Chapter 16: Financial Economics: Investment, Risk, and the Security Market Line

Financial Investment and Economic Investment

  • Economic Investment: Defined as new additions or replacements to the capital stock of an economy.

  • Financial Investment:

    • This concept is broader than economic investment.

    • It involves buying or building an asset specifically for the purpose of financial gain.

    • It can involve either a new asset or an old (existing) asset.

    • It encompasses both financial assets (such as stocks and bonds) and real assets (such as land or buildings).

    • Common examples include various types of securities.

Present Value and the Time Value of Money

  • Time Value of Money: This refers to the specific amount an individual must be compensated for having to wait for a future payment.

  • Compound Interest: The process of earning interest on the interest already earned.= 370.00</p></li><li><p><strong>PresentValueModel:</strong></p><ul><li><p>Thismodelcalculateswhataninvestorshouldpayforanassettodaybasedonitsfutureincomestream.</p></li><li><p>Theassetyieldsaseriesoffuturepayments;itspricetodayshouldideallyequalthetotalpresentvalueofallthosefuturepayments.</p></li></ul></li><li><p><strong>ApplicationsofPresentValue:</strong></p><ul><li><p><strong>LotteryJackpots:</strong>Calculatingthelump−sumvalueofajackpotthatistypicallypaidoutoveraseriesofyears.</p></li><li><p><strong>SalaryCapsandDeferredCompensation:</strong>Determiningthecurrentvalueofathleteorexecutivesalarypaymentsthataredeferredtothefuture.</p></li></ul></li></ul><h3id="ea9e1066−bd98−413c−a765−49675e79844a"data−toc−id="ea9e1066−bd98−413c−a765−49675e79844a"collapsed="false"seolevelmigrated="true">SomePopularInvestments</h3><ul><li><p><strong>GeneralFeaturesofInvestments:</strong></p><ol><li><p>Theinvestormustpaytoacquiretheasset.</p></li><li><p>Thereisachancetoreceivefuturepayments.</p></li><li><p>Futurepaymentsinvolvesomedegreeofrisk.</p></li></ol></li><li><p><strong>Stocks:</strong>Representequityownershipinacompany.</p><ul><li><p>Possibilityofthecompanygoingbankrupt.</p></li><li><p><strong>LimitedLiabilityRule:</strong>Limitsaninvestor′spotentiallosstotheamounttheyinvested.</p></li><li><p><strong>CapitalGains:</strong>Profitfromsellingthestockatahigherpricethanthepurchaseprice.</p></li><li><p><strong>Dividends:</strong>Periodicpaymentsmadebythecompanytoshareholdersfromprofits.</p></li></ul></li><li><p><strong>Bonds:</strong>Debtcontractsissuedbygovernmentsandcorporations.</p><ul><li><p><strong>PossibilityofDefault:</strong>Theriskthattheissuerfailstomakepayments.</p></li><li><p>Theinvestorreceivesregularinterestpayments.</p></li></ul></li><li><p><strong>MutualFunds:</strong>Companiesthatmaintainadiversifiedportfolioofstocksorbonds.</p><ul><li><p>Therearecurrentlymorethan</p></li><li><p><strong>Present Value Model:</strong></p><ul><li><p>This model calculates what an investor should pay for an asset today based on its future income stream.</p></li><li><p>The asset yields a series of future payments; its price today should ideally equal the total present value of all those future payments.</p></li></ul></li><li><p><strong>Applications of Present Value:</strong></p><ul><li><p><strong>Lottery Jackpots:</strong> Calculating the lump-sum value of a jackpot that is typically paid out over a series of years.</p></li><li><p><strong>Salary Caps and Deferred Compensation:</strong> Determining the current value of athlete or executive salary payments that are deferred to the future.</p></li></ul></li></ul><h3 id="ea9e1066-bd98-413c-a765-49675e79844a" data-toc-id="ea9e1066-bd98-413c-a765-49675e79844a" collapsed="false" seolevelmigrated="true">Some Popular Investments</h3><ul><li><p><strong>General Features of Investments:</strong></p><ol><li><p>The investor must pay to acquire the asset.