Diversification is the procedure undertaken by investors in order to cut down hazard via investings in an mixture of assets. The thought of variegation has been around for a long clip, dating back to 935 B.C. where in the Hebrew bible it quotes “ But split your investings among many topographic points, for you do non cognize what hazards might lie in front ” .

Harry Markowitz, a respected economic expert and Nobel Prize victor, in 1952 introduced modern portfolio theories that we are still familiar with today with respects to variegation for efficient portfolio direction. The primary purpose of modern portfolio theory is to maximize returns for a given degree of hazard, or instead, to cut down hazard for a given degree of return. Work by Markowitz led to the development of the “ Capital Asset Pricing Model ” . This theoretical account suggests that there are two types of hazards: diversifiable and non-diversifiable. Diversification is an of import factor to see for hazard averse investors. Such investors are assumed to be rational, intending they would wish to maximize returns whilst understating hazard.

## 2.1. Purposes

This paper chiefly focuses on international markets ; we aim to look into to following affairs:

To separate the degree of international variegation that is required to optimize returns,

Assess the deduction of recessions on the variegation procedure,

3. Literature Reappraisal: ( current word count: 2685 )

The Literature reappraisal is split into three subdivision ; the first paperss surveies focused on domestic variegation, the 2nd documenting surveies on international variegation and the concluding subdivision looking at surveies look intoing variegation during recessions.

## 3.1. Surveies on domestic variegation

There have been several influential surveies in relation to portfolio choice ; a revolutionizing paper in this field was by Markowitz ( 1952 ) in which he introduced the “ Mean-Variance attack ” ( MV ) . He suggested the undermentioned equations for optimum portfolio building: ( Equation 1: Expected return of a portfolio ; Equation 2: Discrepancy of a portfolio )

Equation 1 Equation 23

Markowitz states that the foremost finding factor for ‘good variegation ‘ of a portfolio is the covariance between stocks as opposed to the measure of stocks held, therefore covariance is included in the discrepancy computation ( Equation 2 ) ; a lower correlativity reduces the discrepancy, the predominant thought behind the MV attack is the minimization of portfolio discrepancy.

The survey by Markowitz is focused on one-period analysis ; nevertheless, legion research workers have argued that investors should keep portfolios for a greater figure of old ages. Latane ( 1960 ) stated that the chance of an investor accomplishing the highest degree of public-service corporation is strongest when the figure of old ages that a portfolio is held for nears eternity. This implies that the rational investor is more likely to accomplish the expected return for the securities he is keeping given that they have been held for a long period of clip. Therefore reasoning in his survey that whilst building portfolios, investors must see the expected geometric return. Elton and Gruber ( 1974 ) agree with Latane , they province that the expected geometric mean allows designation of portfolios bring forthing the highest expected public-service corporation of terminal wealth.

Since Markowitz, there have been several surveies with respects to portfolio choice, one that is consistent with the theories behind Markowitz and the benefits gained from variegation is by Evans and Archer ( 1968 ) . They examined the decrease in hazard of portfolio returns whilst increasing the measure of securities. Their survey was based on semi-annual observations from 470 securities listed on the “ Standard and Poor ‘s Index ” between January 1858 and July 1967. Evans and Archer generated 40 portfolios ; foremost they extracted one security out of the 470 at random, computed its return and standard divergence, and therefore produced a portfolio incorporating one security. This procedure was replicated, i.e. for the 2nd portfolio, a choice of two securities was made, one from the staying 469 and one from the original listing of 470 securities. The method of bring forthing these 40 portfolios was so reproduced a farther 60 times, the end point being 2400 portfolios, each with its ain criterion divergence and average return. The consequences they observed indicated that the bulk of unsystematic hazard was removed on the add-on of the 8th security. Further hazard decrease was possible, nevertheless, it required a significant addition in the measure of securities added to the portfolio. Further to this, consequences showed that the benefit gained beyond 19 securities was minimum. The ascertained criterion divergence value dropped by 55 % as figure of securities increased from 1 to 40 ; this allowed them to reason that there is being of a relationship between the measure of securities held and the scattering of that given portfolio.

