International Diversification with Value and Growth Indices

International Diversification

with Value and Growth Indices

Master of Science in Business Administration Specialization: Finance

Profile: Risk and Portfolio Management

International Diversification with Value and Growth Indices

Abstract:

This paper investigates whether there exist possibilities to diversify an internationally constructed benchmark portfolio consisting of MSCI country indices by augmenting this portfolio with either value, growth or both indices. The sample consists of value, growth and MSCI country indices from 9 countries spread all over the world during the period of June 1994- June 2008. The mean-variance tests show that diversification possibilities do exist and the benchmark portfolio can be enhanced in terms of risk and return by both value and growth indices. The largest statistically significant enhancement in mean-variance space comes from adding both value and growth indices to the benchmark, which significantly lowers the risk of the benchmark portfolio, though these results are only attained when short sales are allowed.

JEL-codes: C61, G10 and G11

1. Introduction

Numerous papers have been written about international portfolio diver-sification ever since the traditional studies of Grubel (1968), Levy and Sarnat (1970), and Solnik (1974). They documented that gains from international diversification comes from lower correlation between securities internationally, than from securities within one country. They also argue that these benefits outweigh the higher costs, like higher trading cost, currency risks etc. Although there has been rapid growth in international portfolio diversification in recent years, portfolios remain heavily biased towards domestic assets.

Most of the literature on international portfolio diversification takes a US perspective1_{, this paper however will take a more general view on international} diversification benefits by using a benchmark portfolio consisting of different country indices and not only the local country’s stock index. Also in contrast to Driessen and Laeven (2007) this paper does not only diversify by one regional or country index, but with value and growth indices from every country within the dataset.

Value and growth stocks are not clearly defined. The classification of being either a value or a growth stock depends on some general criteria, most of them are related to a company’s multiples. Value stocks are stocks that trade at a discount with respect to their fundamentals (i.e. dividends, earnings, sales, etc.) and are considered undervalued by the investor. According to Lakonishok, Shleifer, and Vishny (1994) investors can overreact to stocks that have done very well or very bad. Value investors buy the undervalued stocks before the market corrects them. A value investor thus believes that the market is not always efficient and that it is possible to find companies trading for less than their value.

Growth stocks are stocks that have shown a faster-than-average earnings growth rate in the last few years and is expected to continue to show high levels of profit growth. A growth stock usually does not pay a dividend, as the company

1

would prefer to reinvest retained earnings in capital projects. Historically the returns of value and growth stocks do not significantly outperform the other, however empirical studies showed that value stocks outperformed growth stocks2

. Petkova and Zhang (2005) found that value betas tend to covary positively, and growth betas tend to covary negatively with the expected market risk premium. This indicates that value and growth have a low correlation which creates an opening for diversification with value and growth stocks.

The majority of the papers about international diversification is focused on national indices or large-cap stocks, however national indices and large-cap stocks are mostly driven by common global factors and therefore the gains from diversification will be limited. In difference to Eun, Huang and Lai (2006) this paper tries to find diversification benefits through the use of value and growth indices instead of small-cap and mid-cap stocks. Value and growth investing are both well-known and successful investing strategies. It is however still not clear which type of investing is more successful than the other. Empirical evidence found that value stocks outperformed growth stocks. However historically seen there are periods in which the growth stocks outperformed the value stocks. The time period used in this paper, from June 1994 till June 2008, includes the internet bubble of the late 1990’s and during the internet bubble the growth stocks outperformed the value stocks. Since both asset classes can outperform the other from time to time, this creates an opportunity for diversification by using value and growth stocks. Therefore this paper will find out if diversification benefits exist from adding value and/or growth stocks to a benchmark portfolio. Furthermore the empirical evidence about value versus growth investing concentrates mostly on value premiums (within countries). This paper focuses on the international diversification benefits (reduction in risk and increase in return) achieved from augmenting the value and/or growth indices into one international portfolio instead of finding the value premium.

2

The purpose of this paper is therefore to see if an investor who diversified his investments internationally through MSCI3

country indices can benefit from augmenting his investments with international value and/or growth indices. This paper therefore investigates the following central question: Can an investor achieve additional gains from international diversification by adding value indices, growth indices or both to the investor’s portfolio. If an investor can diversify with value and growth stocks, then this paper will also try to find out if value stocks offer more diversification benefits than growth stocks or vice versa.

This paper will investigate the central question on a set of 9 developed countries namely; Australia, Canada, France, Germany, Italy, the Netherlands, Singapore, Sweden, and the United States. The sample consists of two countries from North America, two from Asia/Pacific, and five from Europe. These countries have a relatively open capital market with no formal barriers of investing within these countries. Each country has his own MSCI country, value, and growth index for the 14 year period of June 1994-June 2008.4 _{The analysis} consists of several steps. First the risk-return characteristics and correlation structure are examined, after that value and growth indices of all countries are tested on whether they are spanned or not by the MSCI country indices. Next optimal portfolios are formed by augmenting the benchmark portfolio consisting of MSCI country indices by either value, growth, or both indices. The last step is a mean-variance analysis on different types of portfolios to check if there are improvements in risk and return by augmenting the benchmark portfolio.

First, the correlations seem relatively high (Eun, Huang and Lai (2006) show correlations of as low as 0.08, while in this dataset the lowest correlation is still 0.31). The correlation structure shows that value and growth indices have a lower average correlation internationally with each other than with the MSCI country indices. This is also true for domestic indices. The lowest average correlation exists between international value and growth indices. The spanning

3

MSCI stands for Morgan Stanley Capital International. 4

test results show that some, but not all of the countries value and growth indices cannot be spanned by MSCI country indices; in particular the Netherlands and Sweden.

Next, to assessing the potential of augmenting the benchmark portfolio with value and growth indices in mean-variance space, the optimal portfolios are formed. The Sharpe test shows that only the optimal portfolio comprising value, growth and MSCI country indices with short sales allowed has improved their performance significantly. The mean-variance test shows that the augmented portfolios with short sales allowed perform better in both risk and return space. In the portfolios without short sales allowed the mean-variance test gives no significantly better performance in both risk and return. The results thus show that an investor can diversify by augmenting value and growth indices. The mean-variance test between the portfolios where the value indices are added to the benchmark portfolio and the portfolio where the growth indices are added to the benchmark portfolio shows that the portfolio where the value indices are augmented performs slightly better than the portfolio where the growth indices are augmented, however these results are insignificant with and without short sales allowed. The mean-variance test between value and growth indices indicate that value indices are a more valuable addition to the benchmark portfolio than growth indices. Value indices are slightly better than growth indices in risk and return, however only when no short sales are allowed are the results significant with respect to the risk.

