Diversification is a widely known management technique that aims to reduce the risk of portfolios. The principle underlying the strategy of diversification is that the portfolios created have multiple investments in order to reduce the unsystematic risk. If investments with higher returns are combined with investments with an unfavorable return, the portfolio return would be beneficial to the investor. An important requirement for diversification is the need for securities to be negatively correlated. For example, if the stocks of a country suffer from a downturn, the domestic portfolio comprising these stocks will be affected. If this portfolio comprised stocks from another country, assuming returns of these two portfolios are negative correlated, this diverse portfolio would have reduced the overall potential risk of the investment.

EMPIRICAL EVIDENCE

We start our analysis with a simple example below.

Table 1 Monthly Returns on Asset X and Y

Table 1 shows the monthly return, average return, and standard deviation from investing in asset X and Y, as well as placing equal proportion of funds in each of the two assets. It is evident that after we create a portfolio that includes both X and Y, the risk of our investment has reduced compared with if we invest in either asset X or Y.

An important requirement for efficient diversification is the need for assets to not be perfectly correlated. This technique will enable a diversified portfolio to have less risk than the weighted average risk of its individual component assets, often resulting in a risk less than the least risky asset of the portfolio. (In our example, the portfolio reduces the standard deviation from 7.15 to 6.32).

To see how it works, we would consider more two risky assets, illustrating the principles and considerations that apply to portfolios comprising multiple assets.

A proportion denoted by is invested in the bond fund, and the remainder, 1- denoted. is invested in the stock fund. The rate of return on this portfolio. will be

+ (1)

where is the rate of return on the bond fund and is the rate of return on the stock fund.

The expected return on the portfolio is a weighted average of expected returns on the component securities with portfolio proportions as weights:

(2)

The variance of the two-asset portfolio is

(3)

Equation (3) informs us that variance is reduced if the covariance term is negative. It is important to recognize that even if the covariance term is positive, the portfolio standard deviation remains less than the weighted average of the individual security standard deviations, unless the two securities are perfectly positively correlated.

To see this, notice that the covariance can be computed from the correlation coefficient. as

(4)

Therefore,

(5)

Other things equal, portfolio variance is higher when is higher. In the case of perfect positive correlation, =1, the right-hand side of Equation (5) is a perfect square and simplifies to:

(6)

So, the standard deviation of the portfolio with perfect positive correlation is just the weighted average of the component standard deviations. In all other cases, the correlation coefficient is less than 1, making the portfolio standard deviation less that the weighted average of the component standard deviations.

Equation (2) shows that expected return is unaffected by correlation between returns, as also illustrated in Table 1, the average return remains unchanged. Therefore, other things equal, international diversifiers always aim to constitute their portfolios with assets that have a low or negative correlation with the existing portfolio constituents.

A portfolio’s expected return being the weighted average of its component expected returns and its standard deviation less than the weighted average of the component standard deviations, portfolios of less than perfectly correlated assets always offer better risk-return opportunities than the individual component securities on their own. The lower the correlation is between the assets, the greater the gain in efficiency.

Consider a portfolio with increased number of assets. The expected return and variance of any risky portfolio with weights in each security. can be calculated from the following formulas:

(7)

(8)

(9)

Consider now a diversification strategy in which an equally weighted portfolio is constructed, meaning that = 1/N for each security. In this case Equation (9) may be rewritten as follows,

(10)

We also know that

(11)

(12)

Therefore, we could express portfolio variance as

(13)

Rearrange,

(14)

The contribution to the portfolio variance of the variance of the individual securities goes into zero as N gets very large. However, the as the contribution of the covariance terms approaches the average covariance as N gets larger. So, it shows that the individual risk of securities can be diversified away, while the contribution to the total risk caused by the covariance terms cannot be diversified away.

The risk that remains even after extensive diversification is called market risk, risk that is attributable to market wide risk sources. Such risk is also called systematic risk, or non-diversifiable risk. In contrast, the risk that can be eliminated by diversification is called unique risk, firm-specific risk, non-systematic risk, or diversifiable risk.

Equation (14) plays a crucial role in our analysis, because if we could find an international market whose covariance with our overall portfolio is relatively small, it will give us a very good opportunity to further reduce our risk, which could not be diversified in the domestic market.

Table 2 Effects of diversification

Source: Elton, Gruder, Modern Portfolio Theory and Investment Analysis

Table 2 illustrates how the relationship in Equation (14) results when dealing with U.S. equities. The average variance was 46.619, and the average covariance was 7.058. As more and more securities are added, the average variance on the portfolio declines until it approaches the average covariance.

Table 3 Risk reduction of equally weighted portfolio in correlated and uncorrelated universes

Source: Bodie, Kane, Marcus, Investment 8th Edition

Table 3 presents portfolio standard deviation as we include larger numbers of securities in the portfolio for two cases, ρ=0 and ρ=0.4. As a result, the portfolio risk is greater when ρ=0.4. Besides, we could see from the column ‘Reduction in σ’ that portfolio risk diminishes far less rapidly as n increases in the positive correlation case.

