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hlz-scatter-post-truth.R
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# Setup -------------------------------------------------------------------
rm(list = ls())
# uncomment for pretty fonts
# install.packages('extrafont')
# extrafont::font_import()
library(tidyverse)
library(data.table)
library(ggplot2)
library(extrafont)
library(latex2exp)
dir.create('../results/')
MATBLUE = rgb(0,0.4470,0.7410)
MATRED = rgb(0.8500, 0.3250, 0.0980)
MATYELLOW = rgb(0.9290, 0.6940, 0.1250)
chen_theme = theme_minimal() +
theme(
text = element_text(family = "Palatino Linotype")
, panel.border = element_rect(colour = "black", fill=NA, size=1)
# Font sizes
# , axis.title.x = element_text(size = 26),
# axis.title.y = element_text(size = 26),
# axis.text.x = element_text(size = 22),
# axis.text.y = element_text(size = 22),
# legend.text = element_text(size = 18),
, axis.title.x = element_text(size = 30),
axis.title.y = element_text(size = 30),
axis.text.x = element_text(size = 26),
axis.text.y = element_text(size = 26),
legend.text = element_text(size = 24),
# Tweaking legend
legend.position = c(.80, .15),
panel.grid.major = element_blank(),
panel.grid.minor = element_blank(),
legend.text.align = 0,
legend.background = element_rect(fill = "white", color = "black"),
legend.margin = margin(t = 5, r = 20, b = 5, l = 5),
legend.key.size = unit(1.5, "cm")
, legend.title = element_blank()
)
# Simulate hlz ----------------------------------------------------------------
# true / false labels (for v)
label_true = 'True: [Exp Ret]>0'
label_false = 'False: [Exp Ret]=0'
nport = 1e4
nsim = 500
n = nport*nsim
set.seed(121)
# hlz baseline
v = runif(n) > 0.444 # Table 5, rho = 0.2, p_0
se = 1500/sqrt(12)/sqrt(240) # page 29, N = 240 and page 30, annual volatilty of 15%
mu = rexp(n, 1/55.5); mu[!v] = 0 # Table 5, rho = 0.2, \lambda
theta = mu / se
theta_scatter = theta; theta_scatter[!v] = rnorm(sum(!v), 0, 0.1)
mu_scatter = mu; mu_scatter[!v] = rnorm(sum(!v), 0, 0.05)*se
# Fabian Winkler's fast method for common correlations
rho = 0.2
sigc = sqrt(rho)
sige = sqrt(1-sigc^2)
# simulate common component (in blocks)
c = matrix(rnorm(nsim, 0, sigc), nrow = nsim, ncol = nport) %>% t() %>%
as.vector
# add idiosyncratic noise
e = rnorm(nport*nsim, 0, sige)
Z = c + e
# sanity check
# c2 = rnorm(n, 0, sigc)
# z1 = c2 + rnorm(n, 0, sige)
# z2 = c2 + rnorm(n, 0, sige)
# cor(z2,z1)
# var(z1)
# var(z2)
# assemble into data table
dat = data.table(
Z, theta, v, theta_scatter
) %>%
mutate(
t = theta + Z
, tabs = abs(t)
, mu = mu
, mu_scatter = mu_scatter
) %>%
mutate(
v = factor(
v, levels = c(TRUE,FALSE)
, labels = c(label_true, label_false)
)
) %>%
mutate(
tselect = tabs
)
# fit shrinkage
datsum = dat %>%
mutate(
tgroup = ntile(tselect,1000)
) %>%
group_by(tgroup) %>%
summarize(
tselect_left = min(tselect), tselect_right = max(tselect)
, Etselect = mean(tselect), Etheta = mean(theta), n = dplyr::n()
, nfalse = sum(v == label_false)
)
# fit "cdf"
datsum = datsum %>%
arrange(-Etselect) %>%
mutate(
nfalse_cum = cumsum(nfalse)
, n_cum = cumsum(n)
, fdr_tselect_left = nfalse_cum / n_cum * 100
) %>%
arrange(Etselect)
# find hurdles
hurdle_05 = min(datsum$tselect_left[which(datsum$fdr_tselect_left < 5)])
hurdle_01 = min(datsum$tselect_left[which(datsum$fdr_tselect_left < 1)])
hurdle_bonf05 = qnorm(1-0.05/300/2) # assumes everything is published, as in HLZ's conclusion text
# Plot setup ----------------------------------------------
# find a subset for plotting
nplot = 1500 # close to HLZ's estimate of "total factors" (ignoring unidentified scale)
set.seed(11)
small = dat[sample(1:n,nplot),]
small %>% filter(tabs > hurdle_01) %>% summarize(sum(v==label_false), n())
# plot sizing (shared by below)
texty = 250
