No. of Recommendations: 3

As I wrote to a friend:

You’re right. There are problems with using CAGR to measure investment growth. You’ve pointed that out twice now, which I appreciate as a reminder that I need to solve the problem for myself. But I don’t know how.

I want to use CAGR, because inflation is stated as a CAGR. If CAGR under-reports the investment gains of long-dated bonds, it would seem that it has to also under-state the impact of inflation when inflation is measured over long time frames. I don’t know that is true. But I’m willing to consider it as a working assumption.

The true nemesis for bond investors isn’t their taxes or investment expenses, but the impact of inflation. So what if they are making fat coupons? If prices are rising faster, then they aren’t making money. So that’s what bond returns have to be benchmarked against (when credit-risk is kept constant). The bond with the best CAGR would seem to be the bond best able to overcome inflation.

CAGR is polynomic, not linear, meaning, the rate of increase increases (or decreases). E.g., to get from point A (an earlier and lower point) to point B (a later and higher point) on a chart can be done with either equation. But the predicted successor points of each equation don’t coincide. That, I suspect, is where the trouble lies and where, also, a solution might be found.

Envision a normal yield-curve. Its shape is polynomic, not linear. Why? Why doesn’t a later-maturing bond offer a yield that is linearly-proportional to an earlier-dated bond? In the initial portion of a normal yield-curve –-and in today’s steep yield-curve— the “short” end of the curve is very linear, as, paradoxically, so is the “long” portion of today’s YC for many bonds, which is very flat. Jack has commented on this, as did I previously to him. (But the YC of present days isn’t “normal”.)

Again, why aren’t bond yields linearly-proportional to maturity, when all other factors are held constant? I don’t know, and the problem is of more than theoretical interest. [pun intended]. A CD can be considered to be a zero-coupon bond. For sure it pays a coupon. But the fact is irrelevant structurally. It wouldn’t make any difference to an investor’s returns if he bought a 3-year $1,000 CD with a 5% coupon and ended up with $1,1576.25 (or whatever the result will be), or whether he bought the bond at an appropriate discount to par and ended up with $1,000. His internal rate of gain will be the same. The differences between starting and ending points in each case is irrelevant. That fact makes it possible to benchmark the returns offered by CDs against those offered by zeros and to price credit-risk.

For the same maturity, a CD should offer the same yield as a zero Treasury (when the tax-advantage of a Treasury is properly discounted). That’s the easy case. The harder case is corporate zeros that come in many flavors of credit ratings, triple-AAA to junk. For now, set aside the problem of vetting agency-ratings and the problem of how to interpret market-implied ratings. Just make the counter-factual assumption that the label is accurate and, further, that the historical studies of default-rates can be applied in a straight-forward manner.

Now comes the problem. CDs typically cluster at the short end of the curve. Zeros cluster in the mid to long portion. If ratings can be properly interpreted, and since yields aren’t linearly-proportional to maturity, and if CDs and zeros are plotted on the same yield-curve, where is the sweet spot?

I don’t know, and I should, because I’ll buy CDs if they seem to be one sale, and I’ll buy zeros if they seem to be on sale. But I don’t really know how to determine –-in a disciplined and quantitative manner -- what a good price is. I can make shrewd guesses bases on informed experience. But I can’t (yet) write the equation I’d like to have. I suspect I need something better than CAGR or HPR (Holding Period Return). But I don’t yet know what it is.

Interesting problem.

No. of Recommendations: 0

You might want to read Bernsteins "Investor Manifesto" to look at both the general and quantitative discussions he has on risk and reward with both stocks and bonds. The first two Chapters can be viewed for free here:

http://www.efficientfrontier.com/files/TIM.pdf

The problem, as you correctly state is how to determine value on the day you chose to make the investment, especially since value tends to come at times when risk appears to be higher (like March, 2009).

I think, as others have pointed out you make your decision comparatively (with other opportunities), from trends over time and you guess at the future of a specific bond. If you feel unsure of the trend you bet small. If you feel more confident you bet more. That's the basic secret of poker, and in the day, that's what I was somewhat successful at doing. In my opinion, it takes continuing work, the discipline to examine which investments are best and worst, and can run into the problem that your you're overall size because of success may become too great a drag on your success. What you are doing IMO that is MOST important is examining the numbers.

I congratulate everyone who is successful at understanding (or seeking understanding of) a financial approach which leads to their success. I've had many over time, some more successful than others.

Hockeypop

No. of Recommendations: 0

Hockeypop,

Thanks for the suggestion. I'll look at the book, but I strongly dislike the author. I've dug into his other books --Four Pillars and something on asset allocation-- and had to conclude that he's just a MPT groupie who doesn't know how to use historical data properly. In other worse, he's the worst sort of gambler, someone who under-estimates risks, because he believe returns distribute normally.

The last time I was at Barnes and Nobles, I noticed the book. I didn't pick it up, because of my encounters with his previous books. But it won't hurt me to take a look. (OTOH, Peter Bernstein I like a lot.)

No. of Recommendations: 2

"Envision a normal yield-curve. Its shape is polynomic, not linear. Why?"

You yourself have stated that bonds are puts, so shouldn't you expect their price - and thus their yield - to have the same time-value curve as an option (which is rather non-linear, and borders on something between an S-curve and logarithmic, just like the yield curve)?

Tom