New York University



Debt Markets - Key Concepts

Brief Overview of Key Concepts of Debt Markets

July 5th, 2001

Linda

Debt Markets - Key Concepts

• Inverse relationship of Price vs. Yield

• Sensitivity measures - duration/delta, convexity

• Example 30 year zero vs. high coupon bond

• Importance of Yield curve shape, non-parallel shifts

• Benchmark Yields and Credit Spreads vs. trading on Price basis

Price vs. Yield Relationship

P = (C/Y) + [(100 - C/Y) / (1+ Y/2)^N]

Where:

• C = annual $ coupon paid semi-annually

• Y = annual yield

• N = Number of semi-annual coupons paid in N/2 years

Price vs. Yield Relationship

example

[pic]

Price vs. Yield Relationship

30-yr. 6% coupon example

|Price |Yield |

|115.45 |5.0% |

|100.00 |6.0% |

|87.53 |7.0% |

Price vs. Yield Relationship

Important relationships for convex function:

• The 1st partial derivative (slope of the tangent of the Price vs. Yield curve) is negative:

dP/dY < 0

• The 2nd partial derivative (convexity) is positive:

d2P/dY2 > 0

Price vs. Yield Relationship:

Duration Measures

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

Price vs. Yield Relationship:

30-yr. Bond Duration Comparison

[pic]

Important Duration Rules

• 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

Price vs. Yield Relationship:

Other Duration Measures

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

Dollar Duration:

• = 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%

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

*Note: All duration measures are related to the slope of the tangent to the Price vs. Yield curve

The Importance of the Yield Curve

Term Structure of Interest Rates:

• 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:

• 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

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.

Trading on Yield/Spreads vs. Price Basis

• 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

• 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

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