As discussed antecedently, one of the most widely well-thought-of theories is the MV attack, nevertheless this method faces drawbacks ; one being that the optimal portfolios suggested by the theoretical account have inclinations to incorporate heavy concentrations on a few assets. Bera and Park ( 2008 ) stated that this job is due to statistical mistakes with the input appraisals required for the MV method. To get the better of this, they implemented the cross-entropy ( CE ) method developed by Reuven Rubinstein through usage of the Monte Carlo attack. The CE method, besides recognized as the Kullback-Leibler information standards is defined as “ a step between two chance distributions ( i.e. two portfolio weights ; “ P and Q ” ) , which in nature is non-symmetric ) ” . ( Kullback and Leibler, 1951 )

## Equation 3

Bera and Park examined eight international equity indices ( US, UK, Canada, Italy, Japan, Switzerland and Germany ) extracted from informations supplied by Morgan Stanley Capital International. In order for public presentation analysis of the portfolios, they used a “ peal window ” strategy ; this allowed them to obtain portfolio returns for the following period. The empirical consequences obtained in this survey indicated that there was high quality to the MV attack in the portfolio choice procedure when the CE step was implemented. The two chief grounds they suggested this high quality is due to the freedom in portfolio weighting and the possibilities of immediate extension for the incorporation of greater minutes e.g. dissymmetry.

A more recent survey by Miller and Scholes ( 1972 ) has divulged grounds on the being of positive correlativities between market and non-market hazard of single common stocks. In the instance of such a relationship being present, the variegation procedure would be influenced by the measure of securities in a portfolio every bit good as the mean beta coefficient of the portfolio. A survey by Klemkosku and Martin ( 1975 ) addressed this issue, they aimed to prove this relationship and find the significance of it on the variegation procedure.

Klemkosku and Martin assessed 350 single common stocks from the New York Stock Exchange on a monthly footing between June 1963 and June 1973 ; the beta coefficients were so calculated via arrested developments analysis. This allowed them to do estimates on the per centum monetary value alteration via stock monetary value logarithms, all on a monthly footing. They stated that the step of fluctuation about the arrested development end products would be via the residuary hazard, which is displayed through squares of the standard mistakes. Consequences obtained indicated that portfolios with a higher beta value required a greater measure of securities in comparing to portfolios with a lower beta in order to accomplish the same degree of variegation. This is an of import factor to see for an person who seeks to maximize the benefits of variegation but limit the sum of securities held.

Whilst analyzing the benefits associated with variegation, it is common to measure correlativities amongst the investings ; this is chiefly due to the common cognition that variegation benefits decline with increasing correlativities. However, Statman and Scheid ( 2008 ) claim that comparing via correlativities is non a good indicant of variegation benefits. The two grounds they give to endorse this statement are foremost, because correlativity is non an intuitive index, and secondly variegation benefits are non wholly reliant on correlativities, there is besides dependence on the standard divergence of returns. An alternate step suggested is via return spreads, return spreads are superior since they account for both the standard divergence and correlativity between two securities, therefore will supply an intuitive step of variegation benefits. Statman and Scheid focused their survey around measurement via return spreads and attempted to find the difference between the two steps discussed. Consequences they obtained showed that for a given set of assets ordered by the benefits of variegation, a important difference of that peculiar order was noticed when the two different methods of measurings were implemented.

## 3.2. Diversification into international markets

Levy et Al ( 1970 ) aimed to demo that variegation into international markets can bring on farther benefits. The survey involved the computation of average rates of returns and their corresponding standard divergences from 28 states on an one-year footing between 1951 and 1967. Consequences obtained showed that as a greater degree of international variegation was implemented, the standard divergences of the mean rate of returns declined. Thus connoting that a lower hazard is associated with greater international variegation.

Solnik ( 1974 ) produced consequences consistent to those by Levy. The initial thought brought frontward by him is that the hazard of a portfolio is non entirely dependent on the figure of securities within it, but besides by the single hazards of those securities. Solnik sampled 300 European stocks, taken from The Netherlands, Belgium, Italy, Switzerland, France, Germany and the United Kingdom ; all taken during 1966 and 1971. Within each state, Solnik generated similar sized portfolios dwelling of go uping stock types ; and so measured the hazard of each portfolio as agencies of comparing. Consequences showed that there was a disproportional lessening in hazard with greater variegation. When variegation is expanded into international markets there are important decreases in hazard, chiefly due to the independency of different stock markets. The survey revealed that return on a appropriately diversified international portfolio would be ten times less hazardous in footings of variableness when compared to typical securities. Furthermore, it would be half every bit hazardous as a well-diversified domestic portfolio ( US stocks were used in this analysis ) .

Further to this, Solnik mentioned the presence of exchange hazard, this is the hazard experienced due to changing exchange rates that can potentially impact the value of investings ; a solution to get the better of this would be via the hedge of the foreign investings.

Several surveies that exemplify the additions of variegation into international markets have been conducted since the work of Solnik ; such surveies include those by Errunza ( 1997 ) , DeSantis and Gerrad ( 1997 ) , and Stulz ( 1997 ) .

