One of the most challenging and critical issues that financial managers, academicians and analysts are facing is in estimating a firm's cost of equity Harris, Marston, Mishra and O'Brien (2003). Measuring risk is also a challenging issue as it is not very clear. However, ''portfolio theory tells us that risks to which many securities are exposed to can be associated with a premium in financial markets'' Girard and Omran (2007). Anyhow, Harvey (1995) presents that investors are believed to hold a world market portfolio, where an individual security' risk can be measured with regard to its input to this portfolio. While there are innumerable approaches in estimating the cost of equity and risk, not all are achievable or theoretically justifiable. Therefore, the need to adopt asset pricing models (CAPM, APT, ICAPM etc). Although, according to Harvey (1995) both the single and multifactor CAPM exhibit the risk measures. The Capital asset pricing model (CAPM) was developed and introduced by; Sharpe (1964), Lintner (1965) and Mossin (1966). The competency of CAPM has been analysed by several studies, and it can be argued that CAPM may be a logical model despite the criticism in the literature against it. However, baffling conclusions have been made through the various CAPM tests that correlation between beta and market premium can be contradictory, absolute or irrelevant. As CAPM uses the systematic risk in its framework as a measure of risk, which is measured by beta, it gives some drawbacks which are associated with this risk. Espinosa () suggested that in assessing risks, Scenario analysis could be very beneficial, although the ''risk adjusted discount rates'' will be required with it. However, he then suggested the use of CAPM.
Graham and Harvey (2001) carried out a survey which reported that CAPM is used by financial executives and investors. The popularity of CAPM further increases as its usage is recommended by financial professors for calculating the cost of equity in the capital budgeting purposes (Welch 2008). It is also found in scholarly articles as well as university text books Harris, Marston, Mishra and O'Brien (2003). Girard and Omran (2007) say that CAPM leads to a belief of perfect market integration. Anyhow, this fails in emerging markets as these markets are more volatile than the developed markets and country beta is less than one in these markets Erb, Harvey,and Viskanta (1995), hence, the required rate of returns will also be low in them. Anyhow, Harvey (1991) showed that if beta was allowed to change through time, then this would work for developed markets. Whereas in developed markets, the betas are expressively different from zero and the required returns are obtainable Collins and Abrahamson (2006). However, it may also fail in certain developed markets that are less liquid and smaller in size. Risk can therefore not be accurately measured by beta in emerging markets. Then, Godfrey and Espinosa (1996) put forward that CAPM could be adjusted in two ways, although their approach had problems as it dealt in dollars and not all emerging countries have debt issued in dollars.
There are various methods of measuring the cost of equity as suggested by Estrada (2000). It has been argued by Bekaert, Harvey and Lundblad (2005) that measuring the cost of equity through the asset pricing models will bring about bogus results, because the integration levels are changing over time. However, a solution to this was then proposed by Bekaert and Harvey (1995) to use an approach that varies with time, so that the cost of equity will also change over time. This approach is rather complex and practitioners are not attracted to it. Collins and Abrahamson (2006) proposed another method that could predict the cost of equity by the use of sovereign credit ratings, but these are only pertinent at market level. With this method, it is not even possible to measure the cost of equity at firm-level or sector- level Collins and Abrahamson (2006). Erb, Harvey,and Viskanta (1995) analyse ''risk surrogates such as financial risk, political risk, economic risk and country credit rating from the International Country Risk Guide (ICRG)''. It was observed by them that the higher the risk, the higher the expected returns. In this study, only South Africa (among other African emerging markets) has been given credit ratings by Moody's or Standard &Poor's, Euro money's Country Credit Rating. Lambert, Leuz, Verrecchia, (2005) used the future cash flows' discounted values, hence that is also another possibility that Collins and Abrahamson (2006) proposed, but data again in the African markets is limited as estimates from analysts regarding the future cash flows are required. This data is available for South Africa.
