title: “R Notebook”
output: html_notebook
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Author1 Hendrik Sommer, Germany
Author2 Antoine Putresza, Poland
Date of the project: 30.09.2024-02.12.2024
Date of the submission: 02.12.2024
Date of the revision: 05.12.2024
Date of acceptance:
In the revised version of our draft, we have filled in the missing points with the required answers, revised the existing answers to make them more accessible and made them more specific. We have placed great emphasis on ensuring that the text is fully comprehensible and answers in detail the questions asked in the draft.We have left the old versions of the answers and, for the sake of comparison, placed the new versions of the answers below the old answers
We will now start with doing the basic parameters of the market table
library(quantmod)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo# Define the date range
start_date <- "2024-05-01"
end_date <- "2024-09-30"
# Create an empty data frame
table_data <- data.frame(
Description = character(),
Beginning_of_Term = character(),
End_of_Term = character()
)
# Function to add rows to the table
add_row <- function(category, data) {
table_data <<- rbind(table_data, data.frame(
Description = category,
BoT = as.character(format(round(data[1], 2), nsmall=2)),
EoT = as.character(format(round(data[2], 2), nsmall=2))
))
}
# Get S&P 500 index level
getSymbols("AAPL", src = "yahoo", from = start_date, to = end_date)## [1] "AAPL"sp500_start <- AAPL[1, 4]
sp500_end <- AAPL[nrow(AAPL), 4]
add_row("S&P 500 (stock) index level:", c(sp500_start, sp500_end))
#getsymbols Nasdaq composite index level
getSymbols("^IXIC", src = "yahoo", from = start_date, to = end_date)## [1] "IXIC"start_index_level <- IXIC[1, 4]
end_index_level <- IXIC[nrow(IXIC), 4]
add_row("Nasdaq Composite (stock) index level:", c(start_index_level,end_index_level ))
getSymbols("DPRIME", src = "FRED", from = start_date, to = end_date)## [1] "DPRIME"# Extract the beginning and end prime rates
prime_rate_start <- DPRIME[1, 1]
prime_rate_end <- DPRIME[nrow(DPRIME), 1]
add_row("Prime rate:", c(prime_rate_start, prime_rate_end))
getSymbols("FEDFUNDS", src = "FRED", from = start_date, to = end_date)## [1] "FEDFUNDS"# Extract the beginning and end federal funds rates
fed_funds_start <- FEDFUNDS[1, 1]
fed_funds_end <- FEDFUNDS[nrow(FEDFUNDS), 1]
add_row("Federal funds rate:", c(fed_funds_start, fed_funds_end))
getSymbols("DTB3", src = "FRED", from = start_date, to = end_date)## [1] "DTB3"getSymbols("RIFSPPFAAD90NB", src = "FRED", from = start_date, to = end_date)## [1] "RIFSPPFAAD90NB"Commercial_paper_rate_90days_start <-RIFSPPFAAD90NB[2, 1]
Commercial_paper_rate_90days_end <-RIFSPPFAAD90NB[103,1]
add_row("Commercial paper rate (90 days):", c(Commercial_paper_rate_90days_start, Commercial_paper_rate_90days_end))
add_row("Certificate of deposit rate (3-month):", c(4.91, 5.46))
# Extract the beginning and end rates
tbill_rate_start <- DTB3[1, 1]
tbill_rate_end <- DTB3[nrow(DTB3), 1]
add_row("treasury bill rate (13 weeks):", c(tbill_rate_start, tbill_rate_end))
getSymbols("DTB6", src = "FRED", from = start_date, to = end_date)## [1] "DTB6"# Extract the beginning and end rates
tbill6_rate_start <- DTB6[1, 1]
tbill6_rate_end <- DTB6[nrow(DTB6), 1]
add_row("Treasury bill rate (26 weeks):", c(tbill6_rate_start, tbill6_rate_end))
# Get the 10-year Treasury Bond Yield
getSymbols("DGS10", src = "FRED", from = start_date, to = end_date)## [1] "DGS10"# Extract the beginning and end rates
long_term_yield_start <- DGS10[1, 1]
long_term_yield_end <- DGS10[nrow(DGS10), 1]
add_row("Treasury long-term bond yield:", c(long_term_yield_start, long_term_yield_end))
#we will use a proxy for corporate (master) bond yield, the Moody's Seasoned Aaa Corporate Bond Yeild
# Get the Moody's Seasoned Aaa Corporate Bond Yield
getSymbols("AAA", src = "FRED", from = start_date, to = end_date)## [1] "AAA"# Extract the beginning and end rates
corp_bond_yield_start <- AAA[1, 1]
corp_bond_yield_end <- AAA[nrow(AAA), 1]
add_row("Corporate (Master) bond yield:", c(corp_bond_yield_start, corp_bond_yield_end))
getSymbols("BAMLH0A1HYBBEY", src = "FRED", from = start_date, to = end_date)## [1] "BAMLH0A1HYBBEY"hy_corp_bond_yield_start <- BAMLH0A1HYBBEY [1, 1]
hy_corp_bond_yield_end <- BAMLH0A1HYBBEY[nrow(BAMLH0A1HYBBEY), 1]
add_row("High-yield corporate bond yield:", c(hy_corp_bond_yield_start, hy_corp_bond_yield_end))
add_row("Tax-exempt (7–12-year) bond yield:", c(5.01, 4.63))
print(table_data)## Description BoT EoT
## 1 S&P 500 (stock) index level: 169.30 227.79
## 2 Nasdaq Composite (stock) index level: 15605.48 18119.59
## 3 Prime rate: 8.50 8.00
## 4 Federal funds rate: 5.33 5.13
## 5 Commercial paper rate (90 days): 5.37 4.64
## 6 Certificate of deposit rate (3-month): 4.91 5.46
## 7 treasury bill rate (13 weeks): 5.26 4.52
## 8 Treasury bill rate (26 weeks): 5.17 4.23
## 9 Treasury long-term bond yield: 4.63 3.81
## 10 Corporate (Master) bond yield: 5.25 4.68
## 11 High-yield corporate bond yield: 6.65 5.53
## 12 Tax-exempt (7–12-year) bond yield: 5.01 4.63L2 Financial markets microstructure
Download basic statistic of NASDAQ and London Stock Exchange and compare them
library(quantmod)
getSymbols("NDAQ", src = "yahoo")## [1] "NDAQ"getSymbols("^FTSE", src = "yahoo")## Warning: ^FTSE contains missing values. Some functions will not work if objects
## contain missing values in the middle of the series. Consider using na.omit(),
## na.approx(), na.fill(), etc to remove or replace them.## [1] "FTSE"FTSE<- na.approx(FTSE)
NDAQ <- subset(NDAQ, start = "2024-01-05", end = "2024-30-09")
FTSE <- subset(FTSE, start = "2008-01-05", end = "2024-30-09")
nasdaq_stats <- c(
Mean = mean(NDAQ$NDAQ.Close, na.rm=TRUE),
Median = median(NDAQ$NDAQ.Close, na.rm=TRUE),
StDev = sd(NDAQ$NDAQ.Close, na.rm= TRUE))
lond_stats <- c(
Mean = mean(FTSE$FTSE.Close),
Median = median(FTSE$FTSE.Close),
StDev = sd(FTSE$FTSE.Close))
aligned_data <- merge(NDAQ, FTSE)
cleaned_data <- na.omit(aligned_data)
correlation <- cor(cleaned_data[, 1], cleaned_data[, 7])
print(correlation)## FTSE.Open
## NDAQ.Open 0.7218757stats_comparison <- rbind(nasdaq_stats, lond_stats)
colnames(stats_comparison) <- c("Mean", "Median", "Standard Deviation" )
round(stats_comparison,2)## Mean Median Standard Deviation
## nasdaq_stats 26.55 19.57 20.06
## lond_stats 6545.90 6640.00 952.54print(round(correlation,2))## FTSE.Open
## NDAQ.Open 0.72We will now compare the London Stock Exchange index and the German DAX index
# Download historical data for NASDAQ and TechDAX
getSymbols("NDAQ", src = "yahoo")## [1] "NDAQ"getSymbols("DAX", src = "yahoo") # TechDAX is a component of the DAX index## [1] "DAX"# Fill in missing values with approximations
DAX <- na.approx(DAX)
# Trim data to a specific period
NDAQ <- subset(NDAQ, start = "2024-05-01", end = "2024-09-30")
DAX <- subset(DAX, start = "2024-05-01", end = "2024-09-30")
# Calculate basic statistics
nasdaq_stats <- c(
Mean = mean(NDAQ$NDAQ.Close, na.rm = TRUE),
Median = median(NDAQ$NDAQ.Close, na.rm = TRUE),
StDev = sd(NDAQ$NDAQ.Close, na.rm = TRUE)
)
dax_stats <- c(
Mean = mean(DAX$DAX.Close),
Median = median(DAX$DAX.Close),
StDev = sd(DAX$DAX.Close)
)
# Correlation
aligned_data <- merge(NDAQ, DAX)
cleaned_data <- na.omit(aligned_data)
correlation <- cor(cleaned_data[, 1], cleaned_data[, 2])
# Print statistics and correlation
stats_comparison <- rbind(nasdaq_stats, dax_stats)
colnames(stats_comparison) <- c("Mean", "Median", "Standard Deviation")
round(stats_comparison, 2)## Mean Median Standard Deviation
## nasdaq_stats 26.55 19.57 20.06
## dax_stats 28.13 28.03 3.40print(round(correlation, 2))## NDAQ.High
## NDAQ.Open 1# Visualize the comparison
library(ggplot2)
ggplot() +
geom_line(data = NDAQ, aes(x = index(NDAQ), y = NDAQ.Close), color = "blue") +
geom_line(data = DAX, aes(x = index(DAX), y = DAX.Close), color = "red") +
labs(title = "NASDAQ vs. DAX (TechDAX)", x = "Date", y = "Index Value") +
scale_color_manual(values = c("blue" = "NASDAQ", "red" = "DAX"))## Warning: No shared levels found between `names(values)` of the manual scale and the
