Financial Markets and Investments

Median Voter Theorem: A principle that suggests in a majority rule voting system, the preferences of the median voter will dominate.
- Limitations: Not always applicable in preference spaces with more than two options or when voter preferences are not single-peaked.

Issues that can arise in decision-making processes, including:
- The potential for cyclical preferences leading to indecisiveness.
- Difficulty in knowing how preferences will align when choices exceed two options.

Problems associated with the allocation of scores in ranking or voting systems, leading to:
- Misrepresentation of voter preferences.
- The need for robust methods to aggregate opinions.

Definition: The ability of an entity to produce a good or service at a lower opportunity cost than others, leading to the benefits of trade.
Application: Understanding each person's production in trade scenarios, where:
- Each individual capitalizes on their unique strengths to enhance overall efficiency.

The value associated with holding assets over time, considering factors such as:
- Present value (PV) vs. future cash flows.
- Time value of money principles.

Concepts regarding how capital values are affected by risk, highlighting:
- Trade-offs between potential returns and associated risks.

Risk-Free Assets: Bonds
- Characteristics:
  - Coupon: The periodic interest payment to bondholders; calculated as:
    $ext{Coupon} = ext{Face Value} imes ext{Interest Rate}$ .
  - Maturity Date: The date when the bond's principal must be repaid.
  - Face Value: The amount capital that will be returned to bondholders at maturity.
  - Yield: The total return on investment; inversely related to bond price.
Bond Prices and Rates of Return
- Inversely Related:
  - Higher bond prices lead to lower yields and vice versa.
- Yield to Maturity: Total expected return if the bond is held to maturity.
Bond Pricing Formulas:
- Present value calculations accounting for various interest rates:
  - One year:
    $P = rac{R}{1+i} + rac{F}{(1+i)}$
  - Two years:
    $P = rac{R}{(1+i)} + rac{R}{(1+i)^2} + rac{F}{(1+i)^2}$
  - Three years:
    $P = rac{R}{(1+i)} + rac{R}{(1+i)^2} + rac{R}{(1+i)^3} + rac{F}{(1+i)^3}$

Example: USC Alumni Salaries
- General starting salary: $63,275$ (1 year after graduation).
- Median mid-career salary: $91,408$ (ages 35-45).
- Graduates from Marshall School: Average starting salary: $144,442$ for Class of 2024.
- Gould School of Law: Median mid-career salary: $192,800$ .
- 4% discount rate calculations for present value totaling: $2,094,902$ .

Today’s Rates:
- Series EE Savings Bonds: 2.50%, maturity terms.
- Series I Savings Bonds: 4.03%, federal tax only.
- 30-Year Bonds: 4.625%, with price details.
- 10-Year Notes: 4.000%, issuance details.

Bonds auctioned with varied interest rates, summarized with auction data and results.
- Key auction dates and security details provided.

Rate of Return: The return expressed as a percentage of the initial asset price.
Dividend Yield: The percentage return derived from dividends.
- Example Calculation:
  - Stock Purchase Price: $160, Sale Price: $180, Dividends: $10
  - Rate of Return = rac{(180 - 160 + 10)}{160} imes 100 = 18.75 ext{%}
  - Dividend Yield = rac{10}{160} imes 100 = 6.25 ext{%}.

Portfolio Diversification: Spreading assets to limit exposure to risk.
- Significant reduction in risk demonstrated through comparative analysis of single vs multiple stock holdings.

Definition: Markets are assumed to quickly adjust to new information, negating profitable opportunities.
Counterexample: Insiders performing better due to private information.

Ability to calculate price, yield, and risks.
Understanding the relationship between expected return and risk.
Importance of diversification in investment strategies.
Recognition of market efficiency limitations and asymmetric information effects.