However, in spite of CAPM being an authoritative model, various studies such as those of; Jensen, Black and Scholes (1972) criticized the judgement of Sharpe and Lintner when they took the portfolio into consideration preferably to individual securities. Stock risk premiums can be better explained by various multifactor models that are believed to perform better than the CAPM Girard and Omran (2007). CAPM has been used in the European stock markets by Capaul, Rowley and Sharpe (1993) as well as in the Japanese stocks by Kothari, Shanken and Sloan (1995) among others and these have provided clear results.
According to Bennaceur and Chaibi (2007), CAPM denotes ''that the cross-sectional variation in expected returns'' can only be illustrated by market beta. However, it has been argued by Fama and French (1992 and 1993), Jagannathan and Wang (1996) among others, that only beta cannot be enough to clarify expected return. Fama and French therefore introduced their own model, known as the Fama and French three- factor Pricing model (TFPM) by addition of two more factors to CAPM; size and book- to- market equity ratio Lee and Upneja (2007). Banz (1981) and Rosenberg et al (1985) found that the average stock returns are related to size and book- to- market equity, although along with others they criticised CAPM by adding that beta does not capture the lofty average returns that the stock with soaring book- to- market equity ratios have. However, it was further examined by Fama and French (1997) and Elton (1999) that the evaluations of the expected returns that were added up did not provide certain results.
An alternative CAPM model, the conditional CAPM, is considered better than the ''original'' and ''unconditional CAPM as it allows the beta measure to vary across time'' Vosilov and Bergström (2010). It was found by Jagannathan and Wang (1996) that in a cross-sectional study, where the differences in average returns should be secured, the conditional CAPM performs better. However, Lewellen & Nagel (2006) recently argued, saying that this was untrue, because the abnormalities that the unconditional CAPM missed could not be explained by any alterations in the beta. They found that neither the conditional nor the unconditional CAPM can explain these variations in expected returns Vosilov and Bergström (2010).
Most market anomalies are captured by the three- factor model apart from the momentum anomaly Fama and French (1996). However, Jegadeesh and Titman (1993, 2001) argue that there is sizeable proof indicating that if certain stocks are performing well over a certain period of time, they will continue to do so over that period of time and vice versa (perform negatively). It was also concluded by them that denoting anomalous returns would be earned by "buying past winners and selling past losers"Rustam and Bergström (2010). The implication of this momentum effect was proved by Avramov, Chordia, Jostova & Philipov (2007), who showed why this effect was in existence. In the United States, as well as other developed markets, momentum trading strategies that have attained this fact have regularly been profitable Naceur and Chaibi (2007). Nartea and Ward (2009) had tested the TFPM to see if the short-run past returns pattern extension could be secured, and found that it failed to do so as the TFPM could not describe '' stock return variation related to the continuation of short run return patterns in the future'' Rustam and Bergström (2010).
This momentum factor was thus added to the Fama and French three factor model by Carhart (1997). He put forward that the average stock returns will thus be explained by this model. Carhart, (1997) said that the four factor model does well as it "substantially improves the average pricing errors of the CAPM and the 3-factor model" as it explains the average stock returns cross- sectional variation. Another model for equity valuation was developed by Ohlson (1995), which was used to calculate the rate of capitalisation as a factor for the expected return Lee and Upneja (2007). This model was then used by Botosan (1997) for evaluating the current stock price.
The Arbitrage Pricing Theory (APT) is also an alternative model to CAPM. It was developed by Ross (1976). It is a model that tries to overcome the weaknesses of CAPM. Shanken, 1982, agreed to this as he showed that the APT, unlike the CAPM, has various systematic risks that affect the returns of a security. Roll & Ross (1984) found that there are four systematic factors in the APT, hence the need to appraise the securities sensitivity to each of these factors. In this way, it will be possible to know what risk is affecting a security.
With all the criticisms given to the CAPM model, the multifactor models, with all their additional factors are still suffering from the fact that their extra factors have not been driven by theory. However, there are other studies that have tried by adding two more moments to the standard CAPM. This thus tries to help with the poor performance of the CAPM. These studies thus developed the three-moment CAPM, where, while choosing a portfolio, investors consider skewness Bennaceur and Chaibi (2007). To this three-moment CAPM, Dittmar (2002) added another moment, kurtosis, extending it to a four-moment CAPM. This was added to the preferences of an investor. To my knowledge, apart from that of Bennaceur and Chaibi (2007), there are no other studies that have calculated the cost of equity with the moments of skewness and kurtosis to CAPM. Evidence was provided by Dittmar (2002) and Harvey and Siddique (2000) that better performance was found since the skewness and kurtosis were added to CAPM, extending it.
