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Bond Price Volatility

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  1. Bond Price Volatility

  2. Price Yield Relationship • Recall the earlier discussion… • Inverse relationship between Price and Yield Price Yield

  3. Price Yield Relationship • What do you observe in the given graph? Price Yield

  4. Price Yield Relationship • % Change in Price is not equal for increase in the yield as it is for decrease in the required yield Price Yield

  5. Price Volatility • Lower the coupon rate – greater the volatility • Longer the term to maturity- greater the volatility So what should you be doing if you expect a decline in interest rate?

  6. Price Volatility • Higher the YTM bond trades at- lower its price volatility • An implication of this is: For a given change in yield, price volatility is greater when yield levels are low…

  7. Measures of Bond Price Volatility • Price Value of a Basis Point (PVBP): Change in the price of a bond if the required yield changes by 1 basis point. • Duration • Macaulay Duration (Weighted average) • Modified Duration which is (dp/dy)/p, also equal to [-modified duration/(1+y)]

  8. Approximate Duration • Approximate Duration (P1-P2)/(2* P0* Change in Yield)

  9. Properties of Duration • Duration is less than term to maturity • Duration of a zero coupon bond is equal to its maturity • Lower the coupon greater the duration • Greater the yield lower the modified duration Doesn’t this sound consistent?

  10. Portfolio Duration • How do we calculate the portfolio duration? • How effective is it to its purpose? • Parallel shift in the yield curve • Non- parallel shift in yield curve • Concept of key rate duration

  11. Concerns on Duration • We have assumed flat yield curve- how appropriate is that ? • We have assumed that shift in yield curve is parallel- how appropriate is that? • Misapplication of duration to bonds with embedded options

  12. Don’t think of Duration as measure of Time • Don’t get carried by the weighted average TTM as implied by Macaulay Duration • A bond can have duration in excess of its maturity (leverage effect) • A bond can have negative duration!! • Call can have a duration of 30 even if its TTM is 1 year!

  13. Convexity • Duration fails to capture the entire price change Price Actual Price Tangent line (estimated price) Yield

  14. Convexity • There is an error in estimating price based only on duration Price Actual Price Tangent line (estimated price) Yield

  15. Measuring Convexity • Dollar Convexity Measure = (d2P)/(dy2) • Convexity Measure = Dollar Convexity Measure / Price • Percentage Price change due to convexity = 0.5 * Convexity Measure * (dy)2

  16. Approximate Value of Convexity (P+ + P- -2P0) P0*(Change Yld)2

  17. Value of Convexity • Can two bonds have equal duration but different convexities? • When would convexity be attributed a high value?

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