One curious feature that investors discover when they encounter closed-end funds for the first time is the discount or the, often substantial, differential between the fund’s price and its net asset value. However, while investors know to prefer wider discounts all else equal, there is little guide to any fair-value level.

In this article, we try to quantify fair-value levels of CEF discounts based on a cash flow approach which takes into account fund fees, leverage and funding costs. We use the preferreds CEF sector as a case study.

Odd Man Out

Why do persistent discounts exist in CEFs but not in other investment vehicles like ETFs or mutual funds? The glib answer is, very simply, that they can. Unlike ETFs or mutual funds, CEFs do not have a process which ensures that the price and NAV converge to each other. ETFs manage this convergence via the share creation and redemption arbitrage mechanism while mutual funds simply buy and sell at the closing NAV. Because CEFs lack these mechanisms, it is up to the market to decide at which price the fund will trade.

Do We Really Have To?

CEF discounts seem pretty intuitive so do we really need to quantify their fair value? Investors use a number of heuristics already when thinking about discounts.

One obvious approach is to just use absolute discounts – so a fund at an 8% discount is more attractive than a fund at a 5% discount. As we show below, this approach ignores the key drivers of the discount such as fund fees and funding costs. Within the preferreds sector, which we use as a case study, fair-value discounts range from +4% to -4%, so relying on absolute value is far from ideal.

Another common approach to use is the fund’s historical discount as a guide. We think there are two main problems with this approach. First, it’s not of much help for new funds or funds with a short track record. Secondly, fund discounts do not always revert to mean. There are many reasons why this is the case, but a fund that repeatedly cuts its distribution may tend to see its discount continually come under pressure and is less likely to see it revert to the mean.

Taking A Cash Flow Perspective

So if we cannot rely on absolute values or historic averages to gauge fair value, what can we do? One way to approach this question is through a cash flow perspective which feels appropriate given CEFs are prized particularly because for their relatively high distribution rates. More specifically, this approach relies on the fact that the value of an asset is just the sum of its discounted future cash flows. So, if part of the asset’s cash flows goes to someone other than the investor, then the asset should trade in the market at a discount to its underlying value.

Taking the simplest example – imagine a fund holding a bond portfolio with a yield of 5%. If the fund manager takes 1% as the fund fee, then the investor only receives 80% of the value of the asset, i.e. 4% rather than the full 5%. If the investor can purchase the underlying portfolio in the market at no additional cost, then it would only make sense to buy the fund at a discount of 20% or wider.

Let’s take a more realistic example and assume the investor is not actually going to go into the market and replicate the underlying fund portfolio. Let’s assume instead, to illustrate the point, that the investor can purchase the same portfolio via an ETF. In this case, the discount will be a function of the fee differential between the two funds.

Most investors are aware that CEFs, unlike ETFs, can maintain leverage. This is one of the primary factors that allows CEFs to have their high distribution rates. While individual investors can trade on margin, their margin loan costs can differ from those enjoyed by the CEF. This means we should further adjust the discount calculation by the differential in leverage cost.

A Case Study of The CEF Preferreds Sector

In this section, we take a look at the preferreds CEF sector as a case study. Because leverage figures change daily, due to changes in the NAV, we estimate the fund’s current leverage based on the last published borrowing figures and the latest NAV. Fund fee and leverage costs are taken from the fund fact sheets or reports and calculated using the current LIBOR. For investor leverage cost, we assume a level of Fed Funds + 1.5% which is what is on offer at the cheaper brokerages.

For the base ETF fee, we use the active First Trust Preferred Securities and Income ETF (FPE) over the more popular passive iShares Preferred and Income Securities ETF (PFF). This creates more of an apples-to-apples analysis for two reasons. First, we avoid the passive vs. active difference between the ETF and the CEFs, and secondly, FPE allocates in part to institutional preferreds just as the CEFs, whereas PFF allocates to the retail preferreds sector.

In the chart below, we plot the fair-value discounts against actual discounts for the funds in the sector. The funds are ordered from most “rich” to most “cheap”. To take PDT for example, the calculation suggests that the fair-value discount should be on the order of 4% whereas the fund is trading at a premium of about 3%.

Source: Systematic Income Service

We can also plot the differential between the two metrics.

Source: Systematic Income Service

A Look At The Results

What do the results tell us?

First, all but two of the fair-value discounts are negative, ranging between 1% and 4%. This points to the fact that it is entirely reasonable for CEFs to trade at a discount and just because a given CEF is trading at a discount does not make it a “freebie” or an added argument to hold the fund.

