Interest Rate

The nominal interest rate is the stated rate before adjustment for inflation. When a bank advertises a savings account paying three percent annually, it is quoting the nominal rate. The nominal rate is what borrowers contractually agree to pay and what lenders contractually agree to receive, without reference to the erosion of purchasing power that inflation imposes on the real value of those payments.

The real interest rate is the nominal rate adjusted for inflation, representing the actual increase in purchasing power that the lender achieves after accounting for the inflation that erodes the real value of the nominal interest payments received. The Fisher equation, developed by economist Irving Fisher, describes the relationship between nominal rates, real rates, and inflation: the nominal rate approximately equals the real rate plus the expected inflation rate. More precisely, one plus the nominal rate equals one plus the real rate multiplied by one plus the inflation rate. When nominal rates are low relative to prevailing inflation, real rates are negative, meaning lenders are actually losing purchasing power despite receiving nominal interest payments, a situation that has been relatively common in periods of high inflation or when central banks hold rates near zero in inflationary environments.

The risk-free rate is the theoretical return on an investment with absolutely no credit risk and no uncertainty about the return to be received. In practice, the risk-free rate is approximated by the yield on short-term US Treasury securities, most commonly the three-month Treasury bill, which are backed by the full faith and credit of the US government and are considered to have negligible credit risk. The risk-free rate serves as the baseline against which all other interest rates and investment returns are measured, with higher-risk instruments required to offer yields above the risk-free rate to compensate investors for the additional risk they bear.

The prime rate is the benchmark interest rate that large US commercial banks charge their most creditworthy corporate borrowers, historically set at three percentage points above the federal funds rate and used as the reference rate for many consumer and commercial loan products including credit cards, home equity lines of credit, and certain business loans. Changes in the federal funds rate target typically produce immediate corresponding changes in the prime rate, transmitting monetary policy changes directly to consumer and business borrowing costs.

The London Interbank Offered Rate, once the most important benchmark interest rate in the global financial system, has been replaced by risk-free alternative rates including the Secured Overnight Financing Rate in the United States, the Sterling Overnight Index Average in the United Kingdom, and the Euro Short-Term Rate in the European Union. LIBOR represented the rate at which large international banks could borrow unsecured funds from each other in the interbank market, and its use as a reference rate for hundreds of trillions of dollars of financial contracts made its eventual manipulation scandal one of the most consequential in financial regulatory history. The transition away from LIBOR to SOFR and other risk-free rates was completed in the United States by June 2023 for most purposes.

The Secured Overnight Financing Rate, universally abbreviated as SOFR, is the primary US dollar reference rate that has replaced LIBOR, measuring the cost of borrowing cash overnight collateralised by US Treasury securities in the repurchase agreement market. SOFR is a transactions-based rate derived from actual market activity rather than bank submissions, making it more robust and more resistant to manipulation than LIBOR. The overnight nature of SOFR requires the construction of term rates for use in longer-dated financial contracts through derivatives-based methodologies that approximate the expected average SOFR over specified periods.

The Structure of Interest Rates: The Yield Curve

The relationship between interest rates and the maturity of the underlying obligation at any given point in time is captured by the yield curve, one of the most important analytical tools in fixed income markets and macroeconomic analysis. As discussed in detail in the Government Bond article in Section G, the yield curve plots yields against maturities for bonds of the same credit quality, typically US Treasury securities, revealing the current structure of interest rates across the full spectrum of investment horizons.

The term structure of interest rates, the theoretical framework underlying the yield curve, can be explained by three competing theories that each capture different aspects of why longer-maturity bonds typically yield more than shorter-maturity bonds.

The pure expectations theory holds that the yield on any long-term bond is determined by the market's expectation of the average short-term rate that will prevail over the life of the long-term bond. Under this theory, a two-year bond should yield the same as rolling over two consecutive one-year bonds, and any departure from this relationship would create arbitrage opportunities. The pure expectations theory implies that an inverted yield curve reflects market expectations of falling short-term rates in the future, typically associated with anticipated recession and central bank easing.

