Because closed-end funds [CEF’s] trade largely on sentiment, identifying good buy levels is perhaps subjective. The traditional approach is to look at discounts to Net Asset Value [NAV] as a point of reference, or Z-scores, which are standard deviations on price. If you can buy an asset for 90 cents on the dollar of the true value of the underlying portfolio, what’s not to like about that?

But one limitation of these standard approaches is that, for the popular CEF sites, the premium and discount to NAV data and Z-scores are not very robust. By that I mean that the time ranges for the metrics are fixed and arguably arbitrary. This article describes a simple charting study that can help investors better see price levels when buying shares.

## Discount to NAV and Z-Scores

Let’s look first at discounts to NAV. On *CEFConnect*, for example, probably the most popular data site for CEFs, the table information for price and NAV are the current (last) values, and the 52-week high, average, and low. One can infer relative levels for other times looking at the summary chart, but the time intervals are fixed: 5D, 1M, YTD, 1YR, 3YR, 5YR and SINCE INCEPTION. Their interactive chart provides a few additional time periods, but they are also fixed. From what I see, Seeking Alpha takes the same approach for data aggregation. The larger question is the relevance of any of these arbitrary time periods for price action. Moreover, the fact that NAVs change daily as well as price can mask when a fund is at a relatively-attractive price point, in my view. This might be especially true for a concentrated fund for a sector that is under-performing.

Here’s an example for the Reaves Utility Income Trust (NYSE:UTG), my largest portfolio holding at 4.0%. The price chart to the right clearly shows that both price and NAV have declined for the past year in the wake of the 2022 bear market and the weak performance of the Utilities sector, which is 77% of the fund composition. But the data to the left show that the current discount to NAV is only -0.64% for the 52-week average. The decline in NAV masks that the fund is actually more on sale than one might otherwise think based on the discount alone. There is a look-up table on another page that returns daily values for any 30-day time period, and monthly values for any 5 year period, but this is cumbersome to use and the values can’t be charted.

Now let’s consider Z-scores, looking at the data on *CEFConnect* for UTG. As with NAV, there is a simple chart with a few time period options, and even fewer calculated values to the right of the chart. For the 1-year period, the Z-score is only -0.91 or less than 1 SD below the mean.

Looking at my price chart, UTG reached a low at 23.24 less than 2 weeks ago, and that was 42% below the pre-2020 recession high and 19% above the recession low. So the current price of UTG looks like a better bargain to me than what the discount to NAV and Z-scores indicate. The limitation is not being able to visualize price in relation to time periods that are more meaningful than the standard intervals.

So this had me thinking of a better way to visualize when a CEF is at a good buy level. I wanted an approach that both eliminates the arbitrary time intervals provided by the data sites and where I can better visualize how much price is uncharacteristic of the current or, especially, average price. And I wanted a tool that, once set up, can show these results immediately every time I chart any particular CEF, or stock.

Readers of my previous articles know that I am a basic chart trader and like my current TDAmeritrade ‘thinkorswim’ (tos’) platform, even though I don’t typically use many of the optional tools. But I found one simple approach that fits my needs, by using standard deviation on price, which I like as a metric. But unlike the typical Z-scores, I want to select the time frame for analysis. I haven’t found another source that allows dynamic charting for price divergence from the mean.

## Standard Deviation Channels for Price

Standard deviation basically measures the dispersal of a value point from the mean of the data set. It tells us how meaningful and useful the mean itself is as a representative value of the data range. For data that have a normal distribution, values within 1 standard deviation [SD] each above or below the mean represent about 34.1% of the data points. So the 1 SD channel includes in concept ~68% of the date values. The 2 SD channel adds 13.6% of the data points on each side, so that a total of 95.4% of the values are above or below the mean. Beyond 2 SD, a data value would be fairly unrepresentative of the rest of the data set.

The ‘tos’ chart Studies tools allow users to define standard deviation channels, and I set and overlaid three of these, for 1, 2, and 3 standard deviations. Here’s that chart for UTG using standard deviation channels. I customized this such that SD channel lines are green above the mean (gold line) and dark red below the mean. The 1 SD channel has dotted lines, the 2 SD channel has dashed lines, and the 3 SD channel has solid parallel lines. The slope of a channel is uptrending if the mean of the data increases from the starting point.

This chart shows the period from the Great Recession (aka Great Financial Crisis), a monthly chart from April 2009 to the present. I used this period because it is meaningful regarding market cycles and events. Many stocks and funds essentially experienced a price re-set in early April 2009 and have been in a new price cycle since then. And this period covers a second major market event, the short-lived 2020 recession. So I have a mean price trend for nearly 15 years (actually 14.6) that includes 2 recessions as well as the 2022 bear market, driven in part by large interest rate hikes. The date ranges can be easily modified. I also ran a chart for this fund starting in Nov. 2007 before the GR swoon, which resulted in an even higher mean price, at 35.22, so my date range gives me a more conservative mean price for UTG. The bottom line is that unless I think that there is something meaningful about 3 or 6 months, I prefer to look at data for a reason I can describe.

