Step 10: Financial Assets and Interest Rates
- Every financial asset is a trade-off between liquidity, rate of return and risk. Money is the most liquid but earns the least.
- Bond prices and interest rates move in opposite directions: when market interest rates rise, the prices of existing bonds fall.
- Real interest rate = nominal interest rate − expected inflation: \( r = i – \pi^e \).
- Unexpected inflation helps borrowers and hurts lenders; unexpectedly low inflation does the opposite.
What a financial asset is
Suppose you have saved $500 from a summer job. You could keep it as cash in a drawer, put it in a bank account, lend it to a company by buying a bond, or buy a few shares in a phone maker. Each of these is a financial asset: something you own that is a claim to money, now or in the future. The person or firm on the other side (the bank, the company) has a matching liability.
No asset is best on every count. To choose, savers weigh three features.
- Liquidity: how quickly and cheaply you can turn the asset into money you can spend, without losing value. Cash is perfectly liquid. A house is very illiquid: selling one takes months and costs fees.
- Rate of return: what the asset earns, as a percentage of what you paid. It includes interest or dividends plus any rise (or fall) in the asset’s price.
- Risk: how uncertain that return is. A risky asset might pay a lot or might lose you money.
These features pull against each other. In general, to get a higher expected return you must accept more risk, less liquidity, or both. That is why money pays little or nothing: you are “paying” for its liquidity and safety by giving up the interest you could have earned. This lost interest is the opportunity cost of holding money, an idea you will need for the money market.
Money, bonds and stocks compared
Three assets appear in almost every exam question.
- Money: cash and balances in current (checking) accounts. You can spend it at once.
- Bonds: a bond is a loan. When you buy a bond from a firm or government, you lend it money. In return it promises to pay you a fixed amount of interest each year (the coupon) and to repay the face value (also called par value) on a set date, the maturity date. Bondholders are lenders, not owners.
- Stocks (shares, equities): a share is part-ownership of a company. You may receive a slice of profits as dividends, and the share price can rise or fall. Shareholders are owners, so they are paid only after lenders if the firm fails.
| Asset | Liquidity | Typical return | Risk |
|---|---|---|---|
| Money (cash, current account) | Highest | Zero or very low | Very low (but inflation erodes its value) |
| Bonds | Medium: can be sold, but price may have changed | Medium: fixed interest | Medium: default risk and interest-rate risk |
| Stocks | Medium: easy to sell, but price swings | Highest on average over long periods | Highest: dividends and price both uncertain |
For example, you buy a share for $40. Over the year it pays a $2 dividend, and at the end of the year you sell it for $46. What was your rate of return?
You earned 20%. But if the price had fallen to $34, your return would have been \( (2 – 6) \div 40 = -10\% \). That uncertainty is the risk you accept for the chance of a high return.
Why bond prices and interest rates move in opposite directions
This is the single most tested idea in this topic. Start with an everyday picture. Last year you bought a bond that pays $50 a year on a $1,000 face value: a 5% coupon. This year interest rates rise, and new $1,000 bonds pay $100 a year (10%). You now want to sell your old bond. Who will pay $1,000 for $50 a year when they can buy a new bond paying $100 a year for the same price? Nobody. To sell it, you must cut the price until the buyer’s return matches the new 10% rate.
So when market interest rates rise, the prices of existing bonds fall. When market interest rates fall, existing bonds with their higher fixed coupons become more attractive, and their prices rise. The coupon on an existing bond is fixed, so the only thing that can adjust is its price.
Here \( i \) is the current market interest rate written as a decimal. The formula asks: “How much would I need to put in the bank today, at rate \( i \), to have the bond’s final payment in one year?”
A bond has a face value of $1,000, a 5% coupon and one year left to maturity. In one year it will pay $1,000 + $50 = $1,050. What is it worth if the market interest rate is (a) 5%, (b) 10%, (c) 2%?
When the market rate equals the coupon rate, the bond sells at face value. When rates rise to 10%, the price falls to $954.55: a buyer who pays $954.55 and receives $1,050 gains $95.45, which is \( 95.45 \div 954.55 = 10\% \), the new market rate. When rates fall to 2%, the price rises to $1,029.41.
You can also run the logic the other way. If the price of bonds falls, the return (yield) to anyone buying them rises. So “bond prices fall” and “interest rates rise” are two descriptions of the same event. You will use this in the money market: when people sell bonds, bond prices fall and interest rates rise.
Nominal and real interest rates
Imagine your bank pays 6% a year on savings. After a year, $1,000 grows to $1,060. That sounds like a gain of 6%. But if prices in the shops have risen by 4%, the things you wanted now cost 4% more, so your buying power has grown by only about 2%.
- The nominal interest rate (\( i \)) is the rate stated in money terms: the 6% the bank advertises.
- The real interest rate (\( r \)) is the nominal rate adjusted for inflation: the gain in purchasing power.
When a loan is agreed, nobody knows what inflation will be, so lenders and borrowers base the deal on expected inflation (\( \pi^e \)). This gives the Fisher equation:
The rearranged version shows how lenders set rates: they decide what real return they want, then add the inflation they expect. If expected inflation rises, nominal interest rates tend to rise with it (this is called the Fisher effect). Once the year is over, you can also work out the actual (ex post) real rate using the inflation that really happened: \( r = i – \pi \).
