In barryquinn1/tsfe: Time series financial econometrics

library(learnr)
library(tidyverse) # loads dplyr, ggplot2, and others
library(tidyquant)
library(fpp2)
library(ggpmisc)
library(tsfe)
tutorial_options(exercise.timelimit = 60,exercise.eval = TRUE)
knitr::opts_chunk$set(echo = FALSE,warning = FALSE,message = FALSE)
data("ftse350")

tickers<-c("GRG","BT.A","ULVR")
ftse350 %>% filter(ticker %in% tickers) -> port
port_ret <- port %>%
  filter(variable=="Price") %>%
  arrange(ticker,date) %>% # ensure data is order by stock and then chronologically 
  group_by(ticker) %>% # this ensures the lag operating only operate with each symbol
  mutate(log_return=log(value)-log(lag(value)))

port_ret_ew <- port_ret %>%
  group_by(date) %>%
  summarise(ret=mean(log_return))

port_w <- port %>% 
  select(ticker,date,variable,value) %>%
  spread(variable,value)

port_ret_vw <-port_w %>%
  group_by(date) %>%
  mutate(weight=`Market Value`/sum(`Market Value`))

port_ret_vw <-port_ret_vw %>% 
  arrange(ticker,date) %>% 
  group_by(ticker) %>% 
  mutate(log_return=log(Price)-log(lag(Price))) %>%
  group_by(date) %>%
  summarise(ret=sum(weight*log_return))

port_ret_both<- port_ret_vw %>% rename(vw_ret=ret) %>%
  left_join(port_ret_ew %>% rename(ew_ret=ret),by="date")

ni_hsales_ts<-ts(ni_hsales$`Total Verified Sales`,start = c(2005,1),frequency = 4)
usuk_rate_ts<-ts(usuk_rate$price)

Welcome

In this tutorial, you will learn how to summarise a table of data, including:

• How to rank financial data in terms of size
• How filter stocks filter()
• Calculating and visualisng log returns

Setup

I've preloaded the packages for this tutorial with

library(tidyverse) # loads dplyr, ggplot2, and others
library(tidyquant)
library(ggpmisc)
library(fpp2)

Topic 1 data manipulation

Exercise explore the FTSE350 data

In the tsfe pacakge open the ftse350 data and using the glimpse function to explore the data. Describe what you see? Click Run Code to see the data

tsfe::ftse350 %>% glimpse

What is the top 100 stocks in terms of market capitalisation? Challenge: filter the data to rank stocks on market size (Hint: some code to start ftse350 %>% filter(variable=="Market Value") %>% group_by(date) %>%)

Hint: Userank = min_rank(desc(value))) to rank value (for example) such that the largest market cap will be the top.

ftse350 %>%
  filter(variable=="Market Value") %>%  
  group_by(date) %>% 
  mutate(rank = min_rank(desc(value))) %>% 
  filter(rank %in% c(1:100))

Exercise stocks

Extract the prices and market values for the following three stocks. Name the resultant dataframe port

1. Greggs
2. BT
3. Unilever

tickers<-c("GRG","BT.A","ULVR") ## these are the tickers of the above stocks

tickers<-c("GRG","BT-A","ULVR")
ftse350 %>% filter(ticker %in% tickers) -> port

Topic 2 Calculating and visualising returns

The port data which you created is in tidy form, which is one observation per row. For the purposes of portfolio analytics we will need to filter on one variable to create returns.

Exercise log returns

Create log returns for each daily price series using the mutate function in the dplyr package. Recall the formula

$$r_t=ln(P_t)-ln(P_{t-1})$$

Hint: use the lag() in the mutate to call $P_{t-1}$

port_ret <- port %>%
  filter(variable=="Price") %>%
  arrange(ticker,date) %>% # ensure data is order by stock and then chronologically 
  group_by(ticker) %>% # this ensures the lag operating only operate with each symbol
  mutate(log_return=log(value)-log(lag(value)))

port_ret %>% head() # A sanity check to ensure that log returns are calculated correctly

Exercise how to plot returns for comparison 1

Plot each log returns series in such a way as to compare their volatility over time using the aesthetic colour. Hint: try using facet_wrap in ggplot2 to create separate plots.

port_ret %>% 
  ggplot(aes(x=date,y=log_return,colour=ticker)) + 
  geom_line()

Exercise how to plot returns for comparison 2

Plot each log returns series in such a way as to compare their volatility over time. Hint: try using facet_wrap in ggplot2 to create separate plots.

port_ret %>% 
  ggplot(aes(x=date,y=log_return,colour=ticker)) + 
  geom_line() +
  facet_wrap(~ticker)

Another way to compare these series is to consider the extreme (or outlying) returns. Conventionally, you might want to consider values greater than 95^th^ percentile by using stat_peak() and stat_valley() from the ggpmisc package. The latter package may have to be installed on your machine.

# install.packages("ggpmisc")
library(ggpmisc)
 port_ret %>% 
  ggplot(aes(x=date,y=log_return,colour=ticker)) + 
  geom_line() +
   stat_peaks(colour = "red",ignore_threshold = 0.95) +
   stat_valleys(colour = "blue",ignore_threshold =0.95) +
   facet_wrap(~ticker)

From the plot we can see that Greggs has 2 days where the returns are above the 95th percentile of peak, while BT and ULVR have one.Furthermore, Greggs and ulvr have 2 days where returns are below the 95th percentile of trough. When doing your project how would to deal with outlying observations?

