# Load packages
library(tidyquant)
library(tidyverse)
from <- today() - years(5)
stock_returns_monthly <- c("FB", "AMZN", "NFLX") %>%
tq_get(get = "stock.prices",
from = from) %>%
group_by(symbol) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
col_rename = "Ra")
stock_returns_monthly## # A tibble: 183 x 3
## # Groups: symbol [3]
## symbol date Ra
## <chr> <date> <dbl>
## 1 FB 2015-11-30 -0.0287
## 2 FB 2015-12-31 0.00403
## 3 FB 2016-01-29 0.0721
## 4 FB 2016-02-29 -0.0471
## 5 FB 2016-03-31 0.0672
## 6 FB 2016-04-29 0.0305
## 7 FB 2016-05-31 0.0105
## 8 FB 2016-06-30 -0.0381
## 9 FB 2016-07-29 0.0845
## 10 FB 2016-08-31 0.0176
## # ... with 173 more rowsbaseline_returns_monthly <- "^IXIC" %>%
tq_get(get = "stock.prices",
from = from) %>%
tq_transmute(select = adjusted,
mutate_fun = periodReturn,
period = "monthly",
col_rename = "Rb")
baseline_returns_monthly## # A tibble: 61 x 2
## date Rb
## <date> <dbl>
## 1 2015-11-30 0.000735
## 2 2015-12-31 -0.0198
## 3 2016-01-29 -0.0786
## 4 2016-02-29 -0.0121
## 5 2016-03-31 0.0684
## 6 2016-04-29 -0.0194
## 7 2016-05-31 0.0362
## 8 2016-06-30 -0.0213
## 9 2016-07-29 0.0660
## 10 2016-08-31 0.00990
## # ... with 51 more rows#
stock_returns_monthly_multi <- stock_returns_monthly %>%
tq_repeat_df(n = 10)
stock_returns_monthly_multi## # A tibble: 1,830 x 4
## # Groups: portfolio [10]
## portfolio symbol date Ra
## <int> <chr> <date> <dbl>
## 1 1 FB 2015-11-30 -0.0287
## 2 1 FB 2015-12-31 0.00403
## 3 1 FB 2016-01-29 0.0721
## 4 1 FB 2016-02-29 -0.0471
## 5 1 FB 2016-03-31 0.0672
## 6 1 FB 2016-04-29 0.0305
## 7 1 FB 2016-05-31 0.0105
## 8 1 FB 2016-06-30 -0.0381
## 9 1 FB 2016-07-29 0.0845
## 10 1 FB 2016-08-31 0.0176
## # ... with 1,820 more rows# Assign weights to individual stocks
weights <- c(
0.80, 0.10, 0.10,
0.10, 0.80, 0.10,
0.10, 0.10, 0.80,
0.60, 0.20, 0.20,
0.20, 0.60, 0.20,
0.20, 0.20, 0.60,
0.50, 0.25, 0.25,
0.25, 0.50, 0.25,
0.25, 0.25, 0.50,
0.40, 0.40, 0.20
)
stocks <- c("FB", "AMZN", "NFLX")
weights_table <- tibble(stocks) %>%
tq_repeat_df(n = 10) %>%
bind_cols(tibble(weights)) %>%
group_by(portfolio)
weights_table## # A tibble: 30 x 3
## # Groups: portfolio [10]
## portfolio stocks weights
## <int> <chr> <dbl>
## 1 1 FB 0.8
## 2 1 AMZN 0.1
## 3 1 NFLX 0.1
## 4 2 FB 0.1
## 5 2 AMZN 0.8
## 6 2 NFLX 0.1
## 7 3 FB 0.1
## 8 3 AMZN 0.1
## 9 3 NFLX 0.8
## 10 4 FB 0.6
## # ... with 20 more rows# Aggregate a Portfolio using Vector of Weights
portfolio_returns_monthly <-
stock_returns_monthly_multi %>%
tq_portfolio(assets_col = symbol,
returns_col = Ra,
weights = weights_table,
col_rename = "Ra")
portfolio_returns_monthly ## # A tibble: 610 x 3
## # Groups: portfolio [10]
## portfolio date Ra
## <int> <date> <dbl>
## 1 1 2015-11-30 -0.0239
## 2 1 2015-12-31 -0.00250
## 3 1 2016-01-29 0.0255
## 4 1 2016-02-29 -0.0434
## 5 1 2016-03-31 0.0699
## 6 1 2016-04-29 0.0254
## 7 1 2016-05-31 0.0274
## 8 1 2016-06-30 -0.0407
## 9 1 2016-07-29 0.0758
## 10 1 2016-08-31 0.0205
## # ... with 600 more rows# Merging Ra and Rb
RaRb_multi_portfolio <- left_join(portfolio_returns_monthly ,
baseline_returns_monthly,
by = "date")
RaRb_multi_portfolio## # A tibble: 610 x 4
