Week 22 Day 1: When Rates Go Up, Bond Prices Go Down

Imagine you bought a bond paying 3% interest. Then the Fed raises rates and new bonds pay 5%. Nobody wants your 3% bond anymore -- it has to drop in price until its effective yield matches the 5% available elsewhere. Your bond lost value not because of default risk, but because of interest rate risk.

The math: Bond prices and yields are inversely related. If you own a 10-year Treasury bond paying 3% and rates rise to 5%, your bond's price drops approximately 15% (because the 2% yield gap multiplied by the duration of approximately 7.5 years = 15% price decline). In 2022, the Fed raised the federal funds rate from 0.25% to 4.50% in 10 months -- the fastest rate-hiking cycle in 40 years. The Bloomberg U.S. Aggregate Bond Index fell 13.0% in 2022, its worst year ever. Long-term Treasuries (TLT) fell over 30%. Bonds, normally the safe part of a portfolio, delivered stock-market-level losses. Why it matters: duration is the key measure of bond price sensitivity. Short-duration bonds (1-3 years) barely flinch when rates move. Long-duration bonds (20-30 years) swing violently. If you expect rates to rise: shorten your duration (use SHY or VGSH, short-term Treasuries). If you expect rates to fall: lengthen your duration (use TLT or VGLT, long-term Treasuries). If you do not know (most honest answer): hold an intermediate fund (BND, AGG) and accept moderate rate sensitivity.

The price-yield relationship for a coupon-paying bond is: P = Sum[C/(1+y)^t] + F/(1+y)^n, where C is the coupon payment, y is the yield, F is the face value, and n is the number of periods. This is a convex function: the price sensitivity to yield changes is not linear. For a given yield change, the price gain from a rate decrease is larger than the price loss from an equal rate increase -- this is positive convexity. Modified duration provides a linear approximation: %Change in Price = -ModDur * Change in Yield. For more precise estimates, add the convexity adjustment: %Change = -ModDur * DeltaY + 0.5 * Convexity * (DeltaY)^2. The 2022 bond crash exposed a fundamental risk that many conservative investors had not experienced: rising rates from very low levels create outsized losses because the starting duration of the aggregate bond index was historically high (approximately 6.7 years) due to the prevalence of long-dated bonds issued during the low-rate era. The lesson: 'safe' bonds are only safe from default risk (for Treasuries). Interest rate risk is real and can produce double-digit losses over single years. For liability-matching investors (retirees needing income at specific future dates), individual bonds held to maturity eliminate interest rate risk entirely -- but at the cost of reinvestment risk and opportunity cost.