• No results found

Examining the Deviation to Net Asset Value for Swedish Listed Property Companies

N/A
N/A
Protected

Academic year: 2021

Share "Examining the Deviation to Net Asset Value for Swedish Listed Property Companies"

Copied!
79
0
0

Loading.... (view fulltext now)

Full text

(1)

DEGREE PROJECT,

IN REAL ESTATE AND CONSTRUCTION MANAGEMENT BUILDING AND REAL ESTATE ECONOMICS

MASTER OF SCIENCE, 30 CREDITS, SECOND LEVEL STOCKHOLM, SWEDEN 2016

TECHNOLOGY

DEPARTMENT OF REAL ESTATE AND CONSTRACTION MANAGEMENT

Examining the Deviation to Net Asset Value for Swedish Listed Property Companies

Applying a rational and irrational approach Tomas Shaw

Matilda Wåhlin

ROYAL INSTITUTE OF TECHNOLOGY

DEPARTMENT OF REAL ESTATE AND CONSTRUCTION MANAGEMENT

(2)

Master of Science thesis

Title Examining the Deviation to Net Asset Value

for Swedish Listed Property Companies

Authors Tomas Shaw, Matilda Wåhlin

Department

Master Thesis number

Real Estate and Construction Management TRITA-FOB-ByF-MASTER-2016:29

Archive number 435

Supervisor Herman Donner

Keywords Deviation to NAV, Panel data, Real Estate

Abstract

Net asset value (NAV) is commonly used to represent the value of a property company. For listed property companies a secondary valuation occurs simultaneously as the company’s stocks are traded on the stock market. Historically, a deviation between the NAV and the market capitalisation has been found for property companies implying that the stock market values the company differently. This thesis examines the deviation to NAV for 14 Swedish listed property companies during 2006-2015. The examination explains the deviation from the basis of a rational and an irrational approach. The thesis investigates empirically which factors that have affected the deviation by the use of a panel data regression analysis.

The rational approach investigates the impact of company-specific, share-specific and corporate governance variables. The results of the thesis show that the rational variables can explain the deviation to NAV to some extent. The main contribution comes from company- specific variables. Larger companies, companies focused on fewer locations, companies with a better reputation among asset managers and companies with a higher amount of insider ownership are negatively correlated to the discount to NAV. These company characteristics thus suggest a decrease in discounts to NAV (increase in premiums). At the same time companies with a higher loan to value, focus on property type and systematic risk increase the discount to NAV (decrease in premiums). The final rational model produces an adjusted R-square of 37.4% for the Swedish listed property market during the investigated period.

The irrational approach investigates the impact of noise traders. The results show that the contribution of market sentiment is significant. The confidence indicator for the households has the greatest impact on the discount to NAV and an inclusion of the variable increases the adjusted R-square to 53.6%. An investigation into the justification of using the Noise Trader

Theory is conducted and concludes that the use of a proxy for market sentiment is justified.

(3)

Examensarbete

Titel Substansrabatter och substanspremier hos

svenska börsnoterade fastighetsbolag

Författare Tomas Shaw, Matilda Wåhlin

Institution

Examensarbete Master nivå

Fastigheter och Byggande

TRITA-FOB-ByF-MASTER-2016:29

Arkiv nummer 435

Handledare Herman Donner

Nyckelord Substansrabatt, Substanspremie, Panel data

Sammanfattning

Substansvärdet (NAV) används ofta för att representera värdet av ett fastighetsbolag. För börsnoterade fastighetsbolag sker samtidigt en sekundär värdering eftersom deras aktier köps och säljs på aktiemarknaden. Historiskt sett har fastighetsbolagens substansvärden skilt sig från börspriserna av deras aktier vilket tyder på att aktiemarknaden värderar bolagen annorlunda och det uppstår då en substansrabatt eller substanspremie. Denna uppsats utvärderar detta fenomen för 14 svenska börsnoterade fastighetsbolag under åren 2006-2015 utifrån en rationell och en irrationell utgångspunkt. Uppsatsen testar empiriskt vilka faktorer som påverkar skillnaden under perioden genom en regressionsanalys med paneldata.

Den rationella utgångspunkten undersöker effekterna av variabler knutna till företaget, aktien samt företagets bolagsstyrning. Resultatet visar att rationella variabler kan förklara substansrabatter och substanspremier till en viss grad. Det största bidraget kommer från de företagsspecifika variablerna. Större företag, företag fokuserade på ett mindre antal orter, företag med ett bättre rykte och företag vars styrelse har ett stort aktieinnehav tenderar att ha en minskad substansrabatt alternativt en ökad substanspremie. Å andra sidan tenderar företag med hög belåningsgrad, ett fåtal fastighetstyper och hög systematisk risk att ha en ökad substansrabatt alternativt en minskad substanspremie. Den slutliga modellen av rationella variabler genererar ett justerat R-square om 37,4% för svenska börsnoterade fastighetsbolag.

Den irrationella utgångspunkten i denna uppsats undersöker variabler knutna till ett irrationellt handlande. Resultatet visar signifikant utfall för irrationellt handlande, där en konfidensindikator för hushållen visar störst inverkan och genererar ett justerat R-square om 53,6%. Uppsatsen undersöker möjligheten att använda irrationellt handlande som förklaringsvariabler till varför substansrabatter och substanspremier uppstår. Resultatet visar att det är motiverat att inkludera irrationella förklaringsvariabler.

(4)

Acknowledgement

This master thesis is written as the final part of the master program in Real Estate and Construction Management and the Civil Engineering programme at KTH, the Royal Institute of Technology.

The deviation to NAV for listed property companies has been studied broadly on an international level. The aim of this thesis is to investigate this phenomenon in the Swedish context. Hopefully, the contribution of the report could be of interest to academia, property companies as well as investors in terms of investment strategies and stock market behaviour.

First and foremost, we would like to thank our supervisor Herman Donner for his inspiration, positive guidance and long discussions throughout the process of writing this thesis.

We also want to thank Han-Suck Song and Mats Wilhelmsson for additional guidance as well as for their contribution in discussions.

Feel free to contact us regarding questions about the thesis at tshaw@kth.se (Tomas Shaw) and matwah@kth.se (Matilda Wåhlin).

