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Question 1

What is Money?

Answer 1

Money is a tool people use to buy goods and services. It serves three purposes:
- A medium of exchange: Makes trade easier.
- A store of value: Keeps its value over time.
- A unit of account: Measures the value of things (e.g., $1 = a candy bar).

Question 2

What is a Bank?

Answer 2

• A bank is where people keep money safe. Banks:
  - Take deposits and pay interest.
  - Use deposits to give loans at higher interest rates.
  
  • Banks must keep some money as reserves

Question 3

What is an Interest Rate?

Answer 3

The interest rate is the cost of borrowing money or the reward for saving money.
- Example: Borrow $100 at 5%, and you owe $105.

Question 4

Why is it Bad to Have “Too Much” Money?

Answer 4

• If there’s too much money in circulation, people spend more, which:
  - Increases demand for goods and services.
  - Drives up prices (inflation).
  
  • Excessive inflation reduces the value of money and can destabilize the economy.

Question 5

What is the Federal Reserve (Fed)

Answer 5

• The Fed is the central bank of the United States, responsible for:
  - Managing money supply: Ensuring there’s enough money but not too much.
  - Banking services: Acts as a bank for the government and commercial banks.
  - Regulating banks: Prevents risky behavior by banks.
  - Controlling inflation and unemployment: Balances prices and jobs.

Question 6

What is the Fed’s Dual Mandate?

Answer 6

• The Fed’s two main goals:
  1. Full Employment: Aim for most people to have jobs.
  2. Low Inflation: Prices shouldn’t rise too quickly.
  
  • Why do rising interest rates cause fewer jobs?
    
    • Higher rates increase borrowing costs for businesses and people, reducing spending and investments, which slows the economy and leads to fewer jobs.

Question 7

What is the Fed Funds Rate?

Answer 7

• The Fed Funds Rate (FFR) is the interest rate at which banks lend to each other overnight.
  
  • Why do banks need reserves?
    
    • To meet withdrawals by customers.
    • To comply with Fed requirements.
    • If a bank doesn’t have enough reserves, it risks financial trouble and regulatory penalties

Question 8

How Does the Fed Control the Fed Funds Rate?

Answer 8

• Before 2008: Open Market Operations (OMO)
  - The Fed bought or sold bonds:
  - Buying bonds: Gave banks more money (reserves), lowering interest rates.
  - Selling bonds: Took money from banks, raising rates.
  - What is a bond?
  - A bond is a loan from an investor to a borrower (like the government) that pays back with interest over time.
  • After 2008: Interest on Reserves
    
    • The Fed started paying interest on bank reserves held at the Fed.
    • Banks now decide whether to:
      - Lend to other banks at the FFR.
      - Keep reserves at the Fed and earn a fixed interest rate (default-free).
    • This system:
      - Creates a floor for the FFR, as banks won’t lend to others below the rate they can earn from the Fed.

Question 9

Why Does More Money with Banks Lower Interest Rates?

Answer 9

• Banks compete to lend money when they have excess reserves, which pushes rates down.
  
  • Conversely, less money means banks charge higher rates to borrow funds.

Question 10

What is Quantitative Easing (QE)?

Answer 10

• A tool used during crises to lower long-term interest rates.
  
  • The Fed buys long-term bonds, increasing demand for them. This:
    
    • Raises bond prices.
    • Lowers bond yields (interest rates).

Question 11

Why not use QE often?

Answer 11

It’s typically reserved for crises like the 2008 financial crash or COVID-19, as it risks overheating the economy or creating bubbles.

Question 12

What is the Fed’s Balance Sheet?

Answer 12

• Assets: Treasuries and mortgage-backed securities (MBS).
  
  • Liabilities: Bank reserves and U.S. currency in circulation.

Question 13

Why does the Fed create money?

Answer 13

• To buy assets or inject liquidity into the economy during crises.
  - The amount created depends on economic conditions and policy goals.

Question 14

What are Fed Funds Futures (FFF)?

Answer 14

• Contracts predicting where the FFR will be in the future.
  
  • Used by:
    
    • Investors to hedge risks from unexpected rate changes.
    • Speculators profit from rate predictions.
  • Who calculates FFF prices?
    
    • Market participants (buyers and sellers) based on economic data and expectations.

Question 15

What is Arbitrage?

Answer 15

• Definition: Profiting from price differences in markets.
  
  • Example in the FFR Market:
    
    • Banks borrow at a low FFR and earn a higher rate by keeping reserves at the Fed.
  • The term comes from the French word “arbitrer,” meaning “to judge.”

Question 16

What is Stagflation?

Answer 16

• High inflation and high unemployment at the same time.
  
  • The Fed must carefully balance tools to avoid worsening either issue.

Question 17

What is the FOMC?

Answer 17

• The Federal Open Market Committee sets monetary policy (e.g., target FFR range).
  
  • Members include Fed governors and regional bank presidents.
  • Example: Deciding whether to raise or lower rates based on inflation data.