## data's colour values.
L3 Instrument’s overview and valuation
L3.1 Compare the 13-week Treasury bill rate (which is a proxy for short-term interest rates) at the end of the school term to the rate that existed at the beginning of the school term. (note: 3-Month Treasury Bill Secondary Market Rate, Discount Basis (TB3MS)) https://fred.stlouisfed.org/series/TclB3MS
At the beginning of the school term the 13-week Treasury bill rate was 5.26 and at the end of the school term it was 4.52.
5.26-4.52## [1] 0.74That shows a decrease in the 13-week Treasury bill rate of 0.74.
L3.2 Why interest rates change over time.
REVISED ANSWER
Why did the interest rate change?
The changes may have occurred due to the monetary policy of the Federal Reserve.
1. In order to have control over the inflation rate, the federal reserve raises or lowers the interest rate depending on the inflation expectations. If inflation is high that means there is a lot of money on the market and people can afford to buy. As a result companies raise the prices of their products in order to make bigger profits. The faster the prices go up, the faster the real value of $1 falls. That process can be continuous as long as the amount of money on the market does not decrease.
2. Let’s analyze why there could be a lot of money on the market - that happens when individuals and companies are able to take credits easily. That happens when the interest rates of the credit are low, because in such a situation we say that the credit is cheap (we do not have to give back a lot of money for borrowing it). The interest rate of credits depends on a couple of components but one important component is the interest rate of the Federal Reserve. Why? Because - It is the rate at which the Federal Reserve gives credits to banks. As a result banks will give people and companies credits with an interest rate adding a surplus to it in order to make profit. Knowing that, we can assume that the higher the interest rate of the Federal reserve the higher will the interest rate of a bank credit be.
3. As we said before the higher the interest rate of a credit is the more expensive it is to take it, so the higher the interest rate is the less people and companies will take credit. This way the amount of money on the market changes and the inflation rate is controlled. That is why the interest rate may change.
4. Demand and supply for credit - when there are more units that would like to take credit the demand for credit increases. In that situation there is a risk of the repetition of the case presented in point 2. (the rise of the amount of money on the market). Those units are not only individuals or companies, they can also be governments that want to cover their deficit in the budget. Usually the higher the demand for credit is the more likely it is for the interest rate to go up.
5. Liquidity on the market - what does it mean? Liquidity is the ability to quickly change an asset into cash. The liquidity level depends on the amount of spended and invested money and the number of transactions that took place at a settled price. The more people have money the more likely it is for them to provide such transactions since they can afford it. When the interest rate rises the less credits are given and the less people can afford to buy so the market liquidity lowers. The interest rate is a way to control market liquidity.
6. International capital flows - when the interest rate of a country is higher than others’, investors from other countries may be attracted to invest in the country with a higher interest rate in order to make more money on investments (for example on more favorable bonds). That happens because when the central bank raises the interest rate the result is that the interest rate on bonds also rises so people who buy new bonds will make a better profit on them. Those are some of the possible reasons for the interest rate to change.
L4 Efficiency of market and information
Check if on 26 October 2017 coca cola shares were hit by the advarse information realized on the market. (assume 26 is the information release date)
To provide analysis of the Coca-Cola shares situation on the 26th of October 2017 we will first see the stock price over time to have a base on which we could assume what could happen on the 26th of October 2017.
library(quantmod)
library(ggplot2)
# Specify the date range for October 2017
start_date <- "2017-10-15"
end_date <- "2017-11-15"
# Get the stock data for Coca-Cola
getSymbols("KO", src = "yahoo", from = start_date, to = end_date)## [1] "KO"# Create a data frame with Date and Closing Price
KO_df <- data.frame(Date = index(KO), Price = Cl(KO))
# Create the line plot
ggplot(KO_df, aes(x = Date, y = Cl(KO))) +
geom_line() +
labs(x = "Date", y = "Stock Price", title = "Coca-Cola Stock Price (October- November 2017)") +
theme_classic()## Don't know how to automatically pick scale for object of type <xts/zoo>.
## Defaulting to continuous.
library(quantmod)
library(ggplot2)
# Specify the date range for October 2017
start_date <- "2017-04-15"
end_date <- "2017-11-15"
# Get the stock data for Coca-Cola
getSymbols("KO", src = "yahoo", from = start_date, to = end_date)## [1] "KO"# Create a data frame with Date and Closing Price
KO_df <- data.frame(Date = index(KO), Price = Cl(KO))
# Create the line plot
ggplot(KO_df, aes(x = Date, y = Cl(KO))) +
geom_line() +
labs(x = "Date", y = "Stock Price", title = "Coca-Cola Stock Price (May-December 2017)") +
theme_classic()## Don't know how to automatically pick scale for object of type <xts/zoo>.
## Defaulting to continuous.
library(quantmod)
library(ggplot2)
# Specify the date range
start_date <- "2017-10-22"
end_date <- "2017-10-30"
# Get the stock data for Coca-Cola
getSymbols("KO", src = "yahoo", from = start_date, to = end_date)## [1] "KO"# Create a data frame with Date and Closing Price
KO_df <- data.frame(Date = index(KO), Price = Cl(KO))
# Create the line plot
ggplot(KO_df, aes(x = Date, y = Cl(KO))) +
geom_line() +
labs(x = "Date", y = "Stock Price", title = "Coca-Cola Stock Price (22-30 Oct 2017)") +
theme_classic()## Don't know how to automatically pick scale for object of type <xts/zoo>.
## Defaulting to continuous.
FIRST ANSWER
On October 26 2017 Coca-Cola released its third-quarter earnings for 2017. As we analize the stock price of coca cola company in time we observe that in the period of a month before the 26th of october there is a downtrend but on the 26th of october the price increased for one day and then continued dropping intill the begining of November where it started going up again. The explanation could be that the information comming from the quarterly report influenced a better informed part of the market immidiately on the 26th of october and the rest of the market later in the begining of November.
REVISED ANSWER
What important information do we have about the 26th of October 2017? On that day Coca-Cola released its third-quarter earnings for 2017. As we analyze the stock price of Coca-Cola company in time we observe that in the period of a month before the 26th of october there is a downtrend, which means that more investors sold coca cola shares then bought them, but on the 26th of october the price increased for one day. Then the price continued dropping until the beginning of November where it started going up again. At the time the quarterly report was released we observed an increase of the stock price of Coca-Cola for one day. The explanation for those moves could be that the information coming from the quarterly report influenced a better informed part of the market immediately on the 26th of October which could lead them to buy shares of Coca-Cola then but the rest of the market got to this information later in the beginning of November and started buying those shares only then, which influenced the Coca-Cola share price. There is no reason for thinking that Coca Cola shares were hit by some adverse information.
