Lecture_6

Principles of Macroeconomics

• Instructor: Alvaro Boitier

• Institution: Babson College

• Semester: Fall 2024

Basic Tools of Finance

• Reference: Chapter 14 - Mankiw's Principles of Macroeconomics (10th edition)

Introduction

• Key topics for discussion:

  • Comparing sums of money over time

  • Managing risk

  • Valuing an asset using time and risk analysis

  • Understanding economic bubbles

Present Value vs Future Value

• Understanding Value Over Time:

  • Scenario 1: Choosing between receiving $100 today versus $100 in 10 years.

  • Scenario 2: Choosing between receiving $100 today versus $300 in 10 years.

Essential Definitions

• Future Value: The amount of money a current sum will yield in the future given interest rates.

• Present Value: The current worth of a future sum of money given a specified rate of return.

• Compounding: The process where interest is earned not only on the principal but also on previously earned interest.

Compound Interest

• Formula for Future Value:

  [\text{Future Value} = Pv \times \left(1 + \frac{r}{100}\right)^{N}]

• Yearly Accumulation: Each year, money grows by a factor based on the interest rate.

• Example Calculations:

  • For 1 year: (100 + 100 \times \frac{r}{100} = 100 \times (1 + \frac{r}{100}))

  • For N years: (100 \times (1 + \frac{r}{100})^{N})

Discounting

• Determining how much needs to be invested today to achieve a future value at a given interest rate:

  • Formula: (Pv = Fv \times \left(1 + \frac{r}{100}\right)^{-N})

  • Discount factor: (\frac{1}{(1 + \frac{r}{100})^{N}})

Examples of Future Value Calculation

1. Investing $1000 at 0.04% APR for 5 years.

2. Retirement savings goal: How much to save today to achieve $1 million in 30 years at a 9% return.

Compounding Monthly Rates

• Monthly rates reported by BLS or BEA (e.g., inflation, GDP growth).

  • Yearly inflation calculated from monthly: (\left(1 + \frac{\text{monthly rate}}{100}\right)^{12} - 1)

  • Example: 1% monthly inflation leads to a yearly inflation of approximately 12.68%.

Average Growth Rate

• To find average yearly GDP growth over time lapse:

  • Identifying cumulative growth and using geometric mean formula for calculation.

The Rule of 70

• Formula: Time to double an investment = (\frac{70}{x}) where x is growth rate.

Risk and Its Management

• What is Risk?

  • The uncertainty regarding investment returns.

• Risk Preferences:

  • Risk Averse: Prefers certainty.

  • Risk Seeking: Prefers uncertainty.

  • Risk Neutral: Indifferent towards risk.

Insurance as Risk Management

• Insurance spreads risk rather than eliminates it.

  • Pricing based on probability of risk and expected losses.

Diversification

• Key strategy to reduce investment risk by allocating capital across various assets.

• Impact of standard deviation as a measure of portfolio risk.

• Diversification can eliminate firm-specific risks but not market-wide risks.

Risk-Return Trade-Off

• Higher potential returns correlate with higher risks.

  • Example with portfolios of stocks and bonds demonstrating their risk-return profiles.

Efficient Market Hypothesis (EMH)

• Asset prices reflect all publicly available information.

• Stock prices adjust based on new information, making them unpredictable based on past data.

Limitations of EMH

• Past performance not guaranteed for future results.

• Market anomalies and behavioral factors lead to investor irrationality.

Bubbles and Their Signs

• Definition: Occurrence when asset prices dramatically rise above intrinsic values followed by a significant drop.

• Indicators of a bubble:

  • Rapid price increase without justification.

  • Media hype and stories of wealth.

  • Investor enthusiasm mixed with envy and FOMO (fear of missing out).

Historical Examples of Bubbles

• Tulip Mania: Early 17th-century economic bubble involving tulips in the Netherlands.

• Dot-com Bubble: 1996-2000 tech market boom followed by a crash.

• Housing Bubble: 2002-2006 U.S. housing market bubble results in the 2008 crisis.

• Cryptocurrency Bubbles: Repeated cycles of value surges and collapses in Bitcoin, Ethereum, etc.

Future of Bitcoin?

• Discussion raises questions on sustainability and future valuations.

Questions & Comments

• Open floor for discussion regarding principles of macroeconomics and definitions thereof.