The liquidity preference theory modifies the pure expectations theory by adding a liquidity premium to compensate investors for the greater price risk and uncertainty associated with longer-maturity bonds. Under this theory, investors demand progressively higher yields for longer maturities not only because of interest rate expectations but also because of the greater uncertainty and price volatility that longer maturities entail. The liquidity premium is what typically produces the normal upward-sloping shape of the yield curve even when short-term rates are expected to remain stable.

The market segmentation theory holds that investors and borrowers in different maturity segments of the bond market have specific preferences for particular maturities and do not readily substitute across segments, meaning that supply and demand conditions in each maturity segment independently determine yields in that segment. Under this theory, pension funds that prefer long-duration bonds because of their liability-matching characteristics create demand that lowers long-term yields independently of interest rate expectations, while commercial banks that prefer short-term assets drive demand in the short end.

Factors Determining Interest Rates

The level of interest rates at any given time reflects the interaction of multiple forces operating simultaneously across monetary policy, economic conditions, inflation expectations, credit risk, and the global supply and demand for capital.

Monetary policy is the most direct and most powerful determinant of short-term interest rates in the United States, as the Federal Reserve sets the target range for the federal funds rate that anchors the entire short end of the yield curve. As discussed in the Federal Reserve and Federal Funds Rate articles in Section F, the FOMC adjusts the federal funds rate in response to economic conditions and the pursuit of its dual mandate of maximum employment and stable prices. Changes in the federal funds rate target produce immediate corresponding changes in short-term money market rates and are transmitted to longer-term rates through the expectations and term premium channels described in the yield curve discussion.

Inflation expectations are a critical determinant of longer-term interest rates because lenders require compensation for the expected erosion of the real value of their loan principal and interest payments by inflation over the life of the loan. The Fisher equation establishes that nominal rates must incorporate expected inflation, meaning that increases in inflation expectations are directly reflected in higher nominal interest rates even if the real rate demanded by lenders remains unchanged. The TIPS breakeven inflation rate, the difference in yield between nominal Treasury securities and TIPS of the same maturity, provides a real-time market measure of the inflation expectations embedded in current interest rate levels.

Credit risk is the primary determinant of the interest rate differential between different borrowers of the same maturity, with riskier borrowers required to pay higher rates to compensate lenders for the greater probability of default. The risk-free rate established by Treasury yields is the baseline, and the credit spread above that baseline reflects the market's assessment of the default probability and expected recovery for each specific borrower. Investment grade corporate bonds, high-yield bonds, and speculative grade consumer credit each carry progressively larger credit spreads reflecting the progressively higher default risk of each category.

Economic growth expectations influence interest rates through multiple channels. Strong expected economic growth typically supports higher interest rates by creating strong demand for capital from businesses investing in expansion, increasing the productivity of capital and therefore the rate borrowers can afford to pay, and often generating inflationary pressure that must be reflected in higher nominal rates. Weak economic growth expectations suppress interest rates by reducing capital demand, increasing risk aversion among lenders, and typically prompting central bank accommodation.

The global supply and demand for savings and investment capital influences interest rates through international capital flows that connect the interest rate levels of different countries. When global savings are abundant relative to investment opportunities, as has been the case for much of the past two decades due to high savings rates in Asian economies, ageing populations in developed countries, and the so-called global savings glut identified by Ben Bernanke, the resulting capital flows can suppress interest rates below levels that would prevail in a closed economy even when domestic economic conditions might suggest higher rates.

Interest Rate Risk

Interest rate risk is the risk that changes in prevailing market interest rates will adversely affect the value of a financial instrument or portfolio. It is the most fundamental and most pervasive risk in the fixed income universe, affecting all instruments whose cash flows are fixed in nominal terms and whose value therefore depends on the discount rate applied to those fixed future cash flows.