L5 Financial statements and fundamental analysis
Download to R the financial statements of Microsoft 2018, show the code
Commercial bank operations
For the commercial bank that you selected at the beginning of the term, use its annual report or any other related information to answer the following questions:
For our exercise we chose the Bank of America and took the data from it’s annual report which is available under this link:
https://www.sec.gov/ix?doc=/Archives/edgar/data/70858/000007085824000122/bac-20231231.htm
(in order to open the page you will need to copy the link and paste it in a new web page)
5.1 Identify the types of deposits that the commercial bank uses to obtain most of its funds.
Bank of America raises the majority of its funds through the following types of deposits:
- Demand deposits: checking accounts that allow customers to access their money at any time.
- Time deposits: Time deposit accounts in which customers invest their money for a specific period of time.
- Savings deposits: Savings accounts that are intended for saving and offer higher interest rates.
L5.2 Identify the main uses of funds by the bank. c. Summarize any statements made by the commercial bank in its annual report about how recent or potential regulations will affect its performance.
FIRST ANSWER
The primary uses of Bank of America’s funds include:
- Lending: providing loans to individuals and businesses. - Investment banking: providing corporate finance and capital markets transaction services.
- Asset management: managing assets for private clients and institutions.
Impact of regulations In its annual report, Bank of America emphasises that current and potential regulatory requirements can affect its performance. In particular, reference is made to capital requirements and liquidity requirements, which could restrict the ability to grant loans.
REVISED ANSWER
The primary uses of Bank of America’s funds include:
- Lending: providing loans to individuals and businesses.
- Investment banking: providing corporate finance and capital markets transaction services.
- Asset management: managing assets for private clients and institutions.
Impact of regulations
In its annual report, Bank of America gives us information that current and potential regulatory requirements can affect its performance. In particular, reference is made to capital requirements and liquidity requirements, which could make it harder to grant loans, which are a significant part of the bank’s profit. That means that the bank may have to meet some targets that are more difficult to achieve in order to be able to lend money.
Bank of America is a big bank that helps people and businesses by giving them loans. In their annual report, which is a yearly update about how they’re doing, the bank informs about the rules set by the government. These rules are important because they can affect how well the bank can operate.
Regulatory Requirements: These are the rules that the government makes for banks to follow. They are there to make sure banks are safe and responsible with money.
Capital Requirements: This means the bank has to keep a certain amount of money saved up, like a safety net. This money helps protect the bank and its customers if something goes wrong (for example some borrower is not able to give back the money he got in a credit).
Liquidity Requirements: This means the bank needs to have enough cash available to give to people when they ask for it. It’s like having enough money in your piggy bank to buy something when you want it.
If these rules are very strict, it might limit how much money the bank can lend out to people who need loans. So, if the rules say the bank has to keep more money saved up or have more cash on hand, it might not have as much left over to give out loans. This can affect how well the bank does in helping people borrow money.
L5.3 Does it appear that the bank is attempting to enter the securities industry by offering securities services? If so, explain how.
FIRST ANSWER
Yes, it appears that Bank of America is attempting to enter the securities industry. This is being done by: - Offering securities services: The bank offers trading services for stocks and bonds and has a strong investment banking segment that focuses on capital market transactions.
REVISED ANSWER
Bank of America is trying to get involved in the securities industry by doing a couple of things:
Offering Securities Services: The bank provides services that allow people to buy and sell stocks and bonds, which are types of investments. This means they help clients trade these financial products.
Strong Investment Banking Segment: Bank of America has a solid part of its business focused on investment banking, which means they work on big financial deals and help companies raise money in the capital markets. This includes things like helping companies issue new stocks or bonds.
In summary, Bank of America is expanding its role in the securities industry by offering trading services and focusing on important financial transactions.
L5.4 Does it appear that the bank is attempting to enter the insurance industry by offering insurance services? If so, explain how.
FIRST ANSWER
Yes, there are signs that Bank of America is entering the insurance sector. This is evidenced by:
- Offering insurance products: The bank offers various insurance services to provide comprehensive financial solutions to its customers.
REVISED ANSWER
In the annual report the Bank of America provides information on every sector of its activity (pages 34-43). There is a section called the Global Wealth & Investment Management in which it is said that the Bank of America provides various insurance options, including life and disability insurance, which are part of the benefits offered to employees. Additionally, through its Merrill Wealth Management division, the bank offers life insurance, annuities, and long-term care solutions as part of its wealth management services, indicating a comprehensive approach to financial planning that includes insurance products.
Commercial bank management
L5.5 Assess the bank’s balance sheet as well as any comments in its annual report about the gap between its rate-sensitive assets and its rate-sensitive liabilities. Does it appear that the bank has a positive gap or a negative gap?
The answer to this question may be given after analyzing the Bank’s annual report. Unfortunately in the annual report the bank does not provide any information about its rate-sensitive gap between assets and liabilities.
L5.6 Determine the bank’s interest income as a percentage of its total assets.
REVISED ANSWER
Calculating the interest income percentage is used to get the information on how much money the bank gains on the assets it borrows compared to the total assets it has. It is calculated by dividing the total interest income by the total assets. We get the information about the amounts of the interest income and the total assets from the annual report (page 26 & page 90).
In the case of the Bank of America the calculation would look like this:
(page 90) Interest Income: $130,262 mln
(page 26) Total assets: $3,153,513 mln
Interest Income Percentage = (130,262 / 3,153,513) x 100%=
130262 / 3153513## [1] 0.04130695= 4.13%
An interest result of 4.13% shows that the bank generates 4.13 cents in interest for every dollar of assets. Is that a good result? The average for banks varies between 3-5%, so we can assume this result is in this margin.
In general, the Interest Income percentage provides information on how profitably a bank utilizes its assets. A higher percentage indicates a strong ability to generate income from interest, while a lower value could indicate possible inefficiencies or challenges in lending. In a dynamic market environment, it is crucial to consider this ratio in the context of other financial indicators.
L5.7 Determine the bank’s interest expenses as a percentage of its total assets.
FIRST ANSWER
Interest expenses:
For the year ending December 31, 2023, Bank of America reported interest expenses of $98,581 million
Total Assets: As of December 31, 2023, the total assets for Bank of America were reported as $3,180,151 million
We can now divide the total interest income by the total assets to get a percentage rate:
98581/3180151 ## [1] 0.03099884The bank’s interest expenses were 3,10% of the total assets of the Bank of America
REVISED ANSWER
The interest expenses may inform us how much a society spends money due to borrowed funds - that means if a company issues bonds, it will have to pay the amount of money that the bond represented plus the additional amount of money which is a reward for the borrower - it could differ depending on the rate of the bond and the duration, also it could depend on whether it would be a fixed-rate bond or a floating-rate bond but those are details. In the case of banks the interest expenses often refer mostly to the interest of the deposits as the deposits have a certain rate.
To calculate the interest expenses as a percentage of the bank’s total assets we take the information from the annual report from the consolidated statement of income in which this information is provided (page 90).
The interest expenses for the year 2023 in the Bank of America: $73,331 mln
Interest expenses percentage: (73,331/3,153,513) x 100% =
73331/3153513## [1] 0.02325375= 2.33%
An expenses result of 2.33% shows that the bank loses 2.33 cents in interest for every dollar of assets. Is that a good result? The average for banks varies between 1-2%, so we can assume this result is a little bit worse than the average.
L5.8 Determine the bank’s net interest margin.
FIRST ANSWER
Determine the bank’s net interest margin. NIM = 2.07% (P. 84 / P. 86)
REVISED ANSWER
The information about the net interest margin tells us about the profitability of its activity. That means that it is information on how well the bank uses its assets to generate income. To calculate it we subtract the interest expenses from the interest income.
For the year 2023 the net interest margin was.
NIM = 4.13%-2.33%
4.13-2.33 ## [1] 1.8= 1.8%
This indicator shows us that in the final analysis the Bank of America generates 1.8 cents for every dollar of assets. That means that in this sector the bank is profitable.
L5.9 Determine the bank’s noninterest income as a percentage of its total assets. Determine the bank’s noninterest expenses (do not include the addition to loan loss reserves here) as a percentage of its total assets.
FIRST ANSWER
The noninterest income: For the year ending December 31, 2023, Bank of America reported a noninterest income of $41,650 million Now we will divide this by the total assets to get a percentage rate
41650/3180151 ## [1] 0.01309686The bank’s noninterest income rate was 1,31% of the total assets
Non Interest expenses percentage = 2.09% (P.81)
REVISED ANSWER
The non interest income is the amount of money a bank generates from noninterest services it provides. It may be charged for account maintenance, annual membership fees, wealth management, tax planning services and many other activities. The information about the noninterest income is directly presented in the annual report.
