Macroeconomics

‭Individual‬‭D‬‭decides‬‭to‬‭invest‬‭in‬‭one‬‭of‬‭these‬‭bonds‬‭in‬‭April‬‭2024‬‭at‬‭its‬‭face‬‭value‬‭of‬‭$1,500.‬‭At‬‭the‬‭end‬‭of‬ ‭2024,‬‭2025,‬‭2026,‬‭and‬‭2027,‬‭individual‬‭D‬‭receives‬‭a‬‭4%‬‭coupon‬‭payment‬‭($1,500‬‭x‬‭0.04‬‭=‬‭$60‬‭for‬‭each‬ ‭payment).‬‭In‬‭December‬‭2027,‬‭individual‬‭D‬‭also‬‭receives‬‭the‬‭full‬‭face‬‭value‬‭of‬‭the‬‭bond.‬‭In‬‭total,‬‭individual‬ ‭D‬ ‭earns‬ ‭$240‬ ‭in‬‭coupon‬‭payments‬‭on‬‭the‬‭investment‬‭made.‬‭However,‬‭there's‬‭a‬‭risk‬‭to‬‭the‬‭initial‬‭$1,500‬ ‭investment if GreaTech Inc. does not repay the bond at maturity.‬ ‭Since‬‭a‬‭bond‬‭generates‬‭an‬‭income‬‭for‬‭its‬‭holder,‬‭we‬‭should‬‭be‬‭able‬‭to‬‭calculate‬‭its‬ ‭rate‬‭of‬‭return‬ ‭,‬‭which‬ ‭is‬ ‭the‬ ‭proft‬ ‭made‬ ‭on‬ ‭it,‬ ‭usually‬ ‭expressed‬ ‭as‬‭a‬‭percentage‬ ‭.‬‭A‬‭bond’s‬‭rate‬‭of‬‭return‬‭is‬‭calculated‬‭as‬ ‭follows:‬ ‭× 100%‬ ‭ ‬‭‬‭ ‬‭‬−‭‬‭ ‬‭‬‭ ‬‭‬‭ ‬ ‭ ‬‭‬‭ ‬‭‬‭ ‬ ‭Suppose‬‭that‬‭individual‬‭E‬‭buys‬‭a‬‭bond‬‭with‬‭a‬‭par‬‭value‬‭of‬‭$120‬‭and‬‭pays‬‭$100‬‭for‬‭it.‬‭Let’s‬‭also‬‭assume‬ ‭that this bond doesn’t pay any coupons. Then, the rate of return =‬ ‭× 100% = 20%‬ ‭$120‬‭‬−‭‬‭$100‬ ‭$100‬ ‭This‬‭means‬‭that‬‭upon‬‭purchasing‬‭the‬‭bond,‬‭individual‬‭E‬‭expected‬‭a‬‭20%‬‭return.‬‭This‬‭return‬‭should‬‭be‬‭at‬ ‭least‬ ‭as‬ ‭good‬ ‭as‬ ‭any‬ ‭other‬ ‭return‬ ‭individual‬ ‭E‬ ‭could‬ ‭have‬ ‭gotten‬ ‭for‬ ‭their‬ ‭money,‬ ‭such‬ ‭as‬ ‭a‬ ‭savings‬ ‭account‬‭that‬‭also‬‭pays‬‭20%.‬‭In‬‭fact,‬‭if‬‭individual‬‭E’s‬‭bank‬‭interest‬‭rate‬‭is‬‭less‬‭than‬‭20%,‬‭then‬‭the‬‭bond‬‭is‬ ‭even more appealing.‬ ‭The‬ ‭interest‬ ‭received‬‭from‬‭bonds‬‭or‬‭any‬‭other‬‭fnancial‬‭asset‬‭such‬‭as‬‭savings‬‭accounts‬‭represents‬ ‭the‬ ‭cost‬‭of‬‭borrowing‬ ‭(for‬‭the‬‭borrower)‬‭or‬ ‭the‬‭return‬‭on‬‭saving‬‭and‬‭investment‬ ‭(for‬‭the‬‭lender‬‭or‬‭issuer).‬ ‭Consequently,‬ ‭the‬ ‭interest‬ ‭rate‬ ‭is‬ ‭the‬ ‭opportunity‬ ‭cost‬ ‭of‬ ‭holding‬ ‭money‬ ‭.‬ ‭If‬ ‭people‬ ‭decide‬ ‭to‬‭keep‬ ‭money‬ ‭in‬ ‭their‬ ‭safe‬ ‭or‬ ‭pocket‬ ‭instead‬ ‭of‬‭investing‬‭in‬‭a‬‭bond‬‭or‬‭a‬‭savings‬‭account,‬‭they‬‭would‬‭lose‬‭the‬ ‭interest rate they could have received instead.‬ ‭The Relationship Between Interest Rates and Bond Prices‬ ‭Although‬ ‭the‬ ‭determination‬ ‭of‬ ‭interest‬ ‭in‬ ‭the‬ ‭fnancial‬ ‭market‬ ‭will‬ ‭be‬ ‭discussed‬ ‭in‬ ‭later‬ ‭parts‬ ‭of‬ ‭this‬ ‭chapter,‬ ‭we‬ ‭need‬ ‭to‬ ‭understand‬ ‭the‬ ‭relationship‬ ‭between‬ ‭interest‬ ‭rates‬ ‭and‬ ‭bond‬ ‭prices.‬ ‭This‬ ‭relationship‬ ‭is‬ ‭a‬ ‭fundamental‬ ‭principle‬ ‭in‬ ‭bond‬ ‭investing‬ ‭and‬ ‭is‬ ‭known‬ ‭as‬ ‭the‬ ‭inverse‬ ‭relationship‬ ‭between interest rates and bond prices‬ ‭.‬ ‭Since‬ ‭bond‬ ‭prices‬‭differ‬‭between‬‭the‬‭face‬‭value‬‭and‬‭the‬‭actual‬‭market‬‭price‬‭at‬‭which‬‭they’re‬‭traded,‬‭a‬ ‭calculation‬ ‭is‬ ‭needed‬ ‭to‬ ‭align‬ ‭between‬ ‭the‬ ‭two‬ ‭values.‬ ‭This‬ ‭is‬ ‭known‬ ‭as‬ ‭the‬ ‭yield,‬ ‭which‬ ‭is‬ ‭a‬ ‭simple‬ ‭measure of a bond’s income relative to its current price. It is calculated as follows:‬ ‭Rate of return =‬

‭ ‬‭‬‭ ‬‭‬(‭ ‬‭‬‭ ‭ ‬‭‬‭ ‬‭‬‭ ‬‭ ‬‭ ‬‭ ‬‭ ‬ ‬)

‭Yield =‬

‭× 100%‬

‭Let's say someone has a bond with the following characteristics:‬

‭Par value: $1,000‬

‭Annual coupon payment: $50‬

‭115‬

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