Question 18

Relation Between FFR and Interest on Reserves

Answer 18

• Banks choose between lending to other banks (FFR) or keeping reserves (interest on reserves).
  
  • Non-bank participants (e.g., GSEs) also influence the market, pushing the FFR slightly below the interest on reserves.

Question 19

What is a Mortgage-Backed Security (MBS)?

Answer 19

A bundle of home loans sold to investors, who earn returns as borrowers pay off their mortgages.

Question 20

What are Options on Fed Funds?

Answer 20

• Like FFF, but offer more flexibility to predict rate movements, especially over longer horizons.

Question 21

How Does the Fed Create Money?

Answer 21

• It electronically credits banks when buying assets.
  
  • This expands its balance sheet, injecting money into the economy.

Question 22

Arbitrage Pricing

Answer 22

Determining the value of securities by replicating their cash flows using other assets.

Question 23

Portfolio Optimization

Answer 23

Selecting a mix of investments to maximize returns for a given level of risk.

Question 24

What is Arbitrage Pricing?

Answer 24

What is Arbitrage?
- Arbitrage is the practice of making risk-free profits by exploiting price differences between markets.
- Example: If gold costs $2,650 in New York but $2,700 in London:
- Buy gold in New York for $2,650.
- Sell it in London for $2,700.
- Profit = $50.
- Arbitrage opportunities disappear as prices in different markets adjust.

Question 25

What is the Law of One Price?

Answer 25

• The Law of One Price states that two portfolios with the same future cash flows must have the same price today.
  
  • If prices differ, arbitrageurs can buy the cheaper portfolio and sell the expensive one to earn a profit.

Question 26

Pricing by Replication

Answer 26

• To determine the price of a security, create a replicating portfolio that mimics its cash flows.
  
  • Replicating Portfolio: A combination of other assets whose combined future cash flows are identical to the security being valued

Question 27

Arbitrage Pricing with Two Goods Example

Answer 27

• Scenario: A portfolio of 2 apples and 1 banana costs $7. One apple costs $3.
  
  • What is the price of one banana (PB)?
    - If 2 apples cost $6 (2 × $3), then the remaining $1 ($7 - $6) must be the price of 1 banana.
    - Answer: PB = $1.

Question 28

Methodologies for Solving Arbitrage Pricing Problems

Answer 28

• Method 1: Replicate each asset using portfolios and solve for their prices.
  - Advantage: Identifies replicating portfolios explicitly.
  - Disadvantage: Requires more calculations.
  
  • Method 2: Use fundamental asset prices (e.g., price of 1 apple and 1 banana) to calculate portfolio prices.
    - Advantage: Simpler calculations.
    - Disadvantage: Does not identify replicating portfolios.

Question 29

What is a Bond?

Answer 29

A bond is a loan where the borrower agrees to pay back the principal (face value) and periodic interest (coupon payments).

Question 30

Zero-Coupon Bond

Answer 30

A bond with no periodic interest; it only pays the face value at maturity.

Question 31

Coupon Bond

Answer 31

A bond that pays periodic interest and returns the face value at maturity.

Question 32

Example: Pricing a Coupon Bond

Answer 32

• Scenario: A bond pays $5 in year 1 and $105 in year 2.
  
  • Use replicating portfolios of zero-coupon bonds to determine its price:
    - Cost = (0.05 × $95) + (1.05 × $90) = $99.25.
  • If the bond sells for $100, an arbitrage opportunity exists:
    - Buy the replicating portfolio for $99.25.
    - Sell the bond for $100.
    - Profit = $0.75.

Question 33

What is a Call Option?

Answer 33

• A call option gives the right (but not the obligation) to buy a stock at a specific price (strike price) in the future.
  
  • Payoff: At expiration, the value of the call option is:
    - CT = max(0, ST - K), where ST is the stock price and K is the strike price.

Question 34

Example: Pricing a Call Option

Answer 34

• Scenario:
  - Current stock price (S0) = $60.
  - Strike price (K) = $63.
  - Stock price can rise to $72 or fall to $54.
  
  • Replicating Portfolio:
    - Buy 0.5 shares of stock.
    - Short-sell 0.27 bonds.
  • Cost of Replication:
    - Price = (0.5 × $60) - (0.27 × $100) = $30 - $27 = $3.
  • The call option’s price is $3.

Question 35

What is Portfolio Optimization?

Answer 35

The process of selecting investments to maximize returns for a given level of risk or minimize risk for a given level of returns.

Question 36

Risk and Return

Answer 36

• Expected Return: Average return expected from an investment.
  
  • Risk: Measured by variance or standard deviation of returns.

Question 37

Diversification

Answer 37

• Diversification reduces risk by combining assets whose returns are not perfectly correlated.
  
  • Example: Insurance policies have low returns but reduce the overall risk of a portfolio.

Question 38

What are Fixed Income Securities?

Answer 38

• Definition: Assets that promise future cash flows (CFs) through a contract.
  
