Stock Analysis Theory

Financial Mathematics 1

1 Daily stock prices

1.1 Obtaining data from R packages

Necessary packages in use:

library(tidyverse)

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library(tidyquant)

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library(quantmod)
library(plotly)

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library(DT)

1: Write a R code to obtain stock prices for 4 companies: NETFLIX, TESLA, VINFAST, GENERAL, MOTORS in the latest 4 months.

start_date <- as.Date("2024-01-17")
end_date <- as.Date("2024-05-17")
symbols <- c("NFLX", "TSLA", "VFS", "GM")

prices <- tq_get(symbols, from = start_date, to = end_date)

prices_filtered <- prices %>%
  filter(symbol == "VFS") %>%
  mutate(arithmetic_return = (adjusted - lag(adjusted)) / lag(adjusted),
         log_return = log(adjusted) - log(lag(adjusted))) %>%
  select(symbol, date, adjusted, arithmetic_return, log_return) %>%
  na.omit()

datatable(prices_filtered)

2. Write a R code to plot stock prices for 4 companies: NETFLIX, TESLA, VINFAST, GENERAL MOTORS in the latest 4 months.

start_date <- as.Date("2024-01-17")
end_date <- as.Date("2024-05-17")
symbols <- c("NFLX", "TSLA", "VFS", "GM")

prices <- tq_get(symbols, from = start_date, to = end_date)

prices_filtered <- prices %>%
  filter(symbol == "VFS") %>%
  mutate(arithmetic_return = (adjusted - lag(adjusted)) / lag(adjusted),
         log_return = log(adjusted) - log(lag(adjusted))) %>%
  select(symbol, date, adjusted, arithmetic_return, log_return) %>%
  na.omit()

datatable(prices_filtered)

2 Daily stock return

Write a R code to compute and visualize the daily arithmetic return for VINFAST in the last 4 months.

daily_arithmetic_return_4m <- prices %>%
  filter(date >= start_date, date <= end_date, symbol == "VFS") %>%
  mutate(daily_arithmetic_return = (adjusted - lag(adjusted)) / lag(adjusted)) %>%
  select(symbol, date, adjusted, daily_arithmetic_return) %>%
  na.omit()

datatable(daily_arithmetic_return_4m)

daily_arithmetic_return_4m %>%
  ggplot(aes(x = date, y = daily_arithmetic_return, color = symbol)) +
  geom_line() +
  labs(title = "Daily Arithmetic Return for VINFAST", x = "Date", y = "Arithmetic Return") +
  theme_minimal()

Write a R code to compute and visualize the daily log return for VINFAST in the last 4 months.

daily_log_returns_4m <- prices %>% filter(date < "2024-05-18", date >= "2024-01-18", symbol == "VFS") %>%
    group_by(symbol) %>%
    mutate(daily_log_return=log(adjusted)-log(lag(adjusted,1))) %>% 
    select(symbol, date, adjusted,daily_log_return)%>%
    na.omit() # Remove rows with NA values in arithmetic_return

daily_log_returns_4m %>% datatable()

daily_log_returns_4m %>% ggplot(aes(x=date, y=daily_log_return, col=symbol))+geom_line()+facet_grid(symbol~.)

3 Daily Stock volatility

3.1 Code practice

Compute and visualize the sample daily volatility for 4 stocks NETFLIX, TESLA, VINFAST, GENERAL MOTORS in the last 4 months. Which one has the greatest volatility?

data= daily_log_returns_4s_4m <- prices %>% 
  filter(date <"2024-05-18", date >="2024-01-18", symbol %in%c( "NFLX", "TSLA", "VFS", "GM")) %>%
  group_by(symbol)%>% mutate(daily_log_return=log(adjusted)-log(lag(adjusted,1))) %>%   
  select(symbol, date, adjusted, daily_log_return)%>%na.omit()

data %>% 
  select(symbol,date,daily_log_return)%>% 
  pivot_wider(names_from = symbol, values_from = daily_log_return) ## showing 4 stocks by 4 columns