Stockholm 2nd of June 2016, Tomas Shaw and Matilda Wåhlin

(5)

Table of Contents

1. Introduction ... 1

1.1 Background ... 1

1.2 The Aim of the Thesis ... 4

1.3 Research Question ... 4

1.4 Limitations ... 4

2. Theoretical Framework ... 5

2.1 Modelling Financial Markets ... 5

2.2 The Property Market Versus the Stock Market ... 7

2.3 The Calculation of the NAV Spread ... 8

2.4 Literature Review ... 9

2.5 Expertise Review ... 24

3. Method ... 26

3.1 Methodology ... 26

3.2 The Model ... 26

3.3 Regression Analysis ... 29

3.4 Reliability ... 33

3.5 Validity ... 34

4. Data Description ... 35

4.1 Selection ... 35

4.2 Variables ... 37

4.3 Descriptive Statistics ... 41

5. Results and Discussion ... 48

5.1 Results – Rational Approach ... 48

5.2 Discussion – Rational Approach ... 52

5.3 Results – Irrational Approach ... 57

5.4 Discussion - Irrational Approach ... 63

6. Conclusion ... 67

7. References ... 70

8. Appendix ... 73

(6)

1

1. Introduction

1.1 Background

The value of a property company is to a large extent derived from its underlying assets. The underlying assets, the properties in the company’s portfolio, generate value to the firm primarily through rental income but also indirectly through capital gains. For a company that mainly operates in the field of owning and letting real estate it is thus justified that the value of the company is derived from its underlying assets using a net asset value (NAV) approach (Rehkugler et al., 2012). The NAV of a company is calculated as the sum of the market value of all assets minus liabilities and other claims to the company (Ke, 2015). Since the introduction of IAS-40 accounting standards in 2005 all European companies are obliged to report their investment properties at their fair value in their annual reports (Nordlund, 2008).

The NAV of a property company can therefore be constructed fairly easy via information available in the companies’ annual reports, as the combined fair value of the property portfolio minus all debt and other liabilities. This means that the company displays a justified estimate of their company value on an annual basis. Simultaneously, listed property companies have their shares traded on the stock market, thus enabling that a secondary pricing of the company occurs. This pricing mechanism values the company via supply and demand of the company shares on the stock market. It has been found that the share prices of property companies, the market capitalization, deviate from the companies’ NAV over time, implying that the stock market values the company differently. This deviation varies widely between companies, sectors and over time (Ke, 2015).

The deviation to NAV from market capitalisation is not a phenomenon that is purely related to property companies. In general it is referred to as the closed-end fund puzzle and is an intriguing problem in finance that has been researched on numerous occasions during recent decades (Dimson and Minio-Paluello, 2002). A closed-end fund is a mutual fund that issues a fixed number of shares that are traded at the stock market. Similar to listed property companies, closed-end funds derive most of their value from the underlying assets and are not obliged to buy back (redeem) issued shares. This allows the shares to be priced purely on the stock market and thus differ from the underlying assets of the fund, the NAV (Dimson and Minio-Paluello, 2002). The closed-end fund puzzle is the empirical finding that shares of closed-end funds are being traded at a price that differs from the NAV of the fund, and therefore creating a discount or a premium to NAV. Historically, the closed-end fund puzzle

(7)

2

research has shown that these types of funds have been traded at a significant discount. This is in line with the results of research focusing on discounts on property companies (Barkham and Ward, 1999, Morri et al., 2005 and Rehkugler et al., 2012). According to the efficient market theory this should not be possible since it says that all investors access the same information and act rationally, which would lead to efficiently priced shares (Lee et al., 1991). The puzzle has led to a large body of research on the matter including the most famous works of Malkiel (1977), Lee et al. (1991) and De Long et al. (1990), who all look into how this deviation can be explained.

In broad terms there are mainly two approaches for research into the discount to NAV in closed-end funds and subsequently within the segment of listed property companies: the

“rational approach” and the “noise trader approach”. The rational approach tries to link the discount to company-specific factors such as company size, management quality, leverage ratio and/or portfolio focus via the use of regression analysis techniques. These studies, although relatively intuitive appealing, do not manage to explain more than 30% - 50% of the variance of discounts at its best (Rehkugler et al., 2012). The noise trader approach is mainly based on the works of De Long et al. (1990) and Lee et al. (1991) and basically assume that there are two different types of investors: “rational” and “noise traders”. The noise trader acts irrationally, and this theory implies that market sentiment can play a role in that asset prices can diverge from its fundamental values in the long run (Barkham and Ward, 1999). Even though irrational variables significantly help to explain the variation of the discount, explanatory variables describing market sentiment are hard to define and interpret as they typically are based on proxies to imitate a market sentiment, thus not perfectly corresponding to the true variable.

Studies examining the discount to NAV among property companies have mainly focused on the UK and US property markets. The largest contribution to understanding the UK market is achieved by Barkham and Ward (1999), Morri et al. (2005) and Ke (2015). For the US market Capozza and Lee (1995) and Clayton and MacKinnon (2000) are the main contributors. In recent years the research has shifted to observe a pan-European context.

Brounen and Laak (2005) started this trend which was continued by Rehkugler et al. (2012).

These studies vary in their approach, some focusing on explaining the discount using only rational variables while some only focus on market sentiment. The importance of investigating the existence of noise traders when applying an irrational approach cannot be neglected but very few studies investigate this fully. Muller and Pfnuer (2013) do this on a

(8)

3

European property sector level by investigating if five implications of the Noise Trader Theory can be supported for the property market. Three studies combine the two approaches:

Barkham and Ward (1999) manage to explain 33% with an approach in which a proxy for market sentiment is included. Rehkugler et al. (2012) manage to explain as much as 76% by using a semi-rational approach. Ke (2015) uses traditional rational variables plus variables accounting for corporate governance in order to capture the impact of the company’s management. This in combination with a market average discount as a proxy for market sentiment explains 43% of the deviation as best.

To the best of our knowledge, no research has focused purely on examining the NAV spread for the Nordic context. This thesis aims to fill that gap by looking at annual data for 14 Swedish listed property companies during 2006-2015. The ambition is to explain the NAV spread from the basis of a rational and irrational approach by using a panel data regression methodology. The Nordic property market and Sweden in particular is interesting to examine since it is unique in the sense that the property market is very liquid. According to Leimdörfer (2015), a leading advisory within property related transactions in the Nordic countries, Sweden has been the most liquid property market in Europe during the last decade.