The formula \( r = i – \pi \) is an approximation that works well for low inflation rates, and it is the version AP, Cambridge and IB exams expect. The real rate can be negative: if a savings account pays 1% while inflation is 3%, the real rate is −2%, and your savings buy less each year.
Who gains and who loses from unexpected inflation
If inflation turns out exactly as expected, nobody is surprised: the nominal rate already included it, and the lender gets the real return both sides planned for. Problems arise when inflation is different from what was expected, because most loans fix the nominal rate in advance.
For example, a bank lends a small business $10,000 for one year at a nominal rate of 6%. Both sides expect inflation of 2%. In fact inflation turns out to be 5%. Find the expected and actual real interest rates and say who gains.
The bank planned to earn 4% in real terms but earned only about 1%. The business repays $10,600 as agreed, but those dollars buy less than expected, so its real cost of borrowing fell from 4% to 1%. Unexpected inflation has moved purchasing power from the lender to the borrower.
| Situation | Who gains | Who loses |
|---|---|---|
| Inflation higher than expected | Borrowers (e.g. people with fixed-rate mortgages, governments with large debts) | Lenders and savers; people on fixed money incomes such as some pensions |
| Inflation lower than expected (or unexpected deflation) | Lenders and savers | Borrowers, who repay dollars worth more than they planned |
Two points earn extra marks. First, it is unexpected inflation that redistributes; fully expected inflation is built into the nominal rate. Second, lenders who are caught out once will demand a higher nominal rate next time (an “inflation premium”), which raises borrowing costs for everyone. Loans with variable rates, or bonds whose payments are linked to inflation, reduce this risk.
Practise: 6 questions
Try each one on paper first, then check the worked answer.
EasyQ1. Rank these from most liquid to least liquid: a house, cash, a savings deposit, shares in a company. Show worked answer
Cash is already money. A savings deposit can be withdrawn quickly at full value. Shares can be sold quickly but their price may have fallen. A house takes months to sell and has large selling costs.
EasyQ2. A bank charges a nominal interest rate of 7%. Expected inflation is 3%. What is the expected real interest rate? Show worked answer
MediumQ3. A bond has a face value of $2,000, a 4% coupon and one year to maturity. The market interest rate rises from 4% to 8%. Calculate the bond’s price before and after the rise. Show worked answer
At 4%: price = 2,080 ÷ 1.04 = $2,000.00.
At 8%: price = 2,080 ÷ 1.08 = $1,925.93.
The price falls by $74.07, showing the inverse relationship between interest rates and bond prices. (Check: 1,925.93 × 1.08 ≈ 2,080.)
MediumQ4. A lender wants a real return of 3% and expects inflation of 4%. (a) What nominal rate should she charge? (b) Inflation turns out to be 9%. What real return does she actually earn, and who gains? Show worked answer
(b) Actual real rate = 7% − 9% = −2%. The lender loses purchasing power: the money repaid buys less than the money lent. The borrower gains, because the real cost of the loan is −2% instead of the expected 3%.
MediumQ5. You buy a share for $50. It pays a $1.50 dividend and you sell it a year later for $47. Calculate your rate of return. Show worked answer
Rate of return = −1.50 ÷ 50 × 100 = −3%.
The dividend was not enough to make up for the fall in the share price: this is the risk of holding stocks.
ExamQ6. A bank lends $50,000 for one year at a fixed nominal interest rate of 8%, when expected inflation is 3%. Actual inflation is 6%. (a) Calculate the expected real interest rate. (b) Calculate the actual real interest rate. (c) Identify who gains from the unexpected inflation and explain why. (d) The central bank then raises interest rates. Explain the effect on the price of bonds the bank already holds. [6 marks] Show worked answer
(b) Actual real rate = 8% − 6% = 2%. [1 mark]
(c) The borrower gains [1 mark]. The repayment of $54,000 is fixed in money terms, but because inflation was higher than expected, those dollars have less purchasing power, so the real cost of borrowing is 2% rather than 5% [1 mark].
(d) The price of existing bonds falls [1 mark]. Their coupons are fixed, so to compete with new bonds paying the higher rate, their price must fall until their yield equals the new market rate [1 mark].
Check yourself
1. Market interest rates fall. What happens to the price of existing bonds?
2. The nominal interest rate is 4% and inflation is 6%. The real interest rate is:
3. Inflation turns out lower than expected. Who gains?
Your score: 0 out of 3
The short version
- Financial assets trade off liquidity, rate of return and risk; money is most liquid but earns least, stocks are riskiest but earn most on average.
- A bond is a loan with a fixed coupon; a share is part-ownership of a firm.
- When market interest rates rise, the prices of existing bonds fall, and vice versa.
- Fisher equation: real rate = nominal rate − expected inflation, \( r = i – \pi^e \).
- Unexpectedly high inflation moves purchasing power from lenders to borrowers; unexpectedly low inflation does the reverse.
Further reading on EconTutorials
Older in-depth articles on this topic from our blog:
- Fiscal Policy: Government Spending, Taxation, Multipliers, and the Debt Debate
- Net Present Value (NPV) and Present Value in Economics: Formula, Examples and Investment Decisions
- Compound Interest Formula: Simple vs Compound vs Continuous Compounding with Worked Examples
- Quantitative Easing and the Zero Lower Bound: What Fifteen Years of Evidence Actually Shows