Most of these results remain robust when the data is split into two periods from June 1994-June 2001 and July 2001- June 2008. The only differences are found in the assignment of weights in the optimal portfolios in both periods, and there is no clear winner according to the mean-variance test between the value and growth indices.

mean-variance test methodology the results of these tests are also presented here. Section 6 provides a robustness check of the results. Finally, section 7 offers some concluding comments.

2. Literature

This section first describes the theory behind, and previous literature written, about international diversification plus some empirical results. Also this section describes how this paper is similar and/or different to other papers mentioned. After that the literature and definitions of value and growth stocks is presented. The literature section closes with the presentation of the hypotheses.

A. International diversification

variation in index returns. For industries which produce goods traded internationally the variance of industry factors is relatively larger.

Brooks and Del Negro (2006) however show in their article that the low degree of co-movement across national stock markets has broken down. More large internationally oriented companies feel global shocks in every country, whereas small companies are more sensitive to country-specific shocks. The large companies that all feel the same global shocks determine the national stock market for the largest share. So co-movement between national stock markets becomes stronger as the large companies become more internationally oriented. This should mean that international diversification should become less attractive to investors. Nevertheless, as is shown in Brooks and Del Negro’s (2006) article, this co-movement is mainly for large, internationally oriented companies (the large-cap companies). Eun, Huang and Lai (2006) show in their paper that it is still possible to obtain diversification benefits through the use of small-cap stocks. National indices and large-cap stocks are mostly driven by common global factors and therefore the gains from diversification will be limited, but small-cap stocks are driven by country-specific factors, since they are less internationally exposed, so there are diversification benefits obtainable. This paper generally follows the work done by Eun, Huang and Lai (2006), but with different data. The focus here is not on stocks from companies with different sizes (small-, mid- and large-cap), but on companies who are classified as value or growth stocks. The returns of the value and growth companies are indexed in national value and growth indices. From the viewpoint of an investor who already invested in an international portfolio consisting of MSCI country indices, this paper researches if international diversification benefits exist by adding either value, growth or both indices to the portfolio of MSCI country indices.

expected rate of return for any given level of risk. The costs of international diversification include currency risks (foreign exchange rates have fluctuations which themselves generate variability in foreign returns), political factors, regulatory and cultural differences, and higher trading costs5

. This paper approaches the optimal asset distribution on a theoretical basis and excludes all of the above mentioned costs, its main focus are the international diversification benefits. The only cost that is accounted for is the short sales constraint. This is taken into account for three different reasons; namely illiquidity of the portfolio through excessive short sales, rise of volatility in asset values which could cause alterations in correlations and mean-variance efficiencies, and last because of legal restrictions to short selling by governments. The optimal asset distribution is given with and without short sales constraints, to see whether the diversification benefits disappear through imposing short sale constraints to the portfolio.

Previous empirical evidence6

showed that domestic investors can improve investment performance by including foreign assets in a portfolio when short sales are not allowed. The paper of De Roon et al. (2001) shows by using mean-variance spanning tests that, after imposing short sales constraints, there are still diversification benefits in some individual emerging markets, but not in an optimal combination of these markets. Using either the reduction in risk or the increase in expected return measure, Li et al. (2003) find that the diversification benefits of emerging equity markets remain substantial after imposing short sales constraints in these markets. The results hold when they limit their analysis to investable stocks, that is stocks that are available to nonnative investors and meet minimum size and liquidity criteria. The result is also unaffected by the fact that the U.S. equity index portfolio is not on the efficient frontier spanned by U.S. securities. The integration of world equity markets reduces, but does not eliminate, the diversification benefits of investing in emerging markets subject to short sales constraints.

By using the international CAPM, De Santis and Gerard (1997) estimated that the expected gain from international diversification to a U.S. investor is on

5

These are costs mentioned in Reeb, Kwok, and Baek, (1998). 6

average 2.11% annually. Errunza et al. (1999) further show that the international diversification benefits can be obtained from investment in country funds as well as investing in American Depository Receipts traded in the U.S. Two major theories in the finance literature, the Capital Asset Pricing Model (CAPM) and the Modern Portfolio Theory (MPT), suggest that individual investors should hold a well-diversified portfolio to reduce risk. Individual investors with limited wealth will have to find a way that does not require substantial funds to diversify their portfolios. Mutual funds offer a quick and relatively inexpensive way to diversify for small investors. Mutual fund companies achieved very large rates of return on their investments during the mid to late 1990s. It should be made clear that while performances of these mutual funds over the long haul vary, it is still true that diversification reduces risk at a given level of return. This paper however uses international equity indices instead of mutual funds, because, according to Cumby and Glen (1990), diversifying internationally through investing in mutual funds brings no more gains than investing in an international equity index.

B. Value and growth stocks

How to define stocks as either value or growth stocks? There are no hard definitions, but investors do define both categories on some general criteria and characteristics. Value stocks are stocks that tend to trade at a lower price relative to its fundamentals (i.e. dividends, earnings, sales, etc.) and thus considered undervalued by a value investor. Those value stocks are often neglected by institutional investors and have limited information available (Arbel et al., 1983). Common characteristics of such stocks include:

• A low price to cash-flow (P/C), price to earnings (P/E), and price-to-book (P/B) ratio7_{; the price to earnings ratio (P/E) should be in the bottom 10%} of all companies.

• A price to earning growth (PEG) ratio should be less than 1 (which indicates the company is undervalued).

7

• There should be at least as much equity as debt. • Current assets at twice current liabilities.

• High dividend yield.

According to Lakonishok, Shleifer, and Vishny (1994) investors can overreact to stocks that have done very well or very bad. Value investors buy the undervalued stocks before the market corrects them. A value investor thus believes that the market is not always efficient and that it is possible to find companies trading for less than their value. Value stocks however are not cheap stocks. Investors like to think of value stocks as bargains; the market has under valued the stock for a number of reasons and the investor hopes to get in before the market corrects the price.