In our experience, the unexpected is usually not an "outlier", or an aberrant point by rather a systematic pattern in some part of the data - Gelman et al. (2020)

Topic 3 Portfolio analytics

This topic you will calculate two daily portfolio return series for a portfolio containing the three stocks using log returns and market value.

Exercise 1 equally weighted portfolio returns

Create an equally weighted returns series for the three stocks, then plot the resultant return series Hint: the mean is a equally weighted statistic.

Then using the portfolio return formula

$$r_{p,t} \approx \sum_{i=1}^{N}w_ir_{it}$$

port_ret_ew <- port_ret %>%
  group_by(date) %>%
  summarise(ret=mean(log_return))

port_ret_ew %>%
    ggplot(aes(x=date,y=ret)) +
  geom_line() 

Exercise calculate value weighted

Create an value weighted returns series for the three stocks, then plot the resultant return series Hint: use the data with both price and market value

$$w_{it}= \frac{V_{it}}{\sum V_{it}} \text{ where } V_{it}=Quantity \times P_{it}$$

Then using the portfolio return formula

$$r_{p,t} \approx \sum_{i=1}^{N}w_ir_{it}$$

port_w <- port %>% 
  select(ticker,date,variable,value) %>%
  spread(variable,value)

port_ret_vw <-port_w %>%
  group_by(date) %>%
  mutate(weight=`Market Value`/sum(`Market Value`))

# Sanity check
port_ret_vw %>% 
  summarise(tw=sum(weight)) %>%
  filter(tw>1.0001)

# market value weighted returns
port_ret_vw <-port_ret_vw %>% 
  arrange(ticker,date) %>% 
  group_by(ticker) %>% 
  mutate(log_return=log(Price)-log(lag(Price))) %>%
  group_by(date) %>%
  summarise(ret=sum(weight*log_return))

Exercise merge returns

Combine the portfolio returns using left_join() . Hint: you need to choose a merging variable which unique identifies the portfolio returns time series. Name the new object port_ret_both

port_ret_both<- port_ret_vw %>% rename(vw_ret=ret) %>%
  left_join(port_ret_ew %>% rename(ew_ret=ret),by="date")

Exercise: plot returns and describe

Plot and visually compare the value-weight returns to the equally-weighted returns. Provide some rationale for the differences? Hint: use cumsum to plot the wealth creation in the daily returns series

port_ret_both %>%
  ungroup() %>%
  drop_na() %>%
  mutate(wealth_vw=cumsum(vw_ret),
         wealth_ew=cumsum(ew_ret)) %>%
  select(date,wealth_vw,wealth_ew) %>%
  gather(port,wealth,-date) %>%
  ggplot(aes(x=date,y=wealth,colour=port)) + 
  geom_line()

Topic 4 patterns in correlation

Learning outcomes

We have introduced the following graphics functions:

• gglagplot
• ggAcf

Explore the following time series from the tsfe package using these functions. Can you spot any seasonality, cyclicity and trend? What do you learn about the series?

• ni_hsales_ts
• usuk_rate_ts
• ftse_m_ts

Autocorrelation testing

Firstly create time series objects of the data from tsfe package. Note that ftse_m_ts is already in the package data.

ni_hsales_ts<-ts(ni_hsales$`Total Verified Sales`,start = c(2005,1),frequency = 4)
usuk_rate_ts<-ts(usuk_rate$price)

Plot and visually compare the above time series objects. Then use some visual aids to identify autocorrelation, What do you find? Hint: remember the autocorrelation plots from the lecture

autoplot(ni_hsales_ts)
autoplot(usuk_rate_ts)
autoplot(ftse_m_ts)
gglagplot(ni_hsales_ts)
gglagplot(usuk_rate_ts)
gglagplot(ftse_m_ts)
ggAcf(ni_hsales_ts)
ggAcf(usuk_rate_ts)
ggAcf(ftse_m_ts)

Topic 5 Test your knowledge

question("Explain when it is **not** appropriate to use the above approximation for portfolio returns",
         answer("When the returns are far from zero, for example when the time interval is long, for instance quarterly or annual returns which are likely to be far from zero", correct = TRUE),
         answer("When the returns are close to zero, for example when the time interval is long, for instance quarterly or annual returns which are likely to be far from zero."),
         answer("When the returns are far from zero, for example when the time interval is short, for instance daily."),
         answer("When the returns are far from 1"),
         allow_retry = TRUE
)

question("Why would an analyst prefer to use a total returns rather than price returns when asessing the performance of a portfolio investment?",
         answer("Total returns capture the income gains from holding an stock"),
         answer("Total returns capture the income and capital gains from holding an stock",correct = TRUE),
         answer("Total returns capture the capital and price gains from holding an stock"),
         answer("Total returns capture capital income and CEO turnover activity"),
         allow_retry = TRUE
)

question("What investment assumption does the total return calculation make?",
         answer("In the long term dividend income becomes an increasingly important part of the total return opportunity for investing.", correct = TRUE),
         answer("In the long term dividend income becomes an decreasingly important part of the total return opportunity for investing."),
         answer("In the long term dividend income is not an important part of the total return opportunity for investing."),
         answer("Total returns capture capital income and merger activity"),
         allow_retry = TRUE
)

barryquinn1/tsfe documentation built on Jan. 23, 2025, 2:09 a.m.