In addition, the Nordic property market, and Sweden in particular, is characterized by a high level of transparency as well as stable and high quality institutional environments (Leimdörfer, 2015). This is something that might imply better NAV estimates in comparison to other countries. In addition, it allows investors to have all available information thus setting an interesting platform for examining the NAV spread. The contribution of the report could be of interest to property companies as well as investors in terms of investment strategies and stock market behaviour.

The traditional view when observing the NAV spread is to look at discounts. Previous research has embraced this point of view mainly motivated by the fact that historically closed-end funds and listed property companies have been traded at a discount. However, during this time period the shares of property companies have been traded at both discounts and premiums. For example, 2006 and 2014-2015 are characterized by premiums thus implying an alternating behaviour of the NAV spread. This thesis observes a larger time spectra of ten years and aims to explain the NAV spread in a volatile environment. The period that will be studied, 2006-2015, is particularly interesting since it starts with the end of a boom followed by the large crash in 2007-2008 and sums up with gaining momentum

(9)

4

during the last years. The NAV spread for property companies has thus shifted from a premium to discount and then back to a premium.

1.2 The Aim of the Thesis

This thesis aims at extending the existing literature on the closed-end fund puzzle for property companies on the unique Swedish property market by applying variables and approaches used in previous research. The thesis aims to explain the NAV spread from the basis of a rational and an irrational approach by the use of a panel data regression methodology. In addition the existence and impact of noise traders will be investigated in the thesis, justifying the use of market sentiment in explaining the discount. The data is collected directly from annual reports, which in combination with a standardized method for calculating the NAV spread ensure consistency.

1.3 Research Question

The thesis aims to answer the following questions for Swedish listed property companies during the investigated time period of 2006-2015:

1. How large is the NAV spread (discount or premium to NAV) for the investigated property companies?

2. What can explain the NAV spread for listed property companies?

a. Can a rational approach explain the NAV spread?

b. Can Noise Trader Theory and market sentiment explain the NAV spread?

3. Is the noise trader model justified for explaining the NAV spread?

1.4 Limitations

This thesis will only evaluate Swedish listed property companies and is thus limited to a maximum of approximately 30 listed companies. Via a number of criteria the amount of investigated property companies is narrowed down to 14. An issue can be raised whether a larger data set could increase the contribution of the report. In order to solve this issue the report could choose to use quarterly data thus providing a larger number of observations.

However, quarterly reports have been found to be deficient in terms of information and reporting, and consequently annually data is used. A cornerstone in this report is the appraised value of the property portfolios undertaken by the property companies and displayed in their annual reports. This report assumes that these valuations are done in a professional way and therefore represent the market value of the property. The validity of the results could be increased by taking possible errors or biases in appraisals into account.

(10)

5

2. Theoretical Framework

This chapter will introduce and discuss topics and theories needed to understand the NAV spread as well as discuss and present previous research into the phenomenon. The chapter aims to create a framework in which the NAV spread among property companies can be examined further. First, relevant theories concerning asset pricing are presented as these forms the basis for establishing the two approaches, rational and irrational, to examine the NAV spread. Second, a short explanation into the different characteristics of the property and the stock market is presented as well as the basic techniques for calculating the NAV spread.

This is followed by a literature review of the closed-end fund puzzle and the different approaches applied to explain the NAV spread in listed property companies. The chapter concludes with an expertise review consisting of the view of professionals within the field.

2.1 Modelling Financial Markets

2.1.1 The Rational Investor and the Efficient Market Hypothesis

The traditional models explaining financial markets and asset pricing assume that investors are rational. The meaning of the word rational is in this sense essentially twofold.

- First, when new information is given rational investors update their beliefs correctly.

- Second, based on the new information rational investors make rational decisions based on fundamentals. (Barberis and Thaler, 2003)

One of the more influential theories in the traditional framework is the efficient market hypothesis, developed in part by Fama (1970). The efficient market hypothesis states that since investors are rational the market becomes efficient in its pricing. This statement has one major implication for asset pricing:

- As investors are rational and act rational the price of an asset is correctly set with respect to its fundamental value. The main argument for this is that if a mispricing occurs momentarily due to an actor acting less than fully rational the market will correct for this instantly by the use of arbitrage. (Barberis and Thaler, 2003)

The efficient market hypothesis acts as the base of the literature into the rational approach to the NAV spread, covered in chapter 2.4.2.

(11)

6

2.1.2 Behavioural Finance and the Noise Trader Theory

The traditional framework, resting on the belief that every investor acts in a rational manner, is not confirmed by data in a satisfying way (De Long et al. 1990). In the light of this, the field of behavioural finance started to gain momentum in economic research in the late 20th century. Behavioural finance aims to explain financial markets by stating that financial phenomena can be better understood using models in which some investors are not fully rational. It is hypothesised that there are two types of investors: rational and irrational.

- In contrast to the rational investor, the irrational investor does not trade in consideration of fundamentals but instead on market sentiment. Such market sentiment can be anything from the emotional condition of the investor, rumours in mainstream media, guidance of a friend or just gut instinct. The actions of irrational investors, also called noise traders, distort the pricing mechanisms of assets by producing noise. (Barberis and Thaler, 2003)

Under the efficient market hypothesis the existence of noise traders and distortion of price can only exist for a short period of time. The Noise Trader Theory, put forward by De Long et al. (1990) and extended by Lee et al. (1991), abandons the premises of a perfectly efficient stock market and instead postulates that noise traders exist over time and that their noise distorts the pricing mechanism in such a way that market prices deviate from fundamentals permanently. If asset prices are influenced by noise under the efficient market hypothesis, rational investors will take part in arbitrage. This makes sure that prices return to the levels warranted by current information and fundamentals. Contrary, De Long et al. (1990) argue that rational investors are not able to take part in the arbitrage situation that is created by noise traders because of a number of fundamental assumptions. De Long et al. (1990) put forward three assumptions initially. However, Mueller and Pfnuer, (2013) divide the first assumption into two, which results in the following:

- First and second, rational investors are risk averse (A1) and have reasonably short investment horizons (A2).

