<p> Debt Markets - Key Concepts</p><p>Brief Overview of Key Concepts of Debt Markets</p><p>July 5th, 2001</p><p>Linda</p><p>Debt Markets - Key Concepts</p><p>• Inverse relationship of Price vs. Yield</p><p>• Sensitivity measures - duration/delta, convexity</p><p>• Example 30 year zero vs. high coupon bond</p><p>• Importance of Yield curve shape, non-parallel shifts</p><p>• Benchmark Yields and Credit Spreads vs. trading on Price basis Price vs. Yield Relationship</p><p>P = (C/Y) + [(100 - C/Y) / (1+ Y/2)^N]</p><p>Where: • C = annual $ coupon paid semi-annually • Y = annual yield • N = Number of semi-annual coupons paid in N/2 years</p><p>Price vs. Yield Relationship example Price vs. Yield Relationship 30-yr. 6% coupon example</p><p>Price Yield 115.45 5.0% 100.00 6.0% 87.53 7.0%</p><p>Price vs. Yield Relationship</p><p>Important relationships for convex function:</p><p> The 1st partial derivative (slope of the tangent of the Price vs. Yield curve) is negative: dP/dY < 0</p><p> The 2nd partial derivative (convexity) is positive: d2P/dY2 > 0 Price vs. Yield Relationship: Duration Measures</p><p>Macaulay's Duration:  Average time for a security to payback the original investment on a discounted basis  Weighted-average time to each cash flow  Measures price-elasticity with respect to yield  D = [(I+Y)/Y) - [(I+Y) + T(c-Y)] / c[(I+Y)T-I]+Y Where: c = Coupon rate per payment period Y = Yield per payment period T = Number of payment periods  Note that this is per payment period</p><p>Price vs. Yield Relationship: 30-yr. Bond Duration Comparison Important Duration Rules</p><p>• Macaulay Duration for a zero coupon bond = Term to maturity • Holding maturity constant, duration increases as the coupon rate decreases • Holding all else constant, as yield increases the duration of a coupon paying bond decreases • Holding all else constant, duration increases as maturity increases</p><p>Price vs. Yield Relationship: Other Duration Measures</p><p>Modified Duration: • percentage change in price for a change in yield • Mod D = (dP/P) dy • Mod D = Mac D (I +y/m) where: • y =annual yield • m = number of coupons paid per year Price vs. Yield Relationship: Other Duration Measures</p><p>Dollar Duration:</p><p> = slope of tangent to the P/Y curve at a specific yield  = dP/dY, divide by 100 for percentage yield change -e.g. from 6.0% to 7.0% </p><p>DV01:  $ change in bond price for a I BPS (0.01%) change in yield  = dP/dY x.0001 per $100 par, can adjust scale for notional amount to reflect PVBP position value per basis point PVBP = Mod D * Price</p><p>*Note: All duration measures are related to the slope of the tangent to the Price vs. Yield curve</p><p>The Importance of the Yield Curve</p><p>Term Structure of Interest Rates:</p><p>• Usually upwardly sloping - rates increase as term increases • May have hedged portfolio duration but still have exposures at different maturity levels Non-parallel yield curve shifts:</p><p>• Fixed income assets will re-price based upon movement in rates relative for each assets' maturity. • Cash rates vs. medium term rates vs. long term rates may behave very differently • Seemingly hedged portfolio suddenly not very hedged Benchmarking and Spreads</p><p>Many debt securities priced as a spread to a benchmark  Typical benchmarks include on-the-run US Treasuries, other major sovereigns, LIBOR, etc.  Spreads are generally quoted in basis points above the benchmark yield  Different debt securities are generally analyzed and compared on a yield and spread basis across the same maturity or duration bucket and credit level  Need to be able to adjust from yield/spread basis to price adjustment - most pricing systems such as Bloomberg will convert from yield to price  Example - Mexico Par A (Brady w/ US Treasury 0 collateral) stripped yield/duration comparison to Mexican 5-yr.</p><p>Trading on Yield/Spreads vs. Price Basis</p><p> Remember the Price/Yield Relationship - as prices approach 0 Yield approaches infinity  Therefore for low quality debt, yield basis becomes meaningless and the securities are quotes on a price basis  These are generally high yield category bonds which are in default or have a high probability of default  This high credit risk results in the bond trading more like equity becoming price driven by factors relating to the issuer and are not very interest rate sensitive  Many low credit rated emerging markets bonds appear to trade on a price basis similar to high yield (junk bonds)  Example - Nigeria bond trading at a stripped yield of 35.9%, priced at 53.0 with a collateral value of 40.9! Debt Markets Additional Notes</p><p> Debt Markets account for more dollar value than equity markets but are much less liquid (except benchmarks)  Aside from the markets for major benchmarks such as US Treasuries, most investors are institutional with buy-and-hold strategies  Many bonds do not have a liquid secondary market  Result - arbitrage opportunities may appear to exist but can't always short the bond</p>