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 highbeta funds during up markets and lowbeta funds during down markets. This simple strategy, as I will show, provides consistent longterm returns that are considerably higher than what a static investment in bond funds would achieve.
The reason is simple: Highbeta 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. Lowbeta 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 mathdriven, 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:
 Markets tend to return to the mean over time.
 Excesses in one direction will lead to an opposite excess in the other direction.
 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 longterm trends, as Figure 1, which shows the longterm 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.
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 yieldstomaturity of the 30year Treasury bond and the 10year 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 30year bond exceeds the value change of the 10year 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 bestfit 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 bestfit 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 highbeta 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 highbeta fund alone would provide. I have found the optimum offset limits to be 0.110 for a 10 to 12year investment horizon and 0.040 for a five to 10year 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 highbeta and lowbeta funds in this category, I selected four funds with a reasonably long history: the first is an American Century zerocoupon 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 
Category 
Beta (3y) 
Beta (5y) 
Beta (10y) 
r 
BTTRX 
LongTerm Government 
3.90 
3.78 
3.94 
0.930 
VUSTX 
LongTerm Government 
2.60 
2.47 
2.38 
0.932 
VFIIX 
IntermediateTerm Governmen> 
0.69 
0.74 
0.73 
0.923 
VBISX 
ShortTerm 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.)
The data I’m working with does not go all the way back to fund inception, but it covers a significant time period nevertheless. In order to show the relative performance of the funds, I indexed them to the same starting value as of 12/14/89, the earliest date for which VUSTX data with dividends is available. The indexing date is before the inception date of BTTRX and VBIIX. VUSTX was assumed to be a proxy for BTTRX before 2/15/96 and similarly, VBISX values were assumed to mirror VFIIX values before 6/20/96.
Figure 2 depicts the value of the selected bond funds over time with dividends reinvested. It is evident that the highbeta funds BTTRX and VUSTX appreciated most over time but also have a higher volatility than the low beta funds.
The results
The investment period for this study is from 1/12/1990 to 11/18/2010.
The fund combinations used for evaluating my investment strategy are:
mix 1: VBISX & VUSTX as the lowbeta and highbeta funds, respectively, and
mix 2: VBISX & BTTRX as the lowbeta and highbeta funds, respectively.
Results are presented for two sets of offset limits, “A” and “B”:
“A”: upper offset limit = 0.110 and lower offset limit = 0.110
“B”: upper offset limit = 0.040 and lower offset limit = 0.040
Listed returns are the average annual return from 1/12/1990 to 11/18/2010.
offset limits 
investment horizon 
return mix 1 
return mix 2 
transactions 
Figures 
“A” 
10 to 12 years 
11.16% 
15.06% 
17 
3 & 5 
“B” 
5 to 10 years 
10.44% 
14.61% 
31 
4 
If VFIIX is selected instead of VBISX as the low beta fund in mix 1 and mix 2, the returns are:
offset limits 
investment horizon 
return mix 1 
return mix 2 
transactions 
“A” 
10 to 12 years 
10.92% 
14.80% 
17 
“B” 
5 to 10 years 
10.10% 
14.25% 
31 
Returns are considerably higher than for permanent investments in the highbeta funds, which would have produced average annual returns of 8.04% for VUSTX and 9.24% for BTTRX. (The return for BTTRX does not coincide with its published “since inception return” because of the adjustments made to determine a hypothetical value for BTTRX prior its existence, as mentioned earlier.) Also, since VFIIX has a higher beta than VBISX, the returns with VFIIX as the lowbeta fund in mix 1 and mix 2 are, as expected, lower. The obvious choice is to select respectively the highest and the lowest beta bond funds for the investments in up markets and down markets.
I have investigated combinations with limit settings ranging from 0.160 to 0.010, changing the limits in steps of 0.005. The minimum average annual return from this range of combinations resulted from an offset limit setting of 0.055, which returned 9.66% for mix 1 and 12.85% for mix 2. Even these minimum returns are better than returns from a static investment in the highbeta funds alone.
Figures 3 and 4 depict BVR with offset limits “A” and “B” respectively. Upper switch points are shown when the highbeta fund is sold and the investment is switched into the lowbeta fund, and lower switch points indicate the opposite.
Figure 5 depicts the fund values and the values obtained for mix 1 and mix 2 when using offset limits “A.” The volatility for mix 1 and mix 2 is considerably lower when the investment is in the lowbeta fund, as indicated by the relatively smooth line between the switch points. This, obviously, reduces the overall volatility of the investment.
Figure 6 graphs the investment value after periodic monthly withdrawals based on a withdrawal rate of 6.0% per annum. This is 1.5 times the normally accepted safe withdrawal rate of 4.0%. Over the investment period considered, and with an offset limit setting of 0.110, the return for mix 1 after withdrawals is still a respectable 4.80%, and for mix 2 it is 8.49%. My investment strategy can provide a higher safe withdrawal rate while still producing significant investment growth.
Testing and updating the model
An argument could be made that this method is an exercise in backfitting and that at an earlier end date the bestfit curve for the BVR, derived from the shorter data set, would have had a different shape. A different curve would have resulted in different transaction points than those that the bestfit curve for the full data set produced.
In order to evaluate this criticism, I calculated the bestfit curves for shorter time periods and projected them forward to find the period over which they would still reflect the trend of the BVR correctly. I did this for 16 consecutive oneyear periods starting in 1995 and ending in 2010. I found that the forward projected curves could safely be relied upon for a minimum of three months to produce the same transaction points as the present model did, provided the chosen offset limits did not exceed a value of 0.110.
