Fixed Income Analytics: Pricing and Risk Management

Clarifies the definition of interest rates, principal, and time basis. Demonstrates computing annual interest and year-end debt using the formula (1+R)X, and notes compounding conventions.

Learn to calculate simple interest, the form that accrues interest only on the principal with no compounding, and apply the standard day-count convention for fractional years.

Explore how compound interest grows investments by adding interest to the principal. See annual and semiannual examples and extend to general k times per year compounding and rate equivalence.

Explain continuous compounding as the limit of periodic compounding and demonstrate how investment value becomes e^{rt}, with examples and rate conversions between continuous and periodic forms.

Learn absolute and relative investment return measures, including pnl, gross return, and the annualized return, with time horizons, compounding, and the relation return = pnl / v0.

Explore the structure of coupon bonds within fixed income assets, including face value, maturity, coupon rate, and cash flows, and understand how bonds are issued, traded, and valued.

Explore how bond price reflects the market value of future cash flows and how nominal value and liquidity affect pricing, including the 100-dollar convention.

Show how bond yields measure returns and relate inversely to price, with a one-to-one price-yield link. Illustrate coupon and zero-coupon bonds, and when yields equal realized returns.

Define and apply semiannually compounded yields to price bonds by discounting each semiannual payment by (1+y/2) raised to the number of six-month periods, with coupons and face value.

Learn how accrued interest and discount conventions, especially actual over actual day counts, shape bond pricing, and how to compute dirty price, clean price, and day-count adjustments.

Explore off coupon date yields by applying annual and semiannual price formulas. Learn to compute dirty price, year fraction, and accrued interest on valuation dates.

Explore government bonds and sovereign debt, focusing on long-term securities over one year, including notes, bonds, and zero-coupon strips, with pricing and day-count conventions.

Explore the money market and its short-term instruments, including treasury bills and repos, and apply the bank discount basis yield with actual over 360 and 365 day counts.

Set conventions and notation for interest rates and asset prices, detailing units (decimal, percentage, basis points) and time dependence with R(T) and R(T,t). State simplifying assumptions (zero transaction costs, unrestricted borrowing and short selling) and reference the handout.

The time value of money is the premium for cash now versus later; at 7% interest, a $1000 payable in one year is worth $935 today.

Explain the future value as the time value of money using FV = (1+R)^T V0. Explore how annual, semiannual, and monthly compounding adjust FV for any time T.

Explore the present value concept as the time value of money, deriving PV = X / (1 + R)^T and its generalization for different compounding frequencies and discounting.

Examine how arbitrage enforces present value in fixed income pricing, showing riskless profits when prices diverge from value and the law of one price for cash flows.

price zero coupon bonds using present value, price = f /(1+r)^t; a 5000 face in six months at 4% is about 4903, and portfolios are the sum of component prices.

Extend the time value of money to streams of cash flows, defining future and present values for multi-payment assets like coupon bonds, annuities, and perpetuities.

Learn how forward rates lock in the current market rate for future investments under flat term structures, using borrowing and investing to achieve the future value.

Price bonds by discounted cash flows, treating the bond as a cash flow stream and summing present values of coupons and final par payment under a flat rate curve.

discover how discount factors encapsulate the time value of money by pricing zero-coupon bonds and discounting cash flows; relate them to interest rates under annual, semiannual, and continuous compounding.

The lecture presents a universal bond pricing formula using discount factors to express present value of cash flows, applicable across term structures and payment conventions.

Discover the universal structure of annuities in fixed income, focusing on ordinary annuities in arrears, and derive future and present values by a payment-by-payment approach.

Explore the annuity formula as a method to compress present and future value sums using the geometric sum identity for one-year payments starting today or on the valuation date.

Explore annuity due, the in advance structure of annuities, and derive its present value using discount factors and geometric sums, with applications like a lottery payout.

Explore deferred annuities and annuities in arrears, derive the present value formula, and apply it to examples using annual compounding interest.

Derive the present value formula for annuities with nonannual payments using discount factors and RM, then apply it to a semiannual, nine-year, 15,000-dollar example at 6%.

Examine growing annuities where payments rise at a fixed growth rate; derive present and future values with geometric sums, note the r=g boundary, and apply to IRA examples.

Define perpetuities as annuities with no maturity; derive present value as A over r and growing perpetuities as A/(r−g), with historical bond examples and a philanthropic illustration.

Apply annuity formulas to price bonds by discounting coupon payments and face value. Demonstrate annual and semiannual coupon bonds, including government bonds and treasury notes, using the annuity approach.

Explore spot rates and their link to bond prices, revealing a non-trivial term structure driven by market forces and the concept of implied yields for zero-coupon bonds.

