Inside data at the OSE Finansavisen s portfolio

Transcription

1 Inside data at the OSE Finansavisen s portfolio Bernt Arne Ødegaard Aug 2015 This note shows the actual calculation of some of the results in the article. 1 Descriptives for the portfolio Table 1 Describing the return on the Finansavisen portfolio We describe the return of the Finansavisen Inside Portfolio, together with two market indices, one equally weighted (EW) and one value weighted (VW). Panel A: Returns and Sharpe Ratios Panel B: Information Ratios Rp erp erm(ew) erm(vw) mean Sharpe IR(R p, Rm EW ) IR(R p, Rm V W ) R p

2 1.1 Showing the calculation Implementing the analysis Returns in the file inside_portfolio.csv: "Index";"Rp";"eRp" ; ;NA ; ; ; ; The factors in the file "Index";"eRmEW";"eRmVW";"SMB";"HML" ; ; ; ; ; ; ; ; ; ; ; ; library(zoo) InsidePortf < read.zoo("inside_portfolio.csv", header=true) Rp < na.omit(insideportf$rp) erp < na.omit(insideportf$erp) PricFact < read.zoo("pricing_factors.csv", 10 header=true) ermew < na.omit(pricfact$ermew) ermvw < na.omit(pricfact$ermvw) # take intersection to align the data data < merge(rp,erp,ermew,ermvw,all=false) Rp < data$rp erp < data$erp ermew < data$ermew ermvw < data$ermvw 20 2

3 source("read_data.r") library(stargazer) library(xtable) outdir < "../../results/2015_08_descriptive/" table < matrix(nrow=2,ncol=4) colnames(table) < c("rp","erp","erm(ew)","erm(vw)") rownames(table) < c("mean","sharpe") 10 table[1,1] < mean(rp) table[1,2] < mean(erp) table[1,3] < mean(ermew) table[1,4] < mean(ermvw) table[2,2] < mean(erp)/sd(erp) table[2,3] < mean(ermew)/sd(ermew) table[2,4] < mean(ermvw)/sd(ermvw) filename < paste(outdir,"descriptive_weekly_returns.tex",sep="") print(filename) stargazer(table, out=filename, digits=4, float=false,header=false) 20 table < matrix(nrow=1,ncol=2) colnames(table) < c("$ir(r_p,r_m^{ew})$","$ir(r_p,r_m^{vw})$") rownames(table) < c("$r_p$") 30 ir < mean(erp ermew)/sd(erp ermew) table[1,1] < ir ir < mean(erp ermvw)/sd(erp ermvw) table[1,2] < ir filename < paste(outdir,"descriptive_information_ratios.tex",sep="") print(xtable(table,digits=3,align="lcc"), floating=false,file=filename, type = "latex", sanitize.text.function = function(x){x}) 40 3

4 2 Finansavisen portfolio performance evaluation 2.1 Static Alpha Estimates A standard benchmark for academic studies is the three-factor model of Fama and French (1995). er pt = α p + β p RMRF t + s p SMB t + h p HML t + ε pt where er pt is the time-t excess return on a the managed portfolio (net return minus T-bill return); RMRF t is the time-t excess return on a aggregate market proxy portfolio; and SMB t and HML t are time-t returns on zero-investment factor-mimicking portfolios for size and book-to-market (BTM) equity, repectively. Table 2 shows the results from estimating this model, both with a single factor (the market RMRF) and the three factor model. We investigate two choices for the market portfolio. In (1) we use an equally weighted market index, in (2) a value weighted Implementing the analysis Returns in the file inside_portfolio.csv: "Index";"Rp";"eRp" ; ;NA ; ; ; ; The factors in the file "Index";"eRmEW";"eRmVW";"SMB";"HML" ; ; ; ; ; ; ; ; ; ; ; ; Reading the files into R: library(zoo) InsidePortf < read.zoo("inside_portfolio.csv", header=true) erp < InsidePortf$eRp PricFact < read.zoo("pricing_factors.csv", header=true) 10 4

5 Table 2 Perfomance evaluation - benchmark regression The table shows results from several performance regressions of Finansavisen portfolios. Panel A a single factor model, Panel B a three factor model. We show calculations for the Finansavisen portfolio under the assumptions that trades are done at monday. In each table we shown results for two specifications: (1): EW market index and (2) VW market index. Panel A: Single factor model Dependent variable: EW erp VW (1) (2) Constant (0.001) (0.001) erm (0.044) (0.033) Observations Adjusted R Note: p<0.1; p<0.05; p<0.01 Panel B: Three factor model Dependent variable: EW erp VW (1) (2) Constant (0.001) (0.001) erm (0.050) (0.046) SMB (0.045) (0.059) HML (0.044) (0.045) Observations Adjusted R Note: p<0.1; p<0.05; p<0.01 5

6 Running the Fama French Regression source("read_data.r") library(stargazer) outdir < "../../results/2015_08_estimation/" data < merge(erp,pricfact,all=true) erm < as.matrix(data$ermew) erp < as.matrix(data$erp) regr1 < lm(erp erm) 10 summary(regr1) erm < as.matrix(data$ermvw) regr2 < lm(erp erm) summary(regr2) filename < paste(outdir, "regression_single_factor.tex", sep="") stargazer(regr1,regr2, out=filename, column.labels=c("ew","vw"), 20 float=false,header=false,intercept.bottom=false, omit.stat=c("rsq","f","ser")) erp < as.matrix(data$erp) SMB < as.matrix(data$smb) HML < as.matrix(data$hml) erm < as.matrix(data$ermew) regr1 < lm(erp erm + SMB + HML) erm < as.matrix(data$ermvw) regr2 < lm(erp erm + SMB + HML) 30 filename < paste(outdir, "regression_three_factor.tex", sep="") stargazer(regr1,regr2, out=filename, column.labels=c("ew","vw"), float=false,header=false,intercept.bottom=false, omit.stat=c("rsq","f","ser")) 6

