Chapter 1. Interest Rate Risk and Inflation Risk

1. EIFM LECTURE 1:
INTEREST RATE RISK, INFLATION
RISK & LEARNING FROM
HISTORICAL RETURNS
PRESENTED BY DR YANHUI ZHU
07 OCT 2022

2. OVERVIEW
• In this lecture, we’ll learn about the definition and measurement of bond’s
interest rate risk
• Then, we’ll learn to understand the difference between nominal and real interest
rate before taking a look of the summary statistics of US nominal and real interest
rate and inflation rate in the last 80 years
• Finally, we’ll learn how to compare the returns over different holding periods

3. INTEREST-RATE RISK
• If the bond is not held to maturity, then its holding period return is uncertain at
the time of purchase and the investment in bond is risky
• Interest-rate risk is the risk that arises for bond owners from fluctuating interest
rates
• How much interest rate risk a bond is subject to depends on how sensitive its
price is to interest rate changes in the market
• Interest-rate risk can be quantifiably measured by the concept of duration, which
is mainly determined by the maturity of bond. The longer the maturity of a bond,
the more interest-rate risk its holders would bear

4. ZERO INTEREST RATE RISK?
• While long-term bonds bear substantial interest rate risk, short-term bonds do
not
• If the holding period of bonds matches their maturity, then they have zero
interest-rate risk
• This is because the selling price of these bonds at the end of the holding period
is fixed at face value

5. NOMINAL VS. REAL INTEREST RATE
• Nominal interest rate refers to the interest rate that does not take account of
inflation
• Nominal interest rate measures the return in terms of the money the bond can be
exchanged to, rather than the purchasing power of the bond
• Real interest rate refers to the interest rate that is adjusted by subtracting
expected changes in the price level (inflation) so that it more accurately reflects
the true cost of borrowing

6. EX ANTE VS. EX POST REAL INTEREST RATE
• The ex ante real interest rate refers to the interest rate that is adjusted for
expected changes in the price level
• The ex ante real interest rate is most important to economic decisions, and
typically it is what economists mean when they make reference to the real interest
rate
• The interest rate that is adjusted for actual changes in the price level is called the
ex post real interest rate. It describes how well a lender has done in real terms
after the fact

7. FISHER EQUATION
• The real interest rate is more accurately defined by the Fisher equation, named
for Irving Fisher, one of the great monetary economists of the twentieth century
• The Fisher equation states that the nominal interest rate i equals the real interest
rate ir plus the expected rate of inflation πe
• 𝑖 = 𝑖𝑟 + 𝜋𝑒
• Rearranging Fisher equation
• 𝑖𝑟 = 𝑖 − 𝜋𝑒

8. EXAMPLE
• Data:
• UK Government Bond's Yields (FT) UK government bond's yields (Bloomberg)
• UK Inflation Expectations (Reuters)
• UK Actual Inflation (BBC)
• Q: What’s the ex-ante 1-year real interest rate in the UK now?
• A: 3.89% - 9.5% = -5.61%
• Q: What’s the ex-post 1-year real interest rate in the UK now?
• A: 0.32% - 9.9% = -9.58%

10. MEASURING RETURNS OVER DIFFERENT HOLDING
PERIODS
• For simplicity, let’s consider a zero-coupon bond with a face value of $100
• The price we pay for the zero-coupon bond is less than the face value
• Denote P(T) as the price of the zero-coupon bond with a maturity date of T
• The value of investment will grow by the multiple of
100
𝑃(𝑇)
• The percentage increase in the value of the investment over the holding period is
𝑟(𝑇)
• 𝑟 𝑇 =
100
𝑃(𝑇)
− 1 =
100−𝑃(𝑇)
𝑃(𝑇)

11. EFFECTIVE
ANNUAL RATE
• Effective annual rate (EAR) refers to the interest
rate that is annualized using compound rather
than simple interest
• EAR allows up to compare returns over different
holding periods

12. ANNUAL PERCENTAGE RATE
• Annual percentage rate (APR) is the interest rate annualized using simple rather than
compound interest
• For example, the APR of your credit card is the monthly interest rate you pay
multiplied by 12
• With n compounding periods per year, we can find the EAR from the APR by first
computing the per-period rate as APR/n and then compounding for n periods
• 1 + 𝐸𝐴𝑅 = (1 +
𝐴𝑃𝑅
𝑛
)𝑛
• Equivalently, we can find the APR from the EAR:
• 𝐴𝑃𝑅 = 𝑛 × 1 + 𝐸𝐴𝑅
1
𝑛 − 1

13. EXAMPLE
• Suppose you must pay 1.5% interest per month on your outstanding credit card
balance. The APR would be reported as 1.5% × 12 = 18%, but the effective
annual rate is higher, 19.56%, because 1.01512 − 1 = 0.1956
• Until you pay off your outstanding balance, it will increase each month by the
multiple 1.015, so after 12 months, the balance will increase by 1.01512. This is
why we can EAR an effective rate

14. READING
• Mishkin (2016) Chapter 4
• Bodie, Kane and Marcus (2021) Chapter 5

15. ANY QUESTIONS?