Hw2

#CFA 1.) Define the variables
investment_amount <- 100000

# Equities
equities_expected_return <- (0.6 * 50000) + (0.4 * -30000)

# T-bills
tbills_expected_return <- 1.0 * 5000

# Calculate the expected risk premium
expected_risk_premium <- equities_expected_return - tbills_expected_return

# Print the result
print(paste("Expected risk premium in dollars of investing in equities versus T-bills:", expected_risk_premium))

## [1] "Expected risk premium in dollars of investing in equities versus T-bills: 13000"

#10-12.) Given data
tbill_rate <- 0.05  # T-bill rate
sp_return_difference <- 0.08  # S&P 500 return difference
sp_standard_deviation <- 0.20  # S&P 500 standard deviation

# Weight combinations
weights <- seq(0, 1, by = 0.2)

# Function to calculate expected return of a portfolio
calc_expected_return <- function(weight) {
  weight_tbill <- max(0, 1 - weight)
  return (weight * sp_return_difference + weight_tbill * tbill_rate)
}

# Function to calculate variance of a portfolio
calc_variance <- function(weight) {
  return ((weight^2) * (sp_standard_deviation^2))
}

# Calculate expected returns and variances for each weight combination
expected_returns <- sapply(weights, calc_expected_return)
variances <- sapply(weights, calc_variance)

# Print results for Problem 10
print("Problem 10 - Expected Returns and Variances:")

## [1] "Problem 10 - Expected Returns and Variances:"

print(data.frame(Weight_Tbill = weights, Weight_SP500 = 1 - weights, Expected_Return = expected_returns, Variance = variances))

##   Weight_Tbill Weight_SP500 Expected_Return Variance
## 1          0.0          1.0           0.050   0.0000
## 2          0.2          0.8           0.056   0.0016
## 3          0.4          0.6           0.062   0.0064
## 4          0.6          0.4           0.068   0.0144
## 5          0.8          0.2           0.074   0.0256
## 6          1.0          0.0           0.080   0.0400

# Function to calculate utility level for given A
calc_utility <- function(expected_return, variance, A) {
  return (expected_return - 0.5 * A * variance)
}

# Investor's A values
A_values <- c(2, 3)

# Calculate utility levels for each portfolio for each A value
for (A in A_values) {
  utility_levels <- calc_utility(expected_returns, variances, A)
  # Print results for Problem 11 and 12
  cat("Problem", 11 + which(A_values == A), "- Utility levels for A =", A, ":\n")
  print(utility_levels)
}

## Problem 12 - Utility levels for A = 2 :
## [1] 0.0500 0.0544 0.0556 0.0536 0.0484 0.0400
## Problem 13 - Utility levels for A = 3 :
## [1] 0.0500 0.0536 0.0524 0.0464 0.0356 0.0200

#CFA 1-3.) Given data
expected_returns <- c(0.12, 0.15, 0.21, 0.24)
standard_deviations <- c(0.30, 0.50, 0.16, 0.21)
A <- 4  # Aversion to risk parameter

# Function to calculate utility
calc_utility <- function(expected_return, standard_deviation, A) {
  return (expected_return - 0.5 * A * standard_deviation^2)
}

# Calculate utilities for each investment
utilities <- calc_utility(expected_returns, standard_deviations, A)

# Problem 1: Select investment for risk averse investor
selected_investment_1 <- which.max(utilities)
cat("Problem 1 - Selected investment for risk averse investor (A = 4): Investment", selected_investment_1, "\n")

## Problem 1 - Selected investment for risk averse investor (A = 4): Investment 3

# Problem 2: Select investment for risk neutral investor
selected_investment_2 <- which.max(expected_returns)
cat("Problem 2 - Selected investment for risk neutral investor: Investment", selected_investment_2, "\n")

## Problem 2 - Selected investment for risk neutral investor: Investment 4

# Problem 3: Determine the variable (A) in the utility formula
variable_A <- "b. Investor’s aversion to risk."
cat("Problem 3 - The variable (A) in the utility formula represents:", variable_A, "\n")

## Problem 3 - The variable (A) in the utility formula represents: b. Investor’s aversion to risk.

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