  • Example: Bonds specify the interest and principal repayment schedule.
  • Comparison to Equity:
    
    • Equity offers no guarantees of future dividends.
    • Fixed income securities are more predictable but may involve risks.

Question 39

Types of Fixed Income Securities

Answer 39

• Treasuries: Debt issued by the U.S. government.
  
  • Corporate Bonds: Issued by companies; higher yield but risk of default.
  • Floating Rate Bonds: Interest payments vary with market rates.
  • Convertible Bonds: Can be converted into company equity (stock).
  • Mortgage-Backed Securities (MBS): Securities backed by home loans.
  • Agency Bonds: Issued by government-affiliated agencies (e.g., Fannie Mae).
  • Municipal Bonds: Issued by state or local governments.

Question 40

Bond Features

Answer 40

• Face Value (Principal): The amount paid back at maturity.
  
  • Coupon Rate: The annual interest rate based on face value.
    
    • Example: A bond with a face value of $1,000 and a coupon rate of 5% pays $50 annually.
  • Time to Maturity: The period over which the bond pays interest before the principal is returned.

Question 41

Risks in Fixed Income Securities: Interest Rate Risk

Answer 41

• If rates rise, bond prices fall.
  
  • Example: A bond worth $1,000 at 4% may drop in value if rates rise to 5%.

Question 42

Risks in Fixed Income Securities: Reinvestment Risk

Answer 42

• Uncertainty about the rate at which cash flows can be reinvested.

Question 43

Risk in Fixed Income Securities: Default Risk

Answer 43

• The risk that the issuer cannot meet payment obligations.
  
  • Example: Corporate bonds may default, unlike U.S. Treasuries.

Question 44

Risk in Fixed Income Securities: Inflation Risk

Answer 44

• Inflation reduces the purchasing power of cash flows.
  
  • Example: A 2% bond yield loses value if inflation rises to 3%.

Question 45

Risk in Fixed Income Securities: Liquidity Risk

Answer 45

• Difficulty in selling the bond without losing value.

Question 45

Risk in Fixed Income Securities: Volatility Risk

Answer 45

Price changes due to market volatility.

Question 46

Pricing of Bonds

Answer 46

• Inverse Relationship Between Price and Yield:
  
  • Bond prices fall as interest rates rise.
  • Why? Investors demand a discount to compensate for lower relative returns.
  • Term Structure of Interest Rates (Yield Curve):
    
    • Shows the relationship between yields and maturities.

Question 47

Special Bond Features

Answer 47

• Call Options: Allows the issuer to repay the bond early, exposing investors to reinvestment risk.
  
  • Put Options: Lets investors sell the bond back to the issuer, reducing risk.
  • Convertible Bonds: Can be exchanged for equity, often increasing in value when the stock performs well.

Question 48

Repo Market

Answer 48

• Definition: A repurchase agreement where one party sells a security with an agreement to buy it back later at a higher price.
  
  • Key Terms:
    
    • Repo Rate: The implied interest rate in the agreement.
    • Reverse Repo: The opposite transaction (buy now, sell later).
  • Importance:
    
    • Provides short-term funding and liquidity for financial institutions.

Question 49

Securitization

Answer 49

Repacks cash flows from existing securities into new securities.
Example: Creating floaters/inverse floaters from fixed-rate bonds.

Question 50

Leverage

Answer 50

• Borrowing to increase potential returns.
  
  • Example: Using $100 in equity and $400 in borrowed funds to invest.

Question 51

Present Value (PV)

Answer 51

Present Value is the current worth of a future amount of money or cash flow, discounted at a specific rate of interest to reflect the time value of money.

This concept relies on the principle that money today is worth more than the same amount in the future because it can be invested to earn interest.

Example: If you are promised $1,000 in 3 years and the interest rate is 5%, the present value of that $1,000 is approximately $863.84.

Question 52

Future Value (FV)

Answer 52

Future Value represents how much an investment made today will grow to be worth at a specified date in the future, given a particular interest rate and compounding frequency.

The concept demonstrates how interest accumulation increases the investment’s value over time.

Question 53

Annuity

Answer 53

An annuity is a financial product that provides regular, periodic payments over a specified period. These payments are typically equal and made at fixed intervals (e.g., monthly, quarterly).

Question 54

Ordinary Annuity:

Answer 54

Payments occur at the end of each period (e.g., mortgage payments).

Question 55

Annuity Due

Answer 55

Payments occur at the beginning of each period (e.g., rent payments).

Question 56

Price-Yield Relationship

Answer 56

The price of a bond and its yield (or interest rate) move inversely. This relationship reflects the fundamental market principle that as the opportunity cost of holding a bond (interest rate) increases, the price of the bond must decrease to remain attractive.

Example: A bond with a fixed 5% coupon rate becomes less valuable if new bonds are offering 6% yields, so its price drops.

Question 57

Pull to Par

Answer 57

As a bond approaches its maturity date, its price converges toward its face value (par), regardless of whether it was originally purchased at a premium or discount.

This happens because the bondholder will receive the face value at maturity, which stabilizes its price near par value as the maturity nears.

