3  Risk and Return

This is a book containing all class notes.

Here are some graphs about the evolution of prices through time.

3.1 Insights Ibov

3.1.1 Ibov vs CDI vs Selic in Brazil

#### QUANDL API
# Step to create your key
# 1. Go to https://www.quandl.com/
# 2. Create an account
# 3. Get your key
# 4. Add your key below (I can't give you mine)
library(yfR)
library(ggplot2)
library(GetQuandlData)
library(PerformanceAnalytics)
library(ggthemes)
library(roll)
library(readxl)
library(tidyr)
library(dplyr)
api_KEY <- "Your QUANDL API KEY here"
#Ibov
stock<-'^BVSP' 
start<-'1995-01-01' 
end<-Sys.Date()  
ibov <- yf_get(tickers = stock, 
                         first_date = start,
                         last_date = end)
ibov<- ibov[order(as.numeric(ibov$ref_date)),]
# Cumulative return Ibov
ibov$Ibov_return <- ibov$cumret_adjusted_prices -1
#Selic
selic <- get_Quandl_series(id_in = c('Selic' = 'BCB/11'),
                               api_key = api_key, 
                               first_date = start,
                               last_date = end)
selic<- selic[order(as.numeric(selic$ref_date)),]
selic$value <- selic$value / 100
# Cumulative return Selic
return_selic <- data.frame(nrow(selic):1)
colnames(return_selic)<- "selic_return"
for(i in (2:nrow(selic))) {
return_selic[i,1] <- Return.cumulative( selic$value[1:i] )
}
# CDI
cdi <- get_Quandl_series(id_in =  c('CDI' = 'BCB/12'), 
                         api_key = api_key , 
                         first_date = start ,
                         last_date = end)
cdi<- cdi[order(as.numeric(cdi$ref_date)),]
cdi$value <- cdi$value / 100
# Cumulative return CDI
return_CDI <- data.frame(nrow(cdi):1)
colnames(return_CDI)<- "CDI_return"
for(i in (2:nrow(cdi))) {
return_CDI[i,1] <- Return.cumulative( cdi$value[1:i] )
}
#Inflation Brazil
inf <- get_Quandl_series(id_in =  c('Inflation' = 'BCB/433'),
                         api_key = api_key, 
                         first_date = start,
                         last_date = end)
inf<- inf[order(as.numeric(inf$ref_date)),]
inf$value <- inf$value / 100

# Cumulative return Inflation
return_Inf <- data.frame(nrow(inf):1)
colnames(return_Inf)<- "Inflation_return"

for(i in (2:nrow(inf))) {
return_Inf[i,1] <- Return.cumulative( inf$value[1:i] )
}
# Merging dataframes
selic <- cbind(selic, return_selic)
cdi <- cbind(cdi, return_CDI)
inf <- cbind(inf, return_Inf)

df <- merge(cdi ,selic, by=c("ref_date"))
df <- merge(df ,ibov, by=c("ref_date"))
df2 <- merge(df ,inf, by=c("ref_date"))

df$selic_return[1] <- NA
df$CDI_return[1] <- NA
df$Ibov_return[1] <- NA
df2$Inflation_return[1] <- NA

# Graph cumulated return CDI and IBOV
ggplot(df, aes(ref_date)) + 
  geom_line(aes(y = CDI_return, color = "CDI")) + 
  geom_line(aes(y = Ibov_return, colour = "Ibov")) +
  geom_line(aes(y = selic_return, colour = "Selic")) +
  labs(y='Cumulative return (daily)') +   theme_solarized()

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3.1.2 Ibov vs CDI Vs. Selic vs. Inflation in Brazil

# Graph cumulated return CDI, IBOV, and Inflation
ggplot(df2, aes(ref_date)) + 
  geom_line(aes(y = CDI_return, colour = "CDI")) + 
  geom_line(aes(y = selic_return, colour = "Selic")) +
  geom_line(aes(y = Inflation_return, colour = "Inflation")) +
  geom_line(aes(y = Ibov_return, colour = "Ibov")) +
  labs(      y='Cumulative return (monthly)') +   theme_solarized()

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3.1.3 Ibov vs CDI vs Selic in Brazil 2002-2007

# Graph cumulated return CDI and IBOV
#| label: insights_4
ggplot(df, aes(ref_date)) + 
  geom_line(aes(y = CDI_return, colour = "CDI")) + 
  geom_line(aes(y = Ibov_return, colour = "Ibov")) +
  geom_line(aes(y = selic_return, colour = "Selic")) +
  labs(y='Cumulative return (daily)') +   theme_solarized()

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3.1.4 Ibov vs CDI vs Selic in Brazil 2010-2019

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3.1.5 Closing prices

ggplot(ibov,aes(ibov$ref_date, ibov$price_close))+
        geom_line(color='#801e00') + 
        labs(x = "", 
             y='Closing prices', 
             title="IBOV") +   theme_solarized()

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3.1.6 Daily returns

Daily returns vary a lot.