The benefits of international variegation have been good documented ; accordingly, this has led to a greater integrating of international markets, which has resulted in higher correlativities between them. Therefore, in footings of hazard, international investings can turn out to be unsafe. Longin and Solnik ( 1995 ) conducted a survey into stock market indices from 1960 to 1990. The consequences they obtained indicated instabilities in international covariance and correlativity matrices. Further surveies have shown that these correlativities are even greater during higher economic and fiscal integrating. Based on this work, a survey by Eun et Al ( 2008 ) looked at how small-cap stocks could be used as a drive mechanism for international portfolio variegation. Their findings indicated important benefits for investors if they opted into puting in small-cap stocks.

An interesting issue that arises within international portfolio variegation is whether the benefits gained are consistent regardless of the investors ‘ place state. Previously, smaller states tended to confront limitations on investings so that benefits were received in their place economic system, in these present times authoritiess of such states have eased up on such limitations, therefore giving investors greater freedom. Driessen and Laeven ( 2007 ) conducted a survey that aimed to look into the benefits of variegation from different states from an investor ‘s point of position. Their work was in continuance of that by Huberman and Kandel ( 1987 ) , Bekaert and Urias ( 1996 ) , De Roon et Al ( 2001 ) , and Li et Al. ( 2003 ) . Driessen and Laeven start by saying how international variegation for U.S investors does non demo a big sum of benefits ( measured via the MV attack ) in comparing to investors in developing states or smaller states. This was consistent with the consequences they obtained ; they sampled 23 developed states and 29 developing states. They noticed that when international variegation was applied, the Sharpe Ratio addition is 13.5 % in developing states, yet in developed states it merely increased by 7.8 % . The Sharpe Ratio ( S ) measures the “ reward-to-variability ratio ” ( W. F. Sharpe, 1994 ) :

## Equation 4

The greater the Sharpe ratio, the greater the return for a given hazard, therefore Driessen and Laeven were able to demo that variegation benefits are greater for developing states. Another facet they uncovered was that variegation benefits had a additive relationship to the hazard of a state ; greater possible benefits were associated with riskier states.

Further surveies in international variegation have shown that although investings in developed markets are by and large associated with less hazard, investings in emerging markets can bring forth returns that compensate for the hazards associated to them, therefore a diversified portfolio should incorporate investings from both developed and emerging market equities. Beach ( 2006 ) based a survey on this facet and aimed to demo why emerging market equities should be portion of well-diversified portfolios. Fender ( 2002 ) who motivated Beach ‘s survey explains, “ Why International Equities belong in a Diversified Investment Portfolio ” . In order to find whether emerging market equities are a suited investing option, Beach examines the hazards induced matching to their returns when such equities are contained in a portfolio. Measurement of hazard is carried out via standard divergence, semi-deviation, beta, every bit good as downside betas. Beach used the Capital Asset Pricing Model ( CAPM ) in his analysis and discovered that when puting in an emerging market index a return of 1.27 % per month is provided compared to a significantly less return of 0.775 % per month in an developed market index. Further to this, the emerging market index contained a Sharpe ratio of 0.1282 compared to the 0.087 of the developed market index.

A similar survey by Kim and Singal determined that the returns gained from a globally diversified portfolio incorporating investings from emerging markets was justified by the hazards associated to those markets ; their survey was conducted from the position of U.S. investors. Hence, it is suited to state that when an investor is building an international portfolio, he should include an emerging market index within it since they compensate for their hazard degrees by supplying greater rates of returns.

## 3.3. Diversification during fiscal dazes

Another fascinating subject that arises within portfolio variegation is the behaviour of investings in periods of economic uncertainness. There have been several points in history where extended dazes have hit the fiscal markets, a few of these being the 1987 stock market bubble, the dot com bubble, the Long-Term Capital Management, and of class the most recent “ Credit Crunch ” . During these periods of crises there have been terrible diminutions in equity markets, greater recognition spreads, drastic beads in the assurance of fiscal establishments, greater plus volatility and really high degrees of hazard antipathy. Goldwhite ( 2009 ) examined the behaviour of investings in high volatility periods via analysis of the VIX. The VIX is a step of volatility of the S & A ; P 500. Goldwhite demonstrated that VIX could be a suited classification method for investings. His survey compliments the work by Szado ( 2009 ) , who addressed the undermentioned inquiry in his survey: “ What could hold been done to guarantee that the effectivity of a portfolio ‘s variegation survived in such an environment? ” The survey was conducted between March 2006 and December 2008 ; the clip frame covered was shortly after the constitution of the VIX. The public presentation of the portfolios constructed by Szado showed that there was an undistinguished addition in variegation benefits with the add-on of bonds and other assets. This was the instance shortly after the “ Credit Crunch ” during the 2nd half of 2008. However, the public presentation of VIX observed was solid, therefore demoing the add-on of VIX hereafters to establish portfolios can bring on variegation benefits.