The price sensitivity of a fixed income instrument to interest rate changes is measured by its duration, as described comprehensively in the Duration article in Section D. The inverse relationship between bond prices and interest rates, whereby rising rates reduce bond prices and falling rates increase them, is mathematically derived from the present value relationship between a bond's fixed future cash flows and the discount rate applied to those cash flows. Longer-maturity bonds have higher duration and therefore greater price sensitivity to interest rate changes, making them more appropriate for investors who can tolerate mark-to-market price volatility but less appropriate for those who may need to liquidate positions before maturity.

Reinvestment risk is the complementary dimension of interest rate risk for bond investors who plan to hold their bonds and reinvest the coupon income received. When interest rates fall, the coupon payments received from existing bonds must be reinvested at the lower prevailing rates, reducing the total return from the bond investment below what was anticipated when the bond was purchased at a higher yield. Reinvestment risk and price risk offset each other over a horizon equal to the bond's duration, which is the basis for the immunisation strategies described in the Duration article.

Interest rate risk in equity portfolios operates through the discount rate channel, whereby changes in interest rates affect the present value of future corporate earnings that determines equity valuations. Higher interest rates increase the discount rate applied to future earnings, reducing their present value and creating downward pressure on equity prices. The sensitivity of equity valuations to interest rate changes varies across sectors, with high-duration growth stocks whose value is concentrated in distant future earnings being more sensitive than value stocks with high current earnings that are less dependent on the level of the discount rate.

Interest Rates in Financial Planning

For financial planners and investment advisers working with individual clients, interest rate levels and trends are pervasive and critically important inputs to virtually every financial planning decision.

Mortgage planning is one of the most practically important interest rate applications for individual clients, as the prevailing level of mortgage rates directly determines the monthly payment required to finance a home purchase and therefore the affordable price range for borrowers with given income and savings levels. The decision between fixed-rate and adjustable-rate mortgages involves an explicit trade-off between rate certainty and the potential savings from lower initial adjustable rates, a trade-off that depends critically on the client's expected holding period, their capacity to absorb payment increases if rates rise, and their view on the likely direction of rates over the relevant horizon.

Retirement income planning must account for the interest rate environment's effect on the returns available from fixed income and the income generated by annuities, whose pricing is directly linked to prevailing interest rates. Low interest rate environments reduce the income available from conservative fixed income portfolios and increase the cost of lifetime income annuities, creating challenges for clients who prefer or require conservative investment strategies and are seeking reliable income in retirement.

Debt management decisions including the prioritisation of debt repayment versus investment, the refinancing of existing debt at lower rates, and the structuring of liability profiles across fixed and variable rate instruments all depend critically on the level and direction of interest rates and must be integrated with the broader investment planning process to ensure optimal outcomes.

The opportunity cost of cash and the cost-benefit calculation for maintaining cash reserves versus deploying capital into productive investments changes dramatically with the level of interest rates. In a zero-interest-rate environment, the opportunity cost of holding cash is minimal, while in a five-percent-rate environment the opportunity cost of holding uninvested cash is substantial, affecting the appropriate level of liquid reserves and the urgency of deploying capital from new contributions.

Reading the Forward Rate That Two Spot Rates Imply

Two yields quoted at the same moment for different maturities carry between them a third rate: the rate for the interval that separates them. Because a two-year commitment and a one-year commitment are both available now, the two-year yield must be reconcilable with the one-year yield plus some rate for the second year, and that second-year rate can be recovered from the two quotations by arithmetic alone. The total growth promised by the longer rate is divided by the total growth promised by the shorter one, and what remains is the growth implied for the interval between them. This recovered figure is the forward rate, and it is a property of the two quotations rather than a forecast anyone has published.