Growth stocks are stocks of corporations that have exhibited faster-than-average gains in earnings over the last few years and are expected to continue to show high levels of profit growth. A growth stock usually does not pay a dividend, as the company would prefer to reinvest retained earnings in capital projects. Some general indicators of growth stocks include:

• A high price to cash-flow (P/C), price to earnings (P/E), and price-to-book (P/B) ratio.8

• High growth rate, both historic and projected forward. Historically, you want to see smaller companies with a 10%+ growth rate for the past five years and larger companies with 5% - 7% growth rate.

• High Return on Equity compared to the industry.

• High earnings per share, pre-tax margins should exceed the past five-year average and the industry average.

• Low dividend yield.

8

The investor will usually expect a growth stock to be an ordinary share in a company whose products are selling well and whose sales are expected to expand, whose capital expenditure on new plant and equipment is high, whose earnings are growing, and whose management is strong, resourceful, and investing in product development and long-term research. Most technology companies are growth stocks. The optimal portfolios formed in this paper however do not contain value or growth stocks. Instead national value and growth indices are used to prevent classification errors between value and growth stocks.

Historically, there have been periods when growth stocks have done well and other periods when value stocks outperformed, no one performed clearly better than the other. Empirical evidence about value and growth stocks presents other results. Chan, Hamao, and Lakonishok (1991), Fama and French (1992), Lakonishok, Shleifer, and Vishny (1994) and Fama and French (1998) all performed empirical tests between value and growth stocks on their variables (B/M, E/P, C/P and D/P) and showed that value stocks outperformed the returns of growth stocks. Both Fama and French (1992) and Lakonishok, Shleifer, and Vishny (1994) show that the value premium is associated with relative distress. Furthermore they analysed the betas for these companies and found that the betas have a flat relation with the returns. Petkova and Zhang (2005), on the other hand, find that value betas tend to covary positively and growth betas tend to covary negatively with the expected market risk premium. This indicates that value and growth stocks have a low correlation which creates an opening for diversification with using both value and growth stocks.

C. Hypotheses

As mentioned in the introduction of this paper, the main question of this paper is: Can an investor achieve additional gains from international diversification by adding value indices, growth indices or both to the investor’s portfolio. Also if an investor can diversify with value and growth stocks than this paper will try to find out if adding value stocks offer more diversification benefits than adding growth stocks or vice versa. The review of the literature above does not give a clear cut view as to whether value stocks can always outperform growth stocks or vice versa. Therefore the central question of this paper will be researched by three hypotheses. These hypotheses are:

1

H : Adding value indices to an investor’s portfolio of MSCI country indices offers significant diversification benefits.

2

H : Adding growth indices to an investor’s portfolio of MSCI country indices offers significant diversification benefits.

3

H : Adding growth and value indices to an investor’s portfolio of MSCI country

indices offers significant diversification benefits.

most diversification benefits. This is researched according to another set of hypotheses, namely:

4

H : Adding value indices to an investor’s portfolio of MSCI country indices offers an investor significantly more diversification benefits than adding growth indices.

5

H : Adding growth indices to an investor’s portfolio of MSCI country indices offers an investor significantly more diversification benefits than adding value indices.

3. Data and Descriptive Statistics

This section describes the dataset used in this paper. Their source, availability and legitimacy will firstly be discussed. Next, the descriptive statistics of the dataset will be presented and discussed, as will be the cumulative performance figure of the asset classes.

A. Source, availability and legitimacy

The data set of this paper includes monthly index values and returns of value, growth and MSCI country indices from the nine countries (Australia, Canada, France, Germany, Italy, the Netherlands, Singapore Sweden and the U.S.) used during the sample period of June 1994-June 2008. These index values and returns are obtained from Thomson’s DataStream, as are the U.S. Treasury-Bill rates, which are averaged over the sample period to proxy for the risk-free interest rate. There is no need to form country, value and growth indices by myself since American business bank Morgan Stanley has already done this in the shape of their MSCI country, MSCI value, and MSCI growth indices. These indices are readily available for each country in the sample set. Until the end of May 2003 the value and growth stocks where classified according to one single measure, the price to book ratio. Hereafter is the methodology of determining value and growth stocks improved to a set of eight variables, three for value stocks and five for growth stocks (see Appendix B). The value and growth indices are value weighted indices, each targeting 50% of the free float-adjusted market capitalization of the underlying indices. The market capitalization of each stock is fully represented in either the value, growth or in both indices (without double counting). According to the new set of variables it is possible that a security is represented in both indices at partial weight.

sufficient data for this type of research. The same benchmark for missing values is used as in the paper of Eun, Huang and Lai (2006), where they treat returns greater than 400% as missing values due to errors in DataStream. This leads to zero missing values in this paper’s dataset. The basis for the chosen countries comes also from the paper of Eun, Huang and Lai (2006). In that paper the sample countries are: Australia, Canada, France, Germany, Hong Kong, Italy, Japan, the Netherlands, the U.K. and the U.S. From these countries, Hong Kong and the U.K. are replaced by Sweden and Singapore. Japan was originally a part of the sample countries but was taken out of the country set halfway the research because it led to infeasible results9

. For each country used the data is complete and freely accessible.

B. Descriptive statistics

Summary statistics of each type of index are presented in table 1.

[INSERT TABLE 1 ABOUT HERE]

Panel A of Table 1 reports the annualized mean ( R ) and standard deviation (σ) of the returns, the Sharpe ratio (SHP), and the index’ correlation with the MSCI World market index (ρ_world) for every country within each index. First, if we look at the annualized returns the first thing to mention is that neither value nor growth outperforms the other in all countries. In about half of the countries can we see that the annual return of growth is higher than the annual return of value, in the other half of the countries this observation is reversed. So there can be no straight up conclusions made purely by looking at the annualized return figures about which type of asset class will perform better in an optimal portfolio. The annualized returns of the MSCI country indices generally perform worse than the value indices and better than the growth indices with the exception of Australia (the MSCI country index performs worse than both the

9

value and growth index) and Sweden (the MSCI country index performs better than both value and growth index). The largest returns are shown by the Netherlands (12.4%) for the value indices, Canada (12.6%) for the growth indices, and Sweden (12.3%) for the MSCI country indices. The smallest returns are shown by the U.S. (6.2%) for the value indices, and Singapore for both the growth indices (1.8%) and the MSCI country indices (5.0%). The cross-country average of mean returns is 9.2% for value indices, 7.4% for growth indices, and 8.3% for MSCI country indices.