The non interest expenses are the amount of money a bank loses on non interest costs. Examples of such expenses are salaries and bonuses for employees, training and development expenses, rent or lease payments for bank branches and office spaces and many others. The information about the noninterest expenses is directly presented in the annual report.
To calculate the noninterest income and expenses as a percentage of the bank’s total assets we take the information from the annual report from the Selected Annual Financial Data in which this information is provided (page 30).
The noninterest income for the year 2023 in the Bank of America: $41,650 mln
Interest expenses percentage: (41,650/3,153,513)x100%=
41650/3153513## [1] 0.01320749=1.32%
Non Interest income percentage = 1.32 %
We can do exactly the same operation with the non interest expenses.
The noninterest expenses for the year 2023 in the Bank of America: $65,845 mln
Non interest expenses percentage: (65,845/3,153,513)x100%=
65845/3153513## [1] 0.02087989=2.09%
Non Interest expenses percentage = 2.09%
L5.10 Determine the bank’s addition to loan loss reserves as a percentage of its total assets.
FIRST ANSWER
For the year ending December 31, 2023, Bank of America reported a loan loss reserve of $13,287 million We will now divide it by the amount of total assets to get a percentage rate
13287/3180151## [1] 0.004178103The loans and loss reserve rate was 0,42% of the total assets
REVISED ANSWER
Loan loss reserves are funds that banks set aside to cover potential losses from loans that may not be repaid (also called the provision for credit losses). The addition to loan loss reserves is the amount of money the bank decides to add to the previous loan loss reserve. To calculate the addition to loan loss reserves as a percentage of the bank’s total assets we will first calculate the addition to loan loss reserves by subtracting the previous years Provision for Credit Losses from the actual years Provision for Credit Losses. We can find the information about the Provision for Credit Losses in the annual report on page 93.
Bank’s allowance for loan and lease losses in year 2023: $13,342 mln
Bank’s allowance for loan and lease losses in year 2022: $12,662 mln
Addition to loan loss reserves calculation:
13,342 - 12,662 =
13342 - 12662 ## [1] 680= 680
As we know that the addition to loan loss reserves is $680 mln we can now determine it as a percentage of the total of the bank’s assets.
Calculation of the bank’s addition to loan loss reserves as a percentage of its total assets:
660/3,153,513 =
660/3153513## [1] 0.0002092904= 0,0209%
L5.11 Determine the bank’s return on assets.
FIRST ANSWER
To find out about the return on assets we should find out about the total income of the bank and then divide it by the value of total assets. For the year ending December 31, 2023, Bank of America reported a net income of $26,515 million We will now divide this value by the total assets to get a percentage rate
26515/3180151## [1] 0.008337654The Bank of America’s return on assets was 0,83% of the total assets
RIVISED ANSWER
Calculating the return on assets measures how effectively a bank generates profit from its total assets. In order to calculate it we need information about the net income and the information about the amount of the total assets since the formula for the return on assets is: ROA = net income/total assets. The information is given to us in the annual report on page 30 as the “return on average assets”. We see in the selected annual financial data section that the percentage is 0.84%.
If we would like to double check this information we could calculate it by ourselves
We will find the information about the net income in the annual report on page 30.
Net income for the year 2023: $26,515 mln
Calculation:
26,515/3,153,513=
26515/3153513## [1] 0.008408083= 0,84 %
The average result in the banking sector varies between 1.2% and 1.4% so we can assume that this result is below average.
L5.12 Determine the bank’s return on equity.
FIRST ANSWER
To find out about the return on assets we should find out about the total income of the bank and then divide it by the value of total shareholders equity. As we already have the value of the net income we will now find the data about the total shareholders equity.
For the year ending December 31, 2023, Bank of America reported a total shareholders equity of $291,646 million.
We will now divide the net income by the total shareholders equity.
26515/291646## [1] 0.09091501The Bank of America’s return on equity rate was 9,09%.
REVISED ANSWER
Calculating the return on equity measures how effectively a bank generates profit from the equity invested by its shareholders. In order to calculate it we need information about the net income and the information about the amount of the average shareholders equity since the formula for the return on assets is: ROE = net income/Average shareholders equity.
The information is given to us in the annual report on page 30 as the “return on average shareholders equity”. We see in the selected annual financial data section that the percentage is 9.75 %. However that information takes in account the dividends payed to shareholders
If we would like to check the result without taking in account the dividends we could calculate it by ourselves
Net income for the year 2023: $26,515 mln
Common shareholders equity for the year 2023: $291,646 mln
Calculation:
26,515/291,646=
26515/291646## [1] 0.09091501=9,09%
The average result in the banking sector varies between 8% and 15% so we can assume that this result is in the average.
L5.13 Identify the bank’s income statement items described previously that would be affected if interest rates rise in the next year, and explain how they would be affected.
FIRST ANSWER
Income Statement Items Affected
- net interest income (interest income):
- 2023: $56,931 million
- Impact: An increase in interest rates will increase interest income as the bank benefits from higher income from variable rate loans and new loans. Interest expenses could also increase, but as net interest income is higher than interest expenses, overall net interest income is expected to grow.
- provision for credit losses (loan loss provisions):
- 2023: USD 4.394 million
- Impact: Higher interest rates could increase the risk of default as borrowers may have difficulty servicing their debts. This could lead to higher loan loss provisions.
- non-interest income (non-interest income):
- 2023: USD 41.650 million
- Impact: Fee income could increase as clients increasingly seek financial products to deal with rising interest rates. At the same time, market volatility could negatively impact trading profits.
Summary of the impact
An increase in interest rates would likely lead to an increase in net interest income as interest income exceeds interest expenses. At the same time, the commission for credit losses could increase, which affects the default risk for borrowers. Non-interest income could be affected both positively and negatively, depending on developments in fee income and trading profits. Overall, the bank could benefit from the interest rate increases as long as the income outweighs the risk of credit losses.
This analysis provides a specific overview of the potential financial impact on Bank of America in the context of rising interest rates.
L5.14 Identify the bank’s income statement items described previously that would be affected if U.S. economic conditions deteriorate, and explain how they would be affected
FIRST ANSWER
Income Statement Items Affected
Net interest income: In a situation of crisis the net interest income might register a drop. Usually when the economic conditions deteriorate, individuals and businesses are less likely to take credits because the bank has no guarantee they will be able to pay them back. As a result the demand falls and the interest income becomes lower.There might also be a reaction of the Federal Reserve which could lower the rate which would be a reason for a lower interest income from existing loans.
Provision for Loan Losses: During an economic condition deterioration bank’s might anticipate a higher default rate on credits. That might result in an increase of the provision for loan losses since the expected defaulted loans rate rises, so to cover the potential losses the bank could put more funds into this item.
Non-interest income: During an economic condition deterioration bank’s might experience a drop of fee-generating activities such as asset management or investment banking. That could lead to a decrease of the non-interest income.
Net interest margin: During an economic condition deterioration bank’s might lower the interest rate to stimulate borrowing, that would lead to a drop in the difference between the interest of loans and the interest of deposits which would lead to a drop of the net interest margin.
Net income: As we take the situation of all the items we analyzed above we see that as the net interest income could drop the provision on loan losses could rise and the net interest margin could drop the situation of the net income could also be a decrease in overall.
Mutual funds
For the mutual fund that you selected at the beginning of the term, use its prospectus or any other related information to answer the following questions.
Blackrock treasury Fund - Capital: BCYXX
https://www.blackrock.com/cash/literature/annual-financial-statements/afs-retail-cash-funds-en.pdf
L5.15 What is the investment objective of this mutual fund? Do you consider this mutual fund to have low risk, moderate risk, or high risk?
FIRST ANSWER
We can read about the investment objective of the fund on its official website.
https://www.blackrock.com/cash/en-us/products/282876/blackrock-cash-funds-treasury-fund-capital
The fund’s objective is to invest at least 99.5% of its total assets in cash, U.S. Treasury bills, notes and other direct obligations of the U.S Treasury, and repurchase agreements secured by such obligations or cash. The Fund invests in securities maturing in 397 days or less (with certain exceptions) and the portfolio will have a dollar-weighted average maturity of 60 days or less and a dollar-weighted average life of 120 days or less. In addition, the Fund may invest in variable and floating rate instruments and transact in securities on a when-issued, delayed delivery or forward commitment basis.
We consider this mutual fund to have a low risk since it invests mostly in low risk instruments such as treasury bills, cash equivalents or securities.