Example: A bond trading at $950 with a face value of $1,000 will gradually approach $1,000 as it nears maturity.

Question 58

Price-Time Relationship

Answer 58

Bond prices not only fluctuate with interest rates but also change as time passes, especially if the bond is trading at a premium or discount.

Pull to Par is a component of this concept, where time’s effect on price diminishes as maturity approaches.

This relationship illustrates how bonds “self-correct” in terms of price over time.

Question 59

Accrued Interest

Answer 59

Accrued interest represents the portion of a bond’s coupon payment that has been earned but not yet paid since the last payment date.

When a bond is traded, the buyer compensates the seller for this interest by paying the “dirty price,” which includes accrued interest.

Example: If a bond pays $60 annually in two semiannual payments of $30, and it’s been 3 months since the last payment, accrued interest is $15.

Question 60

Dirty Price vs. Clean Price

Answer 60

The difference between these prices ensures that the seller is compensated for holding the bond during the interest accrual period.

Question 61

Dirty Price

Answer 61

The total price a bond buyer pays, including accrued interest.

Question 62

Clean Price

Answer 62

The quoted price of the bond, excluding accrued interest.

Question 63

Bond at Par, Premium, and Discount

Answer 63

Bonds are sold at par, premium, or discount, depending on how their coupon rate compares to the market interest rate

Example: A bond with a $1,000 face value and a coupon rate of 5% will sell for more than $1,000 if the market rate is 4% (premium).

Question 64

Par

Answer 64

The bond’s price equals its face value because its coupon rate matches the current market rate.

Question 65

Premium

Answer 65

The bond’s price is higher than its face value because its coupon rate is higher than the market rate

Question 66

Discount

Answer 66

The bond’s price is lower than its face value because its coupon rate is lower than the market rate.

Question 67

Convexity in Price-Yield Relationship

Answer 67

Convexity describes the non-linear relationship between bond prices and yields.

It explains why bond prices increase more when yields fall than they decrease when yields rise by the same amount.

Example: A bond’s price might increase by $10 if yields drop by 1% but only decrease by $9 if yields rise by 1%.

Question 68

Price vs. Yield Curve

Answer 68

This curve shows how a bond’s price changes as yields fluctuate.

The curve is downward sloping, reflecting the inverse price-yield relationship. Bonds with longer maturities and lower coupons show greater price sensitivity.

Question 69

Time Value of Money (TVM)

Answer 69

This principle states that money today is worth more than the same amount in the future due to its earning potential.

Implication: Investors demand compensation (interest) for delaying consumption.

Example: If you deposit $1,000 in a savings account earning 5% annually, it will grow to $1,050 after a year, illustrating TVM.

Question 70

Continuous Compounding

Answer 70

A method of calculating interest where it is compounded an infinite number of times.

Question 71

Effective Annual Rate (EAR)

Answer 71

EAR reflects the annualized return of an investment, considering the effects of compounding.

Question 72

Discounting

Answer 72

The process of calculating the present value of future cash flows by applying a discount rate.

Importance: Discounting helps compare investments with different time horizons.

Question 73

Internal Rate of Return (IRR)

Answer 73

The IRR is the discount rate that equates the present value of a bond’s cash flows with its market price.

It represents the bond’s effective return if held to maturity and all cash flows are reinvested at the same rate.

Example: For a 6-year bond priced at $980 with an annual coupon of 5%, the IRR might calculate to 5.2%.

Question 74

Yield to Maturity (YTM)

Answer 74

YTM represents the total return on a bond if held to maturity, assuming all coupons are reinvested at the same rate.

It is a more comprehensive measure of return than the coupon rate or current yield.

Example: A bond priced at $950 with a 4% coupon rate and 5 years to maturity might have a YTM of 5%.

Question 75

Treasury Inflation-Protected Securities (TIPS)

Answer 75

TIPS are bonds issued by the U.S. government that adjust both principal and interest payments based on inflation (measured by the Consumer Price Index).

Key Benefit: They guarantee the preservation of purchasing power.

Example: A $1,000 TIPS bond grows to $1,030 principal if inflation is 3%.

Question 76

Break-Even Inflation Rate

Answer 76

The level of inflation at which the returns on TIPS and nominal Treasury bonds are equal.

Example: If the nominal yield is 3% and TIPS yield is 1%, the break-even rate is 2%.

Question 77

Rolling Down the Yield Curve

Answer 77

A strategy where investors buy longer-term bonds and sell them as they approach shorter maturities. This takes advantage of the typical downward slope in the yield curve for shorter maturities.

\Benefit: Gains from price appreciation as the bond’s yield adjusts downward over time.

Question 78

Duration

Answer 78

A measure of a bond’s sensitivity to interest rate changes, expressed in years. It estimates the percentage price change for a 1% change in yields.

Example: A bond with a duration of 5 years will lose approximately 5% of its value if interest rates increase by 1%.

Question 79

Macaulay Duration

Answer 79

The weighted average time to receive a bond’s cash flows, where the weights are the present values of each cash flow.