The second thing we would highlight is the wide range of fair-value discounts, ranging from a 4% premium to a 4% discount. This is really driven by the significant variation in fund fees and leverage as leverage costs are fairly close to each other. This dynamic suggests that analyzing funds by looking at the largest discounts is not appropriate since different funds will have different fair-value discount levels and ranges.

The third revealing dynamic is the differential between funds of the same family. The 6% fair-value discount differential between FFC and FLC – two Flaherty & Crumrine funds that have 99.96% NAV return correlation – may seem wide; however, this is explained by the large fee differential between the two funds. And if we look at the historic market discount differential between the two funds, we find that is not a million miles away from this 6%, suggesting that in aggregate the market has been pricing this differential reasonably accurately over the last few years.

Source: Systematic Income Service

Finally, there are a number of funds in the sector which appear to be trading at discounts tighter to their fair values such as the Flaherty & Crumrine Preferred Income Fund (PFD). The answer to this is not entirely clear. PFD has a fee in line with the sector average, but well above its sister funds. The fund’s NII and current distribution yield are relatively middling and well below the sector average. Its historic returns are good, but below those of FFC and FLC, suggesting decent but not excessive alpha, and its leverage and leverage costs are in line with other company funds.

This raises an important question. Are there factors beyond our calculation that could justify a discount different from our fair-value calculation? The answer to this is clearly yes in some cases. Term funds, for example, have a discount anchor in the form of the expected maturity date where the discount should move towards zero. This does not appear to be a factor for the two term funds in the sector: JPI and JPT which are not far from zero anyway.

A history of delivering excess alpha is another reason why investors should be willing to pay more for a given fund in the form of a tighter discount. Let’s take a look at fund alphas which we maintain on our service. Here, fund alpha is calculated as a historic pairwise risk-adjusted return differential within the sector. In essence, it represents how well a given fund fares against all the other funds on average in terms of risk-adjusted historic performance. Here, we see that while PFD does have a historic alpha above the sector average, it is not higher than its Flaherty & Crumrine sister funds like FFC, FLC and DFP.

Source: Systematic Income Service

Another reason why fund discounts can diverge from their fair values is due to leverage hedges. Leverage hedges typically take the form of interest-rate swaps where the fund pays LIBOR and receives a fixed-rate. The point of the leverage hedge is to lock in a fixed-rate on the credit facility on which the fund pays LIBOR + spread. This ensures that if short-term rates rise, the fund will be able to preserve its earning power. The downside of a leverage hedge, of course, is that if short-term rates fall, the fund will be unable to take advantage of this, at least not fully.

Within the preferreds sector the amount of leverage hedging varies from zero to 88%. Flaherty & Crumrine funds do not hedge LIBOR while Cohen & Steers funds hedge nearly 90% with the rest of the sector ranging between 25% and 50%. There are two ways to think about leverage hedges. The first way is to roll the hedge into the overall leverage cost and use that in the fair-value discount calculation. Using this approach, all but the Flaherty & Crumrine funds will look slightly worse relative to fair-value because their adjusted leverage costs are higher than the floating-rate credit facility suggests. The second way is to treat the hedge as just another financial asset or bet in the fund’s portfolio, which hasn’t performed well over the last year due to falling short-term rates. In any case, it’s not clear from the pattern of discount differentials that the market is pricing in this dynamic.


An awareness of fair-value discount levels for CEFs can aid the investment process in a number of ways. First, because fair-value discounts can vary widely across a given sector, the approach of picking funds with the widest discounts leaves a lot to be desired. Secondly, this approach allows investors to tie together a number of interconnected fund features such as the fee, leverage and underlying yield into a single metric. Finally, it allows investors to gauge whether using CEFs is attractive versus adopting a potentially cheaper solution of trading on margin.

Check out more in-depth and timely commentary as well as Income Portfolios and interactive Investor Tools at our Premium service.

ADS Analytics LLC / Systematic Income provides opinions regarding securities and other related topics on an impersonal basis; therefore no consideration is made towards your individual financial circumstances.

All content presented here is not to be regarded as investment advice or constitute a client / advisor relationship. It is for general informational purpose only.

Trading securities involves risk, so you must always use your own best judgment when trading securities. You assume the entire cost and risk of any trading you choose to undertake. You are completely responsible for making any investment decisions.