$P_0 ) # 1x9 matrix
- D_s = cbind( D_s , Butterflies[[n]]$Delta ) # 1x9 matrix
- }
-
- Constr = list()
- Constr$Aeq = P_0s # linear coefficients in the constraints Aeq*X = beq (equality constraints)
- Constr$beq = Options$Budget # the constant vector in the constraints Aeq*x = beq
-
- if ( Options$DeltaNeutral == TRUE )
- {
- Constr$Aeq = rbind( Constr$Aeq , D_s ) # 2x9 matrix
- Constr$beq = rbind( Constr$beq , 0 ) # 2x9 matrix
- }
-
- Constr$Aleq = rbind( diag( as.vector( P_0s ) ) , -diag( as.vector( P_0s ) ) ) # linear coefficients in the constraints A*x <= b. an 18x9 matrix
- Constr$bleq = rbind( Options$Limit * ones(N,1) , Options$Limit * ones(N,1) ) # constant vector in the constraints A*x <= b. an 18x1 matrix
-
- # determine expectation of minimum-variance portfolio
- Exps = t(PnL) %*% Probs
- Scnd_Mom = t(PnL) %*% (PnL * (Probs %*% ones(1,N) ) )
- Scnd_Mom = ( Scnd_Mom + t(Scnd_Mom) ) / 2
- Covs = Scnd_Mom - Exps %*% t(Exps)
-
- Amat = rbind( Constr$Aeq , Constr$Aleq ) # stack the equality constraints on top of the inequality constraints
- bvec = rbind( Constr$beq , Constr$bleq ) # stack the equality constraints on top of the inequality constraints
-
- #if ( nrow(Covs) != length( zeros(N,1) ) ) stop("Dmat and dvec are incompatible!")
- #if ( nrow(Covs) != nrow(Amat)) stop("Amat and dvec are incompatible!")
-
- MinSDev_Units = solve.QP( Dmat = Covs , dvec = -1 * zeros(N,1) , Amat = -1*t(Amat) , bvec = -1*bvec , meq = length( Constr$beq) ) # TODO: Check this
- MinSDev_Exp = t( MinSDev_Units$solution ) %*% Exps
-
- # determine expectation of maximum-expectation portfolio
-
- MaxExp_Units = linp( E = Constr$Aeq , F = Constr$beq , G = -1*Constr$Aleq , H = -1*Constr$bleq , Cost = -Exps , ispos = FALSE )$X
-
- MaxExp_Exp = t( MaxExp_Units ) %*% Exps
-
- # slice efficient frontier in NumPortf equally thick horizontal sections
- Grid = t( seq( from = Options$FrontierSpan[1] , to = Options$FrontierSpan[2] , length.out = Options$NumPortf ) )
- TargetExp = as.numeric( MinSDev_Exp ) + Grid * as.numeric( ( MaxExp_Exp - MinSDev_Exp ) )
-
- # compute composition, expectation, s.dev. and CVaR of the efficient frontier
- Composition = matrix( , ncol = N , nrow = 0 )
- Exp = matrix( , ncol = 1 , nrow = 0 )
- SDev = matrix( , ncol = 1 , nrow = 0 )
- CVaR = matrix( , ncol = 1 , nrow = 0 )
-
- for (i in 1:Options$NumPortf )
- {
- # determine least risky portfolio for given expectation
- AEq = rbind( Constr$Aeq , t(Exps) ) # equality constraint: set expected return for each asset...
- bEq = rbind( Constr$beq , TargetExp[i] )
-
- Amat = rbind( AEq , Constr$Aleq ) # stack the equality constraints on top of the inequality constraints
- bvec = rbind( bEq , Constr$bleq ) # ...and target portfolio return for i'th efficient portfolio
-
- # Why is FirstDegree "expected returns" set to 0?