2.3 Risks of investing in emerging markets
Various studies have not been sufficient enough to gain the confidence of investors to invest in emerging markets. Divecha, Drach, Stefek (1992) have also shown examples that these markets have low returns. Barry, Peavy III, Rodriguez (1998) provide a reminiscent evidence that during a crisis time, when diversification is most beneficial, the emerging markets will not really have the ability to provide these benefits. Parashar (2007) mentions that ''Investors prefer to trade in liquid markets.'' Fuss (2002) says that the turnover ratio is an indicator of the market liquidity. The liquidity levels are lower in emerging markets than the developed markets as it's displayed by the overall turnover ratio. Therefore, Fuss (2002) says that a high turnover ratio can be a deceptive pointer of the liquidity in a market, even though these emerging markets have evidenced sizable growth, but as compared to the developed markets, their capitalisation are low. For emerging markets, it is better to invest internationally than domestically, as that would offer considerable benefits. However, under certain economical situations such as high inflation, if investors invest in their home country, it would provide them more benefits than them investing globally Parashar (2007). Hanna, Kiymaz, Perdue (2001) had examined the investor in the Turkish financial markets, and their studies showed that it was more advantageous to invest in the local market rather than internationally. The following are the main risks to be considered when investing in emerging markets.
2.3.1 Volatility
Although the interests of investing in emerging markets is on an increase, but this has been affiliated with the concern about the high volatility levels. In Parashars' (2007) opinion, if the market volatility is high, the ''uncertainty about the future of risky investment and wealth'' increases, and may thus result in ''increased risk and/or shift to less risky investment.'' Therefore, this can thus lead to higher transaction costs and lower liquidity levels in markets that are influenced. Emerging markets are highly volatile as they are known to be disorganised. This is due to the fact that these markets encompass specific patterns of linear behaviour, feeble pricing and regulatory frameworks that have not been improved. Since investors face high risks, they are atoned through increased risk premium Parashar (2007).
It has been shown by French, Schwert, Stambuagh (1987) that volatility and expected risk premium have a direct relationship. If risks are high and there is immense uncertainty, which can lead to an increase in the cost of equity, as well as the costs of new investment activities, thus leading to a decrease in the productive direct investment and conceivably gradually decrease international trade. If markets riskiness increases, some investors may redirect their funds to instruments that are less risky thinking that there will be higher volatility due to the increased risk. Parashar (2007) affirms that the cost of equity to firms will therefore rise ''leading misallocation of resources.'' Black (1976) among others found that the volatility of stock returns acknowledges asymmetrically to news. This hence indicates that greater volatility can be caused by bad news as compared to good news. Parashar (2007) stated that the asymmetries of volatility have traditionally been explained by the leverage effects, that is by a hypothesis that after some bad news, if the prices of stocks decline, a company's operational and financial leverage will increase together with an increase in the stocks volatility and risk.
Sources of Volatility
Volatility in speculative prices can occur due to many reasons. There are three sources, which are agreed upon as being the main contributors of uncertainty:
The expected future investment returns,
The future shape of the yield curve,
The future foreign exchange rates for cross- national investments.
If investments are held in the context of an international portfolio, the variability in the FX exchange rates will add to the volatility of those investment returns as large investors will invest in profitable opportunities regardless of national boundaries. This ultimately increases the hedging costs and reduces the profits.
Why model volatility?
Risk and uncertainty is pivotal to most of modern financial theory. From the CAPM theory, the risk premium is determined by the covariance between returns on the asset and one or more benchmark portfolio.
Volatility clustering can assist in predicting volatility. Large swings in financial markets tend to be followed by more large changes, in both direction, and thus high predictability of volatility trend. Traders measure standard deviation over different periods, and use the most appropriate moving average to predict volatility. Some traders adjust standard deviation to reflect 1990's events (i.e. the Asian crisis).