Example: For a 10-year bond with equal annual cash flows, the Macaulay Duration might calculate to 8 years.

Question 80

Modified Duration

Answer 80

An adjusted measure of duration that accounts for interest rate changes.

Example: A bond with a Macaulay Duration of 7 years and a yield of 5% has a Modified Duration of 6.67 years.

Question 81

Convexity

Answer 81

Convexity measures the curvature in the price-yield relationship. It explains why bonds with higher convexity experience smaller price declines when yields rise and greater price gains when yields fall.

Example: A bond with high convexity will outperform a low-convexity bond in a declining yield environment.

Question 82

Immunization

Answer 82

A strategy to protect a bond portfolio from interest rate changes by matching the portfolio’s duration to the investor’s investment horizon or liabilities.

Example: A pension fund manager aligns portfolio duration with the duration of pension obligations to minimize risk.

Question 83

Negative Convexity

Answer 83

Bonds with embedded options, such as callable bonds, exhibit negative convexity. This means their prices do not increase as much when yields drop compared to similar non-callable bonds.

Why? Callable bonds are likely to be called (repaid early) when yields fall, capping their price potential.

Example: A mortgage-backed security might increase in value less than a non-callable bond in a falling interest rate environment because homeowners refinance their loans, reducing cash flow predictability.

Question 84

Price-Yield Approximation Using Duration

Answer 84

Duration provides a linear approximation of bond price changes for small yield movements.

Question 85

Convexity Adjustment Formula

Answer 85

To improve duration’s accuracy for larger yield changes, convexity is included

Example: A bond with convexity of 50 has a smaller price drop for a 1% yield increase than one with convexity of 20.

Question 86

Barbell Strategy

Answer 86

A portfolio strategy that invests in bonds with both short and long maturities, avoiding intermediate maturities.

Why? Provides a mix of liquidity (from short-term bonds) and higher yields (from long-term bonds).

Example: Allocating 50% of the portfolio to 1-year bonds and 50% to 20-year bonds.

Question 87

Bullet Strategy

Answer 87

Focuses on bonds with maturities close to the investor’s investment horizon, reducing sensitivity to yield curve shifts.

Example: An investor expecting to need funds in 10 years invests primarily in 10-year bonds.

Question 88

Duration Immunization Strategy

Answer 88

Matching the duration of a bond portfolio with the duration of liabilities to hedge against interest rate risk.

Example: A pension fund manager uses bonds with a 10-year duration to cover liabilities due in 10 years.

Question 89

Convexity in Portfolio Management

Answer 89

Adding convexity to a bond portfolio reduces risk in volatile interest rate environments.

Example: A high-convexity portfolio will outperform in a declining interest rate scenario due to its greater price sensitivity.

Question 90

Macauley Duration Weighted Cash Flows

Answer 90

The weighted average maturity of cash flows, where the weights are their present values relative to the bond’s total present value.

Example: A 10-year bond’s duration might calculate to 7 years if earlier cash flows are relatively larger.

Question 91

Rolling Down the Yield Curve

Answer 91

A strategy to profit from the natural decline in yields as bonds approach maturity.

Why It Works: Longer-term bonds typically have higher yields. As they age, their yields converge to lower short-term rates, leading to price appreciation.

Example: A 5-year bond purchased today might yield 4%. After one year, it’s a 4-year bond, and if 4-year yields drop to 3.5%, the bond’s price increases.

Question 92

Yield to Call (YTC)

Answer 92

Similar to YTM but assumes the bond will be called at the earliest possible date.

Importance: For callable bonds, YTC is more relevant than YTM because issuers tend to call bonds when interest rates fall.

Example: A callable bond with a 5% coupon and a call date in 3 years might have a YTC of 4.5%.

Question 93

Real Yield on TIPS

Answer 93

The yield on Treasury Inflation-Protected Securities (TIPS) represents the return after adjusting for inflation.

Example: If a TIPS bond offers a 1% real yield and inflation is 3%, the total return is approximately 4%.

Question 94

Nominal Yield vs. Real Yield

Answer 94

Nominal Yield: Includes inflation, reflecting the total return in dollar terms.

Real Yield: Excludes inflation, showing the true purchasing power of the return.

Example: A 5% nominal yield with 2% inflation results in a real yield of 3%.

Question 95

Breakeven Inflation Rate

Answer 95

The inflation rate at which TIPS and nominal Treasury bonds provide the same return.

Example: A nominal bond yielding 3% and a TIPS yielding 1% have a breakeven inflation rate of 2%.

Question 96

Modified Duration for Callable Bonds

Answer 96

Callable bonds have reduced duration when interest rates fall near the call threshold.

Why? The potential for early repayment limits the bond’s sensitivity to further rate declines.

Example: A callable bond priced at $1,050 with a call price of $1,000 will not increase much if rates drop below 3%.

Question 97

Negative Convexity in Callable Bonds

Answer 97

A callable bond’s price increases more slowly when rates fall, exhibiting “price compression.”

