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Summary The discounts associated with CEFs are at historic highs, with many discounts over 2 standard deviations from the mean. The highly discounted CEFs have been significantly more volatile than high yield bonds. MGU and GLO had the best risk-adjusted performance among the CEFs analyzed. As an income focused investor, I was a fan of high distribution Closed End Funds (CEFs). Many of these funds have been hit hard by the Fed’s plans to increase interest rates. As the prices deteriorated, the discounts of these CEFs have widened to historically large levels. This is evidenced by their Z-score, a statistic popularized by Morningstar to measure how far a discount (or premium) is from the mean discount (or premium). The Z-score is computed in terms of standard deviations from the mean so it can be used to rank CEFs. A good source for Z-scores is the CEFAnalysis website . (Thanks to SA author, Left Bank, for his article on where to find Z-scores). A Z-score more negative than minus 2 is relatively rare, occurring less than 2.25% of the time. However, in today’s environment, there are over 150 CEFs that have one year Z-scores more negative than minus 2, which illustrates the current lack of demand for these CEFs. There were too many CEFs to analyze so I reduced the sample size by using the following selection criteria: A Z-score more negative than minus 2.9. This will occur (assuming a normal distribution) less than 0.2% of the time. A history that includes October 12, 2007 (the beginning of the 2008 bear market) A daily average volume greater than 100,000 shares A market cap of at least $100 million. A distribution of 6% or higher The following CEFs satisfy all these criteria. Clough Global Opportunities Fund (NYSEMKT: GLO ). The CEF sells at a discount of 16.7% and has a Z-score of negative 3.59. This CEF has a “go anywhere” philosophy and has a portfolio of 167 securities, with 60% allocated to the equities, 28% to cash alternatives, and 7% to bonds. The fund may also use an option strategy to increase income. The fund uses a high leverage of 52% and has an expense ratio of 2.2%. The distribution is 10.7%, consisting primarily of gains and Return of Capital (ROC). Over the past year, ROC has been used 50% of the time, with the amount of ROC ranging from 30% to 100%. Invesco Credit Opportunities Fund (NYSE: VTA ). This CEF sells at a discount of 15.3% and has a Z-score of negative 3.59. It has a portfolio of 610 securities invested primarily in senior loans (76%) and high yield bonds (18%). The fund uses 33% leverage and has an expense ratio of 2.5%. The distribution is 8.2% with no ROC. Madison Covered Call and Equity Strategy Fund (NYSE: MCN ). This CEF sells at a discount of 15.1% and has a Z-score of negative 3.3. The portfolio consists of 47 securities, with 78% in equities and 20% in short-term debt. The fund does not use leverage and has an expense ratio of 0.8%. The distribution is 9.7% with no ROC. LMP Corporate Loan Fund (NYSE: TLI ). This CEF sells for a discount of 13% and has a Z-score of negative 3.25. The portfolio consists of 268 securities invested primarily in senior loans (87%) and high yield bonds (8%). The fund uses 33% leverage and has an expense ratio of 1.8%. The distribution is 8.4% with no ROC. Macquarie Global Infrastructure Total Return Fund (NYSE: MGU ). This CEF sells for a discount of 16.9% and has a Z-score of negative 3.09. The fund is concentrated with 51 holdings in infrastructure companies (89%) and 6% in master limited partnerships. The fund uses 30% leverage and has an expense ratio of 2.2%. The distribution is 7%, paid from income and capital gains with no ROC. Calamos Convertible Opportunities and Income Fund (NASDAQ: CHI ). This CEF sells at a discount of 11.2% and has a Z-score of negative 3.04. The portfolio consists of 287 securities, with 57% in convertible bonds and 38% in high yield bonds. The fund uses 28% leverage and has an expense ratio of 1.5%. The distribution is 10.8% with 2 months of ROC during the past year. MS Emerging Markets Debt Fund (NYSE: MSD ). This CEF sells for a discount of 18.3% and has a Z-score of negative 2.95. The portfolio consists of 115 emerging market holdings, with 41% investment grade bonds and the rest in high yield bonds. The fund uses only 8% leverage and has an expense ratio of 3.5%. The distribution is 6.6% with no ROC. GDL Fund (NYSE: GDL ). This CEF sells for a discount of 18.1% and has a Z-score of negative 2.9. The fund seeks total return by using arbitrage transactions and investing in reorganizations and spinoffs. It has 159 holdings, with 75% in equity and 21% in Government bonds. It uses 35% leverage and has an expense ratio of 3%. The distribution is 6.5% with only a small amount of ROC over the past year (the distribution for one quarter had 25% ROC). Based on the Z-score, these high income CEFs appear to be bargains, but Z-score is only one metric to consider. I also like to look at the reward-versus-risk over different time frames. In my mind, the best fund is the one that delivers the highest reward for a given level of risk. This article