One should recalculate the equation of the bestfit line monthly using the entire available data set, so that the most recent data is taken into account. The model should also be regularly updated with the most current bond yields. This is especially important when the BVR is above an upperoffset limit line, which may indicate an imminent signal for a switch into a lowbeta fund. Staying too long in the highbeta fund once the BVR moves below the upper limit line can lead to significant losses. To reduce risk, one can use a lower setting for the upper offset line than for the lower offset line. This would have the effect of selling the highbeta fund earlier, and in exchange for the added security one would expect a slightly lower return. See the Appendix for results of such a strategy.
Recent investment results
Figure 7 is a graph of BVR for the period 2006 to 2010.
The last three switch points occurred on 12/31/08, 12/30/09 and 8/27/10. To demonstrate the effect of my method on investment returns, the actual performance of the funds including dividends, if applicable, is shown below:
The transaction point of 12/31/08 signaled the switch from the highbeta fund to the lowbeta fund.
Fund performance was:
Period 12/31/08 to 12/30/09 
BTTRX 
VUSTX 
VFIIX 
VBISX 
Fund value change % 
20.48% 
12.04% 
+4.93% 
+4.26% 
The next transaction point of 12/30/09 signaled the switch from the lowbeta fund to the highbeta fund. Fund performance was:
Period 12/30/09 to 8/27/10 
BTTRX 
VUSTX 
VFIIX 
VBISX 
Fund value change % 
+26.62% 
+17.22% 
+6.96% 
+3.54% 
The last transaction point of 8/27/10 signaled the switch from the highbeta fund to the lowbeta fund. The BVR has since dropped further, indicating that an investment would have performed better in a lowbeta fund than in a highbeta fund since that date. Fund performance from 8/27/10 to 11/18/10 was:

BTTRX 
VUSTX 
VFIIX 
VBISX 
8/27/2010 fund price/value 
$ 71.81 
$ 12.49 
$ 11.05 
$ 10.66 
dividends paid 
0 
$ 0.076 
$ 0.066 
$ 0.036 
11/18/2010 fund price 
$ 66.68 
$ 11.63 
$ 11.07 
$ 10.67 
11/18/2010 fund value 
$ 66.68 
$11.706 
$11.136 
$10.706 
Fund value change 
($ 5.13) 
($ 0.784) 
$ 0.086 
$ 0.046 
Fund value change % 
7.144% 
6.277% 
+0.778% 
+0.432% 
The most recent change in value of the funds was significant, and in this relatively short period of twelve weeks the highbeta fund VUSTX underperformed the lowbeta fund VBISX by 6.71%. Thus, by switching into the lowbeta fund at the right time, one could improve performance by 6.71% relative to a permanent investment in VUSTX. When most people expected bond yields to fall after Bernanke’s Jackson Hole speech, the BVR dropped immediately from above the upper offset limit line and began a steep fall. Over the last twelve weeks the BVR has fallen and is now below the lower offset limit line. Longbond values have declined by about 7% over this period. When the BVR reverses direction, it will indicate that it should be profitable again to invest in highbeta funds for a while.
In the down market (12/31/08 to 12/30/09), the highbeta funds had large negative returns, while the lowbeta funds provided positive returns. (During previous down markets the lowbeta funds always outperformed the high beta funds, which generated the additional return over a permanent investment in the highbeta funds.) When the BVR was in a rising mode, indicating an up market (12/30/09 to 8/27/10), the returns of the highbeta funds over this period were vastly superior to those of the lowbeta funds. The performance of the funds relative to each other proves that the beta values correctly predicted a fund’s performance under varying market conditions.
Further observations
My investment strategy is based on a quantitative method and does not rely on hope to produce better returns. The superior investment returns of my method do not require an assumption of unusual risks. On the contrary, the volatility risk of my strategy is lower than for an investment in a highbeta fund alone. And recall that I eliminated all default risk by investing in U.S. Treasury bond funds only. The mantra “higher returns with higher risk” does not apply here.
My investment strategy is not limited to U.S. bond funds. The model’s principles apply equally to other welldeveloped bond markets and markets in which funds of various maturity levels are available. If there are no beta values published, then a longmaturity bond fund can be used as a highbeta fund and a shortmaturity bond fund can be used as lowbeta fund. Historical data for bond yields is also necessary to determine the Bond Value Ratios and the BVR trend line, as previously described.
Appendix
Beta vs. Standard Index
(from Morningstar Report: Mutual Fund Data Definitions)
Beta, a component of Modern Portfolio Theory statistics, is a measure of a fund's sensitivity to market movements. It measures the relationship between a fund's excess return over Tbills and the excess return of the benchmark index. Bond funds are compared with the Lehman Brothers Aggregate Bond index. By definition, the beta of the benchmark (in this case, an index) is 1.00. Accordingly, a fund with a 1.10 beta has performed 10% better than its benchmark indexafter deducting the Tbill ratethan the index in up markets and 10% worse in down markets, assuming all other factors remain constant. Conversely, a beta of 0.85 indicates that the fund has performed 15% worse than the index in up markets and 15% better in down markets. A low beta does not imply that the fund has a low level of volatility, though; rather, a low beta means only that the funds marketrelated risk is low.
Returns when upper and lower offset settings are not equal
mix 1: VBISX & VUSTX as the low beta and high beta fund, respectively, and
mix 2: VBISX & BTTRX as the low beta and high beta fund, respectively.
Results are presented for the following offset limits “C”:
“C”:upper offset limit = 0.090 and lower offset limit = 0.110
offset limits 
investment horizon 
return mix 1 
return mix 2 
transactions 
“C” 
long 
11.00% 
14.84% 
17 
(return is the average annual return from 1/12/1990 to 11/18/2010)
Data Source
Fund category and beta data, as well as data on historical fund prices and dividends, were obtained from Yahoo!Finance.
Read more articles by Georg Vrba, P.E.