valuation of closed-end investment vehicles
TRANSCRIPT
Valuation of Closed Investment Vehicles
Guillermo Roditi Dominguez, Managing Director
New River Investments Special Opportunities LP
Introduction In the recent weeks Iโve been analyzing a series of asset-management firms as well as some of
the vehicles they advise, both in the form of bond closed-end funds (CEF) and mortgage real estate
investment trusts (mREIT). As cashflow investors, we are always looking for an opportunity to buy a
cashflow stream and are not faithful to any single structure provided the price is right. As such, I recently
found myself pondering about how to value the management company of a large leveraged bond
portfolio and after a few moments it became obvious that the approach could be extended to
estimating fair deviations from either net asset values (NAV) or tangible book values (TBV).1
My reasoning was simply that if a source of ongoing revenue, like a management contract with a
termination penalty of a closed-end investment vehicle, can be considered an intangible asset to a firm
or to have a non-zero value, then it must also be a liability of the corresponding payer as we are making
the assumption that the revenue generated exceeds the cost of the service provided2.
It is no surprise to our investors that we rely primarily on quantitative tools to identify
investment opportunities and generate expected outcome distributions. In the past, weโve relied
primarily on empirical analysis of deviations from NAV. Over time weโve seen some of our existing
models become less accurate and some of the market outcomes fall in increasingly low probability
zones. As is vital with any quantitative approach, we spend most of our time probing existing models,
trying to find weaknesses, omitted variables, or failed assumptions. This communication is the result of
one of these probes. I send this communication not as a lesson in valuation methods, but as a way to
expose our investment process to our investors.
Permanent capital investment vehicles CEFs, mREITs, and other publically listed investment vehicles that are mostly or wholly invested
in liquid securities often sell at market prices that deviateโsometimes substantiallyโfrom their NAV or
TBV. While a discount may at first look like, โbuying dollars at 90 cents,โ and attract the attention of
value-hunting investors, we believe this is an unnecessarily reductionist approach and the maximum fair
1 I donโt claim to be the first person to think about this, I am sure someone has done this more thoroughly,
elegantly and concisely. Alas, I was never one to shy away from reinventing wheels and, more so, why should we not get to have some fun just because someone else already solved this puzzle before. 2 Geek note: this would be linked to the hurdled return of the management company.
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Valuation of Closed-End Investment Vehicles | July 2015 2
multiple of TBV or NAV can be estimated by comparing internal cost structures with a similarly liquid
substitute, adjusting for leverage, and expected value-added.
To the companies that manage these vehicles and earn a management fee, these types of
entities are commonly referred to as โpermanent capitalโ because the capital canโt be withdrawn by
shareholders and represents potentially very long lived income streams for the management companies.
Tax rules typically require these entities to disburse almost all their income which protects shareholders
from management retaining earnings in order to increase the capital base on which their management
fee is earned. Most of these entities do distribute essentially all of their income. In the case of REITs
where a small % may be retained, it is often offset by an increasing share count due to stock-based
compensation. If the non-interest expenses are closely related to the NAV/TBV of the entity, one could
essentially consider them perpetuity and value them accordingly.
We begin the exercise with a simplified
assumption for an entity, S, with a NAV of $100
per share, selling in markets for $85 per share
which is invested in liquid investment-grade
securities yielding 4% with no leverage and has
a fee of 1% of NAV. In this example, a similar
portfolio could be easily replicated buying
bonds in the open market. To calculate the
maximum fair multiple, we could price as
perpetuity formula for which we would need a
payment and a discount rate. In the case of the payment, we can use c. For the discount rate we can use
r, which will capture the risk-compensation that the portfolio offers to help us internalize the risk of v
declining3. Astute readers will pick-up that as yields fall, the discount rate will too, leading to a lower
maximum fair multiple. This is by design; given that for a fixed management fee a lower yield will result
in a larger percentage of income being deviated away from the investor until, at a management fee
equal to the portfolio yield the investor can expect no future cashflows, rendering the asset worthless4.
Assuming that reproducing the portfolio using cash bonds carries with it a zero recurring cost, the
maximum fair multiple to NAV is described by equation 1.
3 The choice of ฮฒ as a discount rate is probably the weakest part of this model and suggestions for a better
discount rate, preferably one expressed as a function of other inputs, are welcome. 4 This is, obviously, absurd. Boards of directors have a duty to investors and at high enough discounts should either
repurchase shares or pay dividends in excess of income to return capital to shareholders. If a board failed to act, an activist investor could become involved, either to renegotiate the fee or attempt to liquidate the assets. In that the fee is a future income stream to the manager, a liquidation of assets or return of capital to shareholders would constitute a loss of future income to the manager and possibly a write down of an asset, therefore it behooves them to limit that risk. If nothing else, for a fund trading at a large-enough discount, an increase in yields and decline in asset values would lead to an increase in the fundโs fair value, creating a conceptual PUT option on the NAV which we assume would hold *some* value.