will analyze these CEFs in terms of risk-versus-reward to help you determine which may be right for your portfolio. To assess the performance of the selected CEFs, I plotted the annualized rate of return in excess of the risk free rate (called Excess Mu in the charts) versus the volatility of each of the component funds over the past bear-bull cycle (from October 12, 2007 to August 28, 2015). The risk free rate was set at 0% so that performance could be easily assessed. This plot is shown in Figure 1. Note that the rate of return is based on price, not Net Asset Value (NAV). I used the iShares iBoxx $ High Yield Corporate Bond ETF (NYSEARCA: HYG ) as a reference. (click to enlarge) Figure 1. Risk versus Reward over the bear-bull cycle The plot illustrates that these CEFs have booked a wide range of returns. To better assess the relative performance of these funds, 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 HYG. If an asset is above the line, it has a higher Sharpe Ratio than HYG. Conversely, if an asset is below the line, the reward-to-risk is worse than HYG. Some interesting observations are evident from the figure. High Z-score CEFs are substantially more volatile than HYG. This is not surprising since CEFs can sell at discounts and many use leverage. With the exception of VTA, the CEFs had larger absolute returns than HYG. However, when volatility is factored into the calculation, only 4 CEFs (GDL, GLO, MGU, and MSD) beat HYG on a risk-adjusted basis. Two other CEFs (TLI and MCU) had risk-adjusted performances similar to HYG. Among the CEFs, MSD was the best performer followed by GLO, MGU, and GDL. The worst performer on a risk-adjusted and absolute basis was VTA. These funds utilized different investment strategies, so I wanted to assess how much diversification you might receive by buying multiple funds. To be “diversified,” you want to choose assets such that when some assets are down, others are up. In mathematical terms, you want to select assets that are uncorrelated (or at least not highly correlated) with each other. I calculated the pair-wise correlations associated with the funds. For reference, I also included the SPDR S&P 500 Trust ETF (NYSEARCA: SPY ) as a proxy for the overall stock market. The results are presented in Figure 2. (click to enlarge) Figure 2. Correlation over the bear-bull cycle The figure presents what is called a correlation matrix. The symbols for the funds are listed in the first column on the left side of the figure. The symbols are also listed along the first row at the top. The number in the intersection of the row and column is the correlation between the two assets. For example, if you follow VTA to the right for three columns, you will see that the intersection with GLO is 0.650. This indicates that, over the past bear-bull cycle, the price of VTA and GLO were 65% correlated. Note that all assets are 100% correlated with themselves so the values along the diagonal of the matrix are all ones. As shown in the figure, the CEFs were not very correlated with HYG or among themselves. The highest correlation was between SPY and GLO, which was expected since GLO contained a large position in equities. The overall conclusion is that you can obtain diversification by purchasing more than one of these funds. Next, I wanted to see how these funds fared during more recent times so I used a 5-year look-back period. The results are shown in Figure 3 and what a difference a few years made. The CEFs are still more volatile than HYG, but HYG now beats all the CEFs in terms of risk-adjusted performance. MSD fell from being the best performer to the worst, and VTA moved up from being at the bottom to the third best. MGU had by far the best risk-adjusted performance among the CEFs, with GLO coming in second. GDL was again the least volatile but also did not have a high return. (click to enlarge) Figure 3. Risk versus reward over past 5 years My final analysis used a 3-year look-back period, and the results are shown in Figure 4. During this period, GLO, MGU, and MCN were the top performers on a risk-adjusted basis. These CEFs outperformed HYG on both an absolute and risk-adjusted basis. MSD continued its poor performance, booking a negative return. (click to enlarge) Figure 4. Risk versus reward over the past 3 years Bottom Line These large Z-score CEFs had a wide range of performance relative to each other and to HYG. All of these CEFs are much more volatile than high yield bonds so they would only be suitable for risk tolerant investors. These CEFs are at historically wide discounts and may be bargains in terms of discounts but their overall performance left something to be desired. If you want to take a gamble on these funds, I would recommend MGU. GLO could also be considered, but I am a little cautious of this fund’s ROC. No one can predict the future, but based on the past, these two CEFs have consistently outperformed their peers on a risk-adjusted basis. Disclosure: I/we have no positions in any stocks mentioned, but may initiate a long position in MGU over the next 72 hours. (More…) I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.