textsize = 7
linesize = 1.1
# Plot slowly ----------------------------------------------------
p0 = ggplot(small %>%
filter(v==label_false), aes(x=tselect,y=mu_scatter)) +
scale_shape_manual(values = c(1)) +
scale_color_manual(values=c(MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) +
theme(legend.position = 'none')
ggsave('../results/slow-0.jpg', width = 12, height = 8)
p1 = ggplot(small %>%
filter(v==label_false), aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v, color = v, shape = v), size = 2.5) +
scale_shape_manual(values = c(1)) +
scale_color_manual(values=c(MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) +
theme(legend.position = 'none')
ggsave('../results/slow-1.jpg', width = 12, height = 8)
p2 = ggplot(small, aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v, color = v, shape = v), size = 2.5) +
scale_shape_manual(values = c(16, 1)) +
scale_color_manual(values=c(MATBLUE, MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) +
theme(legend.position = 'none')
ggsave('../results/slow-2.jpg', width = 12, height = 8)
p3 = p2 + chen_theme
ggsave('../results/slow-3.jpg', width = 12, height = 8)
p4 = p3 +
geom_vline(xintercept = hurdle_01, size = linesize, color = MATRED, linetype = 'dotdash') +
annotate(geom="text",
label="Discoveries ->",
x=3+1.1, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 0, size = textsize, color = 'black'
)
ggsave('../results/slow-4.jpg', width = 12, height = 8)
p5 = p4 +
annotate(geom="text",
label="FDR = 1%",
x=3, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = MATRED
)
ggsave('../results/slow-5.jpg', width = 12, height = 8)
# plot FDR 5 --------------------------------------------------------------
p6 = p3 +
geom_vline(xintercept = hurdle_01, size = linesize, color = MATRED, linetype = 'dotdash') +
annotate(geom="text",
label="FDR = 1%",
x=3, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = MATRED
)
ggsave('../results/slow-6.jpg', width = 12, height = 8)
p7 = p6 +
geom_vline(xintercept = hurdle_05, size = linesize, color = MATYELLOW, linetype = 'longdash') +
annotate(geom="text",
label="FDR = 5%",
x=hurdle_05, y=texty, vjust=-0.3,
family = "Palatino Linotype", angle = 90, size = textsize, color = MATYELLOW
)
ggsave('../results/slow-7.jpg', width = 12, height = 8)
p8 = p7 +
geom_vline(xintercept = 1.96, size = linesize) +
annotate(geom="text", label="Classical Hurdle",
x=1.95, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'black'
)
ggsave('../results/slow-8.jpg', width = 12, height = 8)
# Plot big data -------------------------------------------------------
p1 = ggplot(small, aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v, color = v, shape = v), size = 2.5) +
scale_shape_manual(values = c(16, 1)) +
scale_color_manual(values=c(MATBLUE, MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)"))
ggsave('../results/hlz-1.jpg', width = 12, height = 8)
# classical hurdle only
p5 = p1 +
geom_vline(xintercept = 1.96, size = linesize) +
annotate(geom="text", label="Classical Hurdle",
x=1.95, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'black'
)
ggsave('../results/hlz-classical-only.jpg', width = 12, height = 8)
# Plot post-truth -------------------------------------------------------
lab_hlz_false = '"False": Insignificant'
lab_hlz_true = '"True": Significant'
# post-truth labels
small = small %>%
mutate(
v_hlz = case_when(
tabs > hurdle_bonf05 ~ TRUE
, tabs <= hurdle_bonf05 ~ FALSE
)
) %>% mutate(
v_hlz = factor(
v_hlz, levels = c(TRUE,FALSE), labels = c(lab_hlz_true, lab_hlz_false)
)
) %>%
mutate(
v_hlz_alt = case_when(
tabs > hurdle_05 ~ TRUE
, tabs <= hurdle_05 ~ FALSE
)
) %>% mutate(
v_hlz_alt = factor(
v_hlz_alt, levels = c(TRUE,FALSE), labels = c(lab_hlz_true, lab_hlz_false)
)
)