The second column of Panel A presents the annualized standard deviations. The same observation as with the annualized returns can be made here. In about half of the countries the value indices have higher return volatility than the growth indices, in the other half this is vice versa. Remarkable is the fact that for France, Germany, Italy, and Sweden the MSCI country indices show lower return volatilities than the growth indices, but have higher returns than the growth indices of these countries. This implies that the MSCI country indices of France, Germany, and Italy are less risky investments than the growth indices of these countries. The largest return volatilities are shown by Singapore for the value indices (29.0%) and the MSCI country indices (25.7%), Sweden has the largest return volatility for the growth indices with a volatility of 35.0%. Australia has the smallest return volatilities for all three asset classes, namely 14.3%, 15.3%, and 12.6% for the value, growth and MSCI country indices respectively. The cross-country average of return volatilities is 20.0% for value indices, 22.7% for growth indices, and 20.0% for MSCI country indices.

The third column presents the Sharpe ratio (SHP). This measure shows that the value indices outperform the growth indices in all countries except the U.S. The Netherlands has a great contrast in performance between their value and growth index. Their Sharpe ratio for the value index is the second best with a ratio of 0.39, while their Sharpe ratio for the growth indices is second worst with a ratio of -0.0410_{. The Sharpe ratio indicates that in most countries the MSCI} country indices outperform the growth indices, and that the value indices

10

outperform the MSCI country and growth indices. This has become a common observation, it appears that the MSCI country indices, as an asset class, fall somewhat in the middle of the value and growth indices through performing somewhat better than the growth indices and somewhat worse than the value indices.

The last column presents the correlation of the indices with the MSCI World market index. The MSCI country indices have the highest correlation to the MSCI World market index with an average correlation of 0.80 and the growth indices the lowest (average correlation of 0.74). The value indices fall in between (with an exception of Italy and the U.S.) with an average correlation of 0.76.

Panel B of Table 1 presents the average correlation between the three asset classes. The up-right triangle corresponds to domestic correlations, while the lower-left triangle corresponds to international correlations. These correlations are averaged from the complete correlation matrix which can be found in Appendix A. The average international correlation is 0.71 between MSCI country indices, 0.67 between value indices, and 0.64 between growth indices. The lowest average international correlation is between value and growth indices, 0.62. The average international correlation of MSCI country indices is 0.68 with value indices and 0.67 with growth indices. These results imply that to achieve the most international diversification benefits, in terms of reducing the portfolio risk, it would probably be more effective to augment both growth and value indices into the benchmark portfolio, than it would be to augment only the value or growth indices into the benchmark portfolio.

To get a better view of how the indices have performed Figure 1 has been made.

[INSERT FIGURE 1 ABOUT HERE]

Figure 1 shows the average cumulative performance of the MSCI country, value, and growth indices over the sample period. Figure 1 shows for all three asset classes that they follow approximately the same pattern throughout the sample period. As can be seen from Figure 1 the patterns show approximately 5 years of value build-up from around June 1995 till June 2000, which can be related to the internet bubble. At the peak of the internet bubble we can see that the growth indices have performed the best. After those 5 years of bull market there is a 3 year ‘market adjustment’ period from around June 2000 until June 2003 where all the stocks from the asset classes are losing their overvalue. Following these ‘market correction’ years, the market starts rising again for about 4 years until June 2007, followed by one last year of decreasing returns. Over the entire sample period it is clear that the value indices performed the best and the growth indices performed the worst, with the MSCI country indices falling in between. This is a common feature of this dataset, which was already mentioned above in the discussion of Panel A of Table 1.

4. Mean-Variance Spanning

test. Huberman and Kandel (1987) provide the regressional framework to test for mean-variance spanning. The second part of this section will present and discuss the results from the mean-variance spanning test.

A. Mean-Variance Spanning Test Methodology

The literature on mean-variance spanning and intersection analyzes the effect that the introduction of additional assets (in this case the value and growth indices) has on the mean-variance frontier of the benchmark portfolio, here consisting of MSCI country indices. If the mean-variance frontier of the benchmark assets and the frontier of the benchmark plus the new assets have exactly one point in common, this is known as intersection. This means that there is one mean-variance utility function for which there is no benefit from adding the new assets11

. If the mean-variance frontier of the benchmark portfolio plus the new assets coincides with the frontier of the benchmark portfolio only, there is spanning. In this case, no mean-variance investor can benefit significantly from adding the new assets to his portfolio of benchmark assets only (DeRoon and Nijman (2001)). However if spanning is rejected, then the additional assets can statistically significant enhance the performance of the benchmark portfolio. By following the framework presented by Huberman and Kandel (1987), an OLS regression of the new asset (value or growth index) on the benchmark assets (the MSCI country indices) is performed to test for mean-variance spanning:

i US US i AU AU i i i MSCI MSCI R =α +β * +...+β * +ε (1)

Where R_i denotes the return of the value or growth index for country i,

AU

MSCI ( US

MSCI ) is the return of the MSCI country index for Australia (the United States), α_iis the estimated intercept of the regression for country i,

11

AU i

β ( US i

β ) is the regression coefficient associated with AU

MSCI ( US

MSCI ) for country i, and ε_iis the residual. To test the regression on spanning, we test the null hypothesis which is a joint hypothesis that α_i is equal to zero and the sum of

i

β is equal to one:

0

H : α_i= 0, and Σ_iβ_i = 1 (2)

If this hypothesis is rejected there is no spanning and the additional asset can statistically significant enhance the performance of the benchmark portfolio. According to Kan and Zhou (2001), when there is only one new asset the distribution of the likelihood ratio test under the null hypothesis is set by12_:

      − −       − = 2 1 1 1 T K U F (3)

Where U denotes the ratio of the determinant of the error covariance matrix of the maximum likelihood estimator for the unrestricted model (no spanning) to that of the constrained model (spanning), T is the number of observations, and K is the number of benchmark assets. The test statistic follows an F-distribution with (2, T-K-1) degrees of freedom13

. These restrictions could also have been tested by the use of a standard Wald test, which is asymptotically chi-squared distributed with two degrees of freedom. However the sample is finite and asymptotic tests can be misleading in finite samples (Galema,

12

The F-statistic used in EViews is given by:

(

)

(

)

, where SSE_Ris the restricted sum of squared errors, SSE_U is the unrestricted sum of squared errors, J is the number of hypotheses, T is the number of observations, and K is the number of benchmark assets. The statistic follows an F-distribution with (J, T-K-1) degrees of freedom. This statistic is used for both the hypothesis of ∑βi =1 where J equals one, and for αi= 0 and Σiβi = 1

where J equals two. 13

Plantinga and Scholtens, 2009). Furthermore the F-statistic of Huberman and Kandel (1987) has a finite sample distribution.