- Third, the incorrect beliefs that noise traders use in order to select their portfolios are unpredictable and create a risk in asset pricing. This means that rational investors cannot with great certainty calculate the outcome of the noise on the asset pricing. In other words, noise trader sentiment is stochastic. As rational investors are risk averse, the implication becomes that they reduce the extent to which they bet against noise

(12)

7

traders in response to this increased risk. This means that rational investors need to take both the fundamental risk and the risk caused by noise traders into account. (A3) - Fourth, the noise trader sentiment is not restricted to just a few individuals. The noise

trader sentiment is systematic in its nature and influences all irrational traders collectively. The imitative and herd behaviour of noise traders snowballs the total effect of the noise traders making them a significant market power that can shift share prices considerably over time (A4). (De Long et al., 1990, Mueller and Pfnuer, 2013) Lee et al. (1991) basically apply the Noise Trader Theory to the closed-end fund puzzle and add a fourth (fifth when using the Mueller and Pfnuer (2013) approach) assumption to the Noise Trader Theory in that off differing clienteles.

- Fifth, noise traders and rational investors hold different types of assets. Noise traders can be generalised as small investors. Small investors usually hold more liquid assets like stocks. Rational investors can on the other hand be generalised as institutional investors. Institutional investors are able to hold assets with a higher transaction cost, less liquidity but stable return. Lee et al. (1991) argue that for the closed-end fund puzzle small investors hold the closed-end fund stocks while institutional investors hold the underlying asset (A5).

De Long et al. (1990) thus postulate that the presence of noise traders in financial markets can permanently deviate price from its fundamental value. The implication is that the closed- end fund stocks are subject to noise trader risk and thus need to be priced higher in equilibrium. The Noise Trader Theory acts as the base of the literature into the irrational approach to the NAV spread, covered in chapter 2.4.4.

2.2 The Property Market Versus the Stock Market

The differing characteristics of the property and stock market are of importance to this thesis as differences allow for a differing pricing to occur. Large property portfolios are typically held for longer time horizons and require special knowledge. This means that typical real estate owners are large investors such as institutional investors and property companies (Barkham and Ward 1999). Unlike real estate, shares on the stock market can be sold quickly and easily to low transaction cost, and investors do not need to take the burden of the purchased assets (Geltner and Miller, 2006).

(13)

8

Although the property market is viewed as being illiquid, the Nordic market and Sweden in particular has proved to be very liquid compared to other countries. Sweden has the highest property investment market turnover ratio in Europe, with an average of 6.3% between 2005- 2014 (Leimdörfer, 2015). However, there is a time lag of about three to six months from the decision to sell property is taken until the assets are actually sold. (Leimdörfer, 2011)

2.3 The Calculation of the NAV Spread

When share prices of property companies (the market capitalization) deviate from the companies’ NAV over time, it is implied that the stock market values the company differently. In this situation, a discount or a premium to NAV arises. As this thesis investigates the differing behaviour of the NAV spread and the explanations for this, it is of utmost importance to understand how it is computed. The discount to NAV is calculated as the percentage difference between the market capitalisation (MC) and the net asset value (NAV) of the firm, see equation 2.1. If the NAV is higher (lower) than the market capitalization, the fund is traded at a discount (premium). (Barkham and Ward, 1999)

DISCOUNT = (NAV-MC)/NAV Equation 2.1

The market capitalization is the total value of shares outstanding and is calculated by multiplying a company’s outstanding shares with the current market price of one share (Investopedia, 2016). The net asset value (NAV) of a company is calculated as the sum of the market value of all assets minus liabilities and other claims to the company (Ke, 2015).

To ensure that an equivalent calculation of the NAV is pursued, the European Public Real Estate Association (EPRA) provides guidelines for how this calculation should be done.

EPRA acts as a non-profit association and was founded in 1999. They work for consistency and transparency in financial reporting in the listed property sector. EPRA continuously observes the NAV spread at a pan-European perspective and has set up two definitions connected to the NAV named EPRA NAV and EPRA NNNAV. The EPRA NAV is intended to reflect the true business of an investment property company, where the assumption is that assets are held for the long term. Therefore EPRA NAV excludes deferred taxes related to future disposals and the fair value of hedging instruments, as both of these are not expected to materialise. The EPRA NNNAV however, is a ’spot’ fair value measure and incorporates management’s view of the fair value of deferred tax and hedging instruments. It also adjusts to fair value debt, which is held at amortised cost in EPRA NAV. (EPRA, 2014)

(14)

9

2.4 Literature Review

2.4.1 The Closed-end Fund Puzzle

The starting point for the research into premiums and discounts to NAV of property companies, and thus in this thesis, lies in the discovery of the closed-end fund puzzle. The closed-end fund puzzle (CEFP) is the empirical finding that shares of closed-end funds are being traded at a price that differs from the NAV of the funds (Dimson and Minio-Paluello, 2002). The NAV spread, as it similarly is referred to, has been found to deviate considerably cross-sectionally, between funds, as well as over time as shown and investigated most famously by Malkiel (1977) and Lee et al. (1991). Historically the deviation has mainly been in the form of a discount implying that investors are only willing to buy shares of closed-end funds for prices less than their fundamental value (Dimson and Minio-Paluello, 2002). The NAV of closed-end funds, and property companies for that matter, can easily be computed and is accessible for investors. This means that the existence of NAV spread goes against the efficient market hypothesis. Consequently, it is considered to be one of the most intriguing problems in finance and has thus inspired a vast body of literature and hypothesis of its origin, which can be applied to the property market (Barkham and Ward, 1999). Dimson and Minio-Paluello (2002) provide a useful overview of the fundamental literature concerning research into the closed-end fund puzzle.

The initial explanations for the NAV spread for closed-end funds attempt to explain the discount within the framework of the efficient market hypothesis, which was presented in more detail in chapter 2.1.1. This rational approach focuses on that purely company-specific factors can warrant that the NAV spread exists. However, as mentioned by several studies, the purely rational approach only manages to explain a part of the NAV spread (Dimson and Minio-Paluello, 2002). In combination with the gaining popularity of behavioural economics in the later 20th century, a shift towards explaining the discount via the noise trader approach, which was presented more in detail in chapter 2.1.2, was imposed. The noise trader approach has managed to explain some parts of the discount, which has not been captured by earlier methods. In summation there are two ways to look at the discount, via a rational approach and noise trader approach (Barkham and Ward, 1999).

Since the late 20th century the theories and hypothesis regarding the explanation for the closed-end fund puzzle has started to be applied to the listed property sector and REITs. The closed-end fund puzzles’ relationship with discounts and premiums to NAV in property

(15)

10

companies comes from the striking resemblance between a listed property company and a closed-end fund in terms of some of their main characteristics (Barkham and Ward, 1999).

