valuation of closed-end investment vehicles

Valuation of Closed Investment Vehicles

Guillermo Roditi Dominguez, Managing Director

New River Investments Special Opportunities LP

Introduction In the recent weeks I’ve 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, we’ve relied

primarily on empirical analysis of deviations from NAV. Over time we’ve 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 deviate—sometimes substantially—from their NAV or

TBV. While a discount may at first look like, “buying dollars at 90 cents,” and attract the attention of

value-hunting investors, we believe this is an unnecessarily reductionist approach and the maximum fair

1 I don’t 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 “permanent capital” because the capital can’t 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 β 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 fund’s fair value, creating a conceptual PUT option on the NAV which we assume would hold *some* value.

Variable Description

𝒑 Per-share market price

𝒗 Net asset value per-share

𝒄 Fee expressed as % of 𝒗

𝒓 Present yield-to-worst of the portfolio

𝜶 Value-added (destroyed) by management

𝜷 Leverage-ratio

𝒊 Funding interest rate

𝒈 Expected Growth rate of NAV

𝒇 Calculated maximum fair multiple to NAV



3

Equation 1

𝑓 = 1 −𝑐

𝑟

In this case the highest fair multiple to NAV would be 1 − .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

𝑓𝑆 = 1 −𝑐𝑆 − 𝑐𝐸𝑇𝐹

𝑟𝑆

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 ETF’s costs giving us:

Equation 3

𝑓𝑆 = 1 −𝑐𝑆 − ((1 + 𝛽𝑆)𝑐𝐸𝑇𝐹 + 𝛽𝑆(𝑖𝐸𝑇𝐹 − 𝑖𝑆))

𝑟𝑆

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 −

1%−0.15%

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 “regulatory arbitrage,” I prefer “financial engineering.” 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% ∗ (1.1% − 0.5%). 9 4% + 30% ∗ (4% − 0.5%)

101-

1%−(0.195%+0.18%)

5.05%



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. I’ll 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

𝑓𝑆 = 1 −𝑐𝑆 − ((1 + 𝛽𝑆)𝑐𝐸𝑇𝐹+𝛼𝑆 + 𝛽𝑆(𝑖𝐸𝑇𝐹 − 𝑖𝑆))

𝑟𝑆

To solve for the outperformance factor implied if we consider the market value fair:

Equation 5

𝛼𝑆 = 𝑐𝑆 − ((1 + 𝛽𝑆)𝑐𝐸𝑇𝐹 + 𝛽𝑆(𝑖𝐸𝑇𝐹 − 𝑖𝑆) + 𝑟𝑆

𝑝𝑆

𝑣𝑆)

Or, if we’ve 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

𝛼𝑆 = 𝑟𝑆 (𝑝𝑆

𝑣𝑆− 𝑓𝑆)

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 I’ve 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.



5

Equation 7

𝑓𝑆 = 1 − ((1 + 𝑔)𝑐𝑆 − ((1 + 𝛽𝑆)𝑐𝐸𝑇𝐹+𝛼𝑆 + 𝛽𝑆(𝑖𝐸𝑇𝐹 − 𝑖𝑆))

𝑟𝑆 − 𝑔)

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,

[email protected]

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.



Exhibit 1: A Real World Example using Municipal Bonds

A simple example is the comparison of a tax-exempt (aka “muni”) 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 sponsors’ 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 ≥ 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%

α Value-added (destroyed) by management 0.00% 0.00%

β 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 α=0 94.76%

Annualized α 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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