Upcoming Thrills: Belgian Women's Super League Matches Tomorrow
Tomorrow promises to be an electrifying day for football fans across Belgium and beyond, as the Women's Super League gears up for a series of matches that are sure to keep spectators on the edge of their seats. With top teams clashing in a display of skill, strategy, and sportsmanship, it's an event that no football enthusiast should miss. In this detailed guide, we'll delve into the matches scheduled for tomorrow, offering expert betting predictions and insights to enhance your viewing experience.
Match Highlights and Expert Predictions
Match 1: Standard Liège vs. Anderlecht
The clash between Standard Liège and Anderlecht is one of the most anticipated fixtures of the day. Known for their tactical prowess, Standard Liège comes into this match with a strong track record at home. However, Anderlecht's recent form has been impressive, making this a potentially close contest.
Betting Predictions:
- Standard Liège to Win: With home advantage and a solid defensive lineup, Standard Liège is favored to secure a victory. Odds are currently at 1.75.
- Draw: Given Anderlecht's resilience and recent performances, a draw is also a plausible outcome. Odds stand at 3.50.
- Anderlecht to Win: If Anderlecht can capitalize on any defensive lapses by Standard Liège, they could pull off an upset. Odds are at 4.20.
Match 2: Gent vs. Bruges
Gent and Bruges are set to battle it out in what promises to be a thrilling encounter. Both teams have shown remarkable consistency this season, making it difficult to predict the outcome.
Betting Predictions:
- Gent to Win: Gent's attacking prowess could give them the edge in this match. Odds are at 2.10.
- Bruges to Win: Bruges' solid defense might just thwart Gent's advances, making them a strong contender. Odds are at 2.80.
- Both Teams to Score: With both teams known for their offensive capabilities, betting on both teams to score seems wise. Odds are at 1.65.
Match 3: Lierse Kempenzonen vs. Beerschot
This match features Lierse Kempenzonen hosting Beerschot, with both teams eager to climb the league table. Lierse Kempenzonen has been in good form lately, while Beerschot looks to bounce back from recent setbacks.
Betting Predictions:
- Lierse Kempenzonen to Win: With home advantage and recent form on their side, Lierse Kempenzonen is favored. Odds are at 1.90.
- Beerschot to Win: If Beerschot can exploit any weaknesses in Lierse's defense, they could secure a victory. Odds are at 3.60.
- Overs/Unders (2.5 Goals): Expect a high-scoring game given both teams' attacking styles. Bet on overs with odds at 1.80.
In-Depth Analysis: Team Form and Key Players
Standard Liège: A Tactical Powerhouse
Standard Liège's success this season can be attributed to their tactical discipline and robust defense. Head coach Jean-Michel Versavel has masterfully orchestrated a team that excels in maintaining possession and launching swift counter-attacks.
Key Player:
Megan De Turck is expected to be pivotal in tomorrow's match against Anderlecht. Her ability to control the midfield and distribute the ball effectively makes her a crucial asset for Standard Liège.
Anderlecht: Resilience Personified
Anderlecht has shown remarkable resilience this season, often pulling off unexpected results against stronger opponents. Their ability to adapt during matches makes them a formidable opponent for any team.
Key Player:
Nicole Vandeputte's leadership on the field is invaluable for Anderlecht. Her vision and passing accuracy are key factors in their attacking plays.
Gent: The Offense Machine
Gent's offensive strategy has been the highlight of their campaign so far. Their forwards have been in exceptional form, consistently finding the back of the net against tough defenses.
Key Player:
Jade Lejeune is expected to be instrumental in Gent's attack against Bruges. Her speed and dribbling skills make her one of the most exciting players to watch.
Bruges: Defensive Solidity Meets Tactical Ingenuity
Bruges has built its reputation on a solid defensive foundation combined with strategic gameplay that often catches opponents off guard.
Key Player:
Sofie Paesens' defensive acumen will be critical for Bruges as they face Gent's potent attack tomorrow.
Tactical Breakdowns and Strategic Insights
The Art of Possession: Standard Liège vs. Anderlecht
This match is expected to be a battle of wits between two tactically astute teams. Standard Liège will likely focus on maintaining possession and controlling the tempo of the game, while Anderlecht will look to disrupt their rhythm with quick transitions.
- Possession Play: Standard Liège's ability to dominate possession could stifle Anderlecht's attacking opportunities.
- Tactical Fouls: Anderlecht might resort to tactical fouls in midfield to break up play and slow down Standard Liège's attacks.
- Crosses and Set-Pieces: Both teams have effective set-piece routines that could prove decisive in this tightly contested match.
Gent vs. Bruges: An Offensive Showdown
The clash between Gent and Bruges is set to be an offensive spectacle, with both teams eager to showcase their attacking prowess.
- Frontline Battles: The forward lines of both teams will be under intense scrutiny as they vie for dominance in attack.
- Midfield Control: Winning control of the midfield will be crucial for both teams as it will dictate the flow of the game.
- Keeper Performance: The performance of both goalkeepers could be pivotal in determining the outcome of this match.
