As a retiree, I am continually looking for sources of more income but I also don't want to court excessive risk. Like most retirees, I have accepted the meager returns from bond funds because of their perceived safe haven against loss of capital. However, as interest began to rise in May, bond funds fell off the cliff and recorded significant losses. To insulate my portfolio as much as possible against interest rate risk, I looked at limited duration Closed End Funds (CEFs). This article discusses my analysis of these funds in terms of their risk-to-reward characteristics.

Duration is a term that helps you to understand the interest rate risks associated with bonds. Duration is different than the maturity; maturity indicates how long a bond will be in existence. For instance, if you buy a 10 year Treasury, the principal will be repaid at the end of 10 years and the maturity is said to be 10 years. Duration is a more complicated concept. Mathematically, duration is a complex formula that represents the weighted average of the time it takes the cash flow from the bond (including the final par value payment) to reimburse the price of the bond. If a bond pays interest at set intervals, the duration is always less than the maturity.

Most bond funds provide an estimate of the average duration of their holdings so investors do not need to know how to calculate this metric. The important thing to understand is that duration is a measure of how sensitive the fund is to interest rate changes. For each 1% rise in interest rates, a bond fund will typically decline an amount equal to the average duration (or vice versa, the fund will increase in value by the average duration if the interest rates fall 1%). As an example, if a fund has a duration of 5 years and interest rates rise by 1%, then you would expect the value of the fund to decrease by 5%. If a fund uses leverage, this will increase the effective duration. The change in price may not exactly track with the duration (there may be other factors at work) but duration is a good indication of interest rate risk.

As the name implies, the managers of limited duration CEFs select bonds that have short durations, typically 5 years are less. If interest rates begin to rise, as they did in May, then these funds should outperform most other bond funds. To analyze the reward-to-risk characteristics of this asset class, I chose funds that were both liquid (an average of at least 50,000 shares traded daily) and had at least 3 years of data. The other criteria that I used were:

- Distributions of at least 6%
- Market Cap of at least $100M
- Premium of no more than 1%

The 5 CEFs satisfying my criteria were:

**BlackRock Limited Duration Income Trust (BLW).**This CEF sells for a discount of almost 2%, which is unusual; it typically sells for an average premium of 4%. This fund uses 32% leverage and has a distribution of 7.3% paid monthly. It has a very low duration of 1.2 years after accounting for leverage. It is comprised of about 775 holdings partitioned among senior loans, high yield bonds, and asset backed bonds. Over 95% of the holdings are from US firms. The fund has a low expense ratio of 1.1% (including interest charges).**Eaton Vance Limited Duration Income Fund (EVV).**This CEF usually sells for a premium (average about 1% over the past year) but it is now selling at a discount of over 6%. This fund uses about 31% leverage and has a distribution of 8% paid monthly. It has a duration of 2.6 years after accounting for leverage. The fund is comprised of more than 1500 holdings partitioned primarily among high yield and asset backed bonds. Virtually all the holdings are from US firms. The fund has an expense ratio of 1.6% (including interest charges).**Eaton Vance Short Duration Diversified (EVG).**This CEF sells for a discount of over 7%, which is less than the average discount of 3%. This fund uses a relatively low 24% leverage and has a distribution of 6.9% paid monthly. It has a short duration of 2.1 years after accounting for leverage. It consists of over 500 holdings partitioned among loans, asset backed and Government bonds. Only about 80% of the holdings are from US firms. The fund has an relatively high expense ratio of 2.1% (including interest charges).**Franklin Limited Duration Income (FTF).**This CEF sells for a discount of over 7% which is significantly less than the average premium of 2%. This fund uses a low 19% leverage and has a distribution of 6.8% paid monthly. It has a duration of 3 years after accounting for leverage and holds almost 400 securities, partitioned among loans, asset backed and high yield bonds. Only about 75% of the holdings are from US firms. The fund has an expense ratio of 1.1% (including interest charges).**Wells Fargo Advantage Multi-Sector Income Fund (ERC).**This fund sells for a discount of over 11% which is well below the average discount of 5%. This fund employs 24% leverage and has a distribution of 8.5% paid monthly. This fund has a relatively large 5.3 year leverage-adjusted duration. It holds more than 700 securities spread among high yield bonds, loans, and Government bonds. Only about 75% of the holdings are from US companies. The fund has an expense ratio of 1.2%.