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3.1.7 Histogram

The returns seems to follow a normal distribution.

ggplot(ibov,aes(ibov$ret_closing_prices))+
        geom_histogram(color='#006600',
                       bins = 100) + 
        labs(x = "",
             y='Daily return', 
             title="IBOV") +   theme_solarized()

---

3.1.8 Standard deviation through time

ibov$sd <- roll_sd(ibov$ret_closing_prices,  
                     width = 100,  
                     min_obs = 100 ) * sqrt(250)
ggplot(ibov,aes(ref_date,sd))+
        geom_line(color='#006600') + 
        labs(x = "",
             y='Standard deviation using 100 daily returns', 
             title="IBOV") +   theme_solarized()

3.2 Insights stocks

3.2.1 Histogram two assets

See below that some stocks have heavier tails than others. The stock with the heavier tail is riskier.

stocks <-c('GOLL4.SA', 'ITUB3.SA') 
start <-'2012-01-01' 
end   <-Sys.Date()  

data <- yf_get(tickers = stocks, 
                         first_date = start,
                         last_date = end)

data<-data[complete.cases(data),] 

ggplot(data, aes(ret_closing_prices,  fill = ticker)) + 
        geom_histogram(bins = 100, alpha = 0.35, position='identity') + 
        labs(x = "",
             y='Daily returns', 
             title="Gol and Itub",
             subtitle = start)+
      xlim(-0.05,0.05) +   theme_solarized()

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3.2.2 Tradeoff risk & return

There are always outliers for a particular time horizon. Also, Brazilian stocks have higher average standard deviation than Berk & Demarzo’s Figure 10.7.

stocks <-c('^BVSP', 'ITUB3.SA', 'WEGE3.SA', 'PETR3.SA', 'VALE3.SA', 'ITSA3.SA' , 'BBDC3.SA', 'BBAS3.SA', 'ABEV3.SA', 'GGBR4.SA', 'LREN3.SA', 'B3SA3.SA', 'CSNA3.SA',  'EMBR3.SA', 'VIVO4.SA', 'CCRO3.SA', 'UGPA3.SA', 'CSMG3.SA', 'HYPE3.SA') 
start <-'2010-01-01' 
end   <-'2023-01-01'
data <- yf_get(tickers = stocks, 
                         first_date = start,
                         last_date = end,
                         freq_data = "yearly",)
data<-data[complete.cases(data),] 
mean_sd  <- data %>%                          
            group_by(ticker) %>%
            summarise_at(vars(ret_adjusted_prices),
                         list(mean = mean,
                              sd = sd)) %>% 
            as.data.frame()
ggplot(mean_sd, aes(x=sd, y=mean,  color = ticker)) + 
      geom_point(size = 4)  + 
        labs(x = "Annualized average standard deviation",
             y='Annualized average return', 
             title="Historical return vs. Historical volatility (selected stocks)") +   theme_solarized()

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3.2.3 Tradeoff risk & return (Ibov)

start <-'2010-01-01' 
end   <-'2023-01-01'
data <- yf_collection_get("IBOV", 
                         first_date = start,
                         last_date = end,
                         freq_data = "yearly",)
data<-data[complete.cases(data),] 
# Get mean & standard deviation by ticker
mean_sd  <- data %>%                          
            group_by(ticker) %>%
            summarise_at(vars(ret_adjusted_prices),
                         list(mean = mean,
                              sd = sd)) %>% 
            as.data.frame()
ggplot(mean_sd, aes(x=sd, y=mean)) + 
      geom_point(size = 2)  + 
        labs(x = "Average standard deviation of annual returns",
             y='Annualized average return', 
             title="Historical return vs. Sd (All Ibov 2010-2022)") +   theme_solarized()

3.3 Insights ESG

3.3.1 Tradeoff risk & return (by ESG level)

The graph below shows the trade-off risk and return by ESG score levels. I can’t see a clear pattern here.

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Let’s exclude the intermediate group to see if there is a more clear pattern.

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Let’s now create the same graph using only the E and the S pillars. Here you have the E Pillar.

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Now you have the S Pillar.