Example: A callable bond might rise from $1,000 to $1,050 when rates fall by 1%, whereas a non-callable bond might rise to $1,100.

Question 98

Convexity and Risk Management

Answer 98

Convexity is an advanced measure used to fine-tune risk assessment in bond portfolios.

Why It’s Important: While duration estimates price changes for small yield shifts, convexity accounts for the non-linear relationship between prices and yields, making it particularly valuable for larger interest rate changes.

Example: A portfolio with high convexity will have a smaller price decline during a sharp rise in yields compared to a low-convexity portfolio.

Question 99

Convexity as a Portfolio Descriptor

Answer 99

In addition to duration, convexity offers a second layer of information about a bond portfolio’s sensitivity to yield changes.

Example: Two portfolios with the same duration but different convexities will respond differently to yield changes. The portfolio with higher convexity will exhibit less risk in volatile markets.

Question 100

Convexity Adjustment for Callable Bonds

Answer 100

Callable bonds have lower convexity (often negative) because their prices are capped at the call price when yields drop.

Example: A callable bond may increase in price by only $10 for a 1% yield drop, while a comparable non-callable bond increases by $15.

Question 101

Duration Approximation Limitations

Answer 101

Duration assumes parallel shifts in the yield curve, small yield changes, and no change in cash flow timing. These assumptions are often unrealistic in practice.

Example: A steepening yield curve will affect long-term bonds more than short-term bonds, a scenario not captured by duration alone.

Question 102

Bullet vs. Barbell Strategy Sensitivity

Answer 102

Bullet Strategy: Concentrates investments in a specific maturity, reducing exposure to yield curve changes.

Barbell Strategy: Spreads investments between short and long maturities, increasing sensitivity to yield curve shape.

Example: A barbell portfolio (50% 2-year bonds, 50% 30-year bonds) may gain if the long end of the curve flattens, while a bullet strategy focused on 10-year bonds may remain stable.

Question 103

Duration Immunization in Practice

Answer 103

Pension funds and insurance companies often use immunization to match the duration of their liabilities with the duration of their assets.

Example: A pension fund expecting a $1 billion payout in 20 years invests in bonds with a 20-year duration to hedge against interest rate risks.

Question 104

Convexity in Immunization Strategies

Answer 104

Convexity adjustments improve the accuracy of immunization strategies, especially during significant yield curve movements.

Example: A portfolio with matched duration but higher convexity than liabilities will better withstand unexpected rate shocks.

Question 105

Effective Annual Yield (EAY)

Answer 105

EAY adjusts nominal yields to reflect compounding, providing a more accurate annualized return.

Question 106

Reinvestment Risk in Bonds

Answer 106

Reinvestment risk arises when cash flows from bonds must be reinvested at lower rates, reducing overall returns.

Example: A bondholder receiving $1,000 in coupons during a period of declining rates may only reinvest at 3% instead of the original 5%.

Question 107

Yield Curve Risk

Answer 107

Yield curve risk reflects the possibility that changes in the shape or slope of the yield curve will affect bond prices differently across maturities.

Example: A flattening yield curve will negatively impact long-term bonds more than short-term bonds.

Question 108

Nominal Yield vs. TIPS Yield

Answer 108

Nominal Yield: Reflects returns without accounting for inflation.

TIPS Yield: Represents real returns, adjusting for inflation.

Example: A nominal bond yielding 4% and a TIPS bond yielding 1% suggest a break-even inflation rate of 3%.

Question 109

Accrued Interest in Transactions

Answer 109

Accrued interest ensures the seller of a bond receives compensation for the interest earned since the last coupon payment.

Example: If a bond pays $50 annually, the accrued interest for 6 months is $25.

Question 110

Clean vs. Dirty Price in Trading

Answer 110

The clean price is the bond’s price without accrued interest, while the dirty price includes accrued interest, representing the actual amount paid.

Example: A bond quoted at $950 with $25 accrued interest has a dirty price of $975.

Question 111

Premium Bonds in Declining Rates

Answer 111

Bonds sold at a premium (price above face value) tend to decline in value faster as they approach maturity due to pull-to-par effects.

Example: A bond purchased for $1,200 with a $1,000 face value will gradually decrease to $1,000 at maturity.

Question 112

Callable Bonds and Reinvestment Risk

Answer 112

Callable bonds expose investors to reinvestment risk because issuers repay them early during falling rate environments, forcing reinvestment at lower yields.

Example: A 5% callable bond repaid early during a 3% rate environment creates reinvestment challenges.

Question 113

Floating Rate Bonds

Answer 113

Bonds with interest payments tied to a benchmark rate like SOFR. Payments adjust periodically, reducing interest rate risk.

Example: A floating rate bond might pay LIBOR + 2%, adjusting payments as LIBOR fluctuates.

Question 114

Mortgage-Backed Securities (MBS)

Answer 114

Bonds backed by pools of mortgages. Investors receive payments from homeowners’ mortgage interest and principal repayments.

