prep.Rmd

---
output: html_document
title: Prescient Coding Challenge Prep 2023
author: Zubair Patel, Shriya Roy
---

### Time Series Data

Financial and economic data is mostly displayed and stored as time series. The time series data in the `csv` file is in long format

```{r}
# libraries
library(data.table)
library(plotly)
library(dplyr)
library(tidyr)

# read file
dt_prices <- fread("price_data.csv")
dt_prices
```

```{r}
# create wide
print("---> csv data in wide form")
dt_prices_wide <- dcast(dt_prices, date ~ stock, value.var = "price")
dt_prices_wide
```

```{r}
# plot
fig1 <- plot_ly(dt_prices_wide, type = "scatter", mode = "lines") %>%
    add_trace(x = ~date, y = ~AAPL, name = "AAPL") %>%
    add_trace(x = ~date, y = ~AMZN, name = "AMZN") %>%
    add_trace(x = ~date, y = ~MSFT, name = "MSFT") %>%
    layout(title = "Stock Price Series", yaxis=list(title="price"), width = 1000)

fig1
```

### Converting To Return Series & Total Return Series

It may be difficult to compare the 3 price series above because the starting price is not the same. To overcome this, calculate the return series $r_t$ for a stock and build a price series from a common base value.

The total return for a stock at time $T$ is defined as

$$ TR(T) = 100 \times \Big[ \Pi_{i=1}^{t\leq T}  \big( 1 + r_{t} \big)\Big]$$

Return at time $t$ is

$$ r_t = \frac{p_t - p_{t-1}}{p_{t-1}}$$

Compare the Total Return series for the 3 stocks

```{r}
dt_returns <- dt_prices_wide %>% 
  mutate(across(!date, ~ .x/lag(.x) -1)) %>% 
  drop_na()
  
fig2 <- plot_ly(dt_returns, type = "scatter", mode = "lines") %>%
    add_trace(x = ~date, y = ~AAPL, name = "AAPL") %>%
    add_trace(x = ~date, y = ~AMZN, name = "AMZN") %>%
    add_trace(x = ~date, y = ~MSFT, name = "MSFT") %>%
    layout(title = "Stock Return Series", yaxis=list(title="returns"), width = 1000)

fig2
```

```{r}

# calc total return
dt_cumulative_returns <- dt_returns %>% 
    mutate(across(!date, ~ 100*cumprod(1+.x)))

# plot
fig3 <- plot_ly(dt_cumulative_returns, type = "scatter", mode = "lines") %>%
    add_trace(x = ~date, y = ~AAPL, name = "AAPL") %>%
    add_trace(x = ~date, y = ~AMZN, name = "AMZN") %>%
    add_trace(x = ~date, y = ~MSFT, name = "MSFT") %>%
    layout(title = "Stock Total Return Seriess", yaxis=list(title="returns"), width = 1000)

fig3

```

### Questions

1. Notice the difference once adjusted to the same reference?
2. Which stock or combination would you have chosen?