Notes, summaries, assignments, exams, and problems for University

Congresses Cons. Powers: Treaty Making, Appointment Powers, War Powers, Commerce Powers.

Financial Ratio Analysis

Usefulness of Ratio Analysis

1. Measure of Profitability

Ratio analysis provides context for evaluating a company's profit, such as comparing it to previous periods or industry averages. Ratios like Gross Profit Margin, Net Profit Margin, and Expense Ratio help assess profitability and identify areas for improvement.

2. Evaluation of Operational Efficiency

Ratios like Turnover Ratios and Efficiency Ratios can reveal how effectively a company manages its assets and resources, helping to identify areas of inefficiency and potential cost savings.

3. Ensure Suitable Liquidity

Ratios such as the Current Ratio and Quick Ratio measure a company's short-term liquidity, indicating its ability to meet immediate cash obligations and... Continue reading "Financial Ratio Analysis: Uses, Benefits, and Limitations" »

ERRONEOUS

Incorrect; mistaken; wrong; filled with errors.

Ferdinand Magellan is credited with proving the earth is spherical in nature, thus dispelling the erroneous notion that the world is flat.

ADMONISH

To counsel against, to earnestly warn.

After reviewing a manuscript J.K. Rowling had submitted, one publisher admonished her by saying that children would not be able to identify with the characters. Needless to say, the publisher’s admonition proved to be erroneous.

DEMARCATE

To clearly set or mark the boundaries of a group or geographic area.

Even after schools were technically integrated, students would quickly demarcate their own boundary lines and sit at cafeteria tables that were either all black or all white.

FOSTER

To promote and encourage.

Consider an European call option with strike equal to 10, T = 1, r = 0.05 and σ = 0.2. Using the following time-series:

1. For every time moment t = 0, 1/360, 2/360:

• Calculate the Black-Scholes price.
• Calculate the corresponding delta.
• Calculate the price of the corresponding replicating portfolio and its composition, if we consider a dynamic hedging.

2. Calculate a static hedging. What is the final value of the portfolio? Compare with the dynamic hedging results.

Solution

• At time 0, time to maturity is 1, and then
  • The Black-Scholes price is given by S0N(d1)−Ke−rT N(d2) = 10N(0.35)−10e−0.05N(0.15) = 1.0450
  • The Delta is given by N(d1) = N(0.35) = 0.6368
  • At time t = 0, the value of the replicating portfolio coincides with the Black-Scholes price

Vocabulary 1

• 1) A mortgage is a loan to buy property.
• 2) Money you put in the bank is called a deposit.
• 3) Money paid to a retired person is called a pension.
• 4) Securities representing part-ownership of a company are called stocks or shares.
• 5) The money invested in a business is its capital.
• 6) Bonds are interest-paying securities issued by companies that need to borrow money.
• 7) A takeover is when a company gains control of another one by buying its stocks.
• 8) A merger is when two formerly separate companies join together.

Vocabulary 2

• 1) Conglomerates: Groups of companies that have joined together.
• 2) Depositors: People who place money in bank accounts.
• 3) Deregulated: Abolished or ended rules and restrictions.
• 4) Fines: Sums of money paid as penalties

Maneuverability of a ship can be defined as the percentage of efficiency that allows the vessel to maintain a course or vary its bow, with the purpose of achieving a certain position with respect to its environment.

Defining Government Capacity

It is the property that the ship must have so that it can change course in the shortest possible time and space.

Maneuvers for Recovery Capacity

The Kempf Maneuver

The Kempf maneuver consists of the following actions:

• When the yaw rate reaches a constant value, the rudder is placed at 20° to the opposite side.
• When the yaw rate reaches a value identical to the previous one in the direction of the turn, the rudder is changed to the opposite side again.

Among the most important factors in this maneuver are:

• Time

Problem 1: European Call Option Valuation

A stock price is currently at 40 euros. It is known that at month-end, the price will be either 42 euros or 38 euros. The risk-free interest rate is 8% per annum, continuously compounded. We have a call option with a strike price of 39 euros.

1. Shares for Riskless Portfolio: Calculate the number of shares to buy to create a riskless portfolio. Given Answer: 0.75 shares.
2. Cash for Replication: Determine the cash needed to replicate the portfolio at the end of the month. Given Answer: -57/2 euros.
3. One-Month European Call Value: What is the value of the one-month European Call option? Given Answer: 1.69 euros.
4. Put Option Value: What is the value of a corresponding put option? Given Answer: 0.43 euros.
5. Call-Put

1. Option Payoffs:

• Call Option: (S_T − K)⁺ = max(S_T − K, 0)
• Put Option: (K − S_T)⁺ = max(K − S_T, 0)
• Call Binary Option: 1 or Q$ when S_T > K, 0 otherwise.

2. Profit and Loss (P&L) Diagrams:

• An asset.
• A Future.
• Call option.
• Put option.
• A Binary option.
• An asset (current value 50 euros) and a Put option on the same asset with Strike 30. This strategy is used to cover potential losses, limiting them to 20 euros plus the option fee.
• Long Call + Put Option with the same Strike and Maturity. This strategy is used when a significant price movement is expected, but the direction is uncertain.
• Long position in a Call option with Strike 50 and Short Position in a Call option with Strike 60. Selling the call option reduces the overall cost of the strategy,

1. Volatility of Returns

- Small company stocks

2. Christine's Return

P0= $42.40, P1= $38.20, Divd= 1.4%

- [(38.20-42.4)/42.4] + 0.014 = -8.51%

3. Scott's Annual Return

200 shares, P0= $48, n= 4 months, dividend= $0.22

HPR= -0.120

- Annual return= (1-0.120417)^(12/4)-1 = -31.95%

4. Annualized Return

Annual returns: 15%, 12%, -18%, 2%, 37%, n=5

- Standard deviation= 20.03%

5. Stock Return Range

Stock return= 14.6%, standard deviation= 19.2%, two-thirds of the time?

- -4.6% to 33.8%

6. Forecasting Returns

Historical dollar-weighted... If you want to forecast, the best:

- Arithmetic average return

7. Jeanette's Future Value

Investment= $12,000, n=4, arithmetic average= 8.72%, geometric average= 8.43%

- FV= 12,000(1+0.0843)^4 = $16,587

8. Black Stone's Geometric Average