TianyuDu/AnnEconForecast

---
title: "Set_12_Portfolio"
output: html_notebook
---

Set data directory path
```{r setup, include=FALSE, cache = FALSE}
if (!require("knitr")) install.packages("knitr")
library(knitr)
opts_knit$set(root.dir = "C:/Teaching/Undergrad/data ECO374")
```
 
Install and load required packages
```{r}
chooseCRANmirror(graphics=FALSE, ind=33)
if (!require("fGarch")) install.packages("fGarch")

library(aTSA)
library(xts)
library(anytime)
library(fGarch)
```

Dowload data on Apple stock (AAPL) for the last five years, daily frequency
Source: https://finance.yahoo.com/quote/AAPL/history/

Load, extract Close price, convert to xts format, and plot
```{r}
setwd("C:/Teaching/Undergrad/data ECO374")
data_AAPL_full <- read.csv(file="AAPL.csv", header=TRUE, sep=",")

xtsdata_AAPL <- xts(x=data_AAPL_full[c("Close")], order.by=anytime(data_AAPL_full$Date))
 
plot.xts(xtsdata_AAPL, plot.type = c("single"), main ="Apple stock price (Close)" , legend.loc = "topleft", grid.col="lightgray")
```

Plot of returns
```{r}
xtsdata_AAPL_returns <- diff(log(xtsdata_AAPL))
xtsdata_AAPL_returns <- na.omit(xtsdata_AAPL_returns)

plot.xts(xtsdata_AAPL_returns, plot.type = c("single"), main ="Apple stock returns" , legend.loc = "topleft", grid.col="lightgray", col="blue")
```

https://finance.yahoo.com/quote/FCX/history/

Dowload data on Freeport-McMoRan Copper stock (FCX) for the last five years, daily frequency
Source: https://finance.yahoo.com/quote/FCX/history/

Load, extract Close price, convert to xts format, and plot
```{r}
setwd("C:/Teaching/Undergrad/data ECO374")
data_FCX_full <- read.csv(file="FCX.csv", header=TRUE, sep=",")

xtsdata_FCX <- xts(x=data_FCX_full[c("Close")], order.by=anytime(data_FCX_full$Date))
 
plot.xts(xtsdata_FCX, plot.type = c("single"), main ="FCX stock price (Close)" , legend.loc = "topleft", grid.col="lightgray")
```

Plot of returns
```{r}
xtsdata_FCX_returns <- diff(log(xtsdata_FCX))
xtsdata_FCX_returns <- na.omit(xtsdata_FCX_returns)

plot.xts(xtsdata_FCX_returns, plot.type = c("single"), main ="FCX stock returns" , legend.loc = "topleft", grid.col="lightgray", col="blue")
```

Apple returns model
```{r}
model_AAPL <- garchFit(~arma(1,0)+garch(1,1), data = xtsdata_AAPL_returns, trace = FALSE)
forecast_AAPL <- predict(model_AAPL, plot=FALSE, n.ahead=1)
forecast_AAPL
```

FCX returns model
```{r}
model_FCX <- garchFit(~arma(1,0)+garch(1,1), data = xtsdata_FCX_returns, trace = FALSE)
forecast_FCX <- predict(model_FCX, plot=FALSE, n.ahead=1)
forecast_FCX
```

Optimal portfolio weights for daily return of 0.1%
```{r}
m_set <- 0.1

m1 <- forecast_AAPL$meanForecast
v1 <- forecast_AAPL$standardDeviation^2

m2 <- forecast_FCX$meanForecast
v2 <- forecast_FCX$standardDeviation^2

denominator <- m1^2/v1 + m2^2/v2
w1u <- m_set*(m1^2/v1)/denominator
w2u <- m_set*(m2^2/v2)/denominator
w1 <- w1u/(w1u+w2u)
w2 <- w2u/(w1u+w2u)

w1
w2

```

Asset Pricing

Approximate market returns with S&P500 index
```{r}
#setwd("C:/Teaching/Undergrad/data ECO374")
data_SP500_full <- read.csv(file="SP500_daily.csv", header=TRUE, sep=",")
xtsdata_SP500 <- xts(x=data_SP500_full[c("Close")], order.by=anytime(data_SP500_full$Date))
xtsdata_SP500_returns <- diff(log(xtsdata_SP500))
xtsdata_SP500_returns <- na.omit(xtsdata_SP500_returns)
model_SP <- garchFit(~arma(1,0)+garch(1,1), data = xtsdata_SP500_returns, trace = FALSE)
forecast_SP <- predict(model_SP, plot=FALSE, n.ahead=1)
s_m <- forecast_SP$standardDeviation
```

Calculate beta of Apple
```{r}
s_AAPL <- forecast_AAPL$standardDeviation
beta_AAPL <- 0.45*s_AAPL/s_m
beta_AAPL
```

Calculate beta of FCX
```{r}
s_FCX <- forecast_FCX$standardDeviation
beta_FCX <- 0.28*s_FCX/s_m
beta_FCX
```