Variable Description
๐ Per-share market price
๐ Net asset value per-share
๐ Fee expressed as % of ๐
๐ Present yield-to-worst of the portfolio
๐ถ Value-added (destroyed) by management
๐ท Leverage-ratio
๐ Funding interest rate
๐ Expected Growth rate of NAV
๐ Calculated maximum fair multiple to NAV
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Valuation of Closed-End Investment Vehicles | July 2015 3
3
Equation 1
๐ = 1 โ๐
๐
In this case the highest fair multiple to NAV would be 1 โ .01/.04 = 0.75, substantially larger
than the observed multiple of 85%. Reality, of course, is never this simple. Creating a portfolio has a
non-zero cost and comes with economies of scale, therefore the fee should be considered with respect
to a suitable substitute. The total expense ratio (TER) of an entity in which capital can be subscribed or
redeemed at NAV with friction costs low enough to ignore (no loads) can be considered as this suitable
substitute. We will use a popular liquid investment grade bond ETF, ETF, has an expense ratio of 0.15%
to arrive at a fair multiple to NAV or 78.75%5 through the expanded formula:
Equation 2
๐๐ = 1 โ๐๐ โ ๐๐ธ๐๐น
๐๐
We can expand the model to account for leverage assuming the cost of leverage is not the same
for the fund and a typical margin investor,6 by subtracting the funding rate of fund S from the cost at
which the ETF could be funded, and scaling up ETFโs costs giving us:
Equation 3
๐๐ = 1 โ๐๐ โ ((1 + ๐ฝ๐)๐๐ธ๐๐น + ๐ฝ๐(๐๐ธ๐๐น โ ๐๐))
๐๐
Assuming the fund borrows funds at 0.5% for 30% of NAV, and leveraging ETF costs 1.1%7 and
both parties are borrowing at otherwise similar terms, the funding advantage would implicitly offset
0.18%8 of the management fee by providing an advantaged access to leverage funding. Expanding our
earlier example to account for a portfolio yield of 5.05%9 we have a new fair ceiling multiple of 87.62%10.
5 78.75% = 1 โ
1%โ0.15%
4%
6 Not only is the cost of leverage to non-institutional investors typically higher, but brokerages require different
levels of margin for different type of securities, often governed by inflexible internal or external rules, leading to constraints or opportunities for regulatory circumvention. Consider the example of an IRA account, where investors are not allowed to borrow money directly but can buy vehicles containing leverage, or a listed fund invested in an asset a prime brokerage may not lend against, like distressed securities, which a broker will let you borrow against in a margin account. Likewise, a fund invested 100% in treasuries would not benefit from the lower margins safer securities typically require. Some call this โregulatory arbitrage,โ I prefer โfinancial engineering.โ 7 Again this is overly simplistic. Funds and REITs often borrow through the use of preferred shares or longer term
repurchase agreements which provide stable term funding not at risk of being called, while margin loans may be called by brokerages at any time. Likewise, a fixed funding rate should be compared not to the prevailing spot rate but to a similar term financing using forward curves. 8 0.18% = 30% โ (1.1% โ 0.5%). 9 4% + 30% โ (4% โ 0.5%)
101-
1%โ(0.195%+0.18%)
5.05%
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Valuation of Closed-End Investment Vehicles | July 2015 4
More realistically, people often invest in actively managed instruments with the expectation
that the management will provide additional value-added, either through an expectation of lower risk or
higher return than a passive substitute. Given the leverage employed in many of these instruments, we
assume that most buyers invest in these structures either as a way to access leverage, management
expertise or an asset-class that would otherwise not be accessible.
Introducing a variable for expectation of outperformance will allow us to either solve for a more
accurate fair discount rate or solve for the price-implied performance differential from the observed
valuation. Iโll spare you the debate of the merits of active vs passive or index construction, and stick to
the equations. To solve for maximum fair multiple with an outperformance factor that is not a function
of yield:
Equation 4
๐๐ = 1 โ๐๐ โ ((1 + ๐ฝ๐)๐๐ธ๐๐น+๐ผ๐ + ๐ฝ๐(๐๐ธ๐๐น โ ๐๐))
๐๐
To solve for the outperformance factor implied if we consider the market value fair:
Equation 5
๐ผ๐ = ๐๐ โ ((1 + ๐ฝ๐)๐๐ธ๐๐น + ๐ฝ๐(๐๐ธ๐๐น โ ๐๐) + ๐๐
๐๐
๐ฃ๐)
Or, if weโve already solved for the fair-ceiling discount, we can shorten it to equation 6, which
becomes handy as we add more items to equation 4.
