m Flashcards
(152 cards)
1
Q
What is Money?
A
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).
2
Q
What is a Bank?
A
- 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
3
Q
What is an Interest Rate?
A
The interest rate is the cost of borrowing money or the reward for saving money.
- Example: Borrow $100 at 5%, and you owe $105.
4
Q
Why is it Bad to Have “Too Much” Money?
A
- 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.
5
Q
What is the Federal Reserve (Fed)
A
- 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.
6
Q
What is the Fed’s Dual Mandate?
A
- 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.
- Why do rising interest rates cause fewer jobs?
7
Q
What is the Fed Funds Rate?
A
- 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
- Why do banks need reserves?
8
Q
How Does the Fed Control the Fed Funds Rate?
A
- 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.
- After 2008: Interest on Reserves
9
Q
Why Does More Money with Banks Lower Interest Rates?
A
- 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.
10
Q
What is Quantitative Easing (QE)?
A
- 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).
- The Fed buys long-term bonds, increasing demand for them. This:
11
Q
Why not use QE often?
A
It’s typically reserved for crises like the 2008 financial crash or COVID-19, as it risks overheating the economy or creating bubbles.
12
Q
What is the Fed’s Balance Sheet?
A
- Assets: Treasuries and mortgage-backed securities (MBS).
- Liabilities: Bank reserves and U.S. currency in circulation.
13
Q
Why does the Fed create money?
A
- To buy assets or inject liquidity into the economy during crises.
- The amount created depends on economic conditions and policy goals.
14
Q
What are Fed Funds Futures (FFF)?
A
- 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.
- Used by:
15
Q
What is Arbitrage?
A
- 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.”
- Example in the FFR Market:
16
Q
What is Stagflation?
A
- High inflation and high unemployment at the same time.
- The Fed must carefully balance tools to avoid worsening either issue.
17
Q
What is the FOMC?
A
- 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.
18
Q
Relation Between FFR and Interest on Reserves
A
- 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.
19
Q
What is a Mortgage-Backed Security (MBS)?
A
A bundle of home loans sold to investors, who earn returns as borrowers pay off their mortgages.
20
Q
What are Options on Fed Funds?
A
- Like FFF, but offer more flexibility to predict rate movements, especially over longer horizons.
21
Q
How Does the Fed Create Money?
A
- It electronically credits banks when buying assets.
- This expands its balance sheet, injecting money into the economy.
22
Q
Arbitrage Pricing
A
Determining the value of securities by replicating their cash flows using other assets.
23
Q
Portfolio Optimization
A
Selecting a mix of investments to maximize returns for a given level of risk.
24
Q
What is Arbitrage Pricing?
A
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.
25
What is the Law of One Price?
- 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.
26
Pricing by Replication
- 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
27
Arbitrage Pricing with Two Goods Example
- 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.
28
Methodologies for Solving Arbitrage Pricing Problems
- 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.
29
What is a Bond?
A bond is a loan where the borrower agrees to pay back the principal (face value) and periodic interest (coupon payments).
30
Zero-Coupon Bond
A bond with no periodic interest; it only pays the face value at maturity.
31
Coupon Bond
A bond that pays periodic interest and returns the face value at maturity.
32
Example: Pricing a Coupon Bond
- 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.
33
What is a Call Option?
- 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.
34
Example: Pricing a Call Option
- 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.
35
What is Portfolio Optimization?
The process of selecting investments to maximize returns for a given level of risk or minimize risk for a given level of returns.
36
Risk and Return
- Expected Return: Average return expected from an investment.
- Risk: Measured by variance or standard deviation of returns.
37
Diversification
- 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.
38
What are Fixed Income Securities?
- 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.
39
Types of Fixed Income Securities
- 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.
40
Bond Features
- 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.
41
Risks in Fixed Income Securities: Interest Rate Risk
- If rates rise, bond prices fall.
- Example: A bond worth $1,000 at 4% may drop in value if rates rise to 5%.
42
Risks in Fixed Income Securities: Reinvestment Risk
- Uncertainty about the rate at which cash flows can be reinvested.
43
Risk in Fixed Income Securities: Default Risk
- The risk that the issuer cannot meet payment obligations.
- Example: Corporate bonds may default, unlike U.S. Treasuries.
44
Risk in Fixed Income Securities: Inflation Risk
- Inflation reduces the purchasing power of cash flows.
- Example: A 2% bond yield loses value if inflation rises to 3%.
45
Risk in Fixed Income Securities: Liquidity Risk
- Difficulty in selling the bond without losing value.
45
Risk in Fixed Income Securities: Volatility Risk
Price changes due to market volatility.
46
Pricing of Bonds
- 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.
47
Special Bond Features
- 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.
48
Repo Market
- 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.
49
Securitization
Repacks cash flows from existing securities into new securities.
Example: Creating floaters/inverse floaters from fixed-rate bonds.
50
Leverage
- Borrowing to increase potential returns.
- Example: Using $100 in equity and $400 in borrowed funds to invest.
51
Present Value (PV)
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.
52
Future Value (FV)
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.
53
Annuity
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).