B. Mean-Variance Spanning Test Results

The results of the mean-variance spanning test are presented in Table 2.

[INSERT TABLE 2 ABOUT HERE]

Table 2 reports the alphas and betas of the mean-variance spanning test, the Wald statistic and its p-value for the hypothesis that Σ_iβ_i=1, and the F-statistic and its p-value for the joint hypothesis that α_i= 0, and Σ_iβ_i = 1. Panel A of Table 2 reports the mean-variance spanning test results for value indices from each country of the sample set and Panel B reports the test results for the growth indices. In Panel A spanning is rejected for the Netherlands at the 1% level of significance, for Sweden at the 5% level of significance, and for France and Singapore at the 10% level of significance. In Panel B spanning is rejected for the Netherlands and Sweden at the 1% significance level, and for Canada at the 5% significance level. The results show that some, but not all, value and growth indices presents diversification possibilities. The extent of these possibilities, whether it will be a reduction in risk or an increase in return of the portfolio, will be examined in the next section where the value and growth indices are added to the benchmark portfolio. The joint restrictions test for spanning of all value or growth indices rejects the hypothesis that all the indices are spanned. Both type of indices reject the joint restrictions test for spanning at the 1% significance level. This result is also found for the joint restrictions test for ∑βi =1.

country index at the 1% significance level. This indicates that the returns of the value and growth indices are for a large share determined by their own MSCI country index. Each value index has a positive and significant beta against the MSCI country index of the Netherlands except Singapore (positive but not significant) and Australia. Also each value index except Sweden has a positive beta against the MSCI country index of the U.S. Each growth index except Australia (negative but significant), the Netherlands (negative), and Singapore (positive but not significant) has a positive and significant beta against Sweden’s MSCI country index. According to the F-statistic and p-value for the hypothesis that ∑β_i =1, the sum of the beta’s is significantly different from 1 for the Netherlands at the 1% significance level and for Canada, France, and Sweden at the 5% significance level for the value indices. For the growth indices is the sum of the beta’s significantly different from 1 for the Netherlands and Sweden at the 1% significance level, for Canada at the 5% significance level, and for the U.S. at the 10% significance level.

provide the results as to which asset class, value or growth indices, provides the most diversification benefits.

A. Modern Portfolio Theory

As can be seen from the results of the mean-variance spanning test, adding international value and growth indices to the benchmark portfolio can provide significant diversification benefits. To examine the extent of these diversification benefits we form optimal portfolios following the framework of modern portfolio theory. Modern portfolio theory (MPT) was first developed by Markowitz (1952,1959) and Tobin (1958), and extended by Sharpe (1964,1973), Lintner (1965) and Mossin (1966).

MPT assumes that investors are rational, and risk averse and markets are efficient. Furthermore MPT assumes that the investors preferences of risk and return can be illustrated through a quadratic utility function, so the investor only cares about the volatility and expected return and not about other characteristics of the return distribution. MPT uses diversification in investing to try to maximize the return and minimize the risk by investing in different types of assets. The different type of assets have collectively lower risk than an individual asset because the different asset types are not perfectly correlated. For specific quantitative definitions of risk and return MPT can explain how to find the best diversification strategy.

Mathematically speaking, the optimal asset allocation rule according to Markowitz under mean-variance preferences is:

[ ]

[

]

α is the optimal portfolio of risky assets, θ is the investors index to risk averseness, P is a given probability measure, X is the vector of returns on the risky assets, R is the return on the risk-free asset, and 1

r

is a vector of ones. This paper adjusts the formula of Markowitz to the following formula with the use of matrices used by Benninga (2008):

{

}

{

}

[

]

Where X is the optimal portfolio of risky assets, −1

S is the inverse of the variance-covariance matrix, E(r) is a vector with the expected returns of the risky assets, and c equals the return of the risk-free asset.14

The portfolio return is the sum of the assets weight in the portfolio times its expected return:

) ( ) ( 1 i i N i p xE r r E = Σ = (6)

Where E(r_p)is the expected return of the portfolio, x_i is the weight in the portfolio of asset i and E(ri)is the expected return of asset i. In matrix notation this comes to:

) ( ) (r X E r E p = T (7) 14

Where E(rp)is the expected return of the portfolio,

T

X is the transposed matrix of the optimal portfolio weights and E(r) is a vector with the expected returns of the risky assets. The portfolios variance is given by the following formula: ij j i j i N j N i p x x σ σ ρ σ2 =ΣΣ or _{i j ij} N j N i p xxσ σ2 =ΣΣ (8) Where 2 p

σ is the variance of the portfolio, σ_i is the volatility of asset i, σ_j is the volatility of asset j, ρ_ij is the correlation between assets i and j, and σ_ij is the covariance between assets i and j. As can be seen from formula (8), with less than perfect correlation the variance of the portfolio is less then the weighted average of each individual asset’s variance, hence showing the major benefit of portfolio diversification. In matrix notation the variance is:

X S XT p 1 2 = − σ (9) Where 2 p

σ is the variance of the portfolio, XT is the transposed matrix of the optimal portfolio weights, −1

S is the inverse of the variance-covariance matrix and X is the optimal portfolio of risky assets. Following from formula (8) and (9) the portfolio’s standard deviation is:

2

p

p σ

σ = (10)

portfolio that can improve both risk and return. The region below the frontier is suboptimal and the region above the frontier is unachievable by holding risky assets alone. Therefore a rational investor will hold only portfolios that are on the frontier. The efficient frontier is convex because the risk-return characteristics of a portfolio change non-linear when the asset weights change.

The portfolio with the highest Sharpe ratio on the efficient frontier is known as the market portfolio. When this portfolio is combined with the risk-free asset you get the Capital Market Line (CML). All points along the CML have superior risk-return profiles to any portfolio on the efficient frontier. Only the special case of the market portfolio with zero cash weighting is on the efficient frontier. This portfolio is the optimal portfolio we are looking for. To verify whether the new portfolio has significantly increased the Sharpe ratio of the benchmark portfolio, a Sharpe ratio test is performed. This is a student’s T-test for equal means in the Sharpe ratio of the benchmark and the augmented portfolio.