Explore the term structure of interest rates and the yield curve, linking spot rates to bond prices, macro factors, and interpolation for practical fixed-income pricing.

Price bonds under a non flat term structure using the universal discount factor formula with spot rates, choosing the appropriate compounding frequency, and applying to coupon and government bonds.

Explore repurchase agreements as collateralized loans used to finance asset purchases, take long positions, or short bonds, with flows, leverage, and practical examples.

Define the annualized holding period return for bonds by including reinvested coupons and the future value, illustrated with a three-year horizon example.

Learn how yield to maturity serves as the bond's price representation, defined as the discount rate that equates present value of coupon cash flows to price, via the annuity formula.

Learn to price and manage fixed income portfolios by using allocations, price notation, and standard conventions to sum bond values, interpolate rates, and handle coupons, zero-coupon bonds, and short positions.

Explain reinvestment risk and market risk that prevent yield to maturity from guaranteeing returns, exploring holding period return under six, eight, and four percent scenarios across five- and nine-year horizons.

examine the carry concept in fixed income, defining carry as yield minus financing costs, and decompose bond returns into carry and capital gains or losses using zero-coupon and coupon examples.

Derive forward rates from the current spot-rate curve using the arbitrage relation and annual compounding to explain and compute key forward rates like F(t1,t2).

Explore forward rates as break-even rates in fixed income, using zero-coupon bonds to link spot and forward curves, and understand arbitrage implications for bond returns.

The pure expectations hypothesis posits that forward rates equal the market's expected future spot rates, linking forward prices to risk-neutral arbitrage across maturities.

Apply break-even rates to trading by comparing projected rates with the implied forward curve to evaluate carry trades in a Lauter portfolio of two-, three-, and four-year zero-coupon bonds.

Explore how a random walk in yields, aligned with the liquidity premium hypothesis, contrasts with the pure expectations hypothesis, showing holding returns equal to forward rates via arbitrage.

Analyze the liquidity premium hypothesis as a risk premium view of the yield curve, contrasting it with the pure expectations hypothesis and their implications for forward rates.

Explain riding the yield curve by earning the roll-down return and term spread from a static yield curve, comparing one-year zero-coupon and four-year coupon bonds.

Explore how interest rate risk drives fixed income prices, and learn to quantify exposure with duration and convexity under a flat term structure to manage bond risk.

Define and apply dollar duration and dv01 to estimate bond price changes from small interest-rate moves using first-order Taylor approximations, with zero-coupon and coupon bond examples.

Calculate a portfolio's dollar duration for interest-rate exposure by applying linearity of derivatives to combine component durations, then value the portfolio under a given rate with semiannual compounding.

Use dollar duration to hedge bond exposure by scaling and shorting a hedging asset until the portfolio's dollar duration is zero.

Explore duration as the core measure of interest-rate risk, linking percentage price changes to rate shifts and illustrating with zero coupon and semiannual bond cases.

Explores duration for coupon bonds, derives McAulay duration as a weighted average of discounted coupon payments, and applies it to standard bullet bonds with practical duration estimates.

Learn how to compute portfolio duration as a value-weighted average of its components' durations, using dollar-value weights and exposure to interest rates.

Explore duration as a central measure of interest rate risk, outlining its properties and how coupon level, market rates, and maturity shape it.

Hedging with duration shows how to set hedge ratios using duration, requiring both asset prices, and a 10-year bond hedged by a 10-year zero coupon reduces interest-rate risk under shocks.

Apply immunization to reduce interest rate risk by aligning your investment horizon with the bond’s McCauley duration. See how duration, convexity, and horizon interact to immunize portfolios.

Apply immunization to a single liability by matching asset duration to a six-year horizon, testing bonds, and identifying a seven-year bond with duration six that immunizes against rate shocks.

Learn how bond portfolio managers use duration to trade on interest rate forecasts, extending or reducing duration to profit from rate moves, illustrated with a 3-year versus 20-year bond example.

Explore convexity, the curvature of the price rate relationship, and how dollar convexity alongside duration improves bond price approximations beyond linear models.

Learn to compute the dollar convexity and convexity of a portfolio by summing constituent bonds' convexities and using a weighted average, with a zero-coupon and coupon example at five percent.

Apply convexity hedging to extend duration hedges, cancel first and second order interest-rate exposures with two hedge instruments, building a portfolio robust to large parallel rate shocks.

Explore the deep connections between convexity, duration, and dispersion, and learn practical methods to increase convexity by adjusting duration or dispersion using bond portfolios.

Apply the Redington conditions to immunize a liability stream with multiple payments, using a two zero-coupon bond portfolio to match present value and duration and exceed liability convexity.