Lierse Kempenzonen vs. Beerschot: A Battle for Survival
This match holds significant importance for both Lierse Kempenzonen and Beerschot as they strive to avoid relegation worries early in the season.
- Tactical Discipline: Both teams will need to maintain tactical discipline throughout the match to avoid costly mistakes.
- Creative Midfield Play: The creativity of midfielders will be essential in breaking down each other's defenses.
- Closing Phases: The closing phases of each half could see decisive moments as both teams push for goals.
Betting Tips and Strategies for Tomorrow’s Matches
Betting Strategy for Standard Liège vs. Anderlecht
<|repo_name|>caryeasterwood/Machine-Learning-for-Financial-Engineering<|file_sep|>/hw_5/solution_5.Rmd
---
title: "HW5"
author: "Cary Easterwood"
date: "Due March XX"
output:
html_document:
toc: true
toc_depth: '5'
toc_float:
collapsed: false
smooth_scroll: true
---
# Problem Setup
## Read data
{r}
# Read data
rm(list = ls())
library(quantmod)
library(tidyverse)
library(zoo)
library(PerformanceAnalytics)
library(ggplot2)
library(gridExtra)
library(knitr)
# Read data
getSymbols("SPY", src = "yahoo", from = "2000-01-01", auto.assign = TRUE)
SPY <- SPY[,6]
getSymbols("IWM", src = "yahoo", from = "2000-01-01", auto.assign = TRUE)
IWM <- IWM[,6]
getSymbols("TLT", src = "yahoo", from = "2000-01-01", auto.assign = TRUE)
TLT <- TLT[,6]
## Create log returns
{r}
# Create log returns
returns <- data.frame(Date = index(SPY), SPY = diff(log(Cl(SPY))),
IWM = diff(log(Cl(IWM))), TLT = diff(log(Cl(TLT))))
returns <- na.omit(returns)
returns <- returns[-1]
returns <- returns %>% mutate(Date = index(SPY))
## Train test split
{r}
# Create train test split
set.seed(12345)
train <- returns %>% filter(Date <= as.Date("2010-12-31"))
test <- returns %>% filter(Date > as.Date("2010-12-31"))
# Problem One
## Mean-Variance Portfolio Optimization
### Fit an optimal portfolio using mean-variance optimization
{r}
# Mean-Variance portfolio optimization
covariance_matrix <- cov(train[,-1])
means <- colMeans(train[,-1])
mu_min <- min(means)
mu_max <- max(means)
optimal_portfolio <- function(mu) {
solve_QP(Dmat = covariance_matrix,
dvec = rep(0,nrow(covariance_matrix)),
Amat = cbind(rep(1,nrow(covariance_matrix)),means),
bvec = c(1,mu),
meq = nrow(covariance_matrix))
}
portfolio_returns <- sapply(seq(from=mu_min,to=mu_max,length.out=100), optimal_portfolio)$primal
portfolio_weights <- sapply(seq(from=mu_min,to=mu_max,length.out=100), optimal_portfolio)$solution[-1]
portfolio_variance <- sapply(seq(from=mu_min,to=mu_max,length.out=100), optimal_portfolio)$value/252
### Plot efficient frontier
{r}
# Plot efficient frontier
plot_data <- data.frame(Returns = portfolio_returns,
Variance = portfolio_variance,
mu = seq(from=mu_min,to=mu_max,length.out=100))
ggplot(data=plot_data) +
geom_line(aes(x=sqrt(Variance), y=(Returns), color=factor(mu))) +
labs(title="Efficient Frontier") +
scale_x_continuous(name="Risk (standard deviation)") +
scale_y_continuous(name="Expected return") +
theme(plot.title = element_text(hjust=0.5))
### Plot risk-return tradeoff by varying expected return
{r}
# Plot risk-return tradeoff by varying expected return
plot_data_2 <- data.frame(Returns = portfolio_returns,
Variance = portfolio_variance,
mu = seq(from=mu_min,to=mu_max,length.out=100)) %>%
mutate(RiskReturnTradeoff =
Returns/sqrt(Variance)) %>%
group_by(mu) %>%
summarize(RiskReturnTradeoff =
mean(RiskReturnTradeoff))
ggplot(data=plot_data_2) +
geom_line(aes(x=sqrt(Variance), y=(RiskReturnTradeoff), color=factor(mu))) +
labs(title="Risk-return tradeoff") +
scale_x_continuous(name="Risk (standard deviation)") +
scale_y_continuous(name="Risk-return tradeoff") +
theme(plot.title = element_text(hjust=0.5))
### Calculate Sharpe ratio
{r}
# Calculate Sharpe ratio
risk_free_rate <- .04/252
sharpe_ratios <- (portfolio_returns - risk_free_rate)/sqrt(portfolio_variance)
optimal_mu <- seq(from=mu_min,to=mu_max,length.out=100)[which.max(sharpe_ratios)]
optimal_sharpe_ratio_index <- which.max(sharpe_ratios)
optimal_sharpe_ratio_mu <- optimal_mu[optimal_sharpe_ratio_index]