54
Ordinary Annuity:
Payments occur at the end of each period (e.g., mortgage payments).
55
Annuity Due
Payments occur at the beginning of each period (e.g., rent payments).
56
Price-Yield Relationship
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.
57
Pull to Par
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.
58
Price-Time Relationship
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.
59
Accrued Interest
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.
60
Dirty Price vs. Clean Price
The difference between these prices ensures that the seller is compensated for holding the bond during the interest accrual period.
61
Dirty Price
The total price a bond buyer pays, including accrued interest.
62
Clean Price
The quoted price of the bond, excluding accrued interest.
63
Bond at Par, Premium, and Discount
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).
64
Par
The bond's price equals its face value because its coupon rate matches the current market rate.
65
Premium
The bond's price is higher than its face value because its coupon rate is higher than the market rate
66
Discount
The bond's price is lower than its face value because its coupon rate is lower than the market rate.
67
Convexity in Price-Yield Relationship
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%.
68
Price vs. Yield Curve
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.
69
Time Value of Money (TVM)
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.
70
Continuous Compounding
A method of calculating interest where it is compounded an infinite number of times.
71
Effective Annual Rate (EAR)
EAR reflects the annualized return of an investment, considering the effects of compounding.
72
Discounting
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.
73
Internal Rate of Return (IRR)
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%.
74
Yield to Maturity (YTM)
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%.
75
Treasury Inflation-Protected Securities (TIPS)
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%.
76
Break-Even Inflation Rate
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%.
77
Rolling Down the Yield Curve
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.
78
Duration
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%.
79
Macaulay Duration
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.
80
Modified Duration
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.
81
Convexity
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.
82
Immunization
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.
83
Negative Convexity
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.
84
Price-Yield Approximation Using Duration
Duration provides a linear approximation of bond price changes for small yield movements.
85
Convexity Adjustment Formula
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.
86
Barbell Strategy
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.
87
Bullet Strategy
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.
88
Duration Immunization Strategy
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.
89
Convexity in Portfolio Management
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.
90
Macauley Duration Weighted Cash Flows
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.
91
Rolling Down the Yield Curve
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.
92
Yield to Call (YTC)
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%.
93
Real Yield on TIPS
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%.
94
Nominal Yield vs. Real Yield
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%.
95
Breakeven Inflation Rate
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%.
96
Modified Duration for Callable Bonds
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%.
97
Negative Convexity in Callable Bonds
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.
98
Convexity and Risk Management
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.
99
Convexity as a Portfolio Descriptor
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.
100
Convexity Adjustment for Callable Bonds
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.
101
Duration Approximation Limitations
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.
102
Bullet vs. Barbell Strategy Sensitivity
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.
103
Duration Immunization in Practice
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.
104
Convexity in Immunization Strategies
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.
105
Effective Annual Yield (EAY)
EAY adjusts nominal yields to reflect compounding, providing a more accurate annualized return.
106
Reinvestment Risk in Bonds
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%.
107
Yield Curve Risk
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.
108
Nominal Yield vs. TIPS Yield
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%.
109
Accrued Interest in Transactions
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.
110
Clean vs. Dirty Price in Trading
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.
111
Premium Bonds in Declining Rates
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.
112
Callable Bonds and Reinvestment Risk
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.
113
Floating Rate Bonds
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.
114
Mortgage-Backed Securities (MBS)
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.
115
Zero-Coupon Bonds
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%.
116
Convexity vs. Duration
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.
117
Dynamic Yield Curve Shifts
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.
118
Duration Limitations in Non-Parallel Shifts
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.
119
Immunization for Multi-Liability Portfolios
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.
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Callable Bonds Price Behavior
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.
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Reinvestment Yield Assumptions
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%.
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Yield Curve Flattening
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.
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Rolling Yield in Bond Strategies
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.
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Breakeven Yield Spread
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.
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Convexity in Volatile Markets
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.
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Convexity and Callable Bonds
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.
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Convexity as a Weighted Average
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.
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Convexity Adjustment in Portfolio Hedging
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.
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Pull-to-Par Dynamics in Premium Bonds
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.
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Price Sensitivity and Maturity
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%.
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Coupon Rate Impact on Volatility
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.
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Interest Rate Sensitivity of Zero-Coupon Bonds
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%.
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Municipal Bonds (Munis)
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.
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Corporate Bonds
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%.
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Treasury Inflation-Protected Securities (TIPS)
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%.
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Repo Agreements
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.
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Duration and Portfolio Risk Management
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.
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Barbell Strategy and Convexity
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.
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Bullet Strategy and Stability
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.
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Callable Bond Price Compression
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.
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Yield Spread Analysis
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.
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Duration Hedging in Bond Portfolios
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.
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Convexity Hedging for Risk Management
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.
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Break-Even Inflation Analysis
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%.
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Inflation Risk in Bonds
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.
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Securitization
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.
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Floating Rate Bonds (Floaters)
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.
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Inverse Floating Rate Bonds
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.
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LIBOR to SOFR Transition
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.
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Treasury Bonds vs. Corporate Bonds
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.
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