Apply it to your data 3

Which of your stock beat the market in 2026

# Load packages
library(tidyverse)
library(tidyquant)

1 Get stock prices and convert to returns

Ra <- c("AAPL", "GOOG", "MSFT") %>%
    tq_get(get  = "stock.prices",
           from = "2026-01-01") %>%
    group_by(symbol) %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Ra")
Ra

## # A tibble: 27 × 3
## # Groups:   symbol [3]
##    symbol date            Ra
##    <chr>  <date>       <dbl>
##  1 AAPL   2026-01-30 -0.0425
##  2 AAPL   2026-02-27  0.0191
##  3 AAPL   2026-03-31 -0.0393
##  4 AAPL   2026-04-30  0.0692
##  5 AAPL   2026-05-29  0.151 
##  6 AAPL   2026-06-30 -0.0727
##  7 AAPL   2026-07-31  0.0676
##  8 AAPL   2026-08-31  0.0266
##  9 AAPL   2026-09-25  0.0764
## 10 GOOG   2026-01-30  0.0736
## # ℹ 17 more rows

2 Get baseline and convert to returns

Rb <- "^IXIC" %>%
    tq_get(get  = "stock.prices",
           from = "2026-01-01") %>%
    tq_transmute(select     = adjusted, 
                 mutate_fun = periodReturn, 
                 period     = "monthly", 
                 col_rename = "Rb")
Rb

## # A tibble: 9 × 2
##   date             Rb
##   <date>        <dbl>
## 1 2026-01-30  0.00973
## 2 2026-02-27 -0.0338 
## 3 2026-03-31 -0.0475 
## 4 2026-04-30  0.153  
## 5 2026-05-29  0.0836 
## 6 2026-06-30 -0.0281 
## 7 2026-07-31 -0.0320 
## 8 2026-08-31  0.0393 
## 9 2026-09-25  0.0265

3 Join the two tables

RaRb <- left_join(Ra, Rb, by = c("date" = "date"))
RaRb

## # A tibble: 27 × 4
## # Groups:   symbol [3]
##    symbol date            Ra       Rb
##    <chr>  <date>       <dbl>    <dbl>
##  1 AAPL   2026-01-30 -0.0425  0.00973
##  2 AAPL   2026-02-27  0.0191 -0.0338 
##  3 AAPL   2026-03-31 -0.0393 -0.0475 
##  4 AAPL   2026-04-30  0.0692  0.153  
##  5 AAPL   2026-05-29  0.151   0.0836 
##  6 AAPL   2026-06-30 -0.0727 -0.0281 
##  7 AAPL   2026-07-31  0.0676 -0.0320 
##  8 AAPL   2026-08-31  0.0266  0.0393 
##  9 AAPL   2026-09-25  0.0764  0.0265 
## 10 GOOG   2026-01-30  0.0736  0.00973
## # ℹ 17 more rows

4 Calculate CAPM

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

## # A tibble: 3 × 18
## # Groups:   symbol [3]
##   symbol ActivePremium   Alpha AlphaRobust AnnualizedAlpha  Beta `Beta-`
##   <chr>          <dbl>   <dbl>       <dbl>           <dbl> <dbl>   <dbl>
## 1 AAPL          0.138   0.0163      0.0163          0.214  0.638   0.965
## 2 GOOG         -0.112  -0.0138     -0.0134         -0.153  1.54    1.95 
## 3 MSFT         -0.0926  0.003      -0.0427          0.0367 0.784   0.677
## # ℹ 11 more variables: `Beta-Robust` <dbl>, `Beta+` <dbl>, `Beta+Robust` <dbl>,
## #   BetaRobust <dbl>, Correlation <dbl>, `Correlationp-value` <dbl>,
## #   InformationRatio <dbl>, `R-squared` <dbl>, `R-squaredRobust` <dbl>,
## #   TrackingError <dbl>, TreynorRatio <dbl>

Which stock has a positively skewed distribution of returns?

Skewness measures whether a stock’s returns are more heavily tilted toward large positive or large negative returns.

RaRb_skewness <- RaRb %>%
    tq_performance(Ra = Ra, 
                   Rb = NULL, 
                   performance_fun = skewness)
RaRb_skewness

## # A tibble: 3 × 2
## # Groups:   symbol [3]
##   symbol skewness.1
##   <chr>       <dbl>
## 1 AAPL        0.142
## 2 GOOG        1.79 
## 3 MSFT        0.238

# All three stocks (AAPL, GOOG, and MSFT) have a positively skewed distribution of returns because their skewness values are all positive. GOOG has the highest skewness at 1.79, followed by MSFT at 0.238 and AAPL at 0.142. This means that Google had the strongest tendency toward larger positive monthly returns during this period.

The SkewnessKurtosisRatio measures the relationship between the asymmetry of returns and the presence of extreme returns.

RaRb_SkewnessKurtosisRatio <- RaRb %>%
    tq_performance(Ra = Ra, 
                   Rb = Rb, 
                   performance_fun = SkewnessKurtosisRatio)
RaRb_SkewnessKurtosisRatio

## # A tibble: 3 × 2
## # Groups:   symbol [3]
##   symbol SkewnessKurtosisRatio.1
##   <chr>                    <dbl>
## 1 AAPL                    0.0667
## 2 GOOG                    0.348 
## 3 MSFT                    0.111

 # All three stocks have a positive ratio, with GOOG having the highest ratio at 0.348, followed by MSFT at 0.111 and AAPL at 0.0667. This indicates that Google had the strongest positive skew relative to its overall level of extreme returns during this period.