optimal_sharpe_ratio_weights <- portfolio_weights[,optimal_sharpe_ratio_index]
optimal_sharpe_ratio_return <- portfolio_returns[optimal_sharpe_ratio_index]
optimal_sharpe_ratio_variance <- portfolio_variance[optimal_sharpe_ratio_index]
optimal_sharpe_ratio_sd_return <- sqrt(optimal_sharpe_ratio_variance)
optimal_sharpe_ratio_return_plot_data <-
data.frame(Returns =
c(optimal_sharpe_ratio_return - optimal_sharpe_ratio_sd_return,
optimal_sharpe_ratio_return,
optimal_sharpe_ratio_return + optimal_sharpe_ratio_sd_return),
Variance =
c(optimal_sharpe_ratio_variance,
optimal_sharpe_ratio_variance,
optimal_sharpe_ratio_variance),
label =
c("Mean - SD",
"Mean",
"Mean + SD"),
mu =
c(optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index]))
ggplot(data=
plot_data[optimal_sharpe_ratio_index,]) +
geom_line(aes(x=sqrt(Variance), y=(Returns), color=factor(mu))) +
geom_point(data=
optimal_sharpe_ratio_return_plot_data,
aes(x=sqrt(Variance),
y=(Returns),
label=label)) +
labs(title=paste("Sharpe ratio maximized at mu=",round(optimal_mu[optimal_sharpe_ratio_index],digits=6))) +
scale_x_continuous(name="Risk (standard deviation)") +
scale_y_continuous(name="Expected return") +
theme(plot.title = element_text(hjust=0.5)) +
geom_text_repel()
### Compute actual sharpe ratio on training set
{r}
# Compute actual sharpe ratio on training set
actual_train_portfolio_returns <- train[,-1] %*% t(as.matrix(optimal_sharpe_ratio_weights))
actual_train_portfolio_returns_sd <- sd(actual_train_portfolio_returns)
actual_train_portfolio_returns_mean <- mean(actual_train_portfolio_returns)
actual_train_portfolio_returns_sharpereatio <-
(actual_train_portfolio_returns_mean - risk_free_rate)/actual_train_portfolio_returns_sd
actual_train_portfolio_returns_quantile_plot_data_1 <=-
data.frame(Returns =
c(actual_train_portfolio_returns_mean - actual_train_portfolio_returns_sd,
actual_train_portfolio_returns_mean,
actual_train_portfolio_returns_mean + actual_train_portfolio_returns_sd),
Variance =
c(actual_train_portfolio_returns_sd^2,
actual_train_portfolio_returns_sd^2,
actual_train_portfolio_returns_sd^2),
label =
c("Mean - SD",
"Mean",
"Mean + SD"),
mu =
c(optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index]))
ggplot(data=
plot_data[optimal_sharpe_ratio_index,]) +
geom_line(aes(x=sqrt(Variance), y=(Returns), color=factor(mu))) +
geom_point(data=
actual_train_portfolio_returns_quantile_plot_data_1,
aes(x=sqrt(Variance),
y=(Returns),
label=label)) +
labs(title=paste("Actual training set Sharpe ratio:",round(actual_train_portfolio_returns_sharpereatio,digits=6))) +
scale_x_continuous(name="Risk (standard deviation)") +
scale_y_continuous(name="Expected return") +
theme(plot.title = element_text(hjust=0.5)) +
geom_text_repel()
### Compute actual sharpe ratio on testing set
{r}
# Compute actual sharpe ratio on testing set
actual_test_portfolio_returns <- test[,-1] %*% t(as.matrix(optimal_sharpe_ratio_weights))
actual_test_portfolio_returns_sd <- sd(actual_test_portfolio_returns)
actual_test_portfolio_returns_mean <- mean(actual_test_portfolio_returns)
actual_test_portfolio_returns_sharpereatio <-
(actual_test_portfolio_returns_mean - risk_free_rate)/actual_test_portfolio_returns_sd
actual_test_portfolio_returns_quantile_plot_data_1 <=-
data.frame(Returns =
c(actual_test_portfolio_returns_mean - actual_test_portfolio_returns_sd,
actual_test_portfolio_returns_mean,
actual_test_portfolio_returns_mean + actual_test_portfolio_returns_sd),
Variance =
c(actual_test_portfolio_returns_sd^2,
actual_test_portfolio_returns_sd^2,
actual_test_portfolio_returns_sd^2),
label =
c("Mean - SD",
"Mean",
"Mean + SD"),
mu =
c(optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index],
optimal_mu[optimal_sharpe_ratio_index]))
ggplot(data=
plot_data[optimal_sharpe_ratio_index,]) +
geom_line(aes(x=sqrt(Variance), y=(Returns), color=factor(mu))) +
geom_point(data=
actual_test_portfolio_returns_quantile_plot_data_1,
aes(x=sqrt(Variance),
y=(Returns),
label=label)) +
labs(title=paste("Actual test set Sharpe ratio:",round(actual_test_portfolio