*A version of this article appeared in the September issue of *Morningstar ETFInvestor*. Download a complimentary copy of* ETFInvestor *here*.

Bond investors require compensation for bearing greater credit and interest-rate risk through higher expected returns, or yields. Fixed-income managers can--and often do--boost returns by taking more credit or interest-rate risk than their benchmarks, but that does not necessarily require skill. Investors can do that on their own with low-cost index funds, so it is hard to justify paying high fees for performance that is simply compensation for risk. And while risk taking can pay off in one period, it may lead to underperformance in another.

Therefore, it is important to distinguish between returns that managers generate through risk-taking and skill (including the skill involved in timing interest and credit risk). We can accomplish this with a factor regression analysis.

To illustrate, consider a simple model that seeks to explain PIMCO Total Return'sPTTRX return as a function of interest-rate risk. To construct this model, we first subtract the returns on short-term Treasury bills from the fund's returns to isolate the extra return investors get for putting their money at risk. We could also subtract the return on Treasuries from the return on the Barclays Intermediate U.S. Treasury Index to determine the payoff the market offers for intermediate-term interest-rate risk (independent of credit risk). This is an interest-rate factor.

The chart below shows the relationship between the fund's excess monthly returns (over Treasuries) and the excess returns on the Barclays Intermediate U.S. Treasury Index over the trailing 10 years through July 2015.

Not surprisingly, there appears to be a positive relationship between the returns on the intermediate-term Treasury bond index and PIMCO Total Return. The slope of the best-fit line through the data measures how much interest-rate risk the fund is taking. A slope of less than 1.0 indicates the fund is taking less interest-rate risk than the index. In this case, the slope is 0.76, indicating that each percentage point return to intermediate-term interest-rate risk tended to contribute 76 basis points to the fund's return. More formally, this is the interest-rate factor coefficient, or beta. The point where the line intersects the y-axis (the y-intercept) captures the return from skill. This figure is better known as alpha. If a fund is not taking more risk (as defined in the model) than Treasuries, it should not generate higher returns. Therefore, if the intercept is significantly positive, either the model is incomplete or the manager is skilled. In this case, the intercept is positive, but it is not statistically significant--meaning that this observation could be due to chance.

This simple model only explains 31% of the variance in the fund's returns, suggesting that there is a lot that it does not capture. The model also has an important limitation--it assumes that there is a linear relationship between interest-rate risk and return. But the yield curve is rarely a straight line. Consequently, the model may over- or understate the return to skill.

**A More Complete Model**

In order to build a more complete model and partially address potential nonlinearity between interest-rate risk and return, I added a long-term interest-rate factor to the model. This factor is defined as the return on the Barclays Long Term U.S. Treasury Index minus the return on the Barclays Intermediate Term U.S. Treasury Index. This adjustment can accommodate different risk/reward profiles for intermediate and long-term bonds and should more accurately capture the type of interest-rate risk managers take.

I also added two credit risk factors. The first captures the returns to investment-grade credit risk. It is measured as 0.5 x (Barclays U.S. Corporate Baa Intermediate Index - Barclays U.S. Intermediate Treasury Index) + 0.5 x (Barclays U.S. Corporate Baa Long Index - Barclays U.S. Long Term Treasury Index). Subtracting the returns of Treasury bonds of comparable maturity should effectively isolate the payoff to credit risk. The second credit risk factor measures the returns to high-yield credit risk. It is defined as the difference between the returns on the Barclays U.S. Corporate High Yield Index and the returns to the Barclays U.S. Corporate Baa Intermediate Index.

This model allows investors to better identify the risks each manager is taking. It can also reveal useful information about a manager's style, particularly when it is difficult to ascertain the fund's credit and duration characteristics from its holdings.

The following table uses the new model to break down the sources of return (over Treasuries) for PIMCO Total Return, Scout Core Plus Bond SCPZX, and Metropolitan West Total Return Bond MWTRX over the past decade.

Exposure to intermediate-term interest-rate risk was the biggest return contributor for each of the three funds. For example, it contributed 23 basis points to PIMCO Total Return's average monthly return. PIMCO Total Return hasn't taken significant long-term interest-rate risk. Investment-grade and high-yield credit risk added a few basis points to the fund's average monthly return. The return from skill (alpha) in this model was 5 basis points, which was not statistically significant. This model could explain 78% of the variance in the fund's returns, which is a considerable improvement over the simple model presented earlier.

Scout Core Plus Bond generated the highest return of the three funds over this time, but that's because it took greater credit and long-term interest-rate risk, both of which paid off. After controlling for these risk factors, the management team did not generate any unique returns from skill. In contrast, Metropolitan West Total Return Bond generated a significant positive alpha, which added 13 basis points to its average monthly return. It took less intermediate-term risk than PIMCO Total Return and Scout Core Plus Bond and comparable credit risk to PIMCO Total Return, leading to a more attractive risk/reward profile.

I ran this analysis on each fund in the intermediate-term bond Morningstar Category that launched on or before Aug. 1, 2005. The chart below shows the contribution of all of the risk factors to each fund's average monthly returns and the portion attributable to manager skill--or not captured in the model (alpha). The funds are sorted by alpha. On average, the model explained 83% of the variance in returns.

Half (100 out of 200) of the funds exhibited a positive alpha, but those figures were only statistically significant for 17 funds. The average fund owed 23 basis points of its typical monthly return to credit and interest-rate risk but generated no return from skill. Of the managers that generated positive returns from skill, their average alpha was only 4 basis points, which was small relative to the returns from the risk factors. While there appear to be some skilled managers, investors should be wary of paying active fees for performance that is simply compensation for credit or interest-rate risk, which may be available more cheaply through index funds.

**Investment Options**SPDR Barclays Intermediate Term Treasury ETF ITE and SPDR Barclays Long Term Treasury ETF TLO offer low-cost (each has a 0.10% expense ratio) exposure to intermediate- and long-term Treasury bonds, respectively. They track the same indexes that I used to construct the intermediate- and long-term interest-rate factors in the model. ITE targets Treasury bonds with between one and 10 years until maturity, while TLO targets Treasuries with more than 10 years until maturity.

SPDR Barclays Intermediate Term Corporate Bond ITR and SPDR Barclays Long Term Corporate Bond ETF LWC offer low-cost (both charge a 0.12% expense ratio) exposure to investment-grade credit risk. ITR targets investment-grade corporate debt with between one and 10 years until maturity. LWC screens for bonds with more than 10 years left until maturity. Neither fund targets BBB rated (or equivalent) debt, so they may not offer as large of a return premium as the Baa indexes featured in the factor model above. According to Morningstar data, the average credit rating of these two funds' holdings is currently A.

Investors can get low-cost exposure to high-yield credit risk through Vanguard High-Yield Corporate VWEAX (0.13% expense ratio). This fund does not track an index, but it is cheaper than its index peers. Index investing in this market segment can also be challenging because many high-yield bonds do not offer good liquidity, which can lead to tracking error and high trading costs for index managers. This fund tilts toward higher-quality bonds in the junk-bond market, which may reduce its expected returns relative to the Barclays U.S. Corporate High Yield Index.

Disclosure: Morningstar, Inc.'s Investment Management division licenses indexes to financial institutions as the tracking indexes for investable products, such as exchange-traded funds, sponsored by the financial institution. The license fee for such use is paid by the sponsoring financial institution based mainly on the total assets of the investable product. Please click here for a list of investable products that track or have tracked a Morningstar index. Neither Morningstar, Inc. nor its investment management division markets, sells, or makes any representations regarding the advisability of investing in any investable product that tracks a Morningstar index.