This example shows how the correlation among security returns limits the power of diversification, and it is quite important to remember that when we hold diversified portfolios, the contribution to portfolio risk of a particular security will depend on the covariance of that security’s return of the portfolio, and not on the security’s variance.

Therefore, when we consider the gains from diversification into developed and emerging markets for U.S. investors, the most important factor to be examined should be the degree of correlation of their performance.

Table 4 and Table 5 present correlations between returns on stock and long-term bond portfolios in various countries. Table 4 shows correlation of returns in U.S. dollars, that is, returns to a U.S. investor when currency risk is not hedged. Table 5 shows correlation of returns in local currencies, that is, returns to a U.S. investor when the exchange risk is hedged.

From Table 4, it is evident that the correlation coefficients between stock indexes of one country and bond portfolio of another are very low, the average correlation between stocks and bonds is -0.16, while the average correlation among various stocks is 0.72, a similar result to as seen in Table 5, suggesting that income portfolios that are balanced between stocks and bonds would greatly benefit from international diversification.

However, the correlation among stock portfolios of the countries in Table 4 is much larger, in the range of 0.44 (Australia-Japan) to 0.96 (France-Germany). We should pay special attention to this result, as stated earlier we need to find a covariance that is small enough to make our international diversification meaningful.

Table 4 Correlation for asset returns (unhedged currencies)

Source: Bodie, Kane, Marcus, Investment 8th Edition

Table 5 Correlation for asset returns (hedged currencies)

Source: Bodie, Kane, Marcus, Investment 8th Edition

According to recent research, increased globalization, which has made the economies of various countries more interdependent, has made available an array of investments whose prices rise and fall independently more increasingly correlated now. This trend is illustrated in Table 7, which shows the correlation of various country indexes with U.S. stocks using monthly excess returns over various periods from 1970 to 2005. The marked increase in correlation is quite striking. For example, Italy markets shows 0.75 correlation to U.S. market, up from just 0.12 ten years ago.

Table 6 Correlation of U.S. equity returns with country equity returns

Source: Datastream

Figure 1: International diversification. Portfolio standard deviation as a percent of the average standard deviation of a one-stock portfolio

Source: B. Solnik, “Why not diversify internationally rather than domestically.” Financial Analysts Journal, July/August 1974, pp. 48-54

Table 7. Percentage of the Risk an individual security that can be eliminated by holding a random portfolio of stocks within selected national markets and among national markets (1975)

Source: Elton, Gruder, Modern Portfolio Theory and Investment Analysis

The observed high correlation across markets addresses the common claim of large diversification benefits from international investing into question. One of the conventional wisdom is depicted in Figure 1, which is based on data for the period 1961-1975. It suggests that international diversification can reduce the standard deviation of a domestic portfolio by as much as half (from about 27% of the standard deviation of a single stock to about 12%). Another study in 1975 is shown in Table 7. According to its research, 89.3% of the risk of an individual security can be eliminated by holding a random portfolio of international stocks.

However, this improvement may well be exaggerated if correlation across markets has markedly increased, as data from Table 6 suggests.

Conclusion

As illustrated above, portfolios of less than perfectly correlated assets always offer better risk-return opportunities than the individual component securities on their own. The lower the correlation is between the assets, the greater the gain in efficiency of returns. However, the correlation among security returns will limit the power of diversification, and when we hold diversified portfolios, the contribution to portfolio risk of a particular security will depend on the covariance of that security’s return with those of other securities, and not on the security’s variance. For this reason, if an international market is identified whose covariance with our overall portfolio is quite small, it will provide an investor a good opportunity to further reduce portfolio risk, which could not be diversified in the domestic market.

EFFICEINT FRONTIER ANALYSIS

The efficient frontier describes all the possible combinations of risky assets based on return and risk of portfolios. In our analysis, the Bond Index and the Developed Market index are computed for the domestic market in USA and the Emerging Market Index is added to these indices to create a diverse portfolio. The risk free rate used is the 3-month treasury bill rate (datastream) .In order to calculate the efficient frontier, we assume that borrowing and lend is done at a risk free rate and short sales are allowed. Using these assumptions, we formed the efficient frontier and estimated the efficient set before and after the diversification.

CONSOLIDATED ANALYSIS

An empirical analysis ranging from a time period between 1991-2010 based on the two portfolios constructed. The first portfolio is the market portfolio constituting the Developed and Bond market indices and the second portfolio constitutes a diversified portfolio into an emerging market.

As supported by empirical evidence, a diversified portfolio into the emerging market is more favorable than a domestic portfolio. This favoritism is a consequence of higher expected returns generated by a diverse portfolio with the same risk constraint as both portfolios.

This is a result of low covariance of returns between the domestic and foreign emerging markets. Factors, both favorable and unfavorable, affecting markets across the globe have a less barring on each other, thus reducing effects of interdependence on each specific market returns. In other words, forces influencing market returns are county specific and diversifying helps nullify the effect of adverse return in the domestic portfolios, assuming market conditions in the emerging market are favorable, resulting in positive returns on an investment.