Three main characteristics can be argued for:

- First, a closed-end fund is a mutual fund that mainly invests assets in other companies’ securities and manages these for long-term income and profit (Dimson and Minio-Paluello, 2002). Listed property companies involved in owning and letting real estate pursue similar business objectives focused on holding the underlying asset for long-term income and profit (Rehkugler et al., 2012).

- Second, the investments of closed-end funds are usually characterized by low levels of liquidity, which is in similarity with the general low liquidity of direct property investments.

- A third resemblance can be found in one of the main characteristics of the closed-end fund, the inelastic supply of shares. The inelastic supply of shares comes from that closed-end funds issue a fixed number of shares that are traded at the stock market.

Once an initial private offering (IPO) has taken place the closed-end fund does not redeem issued shares (Investopedia, 2016). In that sense the closed-end fund can be compared to a listed property company that in the same way as the closed-end fund is under no obligation to redeem issued shares and rarely issue new ones (Barkham and Ward, 1999). This implies that investors that want to buy and sell the stock have to do this at the secondary market at the price set by supply and demand on the stock market. This means that shares are priced on the stock market and subsequently can differ from the NAV of the fund (Rehkugler et al., 2012).

In addition to these similarities the underlying asset of property companies, the properties themselves, are appraised on an annual, even quarterly basis. This is an implication as of the introduction of IAS-40 accounting standards in 2005. Since 2005 all European companies are obliged to report their property portfolios at their fair value in their annual reports (Nordlund, 2008). For a property company the NAV can thus be constructed fairly easy via information available in the companies’ annual reports, as the combined fair value of the property portfolio minus all debt and other liabilities. This means that the company displays a justified estimate of their company value on an annual basis and further motivates why the deviation to NAV is interesting to study within the listed property sector.

(16)

11

2.4.2 The Rational Approach to the Deviation to NAV

The literature attempting to explain the discount in closed-end funds starts by having a strong focus on a framework set up under the efficient market hypothesis and rests on standard economic theories. The divergence of the NAV from the market capitalization is reasoned to be motivated by pure economic company related characteristics (Dimson and Minio-Paluello, 2002). Suggested factors are considered to be either of an endogenous or exogenous nature.

The endogenous approach looks at company-specific factors that could motivate a deviation while the exogenous approach looks outward to external factors to the company that subsequently the company management cannot influence (Rehkugler et al., 2012).

In previous research the rational endogenous approach is often included as the base of most studies. This is a result of its intuitive feel and that it can be computed and analysed with ease. The data used to compute the variables are often key figures that the company is obliged to include in financial reports. The rational approach applied to the deviation to NAV in the real estate sector has been treated in a number of studies, but have mainly focused on REITs (Real Estate Investment Trusts) or the UK, US and recently pan-European markets (Rehkugler et al., 2012).

The main method for investigating the NAV spread has focused on finding a relationship between the discount and different hypothesized explanatory variables through regression analysis on series of cross-sectional set of data over time. This type of data can be considered panel data, but a number of previous studies fail to comment and structure their models after this and instead perform cross-sectional regressions using OLS (Ordinary Least Squares).

Malkiel (1977) is one of the first to study the discounts to closed-end funds and investigates the explanatory power of several company-specific factors. He mainly links the discount to unrealized capital appreciation, number of stock available for trading and amount of foreign assets. In order to test these factors Malkiel employs a cross-sectional regression on a set of 24 closed-end fund stocks for each of the examined years (1967-1974). Adams and Venmore- Rowland (1989) was among the first to study the discount to NAV in property companies.

Although their study is purely theoretical they inspire further research into the problem as they postulate several reasons for the discount to exist. Their main contribution lies in their reasoning of the effects of financial gearing, liquidity and especially how capital gains tax can be a direct factor to the discount. Barkham and Ward (1999) are the next to test the discount in the property sector. They apply a two-step approach in which the first part is of a rational character and the second focuses on a noise trader approach. By the use of data from

(17)

12

44 listed property companies between 1993-1995 they link 15% of the movement of the discount to tax, firm size, holding of trading stock and historical return. Brounen and Laak (2005) investigate the discount in 72 property companies in a large pan-European study.

Although extensive, the study only investigates the discount for one year, thus only looking at a snapshot of the problem. Their main findings are that firm size, historical return and free float (amount of stocks available for trading) decrease the discount, while risk and leverage increase the discount. Morri et al. (2005) provide a purely rational approach to 26 UK listed property companies between 1999 and 2004. The study discusses a noise trader approach but that is not tested empirically. Their main findings are a negative relationship between NAV discounts and leverage, return and equity, while the company’s beta increases the discount to NAV. Rehkugler et al. (2012) extends the literature by using a semi-rational approach to explain the discount. The first part of their study looks at rational variables to explain the deviation to NAV in approximately 40 property companies over 8 years in Europe. They link REIT status, stock price volatility, sectoral and regional concentration, leverage and free float to the discount. The latest contribution to the discount literature within the listed property sector is made by Ke (2015). This thesis focuses on explaining the discount via traditional rational variables such as size, leverage et cetera but aims to highlight the impact of corporate governance mechanisms. It manages to show that some of the corporate governance variables, such as insider ownership and non-executive directors on the managing board, impact the deviation to NAV. At a maximum 43% of the discount could be explained.

However, in order to explain 43% of the movement in NAV spread, an irrational variable accounting for the average market discount was used. (Ke, 2015)

The NAV spread is moreover researched on a large scale at an American level where the main focus is to observe the NAV spreads in REITs. REITs and listed property companies differ in some aspects but do also have similarities, which mean that the REIT research can be applicable in this thesis although with care. Capozza and Lee (1995) contribute largely to the research into the NAV spread in REITs via a rational approach applied to 75 REITs in the US from 1985-1992. The main findings are that focus on property type and size affect the discount. Clayton and MacKinnon (2000) apply a two-step approach to 98 US REITs over three years. The first step is a rational approach that via endogenous rational variables only can explain 7% of the NAV spread in which size plays the biggest part. A summary of the previous literature into the rational approach to the discount to NAV is presented in table 2.1 below.

(18)

13

Table 2.1 – Summary literature rational approach

2.4.3 Rational Variables

The rational approach emphasises that endogenous and exogenous rational variables can warrant a share price that differs from the NAV of the company. If a variable warrants a market capitalisation that is higher (lower) than the NAV it is said to decrease (increase) the discount, thus have a negative (positive) effect on the discount to NAV. In the section below the rationale for the most commonly used variables when performing regression analysis on the discount to NAV is presented and discussed. This chapter concludes with a summary of the findings visualized in table 2.2.

