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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.