PERIODIC ANALYSIS

A consolidated analysis summarizes the benefit of portfolio diversification into an emerging market. Determinants of an efficient return on a diverse portfolio do not stay constant over a period of time. Market influences, political and technological factors play an important role in creating a favorable return. In view of these variances in factors over time, a period analysis would provide an insight on the importance of an investment time frame to be adhered to while making an investment decision.

Period 1. 1991-1997

Period 2. 1998-2003

As the data suggests, benefits of diversification into an emerging market outweigh that of the investment in the domestic market for period 1 and generates similar returns for period 2. Although there is a difference in returns on the two portfolios, it is not very much significant. This may encourage an investor to invest in domestic portfolios as gathering of data on foreign securities are time consuming and expensive in comparison to gathering domestic market information.

Period 3. 2004-2010

In recent years, the benefits of diversification into an emerging market are well described from the historical data obtained. This is primarily due to the rapidly developing nature of world economies with increasing globalization and free transfer of trade and technical “know –how”. This has enabled growing markets to avail resources required to maximize market operations and operate at an efficient level of productivity to developed economies alike. This time period may have also seen suitable conditions in the emerging market from our data on part of transaction costs, exchange rates and interest rates affecting portfolio returns.

RECOMMENDATIONS

Empirical evidence strongly suggests the benefits of international portfolio diversification. But through time, investors have said to prefer domestic portfolio investments over international portfolio diversification. This conclusion is a result of lower percentage of international portfolio holdings in comparison to domestic portfolio holdings by investors (French and Poterba, 1991). Diversification into portfolios in emerging markets are characterized by high volatility, higher returns and extremely high risk. Although, higher returns and lower risks are potentially attainable with international portfolio diversification, investors choose to invest in domestic portfolios as a safer alternative. The reasons for such a bias mainly arises due to lack of information, insufficient exposure to global trends and investment opportunities. Another reason for this favoritism, as supported by finance literature is also transaction costs, exchange rate risks and taxation policies.

In terms of transaction costs, it is viewed as a barrier to international portfolio diversification since investing in domestic portfolios will eliminate these costs being incurred. In the view of Domowitz et al. (2001), the two factors that constitute transaction costs are trading costs and opportunity and timing costs. Although the former might not be tedious in determining. the latter is highly variable in comparison to trading costs and has many factors needing consideration before arriving at an estimate. These factors cannot be easily determined by an individual investor with no in depth and constant up-to-date knowledge on the particular overseas market functioning as this would leave an investor susceptible to ignoring trading subtleties.

In contrast, Tesar and Werner (1995) in their findings. have results confirming high volume of cross border capital flows and the high turnover rate on cross border equity investments relative to turnover on domestic equity markets suggesting that variable transaction costs are an unlikely explanation for lower international portfolio diversification. This indicates that potential investors are not necessarily worried about transaction costs. The explanations proposed in view of high turnover rates in foreign equities are that transaction costs are estimated to be less for institutional investors in comparison to average individual investors and these transactions include derivative securities, which were not included in measurement of domestic turnover rates. These assumptions have not been supported by substantial evidence and have presumed that institutional investors incur less costs, further indicating that individual investors are apprehensive on incurring transaction costs .

On the exchange rate risks faced by an investor due to fluctuations in the price of one currency against another, it is crucial and essential to find out the methods of hedging that can reduce the risk of the portfolio. Hedging strategies can be implemented in three different forms for risk reduction. First, there is the full hedging policy which reduces the unpredictability of returns without decreasing the returns. Second, a unitary hedging strategy can be implemented when there is no correlation between the two exchange rates and the local returns, resulting in the forward premium being a fair predictor of the future exchange rate returns. Finally, the exchange risk rate can be hedged using a conditional hedging strategy, which is based on the forward premium on an assumption that it can predict the expected returns on forward contracts. An example would be a long term investment, when the interest rate currencies are high because the forward premium equals the interest rate differential. Prior information can help us determine the optimal portfolio by analyzing the forward premium using conditional hedging. When we use the fully hedging policy we expect the forward premium to be equal to 1, while the unhedged strategy the forward premium is 0. This result can help us analyze the portfolio weights and therefore the optimal portfolios.(reference)

Moreover, the hedging strategy has contributed to higher mean returns without reducing the risk and in general the performance of the hedging policy is better than that of the unhedged strategy in portfolios.(reference)

LIMITATIONS

The Capital Asset Pricing Model, one of the most accepted asset pricing models, used in our evaluation of expected returns on portfolios, are based on set assumptions that may not hold true under all circumstances. The fundamental basis of the CAPM follows the assumption that investors make decisions only depending on expected return and its variance. Although this might be a major influence on investor decisions, it does not capture all aspects that an investor may consider while making an investment. Also, an assumption of the existence of a risk free asset in the market, is a certain possibility. A risk free rate of return can be obtained, but the real return received by an investor may imaginably be unfavorable if inflationary pressures during that period are high. Moreover, we assume unlimited short sales and lending and borrowing are allowed, which may not hold true in practice. Finally, in view of the estimation on the betas of the stock, variances and covariance’s are obtained using historical data. This does not take into account future changes in these estimates of the beta and are not accurate measures of future unexpected changes.