</p></li><li><p>There is a chance to receive future payments.</p></li><li><p>Future payments involve some degree of risk.</p></li></ol></li><li><p><strong>Stocks:</strong> Represent equity ownership in a company.</p><ul><li><p>Possibility of the company going bankrupt.</p></li><li><p><strong>Limited Liability Rule:</strong> Limits an investor's potential loss to the amount they invested.</p></li><li><p><strong>Capital Gains:</strong> Profit from selling the stock at a higher price than the purchase price.</p></li><li><p><strong>Dividends:</strong> Periodic payments made by the company to shareholders from profits.</p></li></ul></li><li><p><strong>Bonds:</strong> Debt contracts issued by governments and corporations.</p><ul><li><p><strong>Possibility of Default:</strong> The risk that the issuer fails to make payments.</p></li><li><p>The investor receives regular interest payments.</p></li></ul></li><li><p><strong>Mutual Funds:</strong> Companies that maintain a diversified portfolio of stocks or bonds.</p><ul><li><p>There are currently more than9,300mutualfundsinexistence.</p></li><li><p><strong>IndexFunds:</strong>Fundsdesignedtomimictheperformanceofaspecificmarketindex.</p></li><li><p><strong>ActivelyManagedFunds:</strong>Fundswheremanagersselectspecificassetstotryandoutperformthemarket.</p></li><li><p><strong>PassivelyManagedFunds:</strong>Fundsthatfollowasetstrategywithoutactivedailytrading(oftenindex−based).</p></li></ul></li></ul><h3id="52a4b236−f2a8−4379−a423−ef875ac976e2"data−toc−id="52a4b236−f2a8−4379−a423−ef875ac976e2"collapsed="false"seolevelmigrated="true">CalculatingInvestmentReturnsandArbitrage</h3><ul><li><p><strong>RateofReturn:</strong>Thegainorlossofaninvestmentstatedasapercentage.</p><ul><li><p>Calculation:mutual funds in existence.</p></li><li><p><strong>Index Funds:</strong> Funds designed to mimic the performance of a specific market index.</p></li><li><p><strong>Actively Managed Funds:</strong> Funds where managers select specific assets to try and outperform the market.</p></li><li><p><strong>Passively Managed Funds:</strong> Funds that follow a set strategy without active daily trading (often index-based).</p></li></ul></li></ul><h3 id="52a4b236-f2a8-4379-a423-ef875ac976e2" data-toc-id="52a4b236-f2a8-4379-a423-ef875ac976e2" collapsed="false" seolevelmigrated="true">Calculating Investment Returns and Arbitrage</h3><ul><li><p><strong>Rate of Return:</strong> The gain or loss of an investment stated as a percentage.</p><ul><li><p>Calculation:\frac{\text{Selling Price} - \text{Purchase Price}}{\text{Purchase Price}}</p></li><li><p>Afutureseriesofpaymentsisalsofactoredintothereturncalculation.</p></li><li><p>Therateofreturnisinverselyrelatedtotheasset′sprice.</p></li></ul></li><li><p><strong>Arbitrage:</strong>Thesimultaneousbuyingandsellingofassetstoequalizeaverageexpectedreturns.</p><ul><li><p>Investorssellassetswithlowreturnsandbuyassetswithhigherreturnsiftheyhavethesameriskprofile.</p></li><li><p>Throughthisprocess,bothassetswilleventuallygravitatetowardthesamerateofreturn.</p></li></ul></li></ul><h3id="929d2ed2−0d34−460d−8330−3a095b17af90"data−toc−id="929d2ed2−0d34−460d−8330−3a095b17af90"collapsed="false"seolevelmigrated="true">RiskandInternationalDifferences</h3><ul><li><p><strong>Risk:</strong>Futurepaymentsareuncertain.</p></li><li><p><strong>Diversification:</strong>Thestrategyofspreadinginvestmentsacrossdifferentassetstoreducerisk.</p><ul><li><p><strong>DiversifiableRisk:</strong>Riskspecifictoagiveninvestment(e.g.,aspecificcompany′sfailure).