B. Optimal Asset Allocation

The results of the optimal portfolios are presented in Table 3.

[INSERT TABLE 3 ABOUT HERE]

(-129.4%), the U.S. (-127.1%), and Germany’s MSCI country index (-106.5%). The MSCI country indices of Canada and Sweden thus appear to be the best performing indices. This is in line with the descriptive statistics where it is shown that Canada and Sweden have the largest Sharpe ratio of all MSCI country indices. The portfolio has a mean return of 2.990% (1.093%), a volatility of 15.339% (5.985%), and a Sharpe ratio of 0.174 (0.129) for the portfolio with (without) short sales allowed.

The fourth and fifth column represent the optimal portfolios of the value indices with and without short sales. Without short selling the optimal portfolio is comprised with investing 40.8% in Canada’s value index, 35.2% in Sweden’s value index, and also 24.0% in the value index of the Netherlands. With short sales allowed the same 3 countries as without short selling receive positive weights in the optimal portfolio, Canada (300.6%), the Netherlands (171.4%), and Sweden (131.9%). The U.S. has the largest negative position in the portfolio (-313.7%). The value portfolio has a mean return of 2.766% (0.993), which is lower than the benchmark mean return, and a volatility of 13.763% (5.319%), which is lower than the benchmark volatility, for the portfolio with (without) short sales allowed. The Sharpe ratio of the value portfolio with short sales allowed is 0.178. The reduced risk is the main factor for the greater Sharpe ratio. The Sharpe ratio of the value portfolio without short selling is 0.127 which is slightly less than the Sharpe ratio of the benchmark portfolio.

Columns six and seven of Panel A represent the optimal growth portfolios with and without short selling. The growth portfolio without short selling allocates weights of 69.7% to Canada, 6.6% to Sweden, and also 23.7% to Australia’s growth index. With short sales allowed all three above mentioned countries receive positive weight in the portfolio. Remarkable is however that the growth indices of France (386.4%) and the U.S. (264.6%) receive large positive weights when short sales are allowed and no weight when short sales are restricted.

Furthermore Italy (-319.0%), the Netherlands (-586.5%) and Singapore (-409.8%) receive large negative positions in the optimal growth portfolio. These

risk (42.403%) since the Sharpe ratio of the growth portfolio, of 0.172, is smaller than the Sharpe ratio of the benchmark portfolio. The mean return of the growth portfolio without short selling is 1.029% and the volatility is 7.138%. These numbers are both worse than the portfolio of MSCI country indices and thus explain the lower Sharpe ratio of 0.099.

The results of Panel A of Table 3 do not indicate that the value and growth indices on itself are much better investment types in risk-return space than the MSCI country indices. The next step to assessing the potential diversification benefits of the value and growth indices is to augment them into the benchmark portfolio. This is done in Panel B of Table 3. Panel B reports the results of the augmented portfolios of MSCI and value indices, MSCI and growth indices, and MSCI, value and growth indices. Panel B also shows the weights, the mean portfolio return, the portfolio volatility and the Sharpe ratio, but in addition to this Panel B presents a T-statistic with p-value for a Sharpe ratio test. This is a student’s T-test for equal means in the Sharpe ratio of the benchmark (MSCI country indices) and the augmented portfolio and measures whether the increase in the Sharpe ratio is significant.

The second and third column show the optimal portfolios consisting of MSCI country indices augmented with value indices, with and without short sales allowed respectively. Without short sales allowed the optimal portfolio consist of 58.9% invested in the Canada MSCI country index, 22.8% in Sweden’s value index and 18.3% in the value index of the Netherlands. So in contrast to the benchmark portfolio the value indices of Sweden and the Netherlands receive weight in the optimal portfolio and the MSCI country index of Sweden is taken out of the portfolio when the value indices are added. The switch from Sweden MSCI country index to the value index is most likely due to the decrease in risk that Sweden’s value index has opposite to its MSCI country index.

underperformance to the U.S. MSCI country index. The rest of the value indices all receive rather large positive weights when they are augmented to the MSCI country indices, with the Netherlands (635.9%) as the main share of investment. Four MSCI country indices receive a negative weight (Germany, Italy, the Netherlands and Singapore), versus the other five who receive a positive weight. The portfolio has a mean return of 8.123% (1.082%), a volatility of 24.870% (5.583%), and a Sharpe ratio of 0.314 (0.137) for the portfolio with (without) short sales allowed. The increase in the Sharpe ratio from 0.174 to 0.314 for the portfolio with short selling comes from more mean excess return per standard deviation of return. The increase is statistically insignificant with a T-statistic of -1.277 and a p-value of 0.203. The increase in the Sharpe ratio from 0.129 to 0.137 for the portfolio without short sales allowed comes from the decrease in risk. This increase is also statistically insignificant with a T-statistic of -0.067 and a p-value of 0.947. Although the Sharpe ratio of both the portfolio with and without short selling has increased when value indices are augmented to the benchmark portfolio, both ratios have not increased significantly. Therefore hypothesis 1 of this paper can not be confirmed here.

The fourth and fifth column show the optimal portfolios consisting of MSCI country indices augmented with growth indices, with and without short sales allowed respectively. Without short sales allowed the optimal portfolio consist of 84.2% invested in the Canada MSCI country index, 15.8% in the Sweden MSCI country index and no investment in any of the growth indices. So growth indices are redundant if an investor already has a portfolio of MSCI country indices.

short. The other MSCI country indices all receive a positive position in the optimal portfolio with Canada (991.4%) as the main investment.

The portfolio has a mean return of 9.126% (1.093%), a volatility of 28.940% (5.985%), and a Sharpe ratio of 0.304 (0.129) for the portfolio with (without) short sales allowed. The increase in the Sharpe ratio from 0.174 to 0.304 for the portfolio with short selling comes mainly from short selling the growth indices and using the funds for investment in MSCI country indices. The increase is however statistically insignificant with a T-statistic of -1.190 and a p-value of 0.235. The Sharpe ratio of the portfolio without short sales allowed is the same as the Sharpe ratio of the benchmark portfolio. This is because the growth indices are redundant when no short selling is allowed and therefore cannot enhance the performance of the portfolio in mean-variance efficiency. When growth indices are augmented to the benchmark portfolio the Sharpe ratio of the portfolio without short selling has not improved and the Sharpe ratio of the portfolio with short sales allowed did improve, but not statistically significant. Therefore hypothesis 2 of this paper can not be confirmed right now.