L5.16 What was the return on the mutual fund last year? What was the average annual return over the last three years?
FIRST ANSWER
The return of the mutual fund for last year was 5.08% The average annual return over the last three years was 2.22%
REVISED ANSWER
The information about the total return of the mutual fund can be found in its annual financial statement on page 12.
The return of the mutual fund for year 2023 was 5.05%
The average return for funds from the same varies between 1.05% to 4.10% so we can assume that the performance of the fund for the year 2023 was very good in comparison to the average.
The average annual return over the last three years was 2,21% which is within the average for this type of funds.
L5.17 What is a key economic factor that influences the return on this mutual fund? (That is, are the fund’s returns highly influenced by U.S. stock market conditions? By U.S. interest rates? By foreign stock market conditions? By foreign interest rates?)
FIRST ANSWER
As the fund invests most of its assets in treasury bills and obligations it will be mostly affected by the U.S. interest rates.
REVISED ANSWER
As the fund invests most of its assets in treasury bills and obligations it will not be highly influenced by the U.S. stock market conditions. It will be mostly affected by the U.S. interest rates. The foreign stock market should neither be a strongly influencing factor. Foreign interest rates may have a small impact on the funds return since the foreign interest rates may influence the federal interest rate, and the federal interest rates have a major impact on the funds return.
L5.18 Must any fees be paid when buying or selling this mutual fund?
FIRST ANSWER
When buying we pay 0.10% of a management fee and 0.07% of an administration fee, as a sum we pay a 0.17% fee.
REVISED ANSWER
The fund offers a non fee distribution and service system.
L5.19 What was the expense ratio for this mutual fund over the last year? Does this ratio seem high to you?
FIRST ANSWER
The expense ratio for this mutual fund over the last year was 0.02%. This amount seems quite low in comparison with other funds that sometimes have an expense ratio of over 1%. This level of expense ratio gives a possibility to transfer more of the interest to the investors.
REVISED ANSWER
The information about expenses ratio can be found on the page 11 of the annual report. The expense ratio for this mutual fund over the last year was 0.09%. This amount seems quite low considering the comparison with other funds that sometimes have an expense ratio of over 1%. This level of expense ratio gives a possibility to gain more interest for the investors.
Securities firms
For the securities firm that you selected at the beginning of the term, use its annual report or any other related information to answer the following questions.
L5.20 What are the main types of business conducted by the securities firm?
The corporate purpose of Prosegur Cash is to provide the following services through companies focusing on the Cash business:
national and international transport services (by land, sea and air) of funds and other valuables (including jewellery, artworks, precious metals, electronic devices, voting ballots, legal evidence), including collection, transport, custody and deposit services;
processing and automation of cash (including counting, processing and packaging, as well as coin recycling, cash flow control and monitoring systems);
comprehensive ATM solutions (including planning, loading, monitoring, first- and second-tier maintenance and balancing);
cash planning and forecasting for financial institutions;
Cash-Today (including self-service cash machines, cash deposits, recycling and bank notes and coin dispensing services), and cryptocurrency custody services;
added-value services in several countries (AVOS) for banks (including outsourcing of tellers, multi-agency services, cheque processing and related administrative services among others) and
- Correspondent banking activities (collection and payment management and payment of invoices, among others)
Foreign exchange currency services (also includes international payment services, online foreign money, home delivery services for travel money and local cash)
L5.21 Summarize any statements made by the securities firm in its annual report about how it may be affected by existing or potential regulations.
Prosegur acknowledges that the sector in which it provides its services is highly regulated. The firm however sees the need to adapt to those regulations and takes action in introducing changes the regulations address. The reports indicate that the change in regulations affect the business especially in the data protection sector, however it provided important steps to introduce changes in its operational practices. This process may lead to a rise in operational costs since it may need introducing some new technologies and training of the staff. The regulations may however have a positive effect on the business in the domains of cybersecurity and risk management since the changes in regulations may affect the demand on such services provided by this firm.
L5.22 Describe the recent performance of the securities firm, and explain why the performance has been favorable or unfavorable.
Sales in 2023 compared to the year 2022 -21 802 000 €
Post tax profit of ongoing operations in 2023 compared to the year 2022 - 95 488 000 €
EBITDA in 2023 compared to year 2022 - 36 220 000€
The data shows a significant difference between the performance of the firm in the year 2022 and the year 2023. This may have been caused by multiple aspects. First of all, the year 2022 was a very good year in the history of Prosegur and the firm registered some significant profits and a big growth in assets, which could be difficult to outperform. The second aspect could be a difference in demand on the market which could be the reason for the difference in sales and the EBITDA. The firm also has registered an important difference in the post tax profit of ongoing operations which could be caused by a different cost management policy.
L6 Equity
L7 Fixed income
Comparing yields among securities
L7.1 What is the difference between the yield on corporate high-quality bonds and the yield on Treasury bonds at the end of the school term? Explain why the difference exists?
FIRST ANSWER
This difference between the yields is called the credit spread and exists due to the following factors:
1. credit risk a. Corporate high-quality bonds have a higher risk of default compared to Treasury bonds. Therefore, investors demand a higher yield to compensate for this risk
2. liquidity risk a. Corporate high-quality bonds are often less liquid than Treasury bonds. A quick sale at a fair market price is therefore much more difficult than with Treasury bonds.
3. market conditions a. Changes in the economic situation or monetary policy have a different effect on the respective bond.
REVISED ANSWER
The yield on corporate high-quality bonds a the end of the school term was at a level of 4.68%
The yield on Treasury bonds at the end of the school term was at the level of 3.81%
4.68-3.81## [1] 0.87We see a difference of 0.87% between those yields.This difference between the yields is called the “credit spread” and exists due to the following factors:
1. credit risk
- High-quality corporate bonds have a higher risk of default compared to government bonds because government bonds are backed by government money, so there is no chance of bankruptcy. As a result, investors demand a higher yield to compensate for the bankruptcy risk of the corporation issuing the bond.
2. liquidity risk
- Corporate high-quality bonds are often less liquid than Treasury bonds which means they are less likely to be sold. A quick sale at a fair market price is therefore much more difficult than with Treasury bonds.
3. market conditions
- Changes in the economic situation or monetary policy have a different effect on the respective bond.
L7.2 What is the difference between the yield on long-term Treasury bonds and the yield on long-term municipal bonds at the end of the school term? Explain why the difference exists?
FIRST ANSWER
Long-term treasury bonds are 3.81% while long-term municipal bonds yields are between 5% and 6% after counting for their tax-exempt status for investors in higher tax brackets. That means that after taking in consideration the tax implications the municipal bonds offer a higher yield than treasury bonds. The interest from municipal bonds is exempt from federal income tax and also from state taxes if the investor resides in the issuing state. This puts the municipal bonds in a favorable position compared to the treasury bonds which are taxable. There is a difference in risk between the treasury bonds and the municipal bonds since the treasury bonds are considered to be risk-free while the municipal bonds carry some type of credit risk depending on the financial condition of the issuing municipality.
Assessing the forecasting ability of the yield curve
L7.3 What was the difference between the 26-week T-bill yield and the 13-week T-bill yield at the beginning of the school term?
REVISED ANSWER
At the beginning of the school term, the yield of the 13-week T-bill was 5.26% while the 26-week T-bill was 5.17% which is a phenomenon contrary to the usual trend. Usually when a bond has a longer period to maturity it will offer higher yields since there is a higher risk that the person which invests the money in the bond would need it sooner than the bond arrives to maturity. Of course there are many other factors that play a role in setting the yield of bonds such as interest rate changes, economic conditions change and many others, so such situations may take place.
L7.4 Does this imply that the yield curve had an upward or downward slope at that time?
REVISED ANSWER
This information implies that the yield curve had a downward slope at that time. This means that the short-term bonds had a higher yield than the long-term bonds.
L7.5 Assuming that this slope can be primarily attributed to expectations theory, did the direction of the slope indicate that the market expected higher or lower interest rates in the future?
REVISED ANSWER
Such situations occur usually when the interest rates are expected to be lower in the future. When investors anticipate lower interest rates, they may prefer to lock in higher yields from long-term bonds. that increases the demand for these securities which in consequence drives up their prices and lowers their yields.
L7.6 Did interest rates move in that direction over the school term?
REVISED ANSWER
Yes the interest rates lowered. The interest rates were stable during the school term, they only changed in the last month from 5.5% to 5.0%.