Early research put a large emphasis on tax liabilities as a factor that causes a large part of the discount. NAV of closed-end funds are based on the market value of the securities they hold.

Article Year Time Period Companies Region Method Approach R-square Comment

Malkiel 1977 1967-1974 24 - OLS Rational 38% Examining the closed-end fund

puzzle

Adams &

Venmore- Rowland

1989 - - - Discussion Rational -

The first study applying closed-end fund puzzle to the property market

Capozza &

Lee 1995 1985-1992 75 US OLS Rational - Examining REITs

Barkham &

Ward 1999 1993-1995 44 UK OLS Rational/Noise

trader 15% / 33% Rational and testing noise trader assumptions

Clayton &

MacKinnon 2000 1996-1999 98 US OLS Rational/Noise

trader 7% / 44% Examining REITs with a rational and irrational approach

Cronqvist

et al. 2001 1990-1996 32 SWE OLS +

FGLS

Rational

(Diversification) 65% Discount explained by diversification and agency costs

Brounen &

Laak 2005 2002 72 EU OLS Rational 51% Large data set but only for one

year

Morri et al. 2005 2000-2003 26 UK OLS Rational 51% Ungearing NAV spread approach

Rehkugler

et al. 2012 2000-2007 40 (28) EU SEM Rational/Noise

trader 76% Semi-rational approach. Creating country-specific sentiment index plus running a SEM

Ke 2015 2005-2013 41 UK OLS Rational

(corporate gov.) 19% / 43% Corporate governance variables OLS: Ordinary Least Squares, FGLS: Feasible Generalized Least Squares, SEM: Structural Equation Model

(19)

14

If a fund holds securities that have grown in value, i.e. have appreciated, the sale of these securities would incur capital gains tax, which also is applicable for property companies (Barkham and Ward, 1999). However, Malkiel (1977) shows mathematically that only a 6%

discount can be motivated by capital gains taxes, thus shattering the initial thought that the NAV spread was purely a tax issue. Later, investigations into the NAV spread in REITs, that are not subjected to capital gains tax, show that REITs still suffer from discount to NAV, although generally smaller which is in line with Malkiel’s findings. Ke (2015) uses the ratio of contingent tax liabilities as of the total balance sheet value. This was significant in their initial model but insignificant in later models. Barkham and Ward (1999) apply the same approach 15 years earlier and find a significant positive relationship with the discount, as expected, for capital gains tax liabilities for listed property companies in the UK.

Earlier studies also discuss the impact of agency costs and expense ratios on the NAV spread. The results of these contradict each other. Gemmil and Thomas (2002) find that higher management expenses contribute to a larger discount. Malkiel (1977) however, do not find a significant relationship between management fees and discounts. There are some problems in the application of agency costs as a variable affecting the discount to NAV.

Neither current nor future agency costs can explain the wide fluctuation in discount since management fees normally are a percentage of the NAV and do not fluctuate as much as the discount does. In addition, according to Lee et al., (1991) agency costs do not seem to explain much of the cross-sectional variation in discounts.

The core of most literature with a rational or a semi-rational approach is made out by endogenous company-specific factors. These are purely company related and thought to warrant the market capitalisation to differ from the NAV. Company size is probably the most intuitive such company-specific factor and probably the most frequent in previous literature.

The results of the impact of company size on the discount are inconsistent. Property is an asset that can be considered illiquid. For a company with large property holdings this will likely lead to a problem if the company was forced to sell its entire stock instantly. An instant sale of a large amount of properties would lead to a considerable increase in normal flow of properties thus considerably lower the price of the property. Hence, the total value of company’s assets is not necessarily the sum of the values of individual properties. This would lead to that a larger company size would infer a discount to NAV for listed property companies (Barkham and Ward, 1999). On the other hand Adams and Venmore-Rowland (1989) argue that property companies with a large portfolio access capital more easily than

(20)

15

smaller companies. In addition, high value properties can act as a barrier since they require a large amount of capital. Smaller property companies cannot gain access to these properties, which then creates an inefficient pricing. This makes it possible for larger institutions to earn abnormal returns from larger properties. For this reason, larger companies with greater power might be associated with a lower discount to NAV. Ke (2015) and Brounen and Laak (2005) concur that larger companies have smaller discounts. Brounen and Laak (2005) lift the idea that a larger company might benefit from increased popularity, recognition and higher transparency than smaller companies and thus a lower discount.

Studies have found that companies with high levels of leverage tend to have a higher discount to NAV (Ke, 2015, Brounen and Laak, 2005). Rehkugler et al. (2012) confirm the belief that leverage leads to larger discounts as leverage increases the risk for the investor.

Partly in contrast, Adams and Venmore-Rowland (1989), Barkham and Ward (1999) and Morri et al. (2005) argue that leverage can affect the NAV spread in both ways. According to them a higher leverage means an amplified NAV spread.

The trade-off between diversification benefits and loss of economies of scale and other benefits spurring from corporate focus is widely discussed in the literature covering NAV spreads among listed property companies. Previous research measure the degree of corporate focus on property type and geographical location via the construction of a Herfindahl- index. A Herfindahl index is a measurement of the degree of property type focus and geographical concentration and is calculated as shown in equation 2.2.

HERFINDAL!"#$/!"#$%&"' !!!!𝑆!,!,!! Equation 2.2

The Herfindahl index is based on the value of property type/location for company i at time t.

r represents the set of property types or locations, Sr,i,t is the proportion of firm i’s assets invested in property type or location r at time t. The Herfindahl index can vary between close to 0 and 1, where a low Herfindahl index means diversified focus while a number of 1 implies a company focused on one property type or location (Ke, 2015). In regards to property type, previous literature suggest that a larger focus reduces the discount to NAV (Brounen and Laak, 2005 and Ke, 2015). Cronqvist et al. (2001) and Boer et al. (2005) show findings that concur and show that unfocused publicly traded real estate companies are less transparent and more expensive to manage and therefore less successful, which indicate a higher discount. A more focused strategy in this regard could increase both a firm’s return

(21)

16

and risk (Rehkugler et al., 2012). However, the impact of company concentration on geographical location is inconsistent. From purely a theoretical standpoint most researchers argue that the effect of geographical concentration should be similar focus on property type.