Take a one-year rate of four percent and a two-year rate of five percent. One dollar lent for two years at five percent grows to 1.05 multiplied by 1.05, or 1.1025. One dollar lent for one year at four percent grows to 1.04. Dividing 1.1025 by 1.04 gives 1.0601, so the implied rate for the second year is about 6.01 percent. The arithmetic can be read back in the other direction as a check: 1.04 multiplied by 1.0601 returns 1.1025, the same total the two-year rate produces. The implied second-year rate exceeds both quoted rates, which is the ordinary result where the longer quoted rate is above the shorter one, because the second year must carry the whole of the excess.

An investor choosing between a two-year commitment and two successive one-year commitments is therefore not comparing a known rate with an unknown one. The comparison is between the second-year rate the investor expects and the forward rate the two quotations already imply, and the two strategies produce the same total only where those two figures coincide. Where the investor expects a second-year rate below the implied forward, the two-year commitment produces the larger total; where the expected rate is above it, the sequence of one-year commitments does. Nothing in this comparison requires a view about the level of rates, only a view about the second year measured against a figure the market has already supplied.

Separating Expectation from Premium Inside a Quoted Slope

The forward rate recovered from two quotations equals the short-term rate the market expects for that future interval only where lenders demand nothing extra for the longer commitment. Where a premium is demanded for the greater price risk of the longer maturity, that premium is inside the longer quoted yield, and therefore inside the forward rate recovered from it. The forward rate then exceeds the expected future short-term rate by the premium, and the excess is a payment for bearing uncertainty rather than a statement about where rates are going.

The two components can be separated only if one of them is known independently. Suppose the one-year rate is four percent, the two-year rate is five percent, and the market in fact expects the one-year rate twelve months from now to be four and a half percent. The forward rate implied by the two quotations is about 6.01 percent, so the premium is about 1.51 percentage points on the second year's rate. The same premium can be expressed on the two-year yield instead: if the expectation of four and a half percent were the whole story, the two-year yield would be the rate that makes 1.04 multiplied by 1.045 into two equal years, which is about 4.25 percent a year, so the quoted five percent exceeds the pure expectation by about three quarters of a percentage point a year.

In practice neither component is observed, and this is the structural limit on what a slope can be made to say. Two quoted yields supply one equation containing two unknown quantities, the expected future rate and the premium, so any division of the slope between them is consistent with the quotations. A reader who assumes the premium is zero reads the whole slope as an expectation, and a reader who assumes expectations are flat reads the whole slope as a premium; the quotations themselves do not choose between those readings.

One Observed Curve Read Under Each of the Three Theories

The three theories are competing explanations of the same observable, which means a single curve shape yields a different conclusion under each of them. Consider a flat curve on which the one-year and the two-year yields are both four percent. The pure expectations theory reads the two-year yield as the average of the short-term rates expected over its life, so a two-year yield equal to the one-year yield implies that the market expects the one-year rate to be unchanged a year from now: dividing 1.04 multiplied by 1.04 by 1.04 returns 1.04, an implied second-year rate of four percent.

The same flat curve read under the liquidity preference theory implies an expectation of falling rates, because the premium has to be taken out before the expectation can be read. Suppose the premium on the two-year maturity is half a percentage point a year, so the expectations component of the two-year yield is three and a half percent a year rather than four. One dollar compounded at three and a half percent for two years grows to 1.0712; dividing by the 1.04 the first year supplies leaves 1.0300, an expected one-year rate of about three percent for the second year. A flat curve that the first theory reads as an expectation of no change the second theory reads as an expectation of a one-point fall, from the same two quotations.

The market segmentation theory declines the inference altogether. If the yield in each maturity segment is set by the supply of and demand for bonds within that segment, then a flat curve records the relative strength of supply and demand at one maturity against another, and carries no information about the path of short-term rates at all. The three theories are therefore not three vocabularies for one account: a curve shape is evidence about expectations under the first, evidence about expectations blended with a premium under the second, and evidence about segment-level supply and demand under the third.