Explaining shifts in the yield curve over time
L7.7 What was the difference between the long-term Treasury bond yield and the 13-week T-bill yield at the beginning of the school term?
FIRST ANSWER
On May 1st, 2024, the yield for the 30-year Treasury bond was 4.57% Meanwhile, the yield for the 13-week T-bill was 3.81% Difference between those bonds is 4.57 - 3.81 = 0.76% The difference between those two bonds would usually be caused by the risk differences where the risk of the 30-year U.S. treasury bond is higher than the 13-week treasury bill. In such a case the yield of the 30-year treasury bond should be higher to compensate for the risk. Another reason for this difference is the expectation that the interest rate could change in time so investors would prefer to have their money held for a shorter period of time in order not to be locked in their investments.
REVISED ANSWER
On May 1st, 2024, the yield for the long-term Treasury bond was 4.63%
Meanwhile, the yield for the 13-week T-bill was 5.26%
Difference between those bonds is 4.63 - 5.26 = -0.63%
The difference between those two bonds would usually be caused by the risk differences where the risk of the 30-year U.S. treasury bond is higher than the 13-week treasury bill. In such a case the yield of the 30-year treasury bond should be higher to compensate for the risk. In this case however the situation is reversed. The reason is the same as explained in L7.5.
L7.8 What is the difference between the long-term Treasury bond yield and the 13-week T-bill yield at the end of the school term?
FIRST ANSWER
On September 30, 2024, the long-term Treasury bond yield (10-year Treasury rate) was 4.41%. Meanwhile, the 13-week T-bill yield was 3.81%. The difference between these two yields is 0.60% (4.41% - 3.81%)
REVISED ANSWER
On September 30, 2024, the long-term Treasury bond yield was 3.81%.
Meanwhile, the 13-week T-bill yield was 4.52%. The difference between these two yields is -0.71% (3.81% - 4.52%)
L7.9 Given your answers to the two previous questions, describe how the yield curve changed over the school term. Explain the changes in expectations about future interest rates that are implied by the shift in the yield curve over the school term.
FIRST ANSWER
The differences between the yields in the beginning of the school term was 0.76% and at the end of the school term was 0.60%. Over the school term, the yield curve experienced a flattening. That shows that the expectations about the interest rates are that it will drop.
REVISED ANSWER
The differences between the yields in the beginning of the school term was -0.63% and at the end of the school term was -0.71%. Over the school term, the yield curve experienced a steepening. That means that during the school term expectations about the future interest rate changed - at the beginning of the school term investors were less keen on thinking that the interest rates will fall than at the end of the school term.
The Fed’s influence on interest rates
L7.10 Did the Fed change the federal funds rate over the school term?
REVISED ANSWER
The Fed changed the federal funds rate over the school term - at the beginning of the school term the 30-day average rate was 5.33% and at the end of the school term it was 5.13%.
L7.11 Do you think the movements in interest rates over the school term were caused by the Fed’s monetary policy? Explain.
Yes, the movements in the interest rates over the school term were caused by the Fed’s monetary policy. The goals of the Fed’s monetary policy are to keep stable prices and obtain maximum employment. In order to achieve those goals the Fed has instruments it can use such as the influence on the interest rates which it can raise or lower. In this case the Fed lowered the rates.
L7.12 What is the difference between the yield on 90-day commercial paper and the yield on 13-week T-bills at the end of the school term? Explain why this premium exists.
REVISED ANSWER
The yield on 90-day commercial paper at the end of the school term was 4.64% and the yield on 13-week treasury bills was 4.52%. This represents a premium of 0.12%.
This difference exists because of the difference in risk of these two instruments. A treasury bill is backed by the U.S. government and the commercial paper is issued by corporations. The surplus is there to compensate for the credit risk that the buyer takes by purchasing a 90-day commercial paper.
L7.13 Compare the premium on the 90-day commercial paper yield (relative to the 13-week T-bill yield) that exists at the end of the school term to the premium that existed at the beginning of the term. Explain why the premium may have changed over the school term.
REVISED ANSWER
The 90-day commercial paper interest rate at the beginning of the school term was 5.37% and the 13-week T-bill rate was 5,26% which gives us a premium of 0.11%. This result is very similar to the result at the beginning of the school term however it raised by 0.01%. There are multiple reasons for it to happen.
- The yields on both commercial paper and T-bills may have decreased overall due to changes in monetary policy or market conditions, but if commercial paper yields decreased at a slower rate than T-bill yields, this could result in a higher relative premium.
- If investors perceive an increase in credit risk associated with corporate borrowers during the term, they might demand a slightly higher yield on commercial paper compared to T-bills, which are considered risk-free.
Explaining bond premiums and price movements
L7.14 What is the difference between the yield on high-yield corporate bonds at the end of the school term versus the yield on high-quality corporate bonds at the beginning of the school term?
The yield to the high-yield corporate bonds at the end of the school term is 5,53% and the yield on high-quality corporate bonds at the beginning of the school term is 5.25%.
The difference is 5,53% - 5,25% =
5.53 - 5.25## [1] 0.28= 0,28%
However this comparison takes into consideration two different periods of time so it should not be interpreted the same way as two values at the same period.
L7.15 Compare the long-term Treasury bond yield at the end of the school term to the longterm Treasury bond yield that existed at the beginning of the school term. Given the direction of this change, did prices of long-term bonds rise or fall over the school term?
REVISED ANSWER
The long term Treasury bond yield (30 year) at the beginning of the school term represented 4,63%, while at the end of the school term it was 3,81%.
4.63-3.81## [1] 0.82There is a difference of 0,82% between those values.
L7.16 Compare the change in the yields of Treasury, municipal, and corporate bonds over the school term. Did the yields of all three types of securities move in the same direction and by about the same degree? Explain why yields of different types of bonds move together.
REVISED ANSWER
In order to do this comparison we will need to find the values of every type of bonds
Change in treasury bonds over school term: 4,63% - 3,81% =
4.63-3.81## [1] 0.82= 0,82%
Change in municipal bonds over school term: 5,01% - 4,63% =
5.01-4.63## [1] 0.38= 0,38%
Change in AAA corporate bonds over the school term: 5,25% - 4,68% =
5.25-4.68## [1] 0.57= 0,57%
As we can see every type of bond moved in the same direction and almost the same amount. The explanation for this type of event on the market could be an increase in demand for bonds during this specific period of time on the market. As it was said before, the yield of bonds is directly related to the interest rate and expectations towards its changes. At the end of the school term the interest rate decreased by 0,50%. When the interest rates decrease it means that new bonds that will be issued also will have a lower yield, so investors are more interested in buying the bonds that already are on the market. Since the yield of the bonds we took into consideration decreased by around 0,38%-0,60% it would mean that the demand for those bonds is higher - when the demand for the bonds is higher the reward for buying the bond can be smaller so in consequence the yield falls (as we observed). The yield on treasury bonds has fallen slightly more than the municipal and corporate bonds - that could indicate that the demand rose the most in this area. The long-term treasury bonds are considered to be the most risk-free investment so we see that investors chose a safe investment path. The reason for the decreasing of the yields could also be that the inflation rate in the U.S. has fallen in the school term from 3,3% in may to 2,4% in september*. Investors seeing that the value of money rises are more interested in getting returns coming from bonds. It may also be a signal for investors about the anticipated future changes in the interest rates (if inflation is lowering maybe interest rates will fall soon - good time to invest in bonds that still have a high yield).
* https://tradingeconomics.com/united-states/inflation-cpi
L7.17 Compare the premium on high-yield corporate bonds (relative to Treasury bonds) at the beginning of the school term to the premium that existed at the end of the school term. Did the premium increase or decrease? Why this premium changed over the school term.
REVISED ANSWER
In order to compare the premium on high-yield corporate bonds at the beginning of the school term to the premium that existed at the end of the school term we must take data about the yield of corporate bonds and treasury bonds in the beginning of the school term and at the end of the school term to be able to compare the and obtain the premium.
The yield on 30 year treasury bonds in the beginning of the school term was 4.63% and at the end of the school term it was 3,81%
The yield on high-yield corporate bonds in the beginning of the school term was 6,65% and at the end of the school term it was 5,53%.