A farther survey similar to those by Szado and Goldwhite was by Odier and Solnik ( 1993 ) . Consequences they obtained indicated that in periods of worsening markets, the correlativities of U.S and international markets were significantly higher in relation to those of lifting markets ; it is common cognition that with higher correlativities are related to lower benefits from variegation. This shows us that even though variegation is indispensable in clip periods of falling markets, the additions are minimum.

## 4. Datas and Methodology

Financial theory suggests that there are two types of hazards associated with securities: systematic and unsystematic. Systematic hazard is associated with the market whereas unsystematic hazard is associated to the specific security ; the intent of variegation is to cut down the later hazard type.

We can already separate from old surveies mentioned in the literature reappraisal that variegation can be extremely good for rational investors. In this survey I will be look intoing how the benefits of international variegation can be experienced at different points in clip ; I will be sing a clip frame of 15 old ages ; between 1st January 1995 and 15th November 2010. Previous surveies have documented the degree of variegation required within the domestic state in order to optimize returns, in this survey we will be focused on international markets. The primary purpose is to separate the degree of international variegation that is required to optimize returns and to find which clip periods it would be most beneficiary to set about the variegation procedure.

## 4.1. Datas

The information type I will be utilizing in this analysis will be market indices, informations has been extracted from Yahoo Finance for the undermentioned indices on a day-to-day footing: FTSE 100 ( UK ) , S & A ; P 500 ( US ) , Hang Seng ( Honk Kong ) , CAC 40 ( France ) , DAX ( Germany ) , BEL 20 ( Belgium ) , Bovespa ( Brazil ) , ATX ( Austria ) , IPC ( Mexico ) , AEX ( Netherlands ) , Nikkei 225 ( Japan ) , and the STRIATS TIMES INDEX ( Singapore ) . The choice of these major indices is appropriate in that they can be used as placeholders for smaller indices.

## 4.2 Returns, Correlations and Risk

From market monetary values, per centum return for single trading yearss is deliberate via Equation 5. The value obtained shows the capital additions achieved from the given index. In this equation, we are presuming absence of dividend payments ; in world existent received returns from a market index is the summing up of capital additions and dividend payments. In this survey we aim to look into how investing in different markets can be an optimal investment scheme, therefore it is safe to disregard dividend payments and concentrate on the market itself.

## Equation 5

From this, correlativity coefficients ( summarised in Figure 1 ) between different indices are calculated for the period between 1st January 1995 and 15th November 2010. The correlativity coefficient aims to mensurate the additive strength between two assets, for illustration between A and B, see Equation 6. The value is standardised due to the inclusion of standard divergences. It ‘s end product scopes from -1 to 1 ; -1 bespeaking a perfect negative correlativity, bespeaking the return between the given assets move in opposite waies. Alternatively a value of 1 shows perfect positive correlativity, therefore bespeaking return between the given two assets move together in the same way. On the other manus, a correlativity value of 0 indicates that the return between the two given assets is wholly independent.

## Equation 6

## Figure 1

Daily returns are so averaged out to bring forth monthly returns. They are farther summarised into annual returns for graphical intents as can be seen in Figure 2. This was done to cut down the noise in figures ; monthly values besides permit us to cipher correlativities more handily between markets in different old ages ; consequences are displayed diagrammatically in Figure 3. Furthermore, for each month, the standard divergence was computed via Equation 6. This value can be interpreted as the hazard or volatility associated to the given index for the several month. Consequences are compressed in an one-year format and displayed in Figure 4.

## Equation 6

## Figure 2

## ^^^ ( Figure 3 ) Use MONTHLY DATA TO GENERATE A YEARLY CORELATION TIME SERIES

## Figure 4

## Decision

Although, theoretically the benefits of international variegation can to a great extent outweigh strictly domestic investings, there are some disadvantages to see when puting internationally. Sometimes, it is non really convenient to set about international investings, and in the instance they are taken investors are subjected to exchange hazard.

## aˆ¦ .

## In decision reference following: State hazard or political hazard is faced with international investings. Institutional restraints are typically government-imposed, and include revenue enhancements, foreign exchange controls, and capital market controls, every bit good as factors such as weak or nonexistent Torahs protecting the rights of minority shareholders, the deficiency of ordinance to forestall insider trading, or merely unequal regulations on timely and proper revelation of material facts and information to security holders.

## Restrictions:

Not included dividend payments