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Seeking Beta in the Bond Market: A Math-driven Investment Strategy for Higher Returns

November 23, 2010

by Georg Vrba, P.E.

Advisor Perspectives welcomes guest contributions. The views presented here do not necessarily represent those of Advisor Perspectives.

Investors seeking permanent exposure to the bond market should invest in high-beta funds during up markets and low-beta funds during down markets. This simple strategy, as I will show, provides consistent long-term returns that are considerably higher than what a static investment in bond funds would achieve.

The reason is simple: High-beta funds – in other words, funds that are more sensitive to market movements – perform better than their benchmark index in up markets and worse in down markets. Low-beta funds perform worse than the index in up markets and better in down markets.

To implement my strategy, one has to identify turning points in the market and switch one’s investments accordingly. My method of doing so is entirely math-driven, requires little input and does not depend on subjective market interpretation. Relatively few transactions are required – by my metric, the market does not flip often.

Most advisors advocate a conservative bond market investment approach of holding a diversified mix of fixed income securities that offer exposure to all maturities and all types of issuers. For example, the widely used Vanguard Total Bond Market Index Fund seeks to reflect the composition of the entire bond market. This fund has a beta of 1.00 and since 1990 has provided an average annual return of about 7%. In contrast, my investment method over the same time period would have provided, depending on the funds chosen, an average annual return of between 11% and 15% without incurring significant additional risk.

My strategy
My method is based on the first three of Bob Farrell’s rules:

  1. Markets tend to return to the mean over time.
  2. Excesses in one direction will lead to an opposite excess in the other direction.
  3. There are no new eras -- excesses are never permanent.

I establish a mean market direction and exploit deviation from the mean (the up and down markets) for positive investment results.
Interest rates follow long-term trends, as Figure 1, which shows the long-term U.S. interest rates for the last 130 years, illustrates. A recent article in Advisor Perspectives, The Road Ahead: Is It Inflation or Deflation by Martin Pring, makes the same point.

Interest Rates from 1880-2010

There are three clearly defined segments of this graph, each delineated by an interest rate peak: from 1880–1921, from 1921–1981, and from 1981 to now. The interest rate trend for each segment could be expressed as the equation of a curve that fits best to the underlying data. My method, which uses the interest rate trend, applies to the period from 1986 to now. The investment approach I have derived from it can be used as long as the current segment’s interest rate trend continues.

Turning points in the bond market result from interest rate changes alone and nothing else. Therefore, unlike the stock market’s movements, bond market direction is deducible by mathematical analysis.

The daily prognostications on market direction by financial “experts” may be fun to read, but don’t be confused by their predictions. The way to determine bond market direction is to correctly interpret the change of the yield curve over time.  I calculate a “Bond Value Ratio” (BVR), which is based only on the daily yields-to-maturity of the 30-year Treasury bond and the 10-year note. Bond values derive from those yields, and the relationship between those bond values is captured by the BVR, which is an indicator of up or down markets. BVR increases if the value change of the 30-year bond exceeds the value change of the 10-year note, and vice versa.  When BVR is plotted as a graph against time, an upward slope indicates an up market and conversely, a downward slope indicates a down market.

I performed a regression analysis of the BVR to determine its best-fit curve – its trend line. This curve represents the mean market direction referred to in Farrell’s rule one. I then place upper and lower offset lines from the best-fit curve to establish a reference for the directional excesses referred to in Farrell’s rule two. When the BVR turns upwards from below a lower offset line, I invest in a fund with high beta. When the BVR turns downwards from above an upper offset line, I remove my money from the high-beta fund and place it into a fund with low beta. This strategy invokes Farrell’s rule three, which is about excesses never being permanent.

Offset limits can vary depending on the desired time horizon and acceptable volatility of the investment. Lower offset limits result in more turning points, lower volatility and usually, but not always, lower returns. Higher limits result in fewer turning points and more volatility. Only limit settings so high that BVR can never penetrate the offset lines do not provide a higher return than a high-beta fund alone would provide. I have found the optimum offset limits to be 0.110 for a 10- to 12-year investment horizon and 0.040 for a five- to 10-year horizon.

The bond funds
In order to eliminate default risk, I only consider bond funds with investments that are guaranteed by the U.S. Treasury and supported by the full faith and credit of the U.S. government. Seeking high-beta and low-beta funds in this category, I selected four funds with a reasonably long history: the first is an American Century zero-coupon fund and the other three are Vanguard funds with dividends. All funds have a very strong correlation with the BVR, as indicated by the calculated correlation coefficient “r.”

Ticker Symbol


Beta (3y)

Beta (5y)

Beta (10y)


BTTRX Long-Term Government 3.90 3.78 3.94 0.930
VUSTX Long-Term Government 2.60 2.47 2.38 0.932
VFIIX Intermediate-Term Governmen> 0.69 0.74 0.73 0.923
VBISX Short-Term Bond 0.53 0.54 0.56 0.928

(Note: This choice of funds should not be construed as a recommendation to invest in them; my sole purpose is to demonstrate my investment strategy.)