We will now calculate the premiums at the beginning and at the end of the school term:
The premium at the beginning of the school term:
6,65% - 4,63% =
6.65-4.63## [1] 2.02=2,02%
The premium at the end of the school term:
5,53% - 3,81% =
5.53-3.81## [1] 1.72= 1,72%
Difference between the premiums:
2,02% - 1,72% =
2.02-1.72## [1] 0.3= 0,3%
As we can observe in our calculations the premium has changed over the school term - it decreased by 0,3%. Both high-yield corporate bonds and treasury bonds survived a decrease in their yield, however the difference in the premium over the school term shows us the reward for taking a more risky investment is 0,3% lower at the end of the school term. That means that the yield on treasury bonds decreased more slowly than the high-yield corporate bonds yield. That data shows us that the demand on high-yield corporate bonds increased faster than the demand on treasury bonds. That information would indicate that investors for various reasons took riskier instruments such as high-yield corporate bonds as a better opportunity for investment than the safe long-term treasury bonds. The reason might be that at the end of the school term the interest rate decreased by 0,50% which made credits for corporate issuers cheaper. which in consequence lowers the insolvency risk - since this risk decreased the bond yield also decreased. Another reason might be economic stabilization which would be a signal for investors that the conditions on the market are good enough to believe that corporate high-yield bonds are not as risky as they used to be.
L8 Portfolio - Markovitz
Replicate the basic idea of the portfolio case
FIRST ANSWER
Markowitz portfolio theory, which was developed in the 1950s, is a form of portfolio optimization based on structured mathematical and statistical principles.
At its heart is the concept of diversification. Markowitz argues that by combining different assets in a portfolio, the overall risk can be significantly reduced without significantly reducing the expected return. This is based on the assumption that not all investments are equally correlated; by specifically selecting assets with different risk profiles and expected returns, investors can reduce the volatility of their portfolios.
A key element of this theory is the quantification of risk.
REVISED ANSWER
Markowitz theory describes how investors can optimally allocate their money to different investments in order to achieve the best balance between profit (return) and risk. The main aim of the theory is to create a portfolio that either achieves the highest possible return for a certain risk or has the lowest possible risk for a desired return.
A central component of the theory is diversification, i.e. the allocation of money to different investments. The basic idea behind this is that not all investments react in the same way to market changes. If one investment loses value, another could gain value at the same time or remain stable. This reduces the overall risk of the portfolio. This works particularly well if the investments in the portfolio have a low correlation to each other - this means that they develop independently of each other.
The following two variables form the important basis of the Markowitz theory:
1. return: this is the expected profit of an investment or portfolio.
2. risk: Risk is measured by the fluctuations in return (also known as volatility). The more the value of an investment fluctuates, the higher the risk.
The challenge is to reconcile these two variables: Investors want to achieve the highest possible returns while keeping risk low.
According to Markowitz theory, there are certain combinations of investments that are particularly advantageous. These are called efficient portfolios. They offer the highest possible return for a certain risk or the lowest risk for a desired return. These optimal portfolios lie on the so-called efficiency curve (or efficiency frontier). Portfolios that do not lie on this curve are suboptimal - they either offer too little return for the risk taken or they carry an unnecessarily high risk for the return achieved.
Markowitz theory therefore shows how investors can combine their investments in such a way that they achieve their goals - high returns with manageable risk - in the best possible way. It makes it clear that it is not only important which individual investments are selected, but above all how these investments work together. Diversification and the consideration of return and risk are crucial here.
L9 Portfolio - CAPM
State the difference between CAPM and Markovitz
FIRST ANSWER
The Capital Asset Pricing Model (CAPM) is a central concept in finance that describes the relationship between the risk of an asset and its expected return. The basic assumption is that investors must be rewarded for taking risk. It introduces the concept of systematic risk, which cannot be eliminated through diversification. The expected return of an asset is determined by the risk-free rate of return plus a risk premium proportional to the asset’s beta - a measure of its volatility relative to the market as a whole.
In contrast to Markowitz portfolio theory, which focuses on the diversification of investments to reduce risk, the CAPM focuses on the systematic risk of an individual asset in the context of the market as a whole. While Markowitz theory helps investors to create optimal portfolios by using the standard deviation of returns as a measure of risk, the CAPM only looks at risk that cannot be reduced through diversification.
Another difference lies in the application of the two models. The Markowitz theory is often used to optimize the composition of portfolios through diversification, among other things, whereas the CAPM is used to evaluate individual investments. It offers a clear method for determining an appropriate return for the risk taken on an asset. It is therefore very useful for individual investment decisions.
To summarize, both CAPM and Markowitz are important tools in the field of finance. They offer different perspectives on risk and return and complement each other in their application.
REVISED ANSWER
The Capital Asset Pricing Model (CAPM) is a model that shows investors how much return they can expect from an investment based on the risk they take. It distinguishes between two types of risk: systematic risk, which arises from market influences (e.g. economic crises) and cannot be avoided, and unsystematic risk, which can be reduced through diversification (i.e. spreading investments across different assets). The CAPM focuses exclusively on systematic risk, as this is the only risk for which investors are compensated. The expected return is calculated using a formula that combines the risk-free interest rate, the beta factor (which measures how much an investment fluctuates compared to the market) and the market risk premium (the additional return for taking market risk).
In comparison, the Markowitz theory deals with the optimal composition of a portfolio. It shows that investors can reduce their risk by diversifying their investments - i.e. not putting everything into a single investment. The aim is to create an “efficient portfolio” in which the risk is as low as possible for a certain expected return. The theory takes into account both systematic and unsystematic risk.
The main difference between the two models is what they focus on. Markowitz theory looks at the overall risk of a portfolio and shows how to eliminate unsystematic risk through diversification. It therefore helps investors to find an optimal mix of different investments. The CAPM, on the other hand, assumes that investors already have diversified portfolios and that only the systematic risk is relevant. It therefore explains how this remaining risk influences the expected return.
To summarize: Markowitz theory answers the question “How do I construct my portfolio to minimize my risk?”, while the CAPM clarifies “How much return can I expect for a given level of systematic risk?”. Both models complement each other - the Markowitz theory lays the foundation for a smart portfolio composition, while the CAPM helps to evaluate individual investments in the market environment.
L10 WACC
Replicate the book case of WACC
The Weighted Average Cost of Capital (WACC) is an important financial metric that represents the average rate of return a company needs to achieve to satisfy its investors—both equity shareholders and debt holders. It helps determine the minimum return the company should generate on its investments to maintain its value and attract ongoing funding.
Key Components of WACC:
Cost of Equity (Re): This is the return that equity investors expect for taking on the risk of investing in the company. It is typically estimated using the Capital Asset Pricing Model (CAPM), reflecting the opportunity cost of capital.
Cost of Debt (Rd): This represents the interest rate a company pays on its borrowed funds, adjusted for the corporate tax rate because interest payments are tax-deductible.
WACC Formula:
WACC is calculated as a weighted average, where the weights represent the proportion of equity and debt in the company’s capital structure. The formula is:
WACC=EV⋅Re+DV⋅Rd⋅(1−Tc)WACC=VE⋅Re+VD⋅Rd⋅(1−Tc)
Where:
E: Market value of equity
D: Market value of debt
V: Total value (equity + debt)
Re: Cost of equity
Rd: Cost of debt
Tc: Corporate tax rate
Key Takeaways:
Purpose of WACC:
WACC serves as a crucial benchmark for evaluating investment opportunities. It represents the minimum return required to satisfy both equity and debt investors. Projects should only be pursued if their expected return exceeds the WACC, ensuring they create value. By factoring in the company’s overall cost of capital, WACC reflects the risk preferences of both equity and debt holders, supporting informed financial decision-making.
Factors Affecting WACC:
A company’s capital structure plays a major role in determining its WACC, as debt is typically less expensive than equity, but increases financial risk. External factors like interest rates or market risk premiums can influence both the cost of debt and equity. Additionally, the tax rate impacts the after-tax cost of debt, with higher tax rates lowering the effective cost of debt, thus potentially reducing WACC. All these elements collectively shape the company’s total cost of capital and impact its financial strategy.
Implications of WACC:
A lower WACC means cheaper financing for investments, improving the company’s competitive edge.
A higher WACC signals higher financing costs, which could limit growth opportunities.
WACC is a vital metric in corporate finance, guiding investment decisions, valuation models, and performance assessments. It provides a comprehensive view of a company’s financing costs and strategic financial planning.
L11 Derivatives
L11.1 Assume that you purchased an S&P 500 futures contract at the beginning of the school term, with the first settlement date beyond the end of the school term. Also assume that you sold an S&P 500 futures contract with this same settlement date at the end of the school term. Given that this contract has a value of the futures price times $250, determine the difference between the dollar value of the contract you sold and the dollar amount of the contract that you purchased.