7 2.2 Stochasic Discount Factor based performance evaluation A more modern approach to performance analysis is to use stochastic discount factors to do the evaluation. Theoretically, this approach is applicable under a much wider set of distributional assumptions than the previous regression approach. It is also less dependent on the choice of benchmark. The starting point is that any asset pricing model can be written as a condition on the stochastic discount factor m t that prices the risk in the economy at time t. E t 1 [m t R t 1] = 0, where R t is the (gross) return on the primitive assets in the economy. This relationship must also hold for any managed portfolio p: E t 1 [m t R pt 1] = 0 To do performance evaluation we use a two step procedure. First we estimate the discount factor m using data for the crossection of assets. The resulting empirical ˆm is then used to calculate a stochastic discount factor alpha: α p = E t 1 [ ˆm t R pt ] 1 If we use excess returns er pt, the calculation is α p = E t 1 [ ˆm t er pt ] We implement this analysis on the inside portfolios. We first need a parameterization of the discount factor m. We choose a three-factor model m t = 1 + b 1 er mt + b 2 SMB t + b 3 HML t The parameters of this model is estimated using GMM on ten size-sorted portfolios for the Norwegian cross-section over the same period we do performance evaluation. The estimated m is then used to calculate the alpha. The resulting estimates are shown in table 3. Table 3 Estimating performance with a stochastic discount factor approach We estimate the parameters of m t = 1 + b 1eR mt + b 2SMB t + b 3HML t using 10 size based portfolios for Norway. The resulting empirical m is then used to estimate alphas. The alphas are summarized in Panel A. The parameters of the SDF are estimated with GMM. The parameter estimates are shown in Panels B and C. We list parameter estimates and standard deviations. Panel A: Alpha estimates mean p-value InsPort Panel B: The parameters of the estimated stochastic discount factor Stochastic Discount Factor b (4.309) b (2.986) b (12.656) Num. obs. 994 p < 0.001, p < 0.01, p < Implementing the analysis Returns in the file inside_portfolio.csv: 7

8 "Index";"Rp";"eRp" ; ;NA ; ; ; ; The factors in the file factors.csv "Index";"eRmEW";"eRmVW";"SMB";"HML" ; ; ; ; ; ; ; ; ; ; ; ; The size portfolios in size_portfolios.csv "Index";"P1";"P2";"P3";"P4";"P5";"P6";"P7";"P8";"P9";"P10" ; ; ; ; ; ; ; ; ; ; ; e-05; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; Reading the files into R: library(zoo) InsidePortf < read.zoo("inside_portfolio.csv", header=true) erp < InsidePortf$eRp PricFact < read.zoo("pricing_factors.csv", header=true) 10 ermew < na.omit(pricfact$ermew) ermvw < na.omit(pricfact$ermvw) HML < PricFact$HML SMB < PricFact$SMB SizePortfs < read.zoo("size_portfolios.csv", header=true) 8

9 Running the SDF estimation, and alpha estimation source("read_data.r") library(texreg) library(stargazer) outdir < "../../results/2015_08_estimate_sdf/" table < matrix(ncol=2,nrow=1) colnames(table) < c("mean","p-value") rownames(table) < c("insport") 10 er < SizePortfs erm < ermew # take intersection to align the data data < merge(er,erm,smb,hml, all=false) er < as.matrix(data[,1:10]) erm < as.matrix(data[,11]) SMB < as.matrix(data[,12]) HML < as.matrix(data[,13]) X < cbind(er,erm,smb,hml) g < function (parms,x) { 20 b1 < parms[1] b2 < parms[2] b3 < parms[3] m < 1 + b1 * X[,11] + b2 * X[,12] + b3 * X[,13] e < m * X[,1:10] return (e); } library(gmm) t0 < c(0.1,0,0) res < gmm(g,x,t0) 30 filename < paste(outdir,"sdf_estimation.tex",sep="") texreg(res, file=filename, single.row=true, table=false, digits=3, use.packages=false, custom.model.names=c("stochastic Discount Factor"), custom.coef.names =c("$b_1$","$b_2$","$b_3$"), include.obj.fcn=false, 40 dcolumn=true) Theta < as.numeric(res$coefficients) m < 1 + Theta[1] * X[,11] + Theta[2] * X[,12] + Theta[3] * X[,13] m < zoo(m,order.by=index(data)) InsideRets < erp data < merge(m,insiderets,all=false) mhat < data$m InsideRets < data$insiderets 50 alpha < mhat*insiderets tt < t.test(alpha) pval < tt$p.value table[1,1] < mean(alpha) table[1,2] < pval filename < paste(outdir,"sdf_estimation_performance_evaluation.tex",sep="") stargazer(table,out=filename, digits=4, float=false,header=false) 9

10 References Eugene F Fama and Kenneth R French. Size and book-to-market factors in earnings and returns. Journal of Finance, 50 (1):131 56, March