- # Becasuse we capture the equality view in the equality constraints matrix
- # In other words, we have a constraint that the Expected Returns by Asset %*% Weights = Target Return
- Units = solve.QP( Dmat = Covs , dvec = -1*zeros(N,1) , Amat = -1*t(Amat) , bvec = -1*bvec , meq = length( bEq ) )
-
- # store results
- Composition = rbind( Composition , t( Units$solution ) )
-
- Exp = rbind( Exp , t( Units$solution ) %*% Exps )
- SDev = rbind( SDev , sqrt( t( Units$solution ) %*% Covs %*% Units$solution ) )
- CVaR = rbind( CVaR , ComputeCVaR( Units$solution , PnL , Options$Quant ) )
- }
-
- colnames( Composition ) = c( "MSFT_vol_30" , "MSFT_vol_91" , "MSFT_vol_182" ,
- "YHOO_vol_30" , "YHOO_vol_91" , "YHOO_vol_182" ,
- "GOOG_vol_30" , "GOOG_vol_91" , "GOOG_vol_182" )
-
- return( list( Exp = Exp , SDev = SDev , CVaR = CVaR , Composition = Composition ) )
-}
-
-
-MapVol = function( sig , y , K , T )
-{
- # in real life a and b below should be calibrated to security-specific time series
-
- a=-.00000000001
- b= .00000000001
-
- s = sig + a/sqrt(T) * ( log(K) - log(y) ) + b/T*( log(K) - log(y) )^2
-
- return( s )
-}
-
-HorizonPricing = function( Butterflies , X )
-{
- r = .04 # risk-free rate
- tau = 1/252 # investment horizon
-
- # factors: 1. 'MSFT_close' 2. 'MSFT_vol_30' 3. 'MSFT_vol_91' 4. 'MSFT_vol_182'
- # securities: 1. 'MSFT_vol_30' 2. 'MSFT_vol_91' 3. 'MSFT_vol_182'
-
- # create a new row called DlnY and Dsig
- # create a new row called 'DlnY'. Assign the first row (vector) of X to this DlnY for the 1:3 securities
- for ( s in 1:3 ) { Butterflies[[s]]$DlnY = X[ , 1 ] }
-
- # assign the 2nd row of X to a new element called Dsig
- Butterflies[[1]]$Dsig=X[ , 2 ]
- Butterflies[[2]]$Dsig=X[ , 3 ]
- Butterflies[[3]]$Dsig=X[ , 4 ]
-
- # factors: 5. 'YHOO_close' 6. 'YHOO_vol_30' 7. 'YHOO_vol_91' 8. 'YHOO_vol_182'
- # securities: 4. 'YHOO_vol_30' 5. 'YHOO_vol_91' 6. 'YHOO_vol_182'
- for ( s in 4:6 ) { Butterflies[[s]]$DlnY=X[ , 5 ] }
-
- Butterflies[[4]]$Dsig=X[ , 6 ]
- Butterflies[[5]]$Dsig=X[ , 7 ]
- Butterflies[[6]]$Dsig=X[ , 8 ]
-
- # factors: # 9. 'GOOG_close' 10. 'GOOG_vol_30' 11. 'GOOG_vol_91' 12. 'GOOG_vol_182'
- # securities: 7. 'GOOG_vol_30' 8. 'GOOG_vol_91' 9. 'GOOG_vol_182'
- for ( s in 7:9 ) { Butterflies[[s]]$DlnY=X[ , 9 ] }
-
- Butterflies[[7]]$Dsig=X[ , 10 ]
- Butterflies[[8]]$Dsig=X[ , 11 ]
- Butterflies[[9]]$Dsig=X[ , 12 ]
-
- PnL = matrix( NA , nrow = nrow(X) )
-
- for ( s in 1:length(Butterflies) )
- {
- Y = Butterflies[[s]]$Y_0 * exp(Butterflies[[s]]$DlnY)
- ATMsig = apply( cbind( Butterflies[[s]]$sig_0 + Butterflies[[s]]$Dsig , 10^-6 ) , 1 , max )
- t = Butterflies[[s]]$T - tau
- K = Butterflies[[s]]$K
- sig = MapVol(ATMsig , Y , K , t )
-
- # library(RQuantLib) # this function can only operate on one option at a time, so we use fOptions
- # C = EuropeanOption( type = "call" , underlying = Y , strike = K , dividendYield = 0 , riskFreeRate = r , maturity = t , volatility = sig )$value
- # P = EuropeanOption( type = "put" , underlying = Y , strike = K , dividendYield = 0 , riskFreeRate = r , maturity = t , volatility = sig )$value
-
- # use fOptions to value options
- library( fOptions )
- C = GBSOption( TypeFlag = "c" , S = Y , X = K , r = r , b = 0 , Time = t , sigma = sig )
- P = GBSOption( TypeFlag = "p" , S = Y , X = K , r = r , b = 0 , Time = t , sigma = sig )
-
- Butterflies[[s]]$P_T = C at price + P at price
- PnL = cbind( PnL , Butterflies[[s]]$P_T )
- }
- PnL = PnL[ , -1 ]
-
- return( PnL )
-}
-
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