Chapter 3: Time Value of Money - The One-Period Model

basis point (bps, bips)

a unit that is equal to one one-hundreth of 1 percent

• 1.23% is 123 basis points

binomial model

a one-period framework that models uncertainty through 2 random states, up and down

certificate of deposit (CD)

a savings account where the depositor agrees not to withdraw their money for an agreed-upon time period; in return, the depositor receives a higher interest rate than traditional savings accounts

• penalties ensue from early withdrawals

• fed government insures CDs, so they are considered riskless

• large majority of CDs have terms of 1 year or less, making them part of the money market

Consumer Price Index (CPI)

a measure of inflation produced by the U.S. Bureau of Labor Statistics

• average change over time in the prices paid by urban consumers for a market basket of consumer goods and services

core measures of inflation

inflation metrics that strip out the volatile food and energy components from a representative households’s consumption bundle

decimal form

an interest rate expressed in its raw mathematical from without a % symbol

• ex: 12 percent is .12

dual mandate

the Fed’s two primary policy objectives of price stability and maximum sustainable employment

economic bad

all else equal, something that makes economic agents worse off

• ex: crime and pollution

expected value/payout/return

the probability-weighted average of the possible state-contingent outcomes, which may be payouts or returns in the binomial model

federal (fed) funds rate

a money market rate that one bank charges to lend its excess cash to another bank on an overnight basis; market participants widely view the fed funds rate as riskless

• the principal tool the Fed uses to influence interest rates throughout the economy to achieve its objectives of price stability and full employment

Federal Reserve (fed)

the central bank of the United States which is responsible for the nation’s monetary policy

• dual mandate

  • pursues the dual mandate by influencing the federal funds rate

fisher equation/effect

quantitative relationship between nominal interest rates, expected real interest rates, and expected inflation

future value (FV) 

lump sum cash flow that occurs later than the present value

inflation

a continuing rise in the general price level is the reason money is an imperfect store of value; it is a random variable with an expected value

lump sum

a single amount of money at a particular time, as defined by a contract

maximum sustainable/full employment

goal is to achieve the natural rate of unemployment; due to frictions such as workers changing jobs, entering the labor force and then leaving it, there is a natural level of unemployment about 0

• fed achieves full employment when the unemployment rate achieves the natural level of around 4%

money supply

number of dollars held as currency and in checking and saving accounts

• conceptually: money that somebody can convert into consumption quickly; impacting prices and output (concerns of the Fed)

nominal interest rate

the percentage change in dollars per period; random variable with an expected value

• riskless assets: the rate of return you will earn

Personal Consumption Expenditures Price Index (PCE)

measure of inflation produced by the Bureau of Economic Analysis that tracks the prices that people living in the United States pay for goods and services

• known for capturing inflation (or deflation) across a wide range of consumer expenses and reflecting changes in consumer behavior

present value (PV)

a lump sum cash flow that falls earlier than the future value

price stability

goal is to achieve a low and predictable rate of inflation (target around 2% per year)

• one of the Fed’s 2 primary concerns

random variable

a variable whose value is the product of a random process; must have 2 or more possible outcomes that one does not know in advance of their realization

rate of time preference

the degree to which an individual places importance on receiving money today rather than in the future

recession

a period of falling national output, usually for two consecutive calendar quarters

real interest rate

the percentage change in purchasing power for a given period; random variable with an expected value

• anything that affects output can impact the real rate

  • factors include: economy’s growth potential, demographics, productivity. gains, labor force participation, pandemics, and others

realized/holding-period returns

the return the investor receives at the end of the period after time resolves the uncertainty by revealing the true state of the worldr

risk-averse

the behavior of an individual who views risk as an economic good, thus will pay to bear it

• ex: gamblers and entrepreneurs pay more than the expected value to play a risky game

risk-neutral 

the behavior of an individual who is indifferent to risk

• only pay attention to the first moment of a random variable’s distribution (the expected value)

risk premium

the extra compensation a risk-averse person demands to bear risk

risk-reward tradeoff

the result of risk-averse traders who view returns as an economic good and risk as an economic bad; preferences influence asset prices such that low-risk assets pay small returns while riskier assets pay higher returns

state-contingent payout (return)

the payout or return the party receives once time resolves the uncertainty and reveals the state

time value of money (TVM)

the concept that economic agents have preferences over when money is paid or received due to opportunity costs and their unique personal preferences

uncertainty

not knowing which of a least 2 random states the passage of time will reveal