What the Theories Predict When Issuance Shifts Along the Curve

The theories can also be separated by what they predict when the quantity of bonds offered at one maturity changes while expectations about the path of short-term rates do not. Under the market segmentation theory an increase in the supply of bonds at a particular maturity raises the yield at that maturity and leaves the others where they were, because the buyers who would have to absorb the extra supply are the buyers in that segment and investors elsewhere on the curve do not move across to take it up. The yield rises where the supply arrived, and the shape of the curve changes at that point only.

Under the pure expectations theory the same change cannot alter the shape of the curve at all unless it alters the expected path of short-term rates, because every maturity's yield is tied to that single path. A yield that rose at one maturity without a change in expectations would make a holding at that maturity worth more than the sequence of short-term holdings it is supposed to match, and the arbitrage the theory relies on would close the gap. On this account a shift in the composition of issuance is absorbed without a change in relative yields, and the quantity offered at each maturity is not among the things that set the curve's shape.

A Policy Change Reaching a Prime-Linked Borrower

A loan whose rate is stated as the prime rate plus a fixed margin moves point for point with the prime rate. The margin is a term of the credit agreement and is not touched by a policy decision, so the whole of any change in the prime rate reaches the borrower's rate, and the borrower's rate changes by the same number of percentage points as the benchmark it references. This is what makes the prime rate the channel through which a policy decision arrives at a credit card balance or a home equity line of credit: the rate on the loan is not negotiated again, it is recomputed.

Suppose a bank's prime rate stands at seven and a half percent and a borrower holds a line of credit priced at prime plus two percentage points, so the rate charged is nine and a half percent. A three quarter point increase in the policy rate, passed into prime, lifts prime to eight and a quarter percent and the borrower's rate to ten and a quarter percent. On a balance of fifty thousand dollars the annual interest cost rises from four thousand seven hundred and fifty dollars to five thousand one hundred and twenty-five dollars, an increase of three hundred and seventy-five dollars, which is the three quarter point increase applied to the fifty thousand dollar balance.

The same policy increase does nothing at all to the rate owed by a borrower on an existing fixed-rate loan, whose rate was fixed by the contract when it was written. Two borrowers of the same bank, equally creditworthy, carrying the same balance, can therefore experience one policy decision as a full three quarter point increase in their cost of credit and as no change whatever, and the difference between them is which rate their agreement references rather than anything about the decision or about their own circumstances.

What a Cash Reserve Costs at Different Levels of Rates

The annual cost of holding a sum in cash is that sum multiplied by the difference between the rate obtainable on the alternative and the rate the cash itself earns. Written that way the cost is a quantity that can be computed rather than a judgement, and it has two inputs that move for quite different reasons: the size of the reserve, which the holder chooses, and the rate difference, which the holder does not.

Take a reserve of sixty thousand dollars held in a non-interest-bearing account. Where short-term instruments yield five percent, the reserve forgoes five percent of sixty thousand dollars, or three thousand dollars a year. Where short-term instruments yield a quarter of one percent, the identical reserve forgoes one hundred and fifty dollars a year. The reserve has not changed, the holder's intentions have not changed, and the figure has moved by two thousand eight hundred and fifty dollars a year.

Because the cost is the product of the reserve and the rate difference, it is proportional to that difference: five percent against a quarter of one percent is a ratio of twenty to one, so the same reserve costs twenty times as much to hold in the first environment as in the second. The consequence is that a reserve decided once and left alone becomes materially more expensive as rates rise without anybody deciding to spend more, and the cost of the decision changes although the decision does not.

A Borrower and a Depositor in the Same Household

A household that carries floating-rate debt and also holds interest-bearing balances is affected twice by one change in rates, and in opposite directions. A rise raises the interest it pays on the debt and raises the interest it earns on the balances, so the net effect is the rate change applied to the difference between the two amounts rather than to either one of them. The quantity that determines whether the household gains or loses is therefore the difference between what it has lent and what it has borrowed at rates that move.

