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 300in10years.</p></li></ul></li></ul><h5><spanclass="heading−content">EssentialDefinitions</span></h5><ul><liclass="drag"><p><strong>FutureValue:</strong>Theamountofmoneyacurrentsumwillyieldinthefuturegiveninterestrates.</p></li><liclass="drag"><p><strong>PresentValue:</strong>Thecurrentworthofafuturesumofmoneygivenaspecifiedrateofreturn.</p></li><liclass="drag"><p><strong>Compounding:</strong>Theprocesswhereinterestisearnednotonlyontheprincipalbutalsoonpreviouslyearnedinterest.</p></li></ul><h4><spanclass="heading−content">CompoundInterest</span></h4><ul><liclass="drag"><p></p><h3><spanclass="heading−content"><strong>FormulaforFutureValue:</strong></span></h3><p>[Future Value=Pv×(1+r100)N]</p></li><liclass="drag"><p><strong>YearlyAccumulation:</strong>Eachyear,moneygrowsbyafactorbasedontheinterestrate.</p></li><liclass="drag"><p><strong>ExampleCalculations:</strong></p><ul><liclass="drag"><p>For1year:(100+100×r100=100×(1+r100))</p></li><liclass="drag"><p>ForNyears:(100×(1+r100)N)</p></li></ul></li></ul><h4><spanclass="heading−content">Discounting</span></h4><ul><liclass="drag"><p>Determininghowmuchneedstobeinvestedtodaytoachieveafuturevalueatagiveninterestrate:</p><ul><liclass="drag"><p>Formula:(Pv=Fv×(1+r100)−N)</p></li><liclass="drag"><p>Discountfactor:(1(1+r100)N)</p></li></ul></li></ul><h4><spanclass="heading−content">ExamplesofFutureValueCalculation</span></h4><ol><liclass="drag"><p>Investing300 in 10 years.</p></li></ul></li></ul><h5><span class="heading-content">Essential Definitions</span></h5><ul><li class="drag"><p><strong>Future Value:</strong> The amount of money a current sum will yield in the future given interest rates.</p></li><li class="drag"><p><strong>Present Value:</strong> The current worth of a future sum of money given a specified rate of return.</p></li><li class="drag"><p><strong>Compounding:</strong> The process where interest is earned not only on the principal but also on previously earned interest.</p></li></ul><h4><span class="heading-content">Compound Interest</span></h4><ul><li class="drag"><p></p><h3><span class="heading-content"><strong>Formula for Future Value:</strong></span></h3><p>[\text{Future Value} = Pv \times \left(1 + \frac{r}{100}\right)^{N}]</p></li><li class="drag"><p><strong>Yearly Accumulation:</strong> Each year, money grows by a factor based on the interest rate.</p></li><li class="drag"><p><strong>Example Calculations:</strong></p><ul><li class="drag"><p>For 1 year: (100 + 100 \times \frac{r}{100} = 100 \times (1 + \frac{r}{100}))</p></li><li class="drag"><p>For N years: (100 \times (1 + \frac{r}{100})^{N})</p></li></ul></li></ul><h4><span class="heading-content">Discounting</span></h4><ul><li class="drag"><p>Determining how much needs to be invested today to achieve a future value at a given interest rate:</p><ul><li class="drag"><p>Formula: (Pv = Fv \times \left(1 + \frac{r}{100}\right)^{-N})</p></li><li class="drag"><p>Discount factor: (\frac{1}{(1 + \frac{r}{100})^{N}})</p></li></ul></li></ul><h4><span class="heading-content">Examples of Future Value Calculation</span></h4><ol><li class="drag"><p>Investing1000 at 0.04% APR for 5 years.

    • 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.