Assuming equal weight, these CEFs distributed an average of 7.5% annually so they definitely satisfied my desire for higher income. The high distributions were partly attributable to the use of leverage, which was good in bull markets but could result in oversize losses when the bear returns. To analyze risks, I used the Smartfolio 3 program (www.smartfolio.com). Figure 1 provides the rate of return in excess of the risk free rate of return (called Excess Mu on the charts) plotted against the historical volatility over the past 3 years. I also included the following Treasury Bond ETFs to provide a frame of reference:

**iShares Barclay 7-10 year Treasury ETF (IEF).**This fund has a yield of 1.7% and a duration of 7.6 years.**iShares Barclays 20+ Treasury Bond ETF (TLT).**This fund has a yield of 2.7% and has a duration of 16.7 years

## Figure 1: Risk vs. Reward: Limited CEFs over 3 years

As is evident from the Figure, there was a relatively large range of rates of returns and volatilities. For example, BLW had a high rate of return but had a much higher volatility than IEF. Was the increased return worth the increased volatility? To answer this question, I calculated the Sharpe Ratio.

The Sharpe Ratio is a metric, developed by Nobel laureate William Sharpe that measures risk-adjusted performance. It is calculated as the ratio of the excess return over the volatility. This reward-to-risk ratio (assuming that risk is measured by volatility) is a good way to compare peers to assess if higher returns are due to superior investment performance or from taking additional risk. In Figure 1, I plotted a red line that represents the Sharpe Ratio associated with IEF. If an asset is above the line, it has a higher Sharpe Ratio than IEF. Conversely, if an asset is below the line, the reward-to-risk is worse than IEF. Similarly, the blue line represents the Sharpe Ratio associated with TLT.

Several observations are apparent from the Figure. All the CEFs had a Sharpe Ratio equal to or greater than TLT. In other words, all the CEFs provided a better reward-to-risk than buying a long term Treasury fund like TLT. The verdict is not as clear when comparing the CEFs to an intermediate term bond funds like ETF. The risk adjusted return associated with EVG was substantially less than ETF. However, the other CEFs had a similar reward-to-risk profile as IEF. Of the CEFs analyzed, BLW had the best risk-adjusted return.

Based on the data in the Figure, the limited duration CEFs have provided good performance over the past three years with volatilities generally greater than IEF but less than TLT. My next question was: what would happen to the risk-versus- reward if I combined these five CEFs into a portfolio?

In the 1950s, an economist named Markowitz made an amazing discovery. He found that if you combined certain types of risky assets, you could construct a portfolio that had less risk than the components. His work was so revolutionary that he was awarded the Nobel Prize. One of the keys to achieving this reduction in risk is to combine assets that are uncorrelated with one another.

Figure 2 provides the correlation matrix associated with the funds under study. As you can see, the CEFs are relatively uncorrelated with one another, with correlations typically about 50% to 60%. The CEFs are negatively correlated with both IEF and TLT so these CEFs offer an excellent way to diversify a Treasury bond portfolio.

## Figure 2: Correlation Matrix: Limited Duration CEFs 3 years

I combined these CEFs into an equally weighted portfolio, with each component equal to 20% of the total assets. The results are shown as the "green dot" labeled "portfolio" in Figure 1. The resulting portfolio had a rate of return of about 7.4% with a volatility of less than 11%. The portfolio had a Sharpe Ratio that beats both IEF and TLT. Over the past three years, this portfolio truly satisfied my objective of providing higher income with lower risk!

It should be noted that an equally weighted portfolio may not be the absolute best in terms of maximizing the return for a given volatility. The optimum portfolio is said to be on the "efficient frontier". However, the "efficient frontier" can change substantially with relatively small changes in input data. I prefer the simplicity of equally weighted assets, which are easier to rebalance over time.

Bonds have had a rough time lately. Since the beginning of 2012, IEF has not delivered any excess return and TLT has actually lost over 2%. I wanted to see how the limited duration CEFs did in this challenging environment so I plotted the data using a look back period of about 18 months (from the beginning of 2012 to the present). The results are shown in Figure 3 and it is easy to see that the CEFs still had relatively good performance when compared to IEF and TLT. If I combine the CEFs, the resulting portfolio continued to have an excellent risk-adjusted returns, with over a 7.5% rate of return and a volatility of a little over 10%.

## Figure 3: Risk vs. Reward: Limited Duration CEFs 18 months

Past performance is not an indication of future gains but my conclusion is that limited duration CEFs are worthy of consideration for the fixed income portion of a portfolio. Over the periods analyzed, they have delivered relatively high income at a reasonable risk.

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