Most studies do not find a significant result and the concentration variable has found to both increase and reduce the discount. The results of Brounen and Laak (2005), which has a pan- European perspective, show no relationship between the geographical spread and discounts.

They argue that the non-existent relationship could be due to the relatively high degree of regional focus that is presented in their sample.

The variable free float can be used as a proxy for stock liquidity, in other words, how easily the share can be converted to cash (Brounen and Laak, 2005). Investors prefer a liquid share before an illiquid, since an illiquid share would reduce the possibility to sell it. Therefore a higher free float should lead to lower discounts since it will be easier to buy or sell the share.

According to the results of Brounen and Laak (2005), real estate companies with higher free float are linked to lower discounts to NAV. In the study made by Rehkugler et al. (2012), free float is statistically insignificant in the final model, even if pre-test ascribes the variable to lower discounts and some explanatory power.

Brounen and Laak (2005) introduce the belief that an EPRA membership can affect the discount to NAV. EPRA is an organization that works for better transparency and stability in financial reporting for property companies by producing standards and indices. A membership in EPRA should reduce the discount to NAV since the membership entails more stability and transparency for the investor. The results of Brounen and Laak (2005) support the hypothesis of a smaller discount for a company that is a member of EPRA.

Some explanations for the NAV spread to be motivated under the efficient market hypothesis are thought to be of a more exogenous nature, even though they are company related (Rehkugler et al., 2012). These factors are related to the share of the listed property company and are made out by the reputation of the management, volatility and the stock beta.

According to Malkiel (1995) a good reputation of the firm and its management should have a negative relationship to the discount. However, reputation is hard to measure. In order to measure this variable a proxy variable has been used in previous literature. This proxy constitutes a history of good performance. This is calculated as the average daily stock return of the share during the last year. Malkiel (1995), Barkham and Ward (1999), Brounen and Laak (2005) and Ke (2015) expect that this variable would be negatively related to the

(22)

17

discount. After the regression analysis, all authors find a significant and negative relationship.

The stock price volatility is another hypothesized variable that drives the share price away from the NAV. Its importance was first discussed by Adams and Venmore-Rowland (1989) and was picked up by Rehkugler et al. (2012). Both studies predict a positive relationship with NAV discounts, i.e. larger volatility leads to larger discounts. This can be explained by the fact that higher volatility means insecurity for the investor. Volatility is the most explanatory rational variable in the report of Rehkugler et al. (2012). On the other hand, Brounen and Laak (2005) find no significant relationship although showing the right coefficient. In addition to measuring the total risk of the firm, here captured as volatility, the risk associated with the market is also tested for explaining the discount. The Beta of the stock measures the stock’s sensitivity against the market movement and is hypothesized to be positive, as risk tends to lower market values. Although a positive relationship is indicated in the results of Brounen and Laak (2005) a significant relationship cannot be proven. However, Morri et al. (2005) conclude that a higher systematic risk is associated with higher discounts.

Ke (2015) highlights the impact of corporate governance factors on the discount to NAV.

The first corporate governance factor, board size, contains the amount of members in a company’s board. According to Ke (2015), previous studies on REITs seem to suggest that a smaller board can be interpreted as a proxy of a good board, thus having a positive impact on firm performance. Ke (2015) also tests board independence which is constructed by the amount of independent members of the board. The meaning of the word independent is being independent to the company and its governance or independence to larger shareholders. A dependent board might obtain a part of their preferred level of private risk in the company to benefit themselves. Since they are entitled to private benefits of control, they may, for example, implement diversifying investments in property types that are not in line with the company’s business, and support such projects too long despite being less profitable or even unprofitable for the company. (Cronqvist et al., 2001) Insider ownership describes the amount of the company’s shares that are owned by the board as a percentage of the total. Ke (2015) find that a higher insider ownership would lead to higher levels of discount to NAV.

This result is different from the results of Capozza and Seguin (2003), which study investigates the impact of insider ownership on the discount to NAV in US REITs. They find that higher levels of insider ownership convey a signal of higher quality management and therefore a higher REIT valuation. However, Malkiel (1995) argues that insider ownership reduces the likelihood that a fund will be taken over and liquidated at the NAV, which

(23)

18

increases the discount. It is not common that real estate companies are taken over with the aim to be liquidated. However, insider ownership may reduce the prospect of a take-over bid being launched (the opportunity for profitable arbitrage) and therefore widen the discount. On the other hand, if the directors of the company are crucial shareholders, there is a reduced risk of conflicts of interest between the non-directorial shareholders and the management, which would lead to lower discounts (Cronqvist et al, 2001). The last corporate governance variable is similar to insider ownership and free float and proxies ownership concentration. The variable, top three, describes the ownership as the percentage of stocks that is held by top three substantial institutions such as pension funds, insurance companies, private equity funds or other firms that are predominately owned by managers or directors. Although not confirmed empirically, larger ownership by institutions should lead to a negative discount, as these investors are often very rational in their investment strategy (Ke, 2015).

Table 2.2 – Summary rational variables

2.4.4 The Irrational Approach to the Deviation to NAV

The irrational approach to the NAV spread is mainly linked with behavioural finance and the Noise Trader Theory, which was presented in chapter 2.1.2. As previously stated the main part of the theory rests on the abandonment of the premises of a perfectly efficient stock market and instead postulates that noise traders exist over time and that their noise distorts the pricing mechanism in such a way that market prices deviate from fundamentals permanently (Dimson and Minio-Paluello, 2002). For closed-end funds as well as property companies the fundamental values are accessible and thus give an interesting platform for testing the theory of De Long et al. (1990). Lee et al. (1991) elaborate and investigate the findings of De Long et al. (1990) on closed-end funds. They show that the noise trader

YEAR 1989 1995 1999 2000 2001 2005 2005 2012 2015

SIZE - + + + O - O O -

LTV EXAGGERATES N/A O + O O + + +

RETURN N/A N/A - N/A N/A - + O -

VOLATILITY + N/A N/A N/A N/A N/A N/A - +

SYSTEMATIC RISK N/A N/A N/A N/A N/A O - O N/A

TYPE N/A + N/A O - - N/A - -

LOCATION N/A N/A N/A N/A O O N/A - N/A

FREE FLOAT O N/A - N/A O - N/A + N/A

EPRA N/A N/A N/A N/A N/A - N/A O N/A

BOARD SIZE N/A N/A N/A N/A N/A N/A N/A N/A O

INSIDER OWNERSHIP N/A N/A O N/A + N/A N/A N/A -

TOP THREE N/A N/A N/A N/A N/A N/A N/A N/A +

UNREALIZED

CAPITAL GAINS + N/A + N/A N/A N/A O N/A O

AGENCY COST N/A N/A O N/A + N/A O N/A O

Positive significant relationship (+), Negative significant relationship (-), Insignificant relationship (O), Not Accounted for (N/A) BROUNEN &

LAAK MORRI ET AL. REHKUGLER

ET AL. KE

ARTICLE

ADAMS &

VENMORE- ROWLAND

CAPOZZA &

LEE

BARKHAM

&WARD

CLAYTON &

MACKINNON

CRONQVIST ET AL.

