An Application of the Markowitz Theory to Numismatics (The

A n to n io A lcazar B LA N C O U niversity o f E xtrem adura

J o s é Lu is C O C A -P É R E Z U niversity o f Extrem adura

M ig u e l P ra d o R O M Â N Rey Juan Carlos U niversity

J o s é Â lv a re z G A R C IA U niversity o f E xtrem adura

An A pp lica tion o f th e M arkow itz T heory to Num ism atics (The Walking L iberty)

A t a time when the world economy is suffering from the economic crisis, the alter native goods market becomes a reliable investment option. However, these goods

had started to attract attention even before our actual economic situation became unstable. Due to its magnitude, the market o f alternative goods has been studied from different points o f view, and not only focusing on one aspect, as, for example, its expec ted par return.

Due to this fact, this market has been studied from an investment point of view, analyzing the return that came out from this market on a global scale (Sharpe y Alexander, 1990) or from a certain good as, for example, numis matics (Randall, 1981); the return ob tained in the auctions business, using both philately and numismatics as stud ied goods (Mochôn, 2003, 2005), or for goods studied in the individual way, as numismatics (Brown, 2005; Knaus, 2006) or art (Stein, 1977; Ekelund et al., 2001; Vico, 2010). Different studies analyzing behavior

of investment portfolios, which include numismatic assets, in relation to other portfolios, which don't include these characteristic goods, have been car ried out (Lombra, 2003; 2004). Anoth er approach used to study this market is to figure out which variables affect the price of goods and their degree of influence, particularly studies on numis matic goods (Dickie, Delorme y Hum phreys, 1994; Prado, 2009, 2011; Prado, 2012), on philately (Cardell et al., 1995; Coca, 1998), and on art (Pommerehne, 1997; Galenson, 1997). Moreover, some studies aimed

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Gestion 2 0 0 0 mars - avril 2015

to classify these goods according to their features both in the numismatic market (Berman y Shulman, 1983; Coca, 2001) and the philatelic one (Guitiân, 2001 ) were carried out.

It has to be noted that apart from the studies carried out on the cost-benefit analysis, the alternative goods have been studied to develop a model of philatelic values (Guitiân, 2001 ), to be able to identify the factors influencing on the price of works of art (Moureau, 2000), as well as to develop a multi variate logarithmic model to value fine art paintings (Agnello y Pierce, 1996). Also some studies establishing a numis matic asset pricing model have been carried out (Prado, 2012), as well as those establishing the factors that influ ence on the price of numismatic assets both directly and indirectly (Dickie, Delorme y Humphreys 1994; Prado 2009).

After having reviewed existing liter ature, we can prove that besides the investment market of collectable assets has been studied from the investment point of view, there is a need to study the return of this kind of investments during strong economic fluctuations. Given this situation, the aim of this re search is to carry out an analysis of return arising out from the investments in alternative goods during a long pe riod of time, so we can determine its evolution in order to show positive evo lution of the return of these investments,

and to reassert their significance in the investment market.

Our study has the following structure: first of all, we will raise a theoretical framework for our research; than we will analyze the sample we have cho sen for our study, as well as its design. When the points previous to the results are established, we will analyze the obtained results, and we will present the main conclusions, derived from this study. Finally, we will specify the limita tions which we have found out during the research, as well as new lines of research.

Theoretical framework

The selection criterion of investments is one of the most important aspects of the actual market. Investors study different products, offered by the mar ket, to determine which one is the best alternative for the investment of their capital, securing not only its recuper ation, but also some expected return. Within this frame, the investors all over the world are starting to admit alternative goods as a safe way for investment. In evidence, we can ana lyze a significant investment made by the Chinese government in this kind of investments. In 2005 Chinese in vestments represented only 5% in the world market of alternative goods. However, they were increasing, and

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-An Application o f the Markowitz Theory to Numismatics (The Walking Liberty)

finally they achieved 30% in 2011 (TEFAF, 2012). It was possible espe cially due to the Chinese goods' role as a safe haven asset (Coca, 1998), representing a stable investment (Shar pe y Alexander, 1990).

