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.

Magic Numbers

There are a few numbers that are simply magic. They show up all of the time and no one can explain why. Unquestionably, the most magical of them all are e and pi! Both are transcendental constants. Both appear in formulas with such frequency in unrelated areas -- it is staggering. I believe these two numbers are part of the code to understanding the universe. In physics, the Holy Grail for theorists is called the Grand Unified Theory. Very simply put, they want to write the equation that explains everything on the back of a cocktail napkin. I have no idea what that equation will look like but I am certain it will contain e and pi.

In the Long Run...

While the short-term outlook for the US economy is bleak enough, there are some forces at work that may disquiet the long-term prospects as well. The first and most of these forces is the impending demographic transition as the leading edge of the Baby Boomers started receiving Social Security benefits in 2008. The second factor is closely related to the first -- life expectancy is expected to increase in the foreseeable future. Reluctantly, it must be added, there is a countervailing factor that may limit projected increases. Due to the unstable geopolitical situation, the US has a nontrivial exposure to mass mortality risk owing to potential large scale acts of terrorism. Third, the risk of funding the retirement of US workers continues to shift from corporations and governments back to the individual. A manifestation of this risk shifting is the movement away from defined-benefit pension plans towards defined-contribution plans and 401Ks. While I applaud the increase in personal responsibility concerning one's own affairs, I believe that the average American is inadequately prepared to fund a retirement expected to last 13.54 years for men and 16.2 years for women. Moreover, there will be a significant portion of the population facing this dilemma. In 2008, those sixty-five or older comprise 12% of the US population. By 2030, the same cohort is projected to comprise 19%. The current patterns of consumption and savings rates are inconsistent with the underlying reality. Fourth and finally is of those defined-benefit pension plans that remain, a majority are underfunded. These circumstances bring to my mind an oft-quoted statement of the British economist John Maynard Keynes, "In the long run, we're all dead." In the 21st century, this should be revised to "In the long run, we're still alive... and broke."

Year of the Hyena

As we stumble into the new year, I pause to reflect on the foul year of our Lord 2008. With equity markets down almost 40% and Treasury rates near zero, to label these circumstances a bear market seems insulting. Indeed, the terms bull and bear markets are strangely anachronistic. We need some new animals in our zoo of descriptors. I dub 2008 the Year of the Hyena. To atone for our sins of the recent past, market forces moved inexorably from corporation to corporation and asset class to asset class like a marauding pack of hyenas. Asset prices tumbled. Ah yes, the circle of life... The market doing its job in exposing and removing the excesses that inevitably present themselves. The hyena's work will be done in the fullness of time. Meanwhile, the hyena laments "so much carrion, so little time."

Bernie's Ponzi Scheme

When Bernard Madoff was arrested, he reportedly told FBI agents that his eponymous investment advisory firm had bilked investors out of $50 billion and was a "giant Ponzi scheme." So what is a Ponzi scheme? Ponzi schemes are illegal programs to make money by enticing potential "investors" with high expected rates of return which are funded by recruiting more particpants to invest. A pyramid scheme is the classic example. The first wave of participants is paid off with money obtained from the second wave of participants and so forth. Inevitably, the pyramid collapses under its own weight as it becomes exponentially more difficult to recruit enough new participants to pay off earlier ones. A very small group of early participants make the promised return while the rest lose everything. Simply put, it is a redistribution of wealth from new participants to earlier participants. Charles Ponzi was a 1920s swindler who took investors with the scheme that bears his name.