</p></li><li><p><strong>NondiversifiableRisk:</strong>Riskthataffectstheentiremarket,suchasbusinesscycleeffects.</p></li></ul></li></ul><h3id="b292206a−408d−47a9−ac23−b6a0ae176e5c"data−toc−id="b292206a−408d−47a9−ac23−b6a0ae176e5c"collapsed="false"seolevelmigrated="true">ComparingRiskyInvestmentsandtheSecurityMarketLine(SML)</h3><ul><li><p><strong>AverageExpectedRateofReturn:</strong>Aprobability−weightedaverageofallpossiblefuturereturns.</p></li><li><p><strong>Beta:</strong>Arelativemeasureofnondiversifiableriskthatcomparesanasset′srisktotheriskofthemarketportfolio.</p></li><li><p><strong>RiskandReturnRelationship:</strong>Thereisapositiverelationshipbetweenriskandaverageexpectedratesofreturn.</p></li><li><p><strong>Risk−FreeRateofReturn:</strong></p><ul><li><p>Measuredusingshort−termU.S.governmentbonds.</p></li><li><p>Therateofreturnisgreaterthanzerodueto<strong>TimePreference</strong>(compensationforwaiting).</p></li></ul></li><li><p><strong>TheSecurityMarketLineFormula:</strong></p><ul><li><p></p></li><li><p>A future series of payments is also factored into the return calculation.</p></li><li><p>The rate of return is inversely related to the asset's price.</p></li></ul></li><li><p><strong>Arbitrage:</strong> The simultaneous buying and selling of assets to equalize average expected returns.</p><ul><li><p>Investors sell assets with low returns and buy assets with higher returns if they have the same risk profile.</p></li><li><p>Through this process, both assets will eventually gravitate toward the same rate of return.</p></li></ul></li></ul><h3 id="929d2ed2-0d34-460d-8330-3a095b17af90" data-toc-id="929d2ed2-0d34-460d-8330-3a095b17af90" collapsed="false" seolevelmigrated="true">Risk and International Differences</h3><ul><li><p><strong>Risk:</strong> Future payments are uncertain.</p></li><li><p><strong>Diversification:</strong> The strategy of spreading investments across different assets to reduce risk.</p><ul><li><p><strong>Diversifiable Risk:</strong> Risk specific to a given investment (e.g., a specific company's failure).</p></li><li><p><strong>Nondiversifiable Risk:</strong> Risk that affects the entire market, such as business cycle effects.</p></li></ul></li></ul><h3 id="b292206a-408d-47a9-ac23-b6a0ae176e5c" data-toc-id="b292206a-408d-47a9-ac23-b6a0ae176e5c" collapsed="false" seolevelmigrated="true">Comparing Risky Investments and the Security Market Line (SML)</h3><ul><li><p><strong>Average Expected Rate of Return:</strong> A probability-weighted average of all possible future returns.</p></li><li><p><strong>Beta:</strong> A relative measure of nondiversifiable risk that compares an asset's risk to the risk of the market portfolio.</p></li><li><p><strong>Risk and Return Relationship:</strong> There is a positive relationship between risk and average expected rates of return.</p></li><li><p><strong>Risk-Free Rate of Return:</strong></p><ul><li><p>Measured using short-term U.S. government bonds.</p></li><li><p>The rate of return is greater than zero due to <strong>Time Preference</strong> (compensation for waiting).</p></li></ul></li><li><p><strong>The Security Market Line Formula:</strong></p><ul><li><p>\text{Average expected rate of return} = \text{Rate for time preference} + \text{Rate for risk}</p></li></ul></li><li><p><strong>TheSMLGraphComponents:</strong></p><ul><li><p>Thehorizontalaxisrepresentsthe<strong>Risklevel(beta)</strong>.</p></li><li><p>Theverticalaxisrepresentsthe<strong>Averageexpectedrateofreturn</strong>.</p></li><li><p>Thelinestartsat</p></li></ul></li><li><p><strong>The SML Graph Components:</strong></p><ul><li><p>The horizontal axis represents the <strong>Risk level (beta)</strong>.</p></li><li><p>The vertical axis represents the <strong>Average expected rate of return</strong>.