Equation 6
๐ผ๐ = ๐๐ (๐๐
๐ฃ๐โ ๐๐)
Furthermore, we can expound on how distribution management impacts the maximum fair
multiple. While for most of the instruments presented we assume ongoing distributions of income equal
to or greater than the net income of the fund. However, for vehicles that retain a non-zero amount of
income or that return a non-zero amount of capital back to shareholders we can draw inspiration from
the Gordon11 model by accounting for growth or decline in NAV through the discount rate12. For a fund
with a linear expected growth (decline) in NAV we would adjust Equation 4 to:
11
For the sake of brevity and simplicity Iโve stuck to the single step model, but expanding to a multi-step model should be fairly straight forward. 12
This is especially relevant for funds that have a cashflow distribution policy, like some vehicles that invest in amortizing securities and distribute a portion of principal on a monthly basis, or vehicles that retain a specified amount of income, in which case g can be expressed as a function of r. Another relevant example is an asset class where credit losses tend to be clustered but far apart, like corporate credit. Part of the compensation for expected credit loss will be distributed as income in low loss years while NAV will decline in future years.
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Valuation of Closed-End Investment Vehicles | July 2015 5
5
Equation 7
๐๐ = 1 โ ((1 + ๐)๐๐ โ ((1 + ๐ฝ๐)๐๐ธ๐๐น+๐ผ๐ + ๐ฝ๐(๐๐ธ๐๐น โ ๐๐))
๐๐ โ ๐)
Finally, I would like to highlight that this method describes the maximum fair multiple. These
vehicles can and do trade at varying multiples of NAV and with differing depths of liquidity and the
calculation of a fair multiple would involve accounting for differentials in risk. Given the length of this
letter, any additional changes are left as an exercise for the reader13. It is also worth noting that, even
though the fair ceiling multiple is hypersensitive to the discount rate, the growth rate is likely to be low
enough to be almost immaterial for almost all real-world scenarios and its inclusion was mostly for the
sake of completion.
Conclusion The effect expense ratios and leverage have on the fair valuation of closed end funds and similar
investment vehicles can be estimated using traditional DCF valuation techniques. While empirical
analysis based on previous valuations may prove useful at times, the validity of results is likely to be
short lived. A change in leverage ratio, funding rates or the expense ratio of a fund or the least
expensive substitute would lead to a shift in the in the maximum fair multiple to NAV. All else equal, the
introduction of a lower-cost competitor would lead to a permanent decline in fair valuation. Given the
recent focus in the investment industry on fee compression and the popularity of low-cost ETFs, it is
unlikely that CEF valuations will ever return to previous levels absent aggressive cost reduction
measures. Exhibit 1 includes an example from the popular tax-exempt bond sector.
As always, I thank you for your patience with my failure at brevity and welcome your further
questions, comments, suggestions and corrections.
Sincerely,
Guillermo Roditi Dominguez,
13
In the interest of avoiding a holy war, I am abstaining from proposing one; although one certainly could do worse than using a robust statistical measure of price volatility like median absolute deviation.
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Valuation of Closed-End Investment Vehicles | July 2015 6
Exhibit 1: A Real World Example using Municipal Bonds
A simple example is the comparison of a tax-exempt (aka โmuniโ) bond CEF like NEA and a
matching ETF like MLN. Both of these instruments invest in AMT-free municipal bonds of longer
maturities. And while the composition of the portfolios is obviously different given their unlevered
yields, it nonetheless seems like a reasonable comparison. All of the figures used were available directly
on the respective fund sponsorsโ websites.
In order to estimate r we utilize the estimated fund earnings and add the expense ratios back to
obtain a raw portfolio yield14. One way to interpret the results is that, assuming no alpha generation,
and risk of NEA โฅ MLN, it would behoove investors to buy MLN instead above a 94.76% p/v. Another
would be that the present multiple embeds an additional 0.45% of excess return to compensate for
negative value-add, additional premium required to absorb the valuation risk or a combination of both.
Variable Description MLN NEA
y Present Dividend Yield on NAV 3.52% 5.29%
p Per-share market price $ 19.31 $ 12.91
v Tangible book-value per-share $ 19.37 $ 14.69
c Fee expressed as % of V 0.24% 0.98%
r Levered portfolio yield * 3.76% 6.56%
ฮฑ Value-added (destroyed) by management 0.00% 0.00%
ฮฒ Leverage-ratio 0% 35.92%
i Funding interest rate 1.65% 0.81%
g Expected Growth rate of NAV -0.12%
f Calculated fair ceiling p/v for ฮฑ=0 94.76%
Annualized ฮฑ implied by market valuation -0.45%
Total cost differential 0.35%
Funding cost advantage 0.30%
Unlevered Asset Yield 3.76% 4.83%
Current p/v 99.69% 87.88%
*Imputed from distribution yield
User Input
Calculation
Model Output
14
Using the estimated earnings in lieu of net interest income is preferable because it can account for gains from factors like curve roll-down. In this instance, because of the negative convexity embedded in most tax-exempt bond structures, they should be almost the same.
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