Bonds and Fixed Income

Definition

A bond is a debt security promising future payments. Fixed-income analysis classifies bonds, computes the yield that equates present value to price, and weighs the risks of holding or trading them. Notes follow the Derivatives course (Università di Napoli Federico II).

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Core Ideas

Classification

By maturity:

• Short-term — maturity under one year
• Long-term — maturity over one year

By payment structure:

• Pure-discount / zero-coupon — a single payment (nominal value) at maturity
• Coupon bonds — periodic coupons; equivalent to a portfolio of zero-coupon bonds

By issue price vs nominal value:

• At par — price = nominal value
• Above par — price > nominal value
• Below par — price < nominal value

Price, interest rate, and yield

With interest compounded m times per year, after n years 1 + r = (1 + rₐ/m)^{m·n}.

The yield y is the interest rate that makes the present value of all payments equal the current price. For face value F, n coupons per year, maturity T, total payments M = T·n:

$P={\sum }_{i=1}^M\frac{C/n}{(1+y{)}^{i/n}}+\frac{F}{(1+y{)}^T}$

There is a negative relationship between yield and price — when yields rise, prices fall.

Why trade bonds

Saving for future expenditure or retirement (buy), matching liabilities (buy), or anticipating consumption (borrow/sell).

Risks

• Credit / default risk — the debtor defaults; usually higher for corporate than sovereign bonds.
• Inflation risk — rising prices erode the real value of future nominal payments (mitigated by inflation-linked bonds).
• Liquidity risk — losses from selling before maturity.

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Relationships

• Derivatives Pricing — the risk-free/discount leg used to price derivatives
• Portfolio Risk Management — fixed income as a diversifier and tail-risk hedge
• Trading & Finance — parent topic