Suppose a household owes two hundred thousand dollars on a floating-rate obligation and holds fifty thousand dollars in interest-bearing deposits. A rise of one percentage point in rates adds two thousand dollars to the annual interest it pays and five hundred dollars to the interest it earns, leaving it one thousand five hundred dollars a year worse off. The same figure follows directly from the difference: the household's floating debt exceeds its interest-bearing balances by one hundred and fifty thousand dollars, and one percentage point on one hundred and fifty thousand dollars is one thousand five hundred dollars.

Reverse the two amounts and the sign of the result reverses with them. A household holding two hundred thousand dollars of interest-bearing balances against fifty thousand dollars of floating-rate debt gains one thousand five hundred dollars a year from the identical one point rise. The direction in which a household is affected by a change in rates is settled by the composition of its own balance sheet rather than by the direction of the change, which is why the same rise is relief for one household and strain for another.

A Cost Paid Now Against a Lower Rate Later

Where a borrower can pay a sum now to obtain a lower rate on a debt, the two sides of the bargain are in different units: a cost in dollars against a saving in dollars a year. They are made comparable by dividing the cost by the annual saving, which gives the number of years the saving takes to recover the cost. The annual saving is itself a product, the reduction in the rate multiplied by the balance on which interest is charged, so the recovery period is the cost divided by that product.

Suppose a borrower with a balance of two hundred thousand dollars can reduce the rate by half a percentage point by paying three thousand dollars in costs. Half of one percent of two hundred thousand dollars is one thousand dollars, so the first year's interest saving is about one thousand dollars and the three thousand dollars is recovered in about three years. The saving shrinks slightly in each later year, because the balance on which it is computed is reduced by the principal the borrower repays, so three years is a slight understatement of the true recovery period rather than an exact figure.

Because the annual saving is proportional to the balance, the same cost and the same reduction in rate recover at quite different speeds on different debts. On a balance of four hundred thousand dollars the half point saves two thousand dollars a year and the three thousand dollars is recovered in about eighteen months; on a balance of one hundred thousand dollars it saves five hundred dollars a year and recovery takes about six years. Doubling the balance halves the recovery period, so the identical transaction can be recovered quickly or slowly on identical terms.

Examination Relevance and Key Takeaways

Interest rates are tested pervasively across the SIE, Series 7, and Series 65 examinations in the context of fixed income securities, monetary policy, asset valuation, portfolio construction, and financial planning. Candidates must understand the distinction between nominal and real interest rates and the Fisher equation, the types of interest rates including the risk-free rate, prime rate, and SOFR, the yield curve and its three theoretical explanations, the factors that determine the level of interest rates including monetary policy, inflation expectations, credit risk, and economic growth, the concept of interest rate risk and its measurement through duration, and the practical applications of interest rate analysis in financial planning including mortgage decisions, retirement income, and debt management.

The core points to retain are these: an interest rate is the percentage cost of borrowing or return on lending expressed annually; nominal rates are stated rates while real rates adjust for inflation through the Fisher equation which states that nominal rate approximately equals real rate plus expected inflation; the risk-free rate is proxied by short-term Treasury bill yields and serves as the baseline for all other rates and investment returns; SOFR has replaced LIBOR as the primary US dollar reference rate for floating rate financial instruments; the yield curve plots yields against maturities with the pure expectations theory, liquidity preference theory, and market segmentation theory each explaining aspects of its shape; monetary policy through the federal funds rate is the most direct determinant of short-term rates while inflation expectations dominate longer-term rate determination; interest rate risk is the risk that rising rates reduce the value of fixed income instruments, measured by duration; reinvestment risk is the complementary risk that falling rates reduce the returns available on reinvested coupon income; rising interest rates reduce equity valuations through the discount rate channel with growth stocks more sensitive than value stocks; and interest rate levels affect virtually every financial planning decision including mortgages, retirement income, debt management, and the opportunity cost of cash holdings.