## # A tibble: 83 × 5
##    date           NFLX     TSLA      VFS        GM
##    <date>        <dbl>    <dbl>    <dbl>     <dbl>
##  1 2024-01-19 -0.00487  0.00146  0.0619   0.0265  
##  2 2024-01-22  0.00570 -0.0161   0.0263  -0.00536 
##  3 2024-01-23  0.0133   0.00163 -0.00325 -0.00255 
##  4 2024-01-24  0.102   -0.00628 -0.0382  -0.0152  
##  5 2024-01-25  0.0310  -0.129    0.0349   0.0132  
##  6 2024-01-26  0.0149   0.00339 -0.0299   0.000569
##  7 2024-01-29  0.00937  0.0411   0.0282   0.00595 
##  8 2024-01-30 -0.0227   0.00345 -0.0182   0.0751  
##  9 2024-01-31  0.00224 -0.0227  -0.00837  0.0169  
## 10 2024-02-01  0.00601  0.00835 -0.00337  0.00180 
## # ℹ 73 more rows

data %>% ggplot(aes(x=date, y=daily_log_return, col=symbol))+geom_line()+facet_grid(symbol~.)

data%>% 
  mutate(diff=daily_log_return-mean(daily_log_return)) %>% 
  summarize(volatility = sqrt(sum(diff^2) / (n() - 1)))

## # A tibble: 4 × 2
##   symbol volatility
##   <chr>       <dbl>
## 1 GM         0.0159
## 2 NFLX       0.0221
## 3 TSLA       0.0366
## 4 VFS        0.0634

data=daily_log_returns_4s_4m %>% filter(date< "2024-05-18", date >="2024-01-18", symbol %in%c( "NFLX", "TSLA", "VFS", "GM"))
data %>% datatable()

data%>% 
  mutate(diff=daily_log_return-mean(daily_log_return)) %>% 
  summarize(volatility = sqrt(sum(diff^2) / (n() - 1)))

## # A tibble: 4 × 2
##   symbol volatility
##   <chr>       <dbl>
## 1 GM         0.0159
## 2 NFLX       0.0221
## 3 TSLA       0.0366
## 4 VFS        0.0634

4 Daily covariance between two stocks

Consider 4 stocks NETFLIX, TESLA, VINFAST, GENERAL MOTORS in the last 4 months.

a) Plot the scatter plot for each pair of stocks’ log returns?

data1=daily_log_returns_4s_4m %>% select(symbol,date,daily_log_return)%>% pivot_wider(names_from = symbol, values_from = daily_log_return)

data1

## # A tibble: 83 × 5
##    date           NFLX     TSLA      VFS        GM
##    <date>        <dbl>    <dbl>    <dbl>     <dbl>
##  1 2024-01-19 -0.00487  0.00146  0.0619   0.0265  
##  2 2024-01-22  0.00570 -0.0161   0.0263  -0.00536 
##  3 2024-01-23  0.0133   0.00163 -0.00325 -0.00255 
##  4 2024-01-24  0.102   -0.00628 -0.0382  -0.0152  
##  5 2024-01-25  0.0310  -0.129    0.0349   0.0132  
##  6 2024-01-26  0.0149   0.00339 -0.0299   0.000569
##  7 2024-01-29  0.00937  0.0411   0.0282   0.00595 
##  8 2024-01-30 -0.0227   0.00345 -0.0182   0.0751  
##  9 2024-01-31  0.00224 -0.0227  -0.00837  0.0169  
## 10 2024-02-01  0.00601  0.00835 -0.00337  0.00180 
## # ℹ 73 more rows

plot(data1$NFLX[-1],data1$TSLA[-1])

plot(data1$NFLX[-1],data1$VFS[-1])

plot(data1$NFLX[-1],data1$GM[-1])

plot(data1$VFS[-1],data1$TSLA[-1])

plot(data1$VFS[-1],data1$GM[-1])

plot(data1$GM[-1],data1$TSLA[-1])

b) Compute the sample daily covariance for each pair of 4 stocks.

data2=data1 %>% filter(date < "2024-05-18", date >="2023-02-18")  
data2 %>% datatable()

# The sample daily covariance of NFLX and VFS
## Method 1:
 sum((data2$NFLX-mean(data2$NFLX))*(data2$VFS - mean(data2$VFS))) / (nrow(data2) - 1)

## [1] 0.0001859198