## # Groups: portfolio [10]
## portfolio date Ra Rb
## <int> <date> <dbl> <dbl>
## 1 1 2015-11-30 -0.0239 0.000735
## 2 1 2015-12-31 -0.00250 -0.0198
## 3 1 2016-01-29 0.0255 -0.0786
## 4 1 2016-02-29 -0.0434 -0.0121
## 5 1 2016-03-31 0.0699 0.0684
## 6 1 2016-04-29 0.0254 -0.0194
## 7 1 2016-05-31 0.0274 0.0362
## 8 1 2016-06-30 -0.0407 -0.0213
## 9 1 2016-07-29 0.0758 0.0660
## 10 1 2016-08-31 0.0205 0.00990
## # ... with 600 more rows# Sharpe Ratio
RaRb_multi_portfolio %>%
tq_performance(Ra = Ra, Rb = NULL, performance_fun = SharpeRatio.annualized, scale = 12) ## # A tibble: 10 x 2
## # Groups: portfolio [10]
## portfolio `AnnualizedSharpeRatio(Rf=0%)`
## <int> <dbl>
## 1 1 0.909
## 2 2 1.25
## 3 3 0.933
## 4 4 1.04
## 5 5 1.23
## 6 6 1.03
## 7 7 1.09
## 8 8 1.20
## 9 9 1.08
## 10 10 1.16Hint: Use dplyr::arrange().
# Calculate Sharpe Ratio for hundreds of portfolios
RaRb_multi_portfolio %>%
tq_performance(Ra = Ra, Rb = NULL, performance_fun = SharpeRatio.annualized, scale = 12) %>%
arrange(desc(`AnnualizedSharpeRatio(Rf=0%)`))## # A tibble: 10 x 2
## # Groups: portfolio [10]
## portfolio `AnnualizedSharpeRatio(Rf=0%)`
## <int> <dbl>
## 1 2 1.25
## 2 5 1.23
## 3 8 1.20
## 4 10 1.16
## 5 7 1.09
## 6 9 1.08
## 7 4 1.04
## 8 6 1.03
## 9 3 0.933
## 10 1 0.909Hint: Make your argument using the calculated Sharpe
The second portfolio did the best so, the * Facebook(0.10), Amazon(0.80), Netflix (0.10) weighting scheme would have performed the best.When all of the portfolios were put in descending order, the second portfolio had the largest sharpe ratio.
Hint: Calculate Beta from the Capital Asset Pricing Model. Make your argument based on the calculated Beta.
# Beta and Alpha
RaRb_multi_portfolio %>%
tq_performance(Ra = Ra, Rb = Rb, performance_fun = table.CAPM) %>%
t()## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## portfolio 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000
## ActivePremium 0.0511 0.1557 0.1225 0.0790 0.1380 0.1184 0.0921 0.1288
## Alpha 0.0027 0.0090 0.0093 0.0045 0.0080 0.0081 0.0054 0.0075
## AnnualizedAlpha 0.0328 0.1138 0.1170 0.0557 0.1004 0.1012 0.0668 0.0942
## Beta 1.1484 1.2108 1.1353 1.1452 1.1891 1.1414 1.1474 1.1772
## Beta- 0.6889 1.0701 0.8992 0.7752 0.9917 0.8852 0.8162 0.9516
## Beta+ 1.5794 1.3206 1.3370 1.4857 1.3507 1.3588 1.4473 1.3661
## Correlation 0.7716 0.7701 0.5990 0.7893 0.7840 0.6759 0.7865 0.7834
## Correlationp-value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
## InformationRatio 0.3105 0.8846 0.4682 0.5099 0.8366 0.5503 0.5874 0.7886
## R-squared 0.5954 0.5931 0.3588 0.6231 0.6147 0.4569 0.6186 0.6137
## TrackingError 0.1646 0.1760 0.2617 0.1550 0.1649 0.2151 0.1568 0.1633
## TreynorRatio 0.2023 0.2783 0.2676 0.2273 0.2685 0.2625 0.2382 0.2633
## [,9] [,10]
## portfolio 9.0000 10.0000
## ActivePremium 0.1163 0.1099
## Alpha 0.0076 0.0063
## AnnualizedAlpha 0.0945 0.0782
## Beta 1.1458 1.1664
## Beta- 0.8824 0.8876
## Beta+ 1.3707 1.4122
## Correlation 0.7134 0.8008
## Correlationp-value 0.0000 0.0000
## InformationRatio 0.5965 0.7205
## R-squared 0.5089 0.6413
## TrackingError 0.1949 0.1525
## TreynorRatio 0.2597 0.2496After calculating the betas, the second portfolio had the largest beta dn most volatile stock of the 10 portfolios.
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