The sixth and seventh column show the optimal portfolios consisting of MSCI country indices augmented with value and growth indices, with and without short sales allowed respectively. Without short sales allowed the optimal portfolio consist of 58.9% invested in the Canada MSCI country index, 22.8% in Sweden’s value index and 18.3% in the value index of the Netherlands. This is exactly the same portfolio as the one consisting of only MSCI country and value indices without short sales allowed. As already could be seen from column 5 of Panel B, and mentioned above, the growth indices are redundant in a portfolio of MSCI country indices without short sales allowed. Augmenting value indices into that portfolio does not utilize the growth indices, they remain redundant.

value indices; and Australia, France, Singapore and the U.S. receive a positive weight for the growth indices. There is no asset class that receives only positive or negative weights. However there are great differences in the magnitudes per asset class. The MSCI country index of Canada receives a positive position of 2015.6% while the MSCI country index of Singapore receives a negative weight of -1619.4%. For the value indices the largest (smallest) investment is 977.3% (-729.3%) for Singapore (Canada); and for the growth indices the largest (smallest) investment is 475.6% (-916.1%) again for Singapore (Canada). To hold an extreme portfolio like this one is not a realistic investment opportunity for a small investor. Large investment companies however should be able to hold and maintain such an optimal portfolio. The combined investment in the MSCI country indices is 924.2%, in the value indices 91.2%, and in the growth indices -915.4%. These extreme weights can only be obtained if there are unrestricted short sales possibilities. This shows that an investor’s main benefit from augmenting the value and growth indices into the benchmark portfolio comes from short selling growth indices to generate funds for increased investment in MSCI country and value indices.

To get a visual look at how the optimal portfolios perform in mean-variance space Figure 2 illustrates what is analyzed above.

[INSERT FIGURE 2 ABOUT HERE]

Panel A of Figure 2 shows the efficient frontiers of the benchmark and the augmented portfolios with short sales allowed. All three efficient frontiers of the augmented portfolios lie above the efficient frontier of the benchmark portfolio consisting of MSCI country indices. Panel A shows that the efficient frontiers of the MSCI country and value indices, and the MSCI country and growth indices are very similar. It can not be seen from the efficient frontiers which asset class is better to diversify with when short sales are allowed. One thing that is obvious is the performance of the portfolio consisting of MSCI country, value and growth indices which is clearly better than the other portfolio combinations. Panel B of Figure 2 presents the efficient frontiers of the benchmark and the augmented portfolios without short sales allowed. All efficient frontiers lie close to each other, there are no significant differences between the frontiers. The frontiers of the benchmark portfolio and the MSCI country and growth indices portfolio seem to converge. The efficient frontier of the MSCI country and value indices, and the efficient frontier of the MSCI country, value and growth indices15 _{are located} slightly above the frontiers of the other two portfolios but are not significantly better. Again it is not possible to say which asset class is the best to diversify with when short sales are not allowed.

C. Mean-Variance Test

The preceding part about the optimal asset allocation has shown that adding value and growth indices can make a significant improvement to the

15

performances of a benchmark portfolio. What the optimal asset allocation does not show is whether the better performances are due to an increase in return or a decrease in risk. This section tries to find through mean-variance tests, of equal mean or equal variance, which diversification benefits are significant. The procedure to follow is somewhat the same as the forming of optimal portfolios but with one extra restriction. The risk or return of the new portfolio is set equal to the risk or return of the benchmark portfolio to compare with. This creates a new portfolio with equal risk or return as the benchmark portfolio. The new portfolio creates a new stream of returns according to the weights of the new portfolio. These returns are compared to the returns of the benchmark and tested through a student’s T-test and the F-test. The T-statistic and its p-value test the null hypothesis that the new portfolio has the same mean return as the benchmark portfolio (H₀:Ri =Rj), where Ri is the mean return of the benchmark portfolio and

j

R is the mean return of each optimal portfolio to compare with. The F-statistic and its p-value test the null hypothesis that the new portfolio has the same variance as the benchmark portfolio (H0:SDi =SDj) , where SDi represents the standard

deviation of the benchmark portfolio, and SD_j represents the standard deviation of each optimal portfolio to compare with. To conclude this research the value and growth indices are compared to each other to find the superior asset class. The results of the mean-variance tests are reported in Table 4.

[INSERT TABLE 4 ABOUT HERE]

portfolio with MSCI country and value indices and are compared to the portfolio consisting of MSCI country and growth indices to see which funds are better in mean-variance space. In Panel D the benchmark portfolio has changed to the optimal portfolio with MSCI country and growth indices and are compared to the portfolio consisting of MSCI country and value indices to check the results from Panel C. In Panel E the benchmark portfolio has changed to the optimal portfolio with value indices and are compared to the portfolio consisting of growth indices to see which funds are better in mean-variance space. In Panel F this is vice versa to check the results from Panel E.

Panel A reports the results for the single index portfolios (value and growth indices) with and without short sales allowed. The only significant fact from Panel A is that the optimal growth portfolio without short sales is significantly more risky than the benchmark portfolio (F-statistic of 1.713 and p-value of 0.001) when the mean returns of the new and the benchmark portfolio are set equal. Panel B reports the results for the augmented portfolios (MSCI country and value, MSCI country and growth, and MSCI country, value and growth indices) with and without short sales. These results are more interesting to see. When the new portfolios are tested on equal means (i.e. the restriction of equal variance has been applied) only the augmented portfolio of MSCI country, value and growth indices with short sales has a significantly higher return than the benchmark portfolio (5.802% versus 2.990%). This result is significant at the 10% significance level (p-value of 0.095). When the new portfolios are tested on equal variance (H₀:SD_i =SD_j) all the new portfolios without short sales show no

confirms hypotheses 1 and 2. The decrease in risk of the MSCI country, value and growth indices portfolio is 6.323%. Again the results show that the portfolio where both the value and the growth indices are augmented performs the best in both risk and return space. Hypothesis 3 is proven to be true but again only when short sales are allowed.

Since both the value and growth indices can significantly reduce the risk of the benchmark portfolio, there is still no clear cut answer as to which asset class is the best to diversify with. Therefore Panel C and D show the results of the mean-variance tests where respectively the MSCI country and value indices, and the MSCI country and growth indices are the benchmark portfolio16

. The results are not conclusive. Although the portfolio where value indices were added performs slightly better in both risk and return space, with and without short sales allowed, than the portfolio where the growth indices are added, all the results are insignificant. These results do not confirm either hypothesis 4 or hypothesis 5.