</p></li><li><p>The line starts ati^f(therisk−freeinterestrate)whichrepresentscompensationfortimepreference.</p></li><li><p>The<strong>MarketPortfolio</strong>islocatedatabetaof(the risk-free interest rate) which represents compensation for time preference.</p></li><li><p>The <strong>Market Portfolio</strong> is located at a beta of1.0.</p></li><li><p>The<strong>RiskPremium</strong>istheverticaldistancebetweentherisk−freerate(.</p></li><li><p>The <strong>Risk Premium</strong> is the vertical distance between the risk-free rate (i^f)andthelineatagivenbeta() and the line at a given beta (X).</p></li></ul></li></ul><h3id="5e21b1e9−8223−4b2c−933a−7bfe8a59d556"data−toc−id="5e21b1e9−8223−4b2c−933a−7bfe8a59d556"collapsed="false"seolevelmigrated="true">ShiftsintheSecurityMarketLine</h3><ul><li><p><strong>ArbitrageandtheSML:</strong>Ifanasset′sreturnisabovetheSML(PointA),demandwillincrease,pricewillrise,andthereturnwillfallbacktotheline(PointB).Ifbelowtheline(PointC),demandwillfall,pricewilldrop,andthereturnwillrisebacktotheline.</p></li><li><p><strong>IncreaseinRisk−FreeInterestRates:</strong></p><ul><li><p>CausestheSMLtoshiftupwardvertically.</p></li><li><p>Example:Ashiftfrom).</p></li></ul></li></ul><h3 id="5e21b1e9-8223-4b2c-933a-7bfe8a59d556" data-toc-id="5e21b1e9-8223-4b2c-933a-7bfe8a59d556" collapsed="false" seolevelmigrated="true">Shifts in the Security Market Line</h3><ul><li><p><strong>Arbitrage and the SML:</strong> If an asset's return is above the SML (Point A), demand will increase, price will rise, and the return will fall back to the line (Point B). If below the line (Point C), demand will fall, price will drop, and the return will rise back to the line.</p></li><li><p><strong>Increase in Risk-Free Interest Rates:</strong></p><ul><li><p>Causes the SML to shift upward vertically.</p></li><li><p>Example: A shift fromi^f_1totoi^f_2shiftstheentirelinefromshifts the entire line fromSML_1totoSML_2.</p></li></ul></li><li><p><strong>TheSMLDuringtheCOVIDPandemic:</strong></p><ul><li><p>TheFederalReserveimplementedexpansionarymonetarypolicy,leadingtolowerinterestrates.</p></li><li><p>ThiscausedtheSMLtoshiftdownward.</p></li><li><p>However,theslopeoftheSMLincreasedbecauseinvestorsbecamemorerisk−averse.</p></li><li><p>Asaresult,stockpricesfell.</p></li></ul></li></ul><h3id="ef3e50d7−019c−43f7−bd13−27d800f77b61"data−toc−id="ef3e50d7−019c−43f7−bd13−27d800f77b61"collapsed="false"seolevelmigrated="true">IndexFundsversusActivelyManagedFunds</h3><ul><li><p>Afteraccountingforcosts,indexfundstypicallyoutperformactivelymanagedfundsbyapproximately.</p></li></ul></li><li><p><strong>The SML During the COVID Pandemic:</strong></p><ul><li><p>The Federal Reserve implemented expansionary monetary policy, leading to lower interest rates.</p></li><li><p>This caused the SML to shift downward.</p></li><li><p>However, the slope of the SML increased because investors became more risk-averse.</p></li><li><p>As a result, stock prices fell.</p></li></ul></li></ul><h3 id="ef3e50d7-019c-43f7-bd13-27d800f77b61" data-toc-id="ef3e50d7-019c-43f7-bd13-27d800f77b61" collapsed="false" seolevelmigrated="true">Index Funds versus Actively Managed Funds</h3><ul><li><p>After accounting for costs, index funds typically outperform actively managed funds by approximately1\%$$ per year.

  • Management Costs: Significant in actively managed funds, which eats into returns.

  • Role of Arbitrage: Arbitrage makes it very difficult for active managers to consistently beat the market average.

  • The "Boring" Nature of Index Funds: While they offer consistent market averages, they provide no chance to exceed the average rate of return, making them less "exciting" than active management.