Nevertheless, this market has one big inconvenience. It is not formed by ho mogeneous goods, quite the opposite. We can identify a huge variety of sub markets, as collectable coins, numis matics; collectable stamps, philately; the art market, formed by paintings, sculptures, furniture, etc.; ancient books and manuscripts, bibliophily... With all this in mind, consumers will be attracted by one or another alterna tive, depending on the market's nature (Blanco, 2009).

If we focus on the numismatic market, we can observe that this one has be come one of the most important alter native investment markets on the world stage. This fact can be proved, if we analyze some numbers, registered in 2009. During that year, when the market suffered harsh consequences of the economic cuts, British market of bullions presented a significant in crease of the 75% in its sells in com parison with the previous year in the North-American market (Panorama nu- mismdtico, 2009).

If we analyze different parts of the col lectable market, we can observe that all its goods attract special interest, as

it can be the art case of 201 1, when the sales level of the works of art con sidered to be Fine art was very similar to its historical maximum, registered in 2 007 /2 008 (McAndrew, 2012). If we analyze the last 10 years, these goods have a very interesting return, as it can be the case of collectable cars with 456% return over 10 years, or of collectable stamps with 250% return, or of collectable coins with 227% re turn (Knight Frank, 2013). It shows that these goods have been transformed in an attractive investment alternative, which leads to increased number of in vestments in this market.

M ethodo logy

We will focus the sample used for this study on tangible numismatic collecta ble assets. In our case it will be a very important coin for collecting in the USA, The Walking Liberty.

The Walking Liberty was minted for the first time in 1916. Its design is classic, and it was very typical for the most coins in the USA at that time, represent ing a strong American ideology. Table 1 on next page describes briefly this coin.

The source used to know different mar ket values and features of the invest ment assets is US COINS VALUES AD VISOR and STANDAR CATALOGUE OF WORLD COINS 2000-2010.

23


TABLE 1. Definition of the coin

Designer A. Weinman AdolfYears of issue 1916-1921, 1923, 1927, 1929, 1933-1947Mints Denver, Philadelphia and San FranciscoSize 30,61 M M or 16" in diameterW eight 12,5 gramsDensity 10,34Edge reededComposition 90% silver, 10% copperAmount of minted coins 74.400

Source: O w n elaboration

Using this source, we obtained the in formation about revaluation of the nu mismatic good studied in this article, and this way we were able to create an investment portfolio. Regarding our methodology, in the first place we are going to mention the Portfolio Theory and then the Markowitz Model.

When investors make financial invest ments, not always they can achieve the results they are looking for. This point led to a study of a risk level of these financial investments. So we have ar rived to the moment when we have to mention Markowitz's name. This Eco nomics Nobel Laureate speaks about what all the investors want to find: to maximize portfolio expected return for a given amount of portfolio risk. To diversify their investments with the aim to obtain the ideal return where everything is connected with the risk assumed for this process.

For Markowitz, portfolio return is de termined by the asset weighted aver

age, and total portfolio risk depends on three factors:1. The weighting of component assets.2. Return variance of each asset.3. Correlation between all the assets.

We have to accentuate this last point, correlation between all the assets, be cause when there is an increase of assets in a portfolio, there is also an increase of its return, which one is pro portional to the increase of return of each one of the assets forming it, and the risk varies according to the correla tion of different assets.

We will focus on the idea of maxi mizing portfolio's return and minimiz ing portfolio's risk, so we will use the Markowitz model.

Applying the portfolio theory, we will obtain the efficient frontier and we will trace a Capital Market Line, then we will trace out the efficient frontier, using the Toolkit in MatLab software package.

24

An Application o f the M arkowitz Theory to Numismatics (The Walking Liberty)

The Markowitz model presents two scenarios:

To maximize portfolio's expected return through a constant level of risk: Max Rp = X , E (R J + X2 E (R2) + . . . + X N E (RN)

° 2p = 2 i Zj Xj-Xj-Oj, = cte

To minimize portfolio's risk through a constant portfolio's return:Min a2p = 2, 2 j Xj-Xj-Ojj

Rp = X , E (R ,) + X2 E (R2) + . . . + X N E (Rn )= CTE

Results

As we have told, the aim of this study is to create different portfolios formed by numismatic assets of the Walking Liberty from 1950 till 2010, and its classification for every year. The goal is to create a portfolio adapted to an investor's profile, and to maximize

portfolio expected return for the lowest level of risk.

