Mastering Bond Pricing
The Uniform Investment Adviser Law Examination
In a normal interest rate environment, longer-term bonds will pay investors a higher interest rate than short-term bonds of equal quality. As interest rates change the price of existing bonds will move inversely to the change in interest rates. A bond’s duration is a measure of the bond’s price sensitivity to a small change in interest rates and is stated in years. Longer term bonds and bonds with low coupons will generally have a higher duration than shorter term or higher yielding bonds. The higher the bond’s duration, the greater the bond’s interest rate risk and the greater its price volatility. Duration allows investors to compare the interest rate risk associated with bonds of different maturities, quality, and coupons. The bond’s duration may be stated as either modified duration or effective duration. Modified duration assumes that a change in interest rates will not affect the bond’s expected cash flow. Effective or call adjusted duration assumes that a change in interest rates may affect the bond’s cash flow if the bonds are callable or have other options for early retirement. Call adjusted duration is lower than the bond’s duration to maturity. All bonds that make regular interest payments will have a duration that is lower than the number of years to the bond’s maturity. Because a zero coupon bond does not provide any cash flow other than its principal payment at maturity, a zero coupon bond’s duration will be equal to the number of years to maturity. For example a 20-year zero coupon bond would have a duration of 20. To determine a bond’s duration use the following formula:
Bond price change percentage = duration X (change in yield in basis points /100)
If a bond portfolio has an average duration of 7 years and interest rates rise by 1 percent or 100 basis points, the portfolio manager can expect the price of the bonds in the portfolio to fall by 7%.
A bond’s convexity measures its price volatility to large changes in interest rates. A bond’s price will not respond equally to both an increase and decrease in interest rates. As interest rates fall, bonds tend to increase in price, more than they would fall if interest rates were to rise by an equal amount. Bond prices tend to rise faster in response to a fall in interest rates and fall slower in response to a rise in interest rates. Bonds whose prices react in this way are said to have positive convexity. Mortgage backed and callable bonds tend to have negative convexities. A fall in interest rates increases both mortgage pre- payments and the likelihood that the bonds will be called. Convexity is a better risk management tool than duration in volatile interest rate environments or when interest rates are low.
Convexity is only important when comparing two investments with similar durations.
Bond Portfolio Management
Bond portfolios may be either actively or passively managed to meet the needs of different investors. Active portfolio management tends to seek an above average total return for the portfolio. The portfolio’s total return includes:
- Coupon return; the total of all interest payments received by the portfolio plus accrued interest earned during a specific holding period.
- Reinvestment return; the total interest earned from the reinvestment of interest payments during a specific holding period.
- Price return; the total of the portfolio’s appreciation or depreciation during a specific holding period.
For long-term holding periods, the portfolio’s reinvestment return will be the most important factor when determining the portfolio’s return. For holding periods between 2 to 10 years, the coupon return and reinvestment return will be the most important factors. For short term holding periods the price return will be the most important factor.
Passive bond portfolio management includes both indexing and buy and hold strategies. Portfolio managers who use indexing try to match the performance of a given bond index by purchasing bonds that are included in the index. Advantages of indexing include lower management fees, diversification, and more predictable performance. Buy and hold managers tend to purchase bonds in the primary market and hold them for long periods of time or until maturity. By consistently purchasing new issues of bonds the portfolio manager can maintain diversification of terms and coupon rates.
Pension and insurance company portfolio managers will often try to manage the portfolio’s income to meet the current cash obligations of the pension plan or the insurance company’s guaranteed investment contracts. Two methods used to match the portfolio’s income with current cash liabilities are dedicated portfolio management and bond immunization. Dedicated portfolio management matches the portfolio’s monthly income with the monthly cash liabilities. Bond immunization creates a portfolio designed to generate a specific return during a known time horizon. Portfolio managers using bond immunization will match the bonds� maturity dates with the known time when a lump sum payment is due. Because the portfolio’s maturity dates match the time when the payment is due, the portfolio is said to be immunized from interest rate risk.