# plot classical only
p1 = ggplot(small, aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v, color = v, shape = v), size = 2.5) +
scale_shape_manual(values = c(16, 1)) +
scale_color_manual(values=c(MATBLUE, MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
theme(
legend.position = c(.80, .15)
, panel.grid.major = element_blank()
, panel.grid.minor = element_blank()
) +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) +
geom_vline(xintercept = 1.96, size = linesize) +
annotate(geom="text", label="Classical Hurdle",
x=1.95, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'black'
)
ggsave('../results/post-truth-1.jpg', width = 12, height = 8)
# add bonf
p2 = p1 + geom_vline(xintercept = hurdle_bonf05, size = linesize, color = 'darkorchid', linetype = 'dotted') +
annotate(geom="text",
label=TeX("Bonferroni 5\\%"),
x=hurdle_bonf05, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'darkorchid'
)
ggsave('../results/post-truth-2.jpg', width = 12, height = 8)
# relabel
p3 = ggplot(small, aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v_hlz, color = v_hlz, shape = v_hlz), size = 2.5) +
scale_shape_manual(values = c(16, 1)) +
scale_color_manual(values=c(MATBLUE, MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
theme(
legend.position = c(.80, .15)
, panel.grid.major = element_blank()
, panel.grid.minor = element_blank()
) +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) +
geom_vline(xintercept = hurdle_bonf05, size = linesize, color = 'darkorchid', linetype = 'dotted') +
annotate(geom="text",
label=TeX("Bonferroni 5\\%"),
x=hurdle_bonf05, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'darkorchid'
) +
geom_vline(xintercept = 1.96, size = linesize) +
annotate(geom="text", label="Classical Hurdle",
x=1.95, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'black'
)
ggsave('../results/post-truth-3.jpg', width = 12, height = 8)
# add FDR 5%
p4 = p3 +
geom_vline(xintercept = hurdle_05, size = linesize, color = MATYELLOW, linetype = 'longdash') +
annotate(geom="text",
label="FDR = 5%",
x=hurdle_05, y=texty, vjust=-0.3,
family = "Palatino Linotype", angle = 90, size = textsize, color = MATYELLOW
)
ggsave('../results/post-truth-4.jpg', width = 12, height = 8)
# alternative relabelling
p5 = ggplot(small, aes(x=tselect,y=mu_scatter)) +
geom_point(aes(group = v_hlz_alt, color = v_hlz_alt, shape = v_hlz_alt), size = 2.5) +
scale_shape_manual(values = c(16, 1)) +
scale_color_manual(values=c(MATBLUE, MATRED)) +
coord_cartesian(xlim = c(-0.1,10), ylim = c(-0.5,300)) +
scale_x_continuous(breaks = seq(-10,20,2)) +
scale_y_continuous(breaks = seq(0,500,50)) +
chen_theme +
theme(
legend.position = c(.80, .15)
, panel.grid.major = element_blank()
, panel.grid.minor = element_blank()
) +
xlab(TeX("|t-statistic|")) +
ylab(TeX("Expected Return (bps p.m.)")) + geom_vline(xintercept = hurdle_bonf05, size = linesize, color = 'darkorchid', linetype = 'dotted') +
annotate(geom="text",
label=TeX("Bonferroni 5\\%"),
x=hurdle_bonf05, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'darkorchid'
) +
geom_vline(xintercept = hurdle_05, size = linesize, color = MATYELLOW, linetype = 'longdash') +
annotate(geom="text",
label="FDR = 5%",
x=hurdle_05, y=texty, vjust=-0.3,
family = "Palatino Linotype", angle = 90, size = textsize, color = MATYELLOW
) +
geom_vline(xintercept = hurdle_bonf05, size = linesize, color = 'darkorchid', linetype = 'dotted') +
annotate(geom="text",
label=TeX("Bonferroni 5\\%"),
x=hurdle_bonf05, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'darkorchid'
) +
geom_vline(xintercept = 1.96, size = linesize) +
annotate(geom="text", label="Classical Hurdle",
x=1.95, y=texty, vjust=-1,
family = "Palatino Linotype", angle = 90, size = textsize, color = 'black'
)
ggsave('../results/post-truth-5.jpg', width = 12, height = 8)