FINA5526 Workshop Week 4

Download monthly stock prices for the previous 5 years for Wesfarmers (WES), Woolworths (WOW), Rio Tinto (RIO), BHP (BHP), and Telstra (TLS). Download monthly values of the ASX 200 for the same period.

Required:

• Calculate the beta for each of the stocks.
• Assuming the expected market return is equal to the historical long-term average return of 12%, and the average risk free return is 3%, what is the risk aversion parameter for the average investor in Australia according to the CAPM model?

Download historical stock prices from Yahoo finance and calculate monthly returns

# Wesfarmers, Woolworths, Rio Tinto, BHP Billiton, Telstra.
Ra <- c("BHP.AX", "WES.AX", "WOW.AX", "RIO.AX", "TLS.AX") %>% 
  tq_get(get  = "stock.prices", 
         from = "2012-08-21",
         to   = "2017-08-21") %>% 
  group_by(symbol) %>% 
  tq_transmute(select     = adjusted,
               mutate_fun = periodReturn,
               period     = "monthly",
               col_rename = "Ra")
head(Ra)

## # A tibble: 6 x 3
## # Groups:   symbol [1]
##   symbol       date          Ra
##    <chr>     <date>       <dbl>
## 1 BHP.AX 2012-08-31 -0.04448536
## 2 BHP.AX 2012-09-28  0.06759746
## 3 BHP.AX 2012-10-31  0.02360914
## 4 BHP.AX 2012-11-29  0.01685279
## 5 BHP.AX 2012-12-30  0.07880419
## 6 BHP.AX 2013-01-31  0.02210116

# ASX200
Rb <- "^AXJO" %>%
  tq_get(get  = "stock.prices",
         from = "2012-08-21",
         to   = "2017-08-21") %>%
  tq_transmute(select     = adjusted, 
               mutate_fun = periodReturn, 
               period     = "monthly", 
               col_rename = "Rb")
head(Rb)

## # A tibble: 6 x 2
##         date          Rb
##       <date>       <dbl>
## 1 2012-08-31 -0.01535333
## 2 2012-09-28  0.01642684
## 3 2012-10-31  0.01609302
## 4 2012-11-29  0.01085784
## 5 2012-12-30  0.03173546
## 6 2013-01-31  0.05852874

CAPM Calculations

# Combine the two data sets using the “date” field and left_join (dplyr). 
RaRb <- left_join(Ra, Rb, by = c("date" = "date"))

# Calculate CAPM metrics 
RaRb_capm <- RaRb %>%
  tq_performance(Ra = Ra, 
                 Rb = Rb, 
                 performance_fun = table.CAPM)
RaRb_capm

## # A tibble: 5 x 13
## # Groups:   symbol [5]
##   symbol ActivePremium   Alpha AnnualizedAlpha   Beta `Beta-` `Beta+`
##    <chr>         <dbl>   <dbl>           <dbl>  <dbl>   <dbl>   <dbl>
## 1 BHP.AX       -0.0353 -0.0012         -0.0139 1.0640  1.2217  1.7092
## 2 WES.AX        0.0405  0.0038          0.0466 1.0102  0.7319  0.5508
## 3 WOW.AX       -0.0133 -0.0001         -0.0011 0.9067  1.0862  0.6476
## 4 RIO.AX        0.0406  0.0052          0.0647 0.9046  0.8767  1.4248
## 5 TLS.AX        0.0272  0.0038          0.0461 0.7273  0.4970  0.8500
## # ... with 6 more variables: Correlation <dbl>,
## #   `Correlationp-value` <dbl>, InformationRatio <dbl>, `R-squared` <dbl>,
## #   TrackingError <dbl>, TreynorRatio <dbl>

## Adding missing grouping variables: `symbol`

symbol	Alpha	Beta
BHP.AX	-0.0012	1.0640
WES.AX	0.0038	1.0102
WOW.AX	-0.0001	0.9067
RIO.AX	0.0052	0.9046
TLS.AX	0.0038	0.7273

Plots of stock returns against the ASX 200

RaRb %>% 
  ggplot(aes(Rb, Ra, group = symbol, color = symbol)) +
  geom_point() +
  facet_wrap(~ symbol, ncol = 2) +
  labs(title = "Stock Betas",
       x = "ASX 200 Return", y = "Stock Returns") +
  geom_smooth(method = "lm") +
  scale_y_continuous(labels = scales::percent) +
  guides(color = FALSE)

Ra %>% 
  ggplot(aes(date, Ra, group = symbol, color = symbol)) +
  geom_line() +
  facet_wrap(~ symbol, ncol = 2, scale = "free_y")

Rb %>% 
  ggplot(aes(date, Rb, fill = Rb)) +
  geom_bar(stat = "identity") +
  labs(title = "ASX200 Returns",
       x = "", y = "Monthly Returns") +
  geom_smooth(method = "lm") +
  theme_tq() +
  scale_color_tq() +
  scale_y_continuous(labels = scales::percent) +
  guides(fill = FALSE)