In the first place, we will simulate 5.000 investment portfolios and we will calculate two variables we are go ing to study: risk and expected return of all the portfolios. They are represent ed on the Figure 1.

Figure 1. Portfolio's risk and expected return

48,50% j — ...... ..................................................................................

48,00%

47,50%

47,00%

46,50%

46,00%

45,50%

45,00%

24,00% 26,00% 28,00% 30,00% 32,00% 34,00% 36,00% 38,00%

Source: Own elaboration

25


Using financial Toolkit in MatLab soft ware package we will calculate the efficient frontier, maximizing expected return for different levels of risk. This way we will have some alternatives for increasing expected return with a constant level of risk, and we will have 20 portfolios of the efficient frontier.

Using these data (expected return and risk level) we will trace out the efficient frontier, so if we apply a free 4% risk, the portfolio will have 50,38% expect ed return per year with the standard deviation of 37,1 1%. As a result, we will have the same expected return, but the level of risk will be lower, because

Figure 2

70,00%

60,00%

50,00%

40,00%

30,00%

20,00%

10,00%

0,00%0,00% 20,00% 40,00% 60,00% 80,00% 100,0)%


♦ Seriesl

Figure 3


26

An Application o f the M arkowitz Theory to Numismatics (The Walking Liberty)

the theory says that the CML doesn't have self risk, only systematic one.

In other words, investing:7,43% in 1919VG-8

17,69% in 1921VG-8

21,28% in 1921AU-50

20,97% in 1921 MS-60 25,48% in 1947XF-40

7,15% in 1 947MS-60

We maximize expected return up to 50,38% for 37,11% of risk.

According to the investor's profile, more conservative or more aggressive, the level of desired risk will be established, calculating the result between risk-free rate of return and market portfolio. If the combination of the portfolio we want to create is situated in the direct line of the efficient frontier, we will obtain better return/risk properties than any point of 5.000 drawn portfolios.

Discussion and conclusions

We can figure out the following con clusions we have made as a result of this study:

• Portfolio Theory offers us a possibil ity to manage better the risk in the numismatic market, applying diver sification according to the level of conservation of a numismatic good.

• In portfolio construction not all the selected assets are used to create

an efficient portfolio. Those we have used are the Walking Liberty from 1950 till 2010 for 1919VG-8, 1921VG-8, 1921 AU-50, 192 IMS- 60, 1947XF-40 y 1947MS-60. VG (very good) designates a worn coin, XF (Extremely Fine) designates a coin which one had been circulat ing for a short period of time and it is exceptionally well conserved, AU (About/Almost Uncirculated) desig nates a coin which one has never or almost never circulated, that's why the signs of wear are hardly seen, MS (Mint State) means an uncirculated coin with no trace of wear.

• Investment in tangible goods is a good safe haven asset, because fi nancial crisis doesn't affect them as other investments, due to the fact that the investment in collectable as sets, numismatic ones in our case, doesn't governed by evolution of the financial markets.

• This is an accessible kind of in vestment for any investor, and the grade of accessibility depends on the cataloguing of the collectable asset. At global level the market of collectable assets is divided be tween the USA, the UK, France and China.

• This is a medium- to long-term invest ment, because the older the asset is, more valuable it will be considered in the collectable market. These in vestments obtain their maximum re turn on a long-term basis.

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Carried out this research, we would like to mention different limitations and new lines of research:a) To include new numismatic as

sets into the investment portfolio. For example, a new kind of coin minted in other period of time and composed of a different metal as, for example, gold numismatic as set, to increase expected return, to reduce the volatility and to have a more diversified investment portfo lio, as this study was carried out using only one collectable numis matic asset.

b) We can also suggest analyzing monetary policies in Europe, be cause at global level the collecting and investment market of tangible assets is a market where turnover is constantly increasing, while the Eu ropean market is reducing its turno ver.

c) Finally, to work out this investment portfolio of the Walking Liberty including all the years of reval uation for more accurate results and to carry out a more detailed research about investment in this asset.

d) It would be also possible to work out the investment portfolios not only of collectable numismatic as sets, but also to try to diversify and to mix different collectable assets, as, for example, investment port folios of numismatic and philatelic assets.

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An Application of the Markowitz Theory to Numismatics (The