The UTG chart tells me several things. First, I notice that the current price of UTG, despite being only a -0.64% discount to NAV, is -2 SD below the mean price line of the entire period from 2009 to present. The current price (24.97) is actually 28.4% below the 15 year mean price of 34.90. That divergence is now the second lowest other than for the 2020 recession (COVID) low. Second, from 2011 to 2022, most of the price action of UTG has been above its nearly 15-year average price. Overall, this chart tells me that now is a great time to add to my position in UTG, trading at ~$10 per share below the longer-term average price. The current distribution yield on cost, at 9.13%, is also nice for those who want current income and from a fund that has no ROC. Finally, I notice that every time that the monthly price of UTG rose above the +1 SD level, it reversed within a few months. The +1 SD level might then be viewed as a potential sell level for UTG. Take some profits at +1 SD and re-build the position at the mean price and lower seems to be a good pattern. Adding more aggressively from -1 SD to -2 SD builds the position further and lowers the average unit cost, increasing yield. The relative buy and sell levels will likely differ for each fund and any clear chart patterns would have to be identified for each case.

I also see an interesting volume trend on that price chart. Beginning in late 2015, monthly volumes increased over the previous years, and another increase in volumes occurred post-2020. I suspect that this fund has become more popular as the monthly distributions have increased over recent years, as shown below.

This is a simple approach, but it provides for me a better view of when I’d want to add to a fund than just the traditional discount to NAV or Z-scores for arbitrary time periods.

For those who are not ‘swimmers,’ other on-line brokerage platforms can probably be customized to do this type of analysis.

## Current CEF Portfolio

My Roth IRA portfolio has an income portion comprised of CEFs, REITs, and selected dividend stocks, and a swing & position trading portion wherein I look to take profits on price appreciation of mostly over-sold S&P 500 stocks in sectors under-performing relative to the index.

As of November 1, I hold 60% in CEFs and 40% in individual stocks. My CEF portfolio consists of >42,000 shares across 61 CEFs.

The 10 largest CEFs in the portfolio by cost are:

UTG | Reaves Utility Income Trust |

BDJ | BlackRock Enhanced Equity Dividend Fund |

BST | BlackRock Science and Technology Trust |

RQI | Cohen & Steers Quality Income Realty Fund |

DSL | DoubleLine Income Solutions Fund |

HQH | abrdn Healthcare Investors |

UTF | Cohen & Steers Infrastructure Fund |

USA | Liberty All-Star Equity |

RVT | Royce Value Trust |

HTD | John Hancock Tax-Advantaged Dividend Income Fund |

The ticker symbols for the next 15 largest CEFS are: BMEZ, DLY, PDO, GDV, BIGZ, EMD, EOS, LDP, BSTZ, BIT, RMT, CSQ, DNP, ECAT, and HYT.

## Another Good CEF Buy Now

I applied my simple but easy-to-use charting set-up to some other CEFs that I suspect are over-sold but not showing a large discount to NAV or Z-score.

The REIT space is covered well by the Cohen & Steers Quality Income Realty Fund (RQI). It is trading at a good -9.25% discount to NAV and has a non-ROC distribution yield of 9.59%. But the Z-score for the inflexible 6-month and 1-year periods are in the neighborhood of -1.6, and it is better (-1.2) for the 3-month period.

But looking at my standard deviation channels chart from the 2009 Great Recession, below, RQI is at nearly -2 SD from the mean price for that 15 year period. At 10.01 per share, RQI is trading at -32% below the 15-year mean price. It also has similar patterns regarding topping at the + 1 SD level. For me, RQI is another CEF for which I am adding shares. The price SD channels chart confirms the discount to NAV and Z-score data but also makes the buy case clearer.

Many times, the discount to NAV and/or Z-scores work well for indicating when a CEF is on sale. But as I found for UTG and somewhat for RQI, the longer-term price SD channels provide a more useful picture.

A final example is for the Calamos Strategic Total Return Fund (CSQ), which is trading at a moderate discount to NAV of -4.71%. But the Z-scores are wide: -1.91 for 3 months, -2.24 for 6 months, and -2.53 for 1 year. Looking at the price SD channels below, the current price is ‘only’ just above -1 SD for the 15 year mean price. With 6 of the leading large caps comprising about 19% of the fund, price dropped rapidly during the 2022 bear market after spiking in 2021, resulting in high Z-scores for these short time frames. The current price is -12.9% below the 15-year mean of 15.55. I might want to wait for shares to at least drop below the -1 SD level before adding shares. For me, investing and trading actions are always based on charts, and the SD price channels help clarify the price pattern in addition to my traditionally technical indicators such as moving averages, volume, support/resistance, etc.

Having mentioned volume, I also note that monthly volumes for CSQ are generally lower recently, which is curious given that the fund has out-performed the SPY on a total return basis (683.51% for CSQ, 612.93% for SPY) for the past 14.62 years.

## Investor Takeaways

CEF investors have been taught to buy funds at discounts to NAV and/or when Z-scores are significant. But the available data sources only provide these measures for arbitrary time periods. It is preferable, in my view, to consider price points using meaningful cycle-level market events such as the end of recessions. The mean price trend for longer time periods that include recessions can provide a better way to evaluate the degree to which current prices are truly significantly below average.

A simple series of standard deviation price channels was created using my TD Ameritrade ‘thinkorswim’ charting platform. Using the tool, I think that both UTG and RQI are currently attractively-priced non-ROC CEFs, trading at about -2 SD from their 15-year means.

I hope that this article has been of interest and provided some thoughts about buying CEFs. Please do your own due diligence before making any investment decisions.

Best to your investing/trading!

=Green=