Finally to investigate which asset class is superior over the other in risk and return space, Panels E and F show the results of the mean-variance tests with the optimal value or growth portfolio as the benchmark portfolio17_{. Again the} value indices perform slightly better in both risk and return with and without short sales allowed, however when no short sales are allowed are the value indices significantly better at the 1% significance level with respect to lower risk. In Panel E the value indices have a standard deviation of 5.319% corresponding to a return of 0.993% while the standard deviation of the growth portfolio is 6.795%. This corresponds to a F-statistic of 1.632 and a p-value of 0.002. In Panel F the growth portfolio has a standard deviation of 7.138% corresponding to a return of 1.029% while the value portfolio shows a standard deviation of 5.669%. This leads to a F-statistic of 1.586 and a p-value of 0.003. Value indices thus appear to be the better performing asset class. However these results are only significant when no short sales are allowed and with respect to the reduction in risk not an increase in return. Previous literature about value and growth stocks

16

The benchmark portfolio is the optimal MSCI country and value indices, or the MSCI country and growth indices portfolio in Panel C and Panel D respectively. These optimal portfolios can be found in Panel B of Table 3.

17

of Chan, Hamao, and Lakonishok (1991), Fama and French (1992), Lakonishok, Shleifer, and Vishny (1994) and Fama and French (1998) all found significant results in favour of value stocks. They showed that value stocks outperformed the returns of growth stocks. The results of this paper are also in favour of value stocks but most results are not significant and there are no significant results of outperformance in the returns of value indices versus the returns of the growth indices.

6. Robustness Check

The preceding sections have shown that investors can significantly benefit from augmenting value and growth indices into a benchmark portfolio consisting of MSCI country indices. The robustness of these findings will be checked here. This will be done by splitting the sample period. Two periods of equal length will be evaluated to see if the results remain constant. The first period is from the start of the dataset, June 1994, until June 2001. This period contains the internet bubble or dot-com bubble. The internet bubble caused stock prices of internet based firms to skyrocket. Even firms that had nothing to do with the internet but who added an e-prefix to their company’s name saw their stock prices go through the roof. Traditional metrics were overlooked and this eventually led to the burst of the bubble. As mentioned in the section about value and growth stocks, most technology companies are growth stocks. The expectation therefore is that the growth stocks will outperform the value stocks in this period. The second period is from July 2001 until June 2008. This check will show if the results are sensitive to period changes or if they remain robust throughout the dataset.

A. Period of June 1994 - June 2001

of 13.0% and a Sharpe ratio of 0.42. This is because at the end of this sub period the bubble already started to burst and the growth stocks lost a lot of value18

. Furthermore the value indices performed the best with an average mean return of 14.9% and a Sharpe ratio of 0.64, and the MSCI country indices performed second best with an average mean return of 14.1% and Sharpe ratio of 0.60, which is the same order as in the entire dataset. Panel B of Appendix C shows that the correlations, both domestic and international, are less than the correlations of the entire dataset, which could mean that in this period there could be more diversification benefits achievable.

The results of the mean-variance spanning test for the period June 1994- June 2001 are presented in Table 5.

[INSERT TABLE 5 ABOUT HERE]

Panel A reports the results of the mean-variance spanning test for the value indices. Only the value index of the Netherlands is not spanned by the MSCI country indices. Spanning is rejected for the Netherlands at the 5% significance level. Panel B shows the results for the growth indices. Again spanning is only rejected for the Netherlands at the 1% significance level. These results show that only the Netherlands should be able to statistically significant enhance the performance of the benchmark portfolio when added. The joint restrictions test for spanning of all value or growth indices accepts the hypothesis that all the indices are spanned. Both type of indices indicate that all the indices together are spanned by the MSCI country indices. This result is also found for the joint restrictions test for ∑β_i =1. This result is different from the result of the entire dataset where was found that at least three or four of the value or growth indices were not spanned and all the value and all the growth indices together tested for joint restrictions proved to be not spanned by the MSCI country indices.

18

The next step is to investigate if it is possible to significantly enhance the benchmark portfolio in mean-variance efficiency by adding the value and/or growth indices. Table 6 presents the results for the optimal portfolios.

[INSERT TABLE 6 ABOUT HERE]

From Panel A it can be seen that the growth portfolio with short sales allowed is the best performing portfolio with a mean return of 17.160%, a standard deviation of 39.901%, and a Sharpe ratio of 0.422. The major share of investment goes to the U.S and Sweden’s growth index. The optimal growth portfolio without short sales only distributes weights to the U.S. and Sweden’s growth indices. For the optimal MSCI country indices, and value indices portfolio the main share of investment is divided between the Netherlands and the U.S. When short sales are not allowed those two countries are the only countries that receive investment in the optimal portfolios.

These results can also be seen in Figure 3.

[INSERT FIGURE 3 ABOUT HERE]

Panel A shows that all three efficient frontiers of the augmented portfolios lie above the efficient frontier of the MSCI country indices portfolio and perform quite similar when short sales are allowed. When short sales are not allowed, in Panel B, only two lines are visible. This is because the growth indices are redundant when no short selling is allowed. The efficient frontiers of the portfolios consisting of MSCI country and value indices, and MSCI country, value and growth indices are thus the same. As are the efficient frontiers of the portfolios consisting of MSCI country indices, and MSCI country and growth indices.

The outcomes of the mean-variance tests are reported in Table 7.

[INSERT TABLE 7 ABOUT HERE]

The outcomes of Panel A are about the same as for the entire dataset, only the growth indices are not significantly more risky than the MSCI country indices. Furthermore in Panel B, the portfolio consisting of MSCI country, value and growth indices does not have a statistically higher return than the benchmark portfolio. The decrease in risk of 2.542% remains statistically significant at the 1% level. The other two augmented portfolios also have a statistically significant decrease in risk at the 5% level of 2.069% and 2.058% for the MSCI country and value indices, and the MSCI country and growth indices respectively. When looking between the MSCI country and value indices portfolio, and the MSCI country and growth indices portfolio the only difference opposed to the entire dataset results is that the portfolio of MSCI country and value indices without short sales is statistically significantly less risky. Panel E and F provides about the same results as Panel E and F of Table 4. The value indices are significantly less risky without short sales.