Class Business Upcoming Homework

Bond Page of the WSJ and other Financial Press Jan 23, 2003

Bond Page of the WSJ contd. Jan 23, 2003

Alternative Measures of Yield Yield to Call – Call price replaces par – Call date replaces maturity Holding Period Yield (actual return) – Considers actual reinvestment of coupons – Considers any change in price if the bond is held less than its maturity Realized Compound Yield – Reinvestment rate of coupons

Default Risk Agency Assessment – Coverage ratios – Leverage ratios – Liquidity ratios – Profitability ratios – Cash flow to debt Company’s Protection Against – Sinking funds – Subordination of future debt – Dividend restrictions – Collateral Risk Premiums – Corporate Yields over T-bill Yields

Term Structure of Interest Rates Relationship between yields to maturity and maturity Yield curve - a graph of the yields on bonds relative to the number of years to maturity – Usually Treasury Bonds – Have to be similar risk or other factors would be influencing yields

Expectations Hypothesis Key Assumption: Bonds of different maturities are perfect substitutes Implication: Expected Return on bonds of different maturities are equal For n-period bond: y t + y t+1 + y t y t+(n–1) y nt = n In words: Interest rate on long bond = average short rates expected to occur over life of long bond Numerical example: One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9%: Interest rate on two-year bond: (5% + 6%)/2 = 5.5% Interest rate for five-year bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Interest rate for one to five year bonds: 5%, 5.5%, 6%, 6.5% and 7%.

Liquidity Premium Theory Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes Implication: Modifies Expectations Theory with features of Segmented Markets Theory Investors prefer short rather than long bonds  must be paid positive liquidity (term) premium, l nt, to hold long-term bonds Results in following modification of Expectations Theory y t + y e t+1 + y e t y e t+(n–1) y nt = + l nt n

Relationship Between the Liquidity Premium and Expectations Theories

Innovations in the Bond Market Reverse floaters Asset-backed bonds Pay-in-kind bonds Catastrophe bonds Indexed bonds – TIPS (Treasury Inflation Protected Securities)

Managing Fixed Income Securities: Basic Strategies Active strategy – Trade on interest rate predictions – Trade on market inefficiencies Passive strategy – Control risk – Balance risk and return

Bond Pricing Relationships Inverse relationship between price and yield An increase in a bond’s yield to maturity results in a smaller price decline than the gain associated with a comparable decrease in yield Long-term bonds tend to be more price sensitive than short-term bonds As maturity increases, price sensitivity increases at a decreasing rate Price sensitivity is inversely related to a bond’s coupon rate

Duration A measure of the effective maturity of a bond The weighted average of the times (periods) until each payment is received, with the weights proportional to the present value of the payment Duration is equal to maturity for zero coupon bonds Duration of a perpetuity is (1+r)/r

Duration Formula

Duration Formula Another Perspective

Workout Problem-Duration Calculate the duration of an asset that makes nominal payments of $120 one year from now, $140 two years from now, and $160 three years from now. Assume the YTM is 10%. Calculate the duration of another asset that makes nominal payments of $160 one year from now, $140 two years from now, and $120 three years from now, also with an YTM of 10%. – Spreadsheet Spreadsheet

Duration Properties The longer the term to maturity of a bond, everything else being equal, the greater its duration. When interest rates rise, everything else being equal, the duration of a coupon bond falls. (convexity) The higher the coupon rate on the bond, everything else being equal, the shorter the bond’s duration. Duration is additive: The duration of a portfolio of securities is the weighted average of the durations of the individual securities, with the weights reflecting the proportion of the portfolio invested in each.