Example: A homeowner refinancing their mortgage impacts the cash flows of the associated MBS.

Question 115

Zero-Coupon Bonds

Answer 115

Bonds that do not pay periodic interest but are issued at a discount and repay their face value at maturity.

Example: A zero-coupon bond issued for $500 and maturing at $1,000 in 10 years effectively offers a return of approximately 7.18%.

Question 116

Convexity vs. Duration

Answer 116

Convexity enhances the accuracy of duration by accounting for the bond’s non-linear price-yield relationship.

Example: Duration may predict a $10 price change for a 1% yield shift, but convexity adjusts this to $12 for downward shifts due to the bond’s curvature.

Question 117

Dynamic Yield Curve Shifts

Answer 117

Yield curves do not always shift in parallel; they may steepen, flatten, or twist, impacting bonds differently depending on their maturities.

Example: A steepening curve hurts long-term bonds more than short-term bonds, increasing reinvestment risk for longer maturities.

Question 118

Duration Limitations in Non-Parallel Shifts

Answer 118

Duration assumes all yields move by the same amount, which is often not true in real markets.

Example: If long-term yields rise while short-term yields fall, duration inaccurately predicts the overall price impact.

Question 119

Immunization for Multi-Liability Portfolios

Answer 119

To hedge against interest rate risk, a portfolio’s duration must equal the weighted average duration of all liabilities.

Example: A pension fund with payouts in 5 and 10 years balances its portfolio duration accordingly.

Question 120

Callable Bonds Price Behavior

Answer 120

The price of a callable bond is capped because issuers call the bond when it becomes favorable for them to refinance at lower rates.

Example: A callable bond priced at $1,050 may only increase to $1,080 if rates drop further, while a comparable non-callable bond could rise to $1,150.

Question 121

Reinvestment Yield Assumptions

Answer 121

Yield to maturity assumes that all coupon payments are reinvested at the same rate as the bond’s YTM, which is often unrealistic.

Example: A bond with a 5% YTM may not achieve this return if reinvestment rates drop to 3%.

Question 122

Yield Curve Flattening

Answer 122

A flattening yield curve occurs when the difference between short- and long-term yields narrows.

Impact: Reduces the attractiveness of long-term bonds compared to short-term bonds.

Example: A 10-year bond yielding 4% and a 2-year bond yielding 3.8% offer similar returns, discouraging long-term investments.

Question 123

Rolling Yield in Bond Strategies

Answer 123

The additional return earned when a bond “rolls down” the yield curve as its maturity shortens, reducing its yield and increasing its price.

Example: A 5-year bond yielding 3% becomes a 4-year bond yielding 2.8%, creating a price gain.

Question 124

Breakeven Yield Spread

Answer 124

The yield difference at which two bonds provide the same return after accounting for their durations and risks.

Example: A 5-year corporate bond and a 5-year Treasury may have a spread of 0.5% to reflect the corporate bond’s higher credit risk.

Question 125

Convexity in Volatile Markets

Answer 125

Bonds with higher convexity perform better in volatile markets because they gain more from yield decreases and lose less from yield increases.

Example: A bond portfolio with convexity of 150 will outperform one with convexity of 100 during large yield changes.

Question 126

Convexity and Callable Bonds

Answer 126

Callable bonds have negative convexity in falling rate environments because their price gains are capped by the call feature.

Example: A callable bond’s price may stabilize at $1,050, while a similar non-callable bond rises to $1,100.

Question 127

Convexity as a Weighted Average

Answer 127

Convexity is calculated as a weighted average of squared cash flow maturities, reflecting how price changes accelerate as yields deviate.

Example: A 10-year bond has a convexity of 80, while a 30-year bond may have a convexity of 200, making it more sensitive to yield curve changes.

Question 128

Convexity Adjustment in Portfolio Hedging

Answer 128

Convexity ensures that portfolios remain balanced even during significant yield changes, complementing duration for better risk management.

Example: A portfolio manager uses bonds with high convexity to offset liabilities with unpredictable cash flows.

Question 129

Pull-to-Par Dynamics in Premium Bonds

Answer 129

Premium bonds gradually lose their extra value as they approach maturity, converging to their face value.

Example: A bond trading at $1,200 with a face value of $1,000 will decline to $1,000 at maturity.

Question 130

Price Sensitivity and Maturity

Answer 130

Bonds with longer maturities are more sensitive to interest rate changes because their cash flows are discounted over more periods.

Example: A 30-year bond’s price might drop by 15% for a 1% increase in yields, while a 5-year bond’s price drops by only 5%.

Question 131

Coupon Rate Impact on Volatility

Answer 131

Bonds with lower coupon rates are more sensitive to yield changes because a larger portion of their value is derived from the final principal repayment.

Example: A zero-coupon bond is more volatile than a 10% coupon bond with the same maturity.

Question 132

Interest Rate Sensitivity of Zero-Coupon Bonds

Answer 132

Zero-coupon bonds are highly sensitive to interest rate changes because their entire value comes from the lump-sum payment at maturity.