The price of futures contract in the beginning of the school term: $ 5046,5
The price of futures contract in the end of the school term: $5814,25
Futures value of purchase: 250 * 5046,5=
250 * 5046.5## [1] 1261625=$1 261 625
Futures value of sale: 250 * 5814,25=
250 * 5814.25## [1] 1453562= $1 453 562
We will now calculate the difference:
$1 261 625 - $1 453 562 =
1261625 - 1453562## [1] -191937= - $191 937
L11.2 Assume that you invested an initial margin of 20 percent of the amount that you would owe to purchase the S&P 500 index at the settlement date. Measure your return from taking a position in the S&P 500 index futures as follows. Take the difference determined in the previous question (which represents the dollar amount of the gain on the futures position) and divide it by the amount you originally invested (the amount you originally invested is 20 percent of the dollar value of the futures contract that you purchased).
Initial investment: 0.2 * $1 261 625 =
0.2 * 1261625## [1] 252325= $252 325
Return = difference/initial investment
Return = 191 937,5/252 325 =
191937.5/252325## [1] 0.7606757= 76,07%
L11.3 The return that you just derived in the previous question is not annualized. To annualize your return, multiply it by 12/m, where m is the number of months in your school term.
Annualized return = 76% *12/5 =
76 *12/5## [1] 182.4= 76% * 3 = 182,4%
L11.4 Assume that you purchased a call option (representing 100 shares) on the specific stock that you identified for this project. What was your return from purchasing this option? [Your return can be measured as
Return = max(market price - K,0)/P
Premt represents the premium at which the same option can be sold at the end of the school term.] If the premium for this option is not quoted at the end of the school term, measure the return as if you had exercised the call option at the end of the school term (assuming that it is feasible to exercise the option at that time). That is, the return is based on purchasing the stock at the option’s strike price and then selling the stock at its market price at the end of the school term.
To calculate the return from purchasing a call option on Apple Inc. (AAPL) shares, we will assume specific values for the strike price and premium paid for the option. Based on the most recent stock price data, we will use the closing price of Apple shares at the end of the school term, which is $237.33.
Assumptions:
Strike Price (K): Let’s assume a strike price of $230.
Premium Paid (P): We will assume we paid a premium of $5 per share
Market Price at Expiration: The market price of Apple shares on September 30 2024 is $237.33.
Calculating return:
- Selling the option
If you decide to sell the call option at market price:
Return=max(Market Price−K,0)−P /P
K - strike price
P - premium
Calculating:
max(237.33−230,0)=max(7.33,0)=7.33
Return=(7.33−5)/5=2.33/5=
2.33/5## [1] 0.466=0.466 or 46.6%
Exercising the option:
If you decide to exercise the call option:
Return=max(Market Price−K,0)/P
Calculating:
Return=7.33/5=
7.33/5## [1] 1.466=1.466 or 146.6%
Summary of returns
Return if Sold: 46.6%
Return if Exercised: 146.6%
L11.5 Annualize the return on your option by multiplying the return you derived in the previous question by 12/m, where m represents the number of months in your school term.
If sold: 46,6% * 12/5 =
46.6 * 12/5## [1] 111.84= 111,84%
If exercised: 146,6%*12/5=
146.6*12/5## [1] 351.84= 351,84%
L11.6 Compare the return on your call option to the return that you would have earned if you had simply invested in the stock itself. Notice how the magnitude of the return on the call option is much larger than the magnitude of the return on the stock itself. That is, the gains are larger and the losses are larger when investing in call options on a stock instead of the stock itself.
REVISED ANSWER
To Compare the return on the call option to the return that we would have earned if we had simply invested in the stock itself we will have to look at the performance of the stock itself. In the beginning of the school term the Apple stock index represented a value of 169.30 and at the end of the school term it represented a value of 227.79.
The difference:
Value at the end of investment - value at the beginning = difference
227.79 - 169.30=
227.79-169.3## [1] 58.49= 58,49
The growth percentage:
Difference/Value at the beginning = growth percentage
58,49/169,3 =
58.49/169.3## [1] 0.3454814= 34,55%
Annualized result
Growth percentage * 12/m = Annualized return
34,55% *12/5 =
34.55*12/5## [1] 82.92= 82,92%
Comparison to call option
Sold call option: 111,84% - 82,92% =
111.84-82.92## [1] 28.92= 28,92%
Exercised call option: 351,84% - 82,92%=
351.84-82.92## [1] 268.92= 268,92%
Determining swap payments
L11.7 Assume that, at the beginning of the school term, you engaged in a fixed-for-floating rate swap in which you agreed to pay 6 percent in exchange for the prevailing 26-week T-bill rate that exists at the end of the school term. Assume that your swap agreement specifies the end of the school term as the only time at which a swap will occur and that the notional amount is $10 million. Determine the amount that you owe on the swap, the amount you are owed on the swap, and the difference. Did you gain or lose as a result of the swap?
REVISED ANSWER
In order to calculate the amount that we would owe on the swap, the amount we would be owed and the difference we must provide some information for the calculation:
Investment: $10 000 000
Fixed rate: 6%
Floating rate (rate at the end of the school term): 4.23%
Calculation:
Amount we would owe - $10 000 000 * 6% =
10000000 * 0.06## [1] 6e+05= $600 000
Amount we would be owed - $10 000 000 * 4.23% =
10000000 * 0.0423## [1] 423000= $423 000
Difference: $600 000 - $423 000=
600000 - 423000## [1] 177000= $177 000
The swap would generate a loss of $177 000.
Measuring and explaining exchange rate movements
L11.8 Determine the percentage change in the value of the British pound over the school term. Did the pound appreciate or depreciate against the dollar?
REVISED ANSWER
In the beginning of the school term one British Pound costed 1,27 USD
In the end of the school term one British Pound costed 1,34 USD
The British Pound appreciated (1,34-1,27)/1,27=
(1.34-1.27)/1.27## [1] 0.05511811= 0,05512 = 5,512%
L11.9 Determine the percentage change in the value of the Japanese yen over the school term. Did the yen appreciate or depreciate against the dollar?
In the beginning of the school term one Japanese Yen costed 0,0064 USD
In the end of the school term one Japanese Yen costed 0,0070 USD
The Japanese Yen appreciated (0,0070-0,0064)/0,0064 =
(0.0070-0.0064)/0.0064## [1] 0.09375= 0,09375 = 9,38%
L11.10 Determine the percentage change in the value of the Mexican peso over the school term. Did the peso appreciate or depreciate against the dollar?
In the beginning of the school term the Mexican Peso costed 0,59 USD
In the end of the school term the Mexican Peso costed 0,51 USD
The Mexican Peso depreciated (0,51-0,59)/0,59= -0,13559=
(0.51-0.59)/0.59## [1] -0.1355932= -13,56%
L11.11 Determine the per unit gain or loss if you had purchased British pound futures at the beginning of the term and sold British pound futures at the end of the term.
In the beginning of the school term one British Pound costed 1,27 USD
In the end of the school term one British Pound costed 1,34 USD
Gain or loss per unit: 1,34 - 1,27=
1.34 - 1.27## [1] 0.07= 0,07 USD
That represents a gain of $0,07 per British Pound
L11.12 Given that a single futures contract on British pounds represents 62,500 pounds, determine the dollar amount of your gain or loss.
To calculate the dollar amount of gain or loss we must multiplicate the amount of GBP per the gain or loss per British Pound in USD
Calculation:
62 500 * 0,07=
62500 * 0.07## [1] 4375= $4 375
L12 Capital requirements
L12.1 Calculate the operational, market and credit risk capital requirements for Bank of America and Deutsche Bank as of December 31, last year, which bank has a better capital base?
Bank of America (BoA):
Common Equity Tier 1 (CET1) Capital Ratio: 11.8%
Deutsche Bank:
Common Equity Tier 1 (CET1) Capital Ratio: 13.7%
Risk-weighted Assets (RWA): €350 billion
Operational Risk RWA: €57 billion
Credit Risk and Market Risk RWA: Remaining amounts after operational RWA deduction.
Comparison
CET1 Ratios:
Deutsche Bank: 13.7%
BoA: 11.8%
Better CET1 Ratio: Deutsche Bank, indicating a stronger capital position relative to risk-weighted assets.
Breakdown of Risks (Deutsche Bank):
Operational Risk: €57 billion.
Remaining RWA (likely split between Credit and Market Risk): €293 billion.