Why Par Bonds Don't Sell at Par

On the morning of October 30, the current thirty year Treasury that matures August 15, 2039 was priced to yield 4.283%. This Treasury pays a coupon at the rate of 4.5%. Suppose the bond were yielding the same rate as the coupon rate. What is the price (specfically the flat price) of the bond? Well, that's an easy one. In an introductory finance class, we learned that when the yield equals the coupon rate, the bond price sells at par. The question is so simple the obvious answer of par must be wrong and it is. When the current 30-year is priced at 4.5%, the flat price is 99.99387 tantalizingly close to par but not exactly. What the hell happened? Simply put, accrued interest is the culprit. When a bond is traded between two coupon payments attention must be given to how the next coupon payment should be divided between buyer and seller. Coupon interest accrues linearly during the period. Accordingly, if the bond is sold halfway through the period, the seller is entitled to half the next coupon payment. Note that the seller is paid coupon interest for his/her without a discount even though the coupon payment is still three months away. If the seller keep the bond rather than selling it their half of the coupon payment would worth its present value discounted back three months. The accrued interest grows linearly on a simple interest basis while the present value of the next coupon payment follows a slightly curved path due to the impact of compounding. The market convention (i.e., linear accrual) introduces a slight wrinkle into bond valuation. If the yield and the coupon rate are the same, the bond's flat price will sell at slight discount to par between coupon payment dates. A par bond will sell at par only on coupon payment dates when accrued interest equals zero.

How Managers Add Value to a Bond Portfolio

The performance of an actively managed fixed-income portfolio is measured against a designated benchmark (e.g., an index or liability structure). Portfolio managers employ five basic strategies to add value relative to the benchmark. First, bond portfolio managers may seek to outperform by extending duration before a rally and shortening duration before a sell off. That is, they can take a directional view on the interst rates. Unfortunately, portfolio managers who possess the skill need to successfully employ this strategy on a consistent basis are scarce. Consequently, guidelines for most managed funds impose fairly tight duration targets on portfolio managers.

A second strategy to outperform is to take views on the future slope of the yield curve as opposed to the future level of interest rates. Managers would put on steepening trades before the yield curve steepens and flattening trades before the yield curve flattens. Barbells and bullets are among the most commonly used vehicles. Specifically, a flattening yield curve tends to favor barbells while a steepening yield curve tends to favor bullets. Most portfolio managers have more latitude to express curve-shaping views than directional views but they are still constrained. Perhaps they are merely reluctant to do so.

The third strategy that can be employed is one when there is a mismatch between a manager’s view on expected volatility and the implied volatility of bonds with embedded options, This strategy involves buying or selling convexity before realized volatility increases or decreases can enhance return. The convexity and volatility trades can be implemented through bullets and barbells, through bonds with embedded options like structured products or through the interest rate derivatives markets.

Sector selection is the fourth strategy. Fixed-income markets are comprised of various sectors which include Treasuries, agencies. corporates, structured products, etc. Since the returns across sectors are imperfectly correlated, managers can add value by overweighting sectors expected to outperform and underweighting expected to underperform.

The fifth strategy, and probably the most common one, portfolio managers attempt to outperform benchmarks through security selection. When pursuing a security selection strategy, managers attempt to overweight cheap issues and underweight rich issues to enhance total rate of return relative to their benchmark. For this to occur, one or more of the bond’s risks must be mispriced.

The Rules of Life

1. People respond to incentives.
2. Everything is connected with everything else.
3. You cannot just change one thing.
4. Options are valuable.
5. Reputation is valuable be as honest as the local custom dictates.
6. Life has a large random component -- be flexible.
7. Travel is the best education value.
8. Acknowledge that every one is self-interested including you.