(24)

19

approach is more successful in explaining the closed-end fund puzzle than the rational approach.

Table 2.3 summarizes previous literature on the irrational approach. There are mainly two ways of applying the Noise Trader Theory. Rehkugler et al. (2012) engage in the first type that focuses on combining rational factors and irrational variables such as market sentiment indicators to be able to explain the NAV spread via noise trader behaviour of investors.

Rehkugler et al. (2012) create a country-specific market sentiment indicator that is combined with rational variables in a structural equation model. The complete set was given by REIT status, volatility, regional and sectoral concentration, leverage, free float as well as a market sentiment variable. To some extent also Barkham and Ward (1999) and Ke (2015) make use of this approach. They both add average sector discount to their calculation with rational variables in order to explain a part of the NAV spread via noise trader behaviour of investors.

The second approach follows from the five assumptions (A1-A5) of the Noise Trader Theory that was presented in chapter 2.1.2. Essentially this approach investigates the presence of noise traders on closed-end funds or property market and if found to be true it justifies the use of market sentiment in models trying to explain the NAV spread. These assumptions lead to a number of consequences such as long-term mispricing and the continued existence of noise traders. Figure 2.1 shows the complete summary of assumptions and consequences as modelled by Mueller and Pfnuer (2013). In turn these consequences lead to five implications (I1-I5) that can be tested. These implications are: (I1) NAV spreads have a negative long- term average, (I2) alternation of premium/discount, (I3) correlation among NAV spreads, (I4) correlation with other sentiment indicators and (I5) equity issues in premium periods.

Barkham and Ward (1999) (although not I1) and Mueller and Pfnuer (2013) apply the approach to test the Noise Trader Theory on the property sector by investigating these five implications. Several studies focus on examining one or two of the implications but do not apply a holistic approach on the same data set. The framework for analysing the existence of noise traders can be summarized in the following figure 2.1.

(25)

20

Figure 2.1 – Methodology for the justification of the irrational approach

Mueller and Pfnuer (2013) test the Noise Trader Theory by looking at the property sector and the five implications as stated in figure 2.1. They manage to test and find positive significant results for all observable implications. For (I1), (I2) and (I5) an aggregated data analysis is made in which all cross-sectional entities are bundled together. For (I3) and (I4), a panel data GLS (General Least Squares) regression model with random effects is used. Barkham and Ward (1999) try to investigate the existence of noise traders in the same way as Mueller and Pfnuer. They investigate if market sentiment is important in explaining the discount by testing four of the implications implied by the Noise Trader Theory (I2-I5).

The first implication (I1) of the Noise Trader Theory is that NAV spread has a negative long- term average. The rationale for this lies in that if noise traders exist they create long-term mispricing due to the permanent deviation of price from fundamentals due to systematic noise. Thus an additional risk is created by the noise trader which means that the stock, in contrast with the underlying asset, should be burdened with a risk premium which in turn leads to a negative long-term average discount (Dimson and Minio-Paluello, 2002). In order to test whether this long-term average exists or not a market sector average NAV spread is computed for the studied period. Liow and Li (2006) show a long-term discount among Asian and Pacific property companies between 1995 and 2003. Mueller and Pfnuer (2013) show a long-term average discount of 4.62% for EU-REITs between 2005-2010. Barkham and Ward (1999) estimate an equilibrium long-term average discount of 25% for UK property companies between 1993-1995 via a Vector Error Correction Model.

ASSUMPTIONS NTM CONSEQUENCES OBSERVEABLE IMPLICATIONS

(A1) Risk aversion (i) (I1) NAV spread, negative long-

term average (A2) Finite investment

horizons (i) (I2) Alternation of

premium/discount (iii) (A3) Noise trader

sentiment is stochastic Equal probability for optimistic and pessimistic

sentiment (I3) Correlation among NAV

spreads (A4) Noise trader

sentiment is systematic Homogeneity of sentiment (I4) Correlation with other

sentiment-indicators (A5) Divergent

investment preferences (ii)

Rational investors have higher funds in direct

investments (I5) Equity issues in premium

periods

Noise trader model published by Mueller and Pfnuer (2013), based on the NTM of De Long et. al, (1990) and Lee et.al, (1991), Barkham and Ward (1999)

(iii) Mean reversion

Long-term mispricings Continued existence of noise traders Noise trader sentiment:

- Additional risk, not diversifiable - Affects direct and indirect investments differently

(ii) Divergent investment preferences of institutional and private investors, whereas institutional investors are identified with rational investors while private investors are identified with noise traders

(i) Assumption regarding rational investors

References

Related documents

46 Konkreta exempel skulle kunna vara främjandeinsatser för affärsänglar/affärsängelnätverk, skapa arenor där aktörer från utbuds- och efterfrågesidan kan mötas eller

The increasing availability of data and attention to services has increased the understanding of the contribution of services to innovation and productivity in

På många små orter i gles- och landsbygder, där varken några nya apotek eller försälj- ningsställen för receptfria läkemedel har tillkommit, är nätet av

In this thesis we investigated the Internet and social media usage for the truck drivers and owners in Bulgaria, Romania, Turkey and Ukraine, with a special focus on

Results: In our case study we have found that the biggest barriers to entry the Brazilian market for Swedish companies are high import duties, bureaucracy, expensive

French 5-Factor Model are explained. Furthermore, the price multiples P/E and P/B and GPA are described. These are the base of the later described portfolio construction. This

In the statistically chosen model, a change in EQT’s share of Investor’s total net asset value has the largest impact on the discount and a change in IGC’s share of Investor’s to-

Even though companies normally trade at a discount or premium to NAV, previous studies indicate that the stock price for a company over time strongly correlates with the