Example: A 10-year zero-coupon bond priced at $500 may drop to $450 if rates rise by 1%.

Question 133

Municipal Bonds (Munis)

Answer 133

Debt issued by state and local governments, often tax-exempt. Investors favor them for their tax advantages and safety.

Example: A municipal bond yielding 3% tax-free is equivalent to a taxable bond yielding 4.5% for an investor in a 33% tax bracket.

Question 134

Corporate Bonds

Answer 134

Bonds issued by companies to raise capital, offering higher yields but with added credit risk compared to government bonds.

Example: An AA-rated corporate bond might yield 4%, while a Treasury bond yields 3%.

Question 135

Treasury Inflation-Protected Securities (TIPS)

Answer 135

TIPS adjust their principal and interest payments based on inflation, preserving purchasing power.

Example: A $1,000 TIPS bond grows to $1,050 if inflation is 5%.

Question 136

Repo Agreements

Answer 136

Short-term loans where securities are sold with an agreement to repurchase them later. Used by banks for liquidity.

Example: A bank sells Treasury bonds for $1 million and agrees to repurchase them the next day for $1.001 million, reflecting a 0.1% repo rate.

Question 137

Duration and Portfolio Risk Management

Answer 137

Duration helps investors balance interest rate sensitivity in portfolios, ensuring alignment with investment objectives or liabilities.

Example: A 7-year duration portfolio matches a liability due in 7 years, minimizing risk from rate changes.

Question 138

Barbell Strategy and Convexity

Answer 138

The barbell strategy inherently has higher convexity because it includes bonds with both short and long maturities, avoiding intermediate durations.

Example: A portfolio with 50% short-term bonds and 50% long-term bonds will gain more from falling yields than one with mid-term bonds due to its higher convexity.

Question 139

Bullet Strategy and Stability

Answer 139

A bullet strategy focuses on bonds with maturities around a specific target, making it less sensitive to shifts in the shape of the yield curve.

Example: Investing solely in 10-year bonds reduces exposure to steepening or flattening of the curve compared to barbell strategies.

Question 140

Callable Bond Price Compression

Answer 140

Callable bonds experience price compression, meaning their prices stop rising as much when yields fall. This limits potential gains compared to non-callable bonds.

Example: A callable bond capped at $1,050 will not benefit further if rates drop significantly below the call threshold.

Question 141

Yield Spread Analysis

Answer 141

Yield spread reflects the difference between the yields of two bonds, often indicating credit or liquidity risk.

Example: A corporate bond yielding 5% and a Treasury bond yielding 3% have a spread of 2%, representing the corporate bond’s higher risk.

Question 142

Duration Hedging in Bond Portfolios

Answer 142

Matching the portfolio duration with liabilities minimizes interest rate risk. Duration-based hedging is essential for pension funds and insurers.

Example: A portfolio manager aligns the duration of assets to a liability stream due in 15 years to protect against rate changes.

Question 143

Convexity Hedging for Risk Management

Answer 143

Adding high-convexity bonds to a portfolio reduces exposure to large interest rate changes.

Example: A high-convexity portfolio is better suited for volatile rate environments, offering more consistent returns.

Question 144

Break-Even Inflation Analysis

Answer 144

Compares nominal and real bond yields to estimate the expected inflation rate where both bonds perform equally.

Example: A nominal bond yielding 4% and a TIPS yielding 2% imply a break-even inflation rate of 2%.

Question 145

Inflation Risk in Bonds

Answer 145

Inflation erodes the purchasing power of fixed cash flows, making nominal bonds less attractive in rising inflation scenarios.

Example: A bond yielding 3% in a 4% inflation environment results in a negative real return.

Question 146

Securitization

Answer 146

The process of pooling financial assets (like mortgages) and issuing securities backed by those assets, diversifying risk.

Example: Mortgage-backed securities (MBS) are created by bundling home loans and selling them to investors.

Question 147

Floating Rate Bonds (Floaters)

Answer 147

Bonds with interest payments tied to a benchmark rate, adjusting periodically to reflect market changes.

Example: A floater paying SOFR + 1% adjusts its rate every quarter based on the prevailing SOFR.

Question 148

Inverse Floating Rate Bonds

Answer 148

Bonds where interest payments decrease as benchmark rates rise, making them sensitive to rate increases.

Example: If benchmark rates rise by 1%, the bond’s interest payment decreases proportionally.

Question 149

LIBOR to SOFR Transition

Answer 149

The transition from LIBOR (based on bank estimates) to SOFR (based on actual transactions) improves accuracy in benchmark rates.

Example: A floating rate bond previously tied to LIBOR now adjusts based on SOFR, reducing manipulation risks.

Question 150

Treasury Bonds vs. Corporate Bonds

Answer 150

Treasury bonds are considered risk-free because they are backed by the U.S. government, while corporate bonds carry credit risk due to potential defaults.

Example: A Treasury bond yielding 2.5% offers lower risk than a corporate bond yielding 5% with a BB rating.