How to model Volatility
Researchers have progressed from relating asset return volatilities to macroeconomic environmental factors, as in Schwert (1989), and moved towards modelling time series variation in second or higher order models. One of the most popular methods is ARCH as detailed here after.
Autoregressive Conditional Heteroskedasticity (ARCH) Models
The ARCH acronym stands for:
Autoregressive: Consistent relationship between past and present data.
Conditional: Estimate of variance depends on the information available.
Heteroskedasticity: Changing Variance.
Robert Engle introduced this concept in his seminal paper in 1982. In ARCH models, the volatility at time t is considered to be conditional (i.e. dependent) upon the price information up to time interval t-1.
The conditional volatility random variable, ht is related to a specific function of past return residuals єt. The return residual is defined as the difference between the return at time t and the expected value of return E (Xt). The simplest ARCH model is the linear ARCH (q).
t = 0 + i є2 t-i
Where 0 and the i 's are all positive constants. These are estimated by using maximum likelihood techniques.
GARCH model was generalised from ARCH by Tim Bollerslev in 1986. In the generalised GARCH (q,p) model, past estimates of conditional volatility are included as well as the past squared disturbances.
t = 0 + i є2 t-i + j ht-j
Why ARCH is selected?
ARCH seems to be more popular due to its success in modelling volatility compared with other models available.
Financial data have been found to have ARCH properties, such as volatility persistence and leptokurtick return distributions.
However, Since the ARCH is not directly going to fit in to the scope of my dissertation, I will therefore not discuss it further in detail, but for more details concerning the ARCH, see R. F. Engle: Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of UK.
Governments, modulators and investors have presumptions with the awareness of the volatility dynamics. Butler and Malaikah (1992) said that it is important for the modulators of stock markets to understand their market volatility, so as to define the applicable policy and regulatory decisions that are conducive to the blooming and brisk development of their markets. It is usually difficult for investors to know whether the returns of investing will be high enough to repay them for the risks they hold, as the emerging markets carry a range of risks that are usually not present in the developed markets. Essentially, there are two types of risks involved in the emerging markets as said by Micheal Pettis. These are mentioned below;
2.3.2 The Default Risk
Crosbie (2003) defines this risk as the ''uncertainty that surrounds a firm's ability to service its debts and obligations''. There is a large impact of this risk on fixed- income yields and a complete industry - ratings agencies- ha evolved to measure this risk. The risk premium that a market demands for the default risk approximately follows the credit ratings, which is why there is high interaction between the default rates and agencies' ratings Parashar (2007). The risk premium can be reduced by upgrading the issuers' ratings; therefore they are usually very anxious about it.
2.3.3 The Currency Risk
This is the risk that several investors face when they make investments in local currency denomination. The risks that arise from cross-border, cross-currency nature of sovereign emerging-market instruments are a set of risks that fall under this term; currency risk Parashar (2007). Convertibility and index risk are the main aspects of currency risk.
Convertibility risk
In various emerging markets, many of the local (domestic) foreign exchange markets are interceded by various administrations and/ or managements as part of the budgetary policy. Therefore, to balance out the market propensities, there may be interference in the foreign exchange markets as well as involvement of a fixed exchange rate. Convertibility risk can be caused by the policy of exchange rates, which frequently has restrictions of capital flows included in it, either to maintain the reserves of foreign exchange or to ward off the runs on a fixed exchange- rate. This is the risk where investors' funds are obstructed in a country, due to restrictions by the government hampering the repatriation and the funds being converted in to a foreign currency. There can be extreme cases with the convertibility risk, some of which can be if the government is facing a shortage of foreign exchange; it could have the capital outflows held up completely.
Index risk
All investors, either local or foreign face the risk of losing the value of their investment to either movements in the exchange rates, or inflation. It is therefore natural for these investors to ask for flexible interest rates, so as to consider the expected changes of the currency's real value. Both foreign and local investors have different perspectives on the returns. The local investors worry about how the inflation could affect their returns and are interested in knowing the currency's purchasing power. Whereas the foreign investors are more worried about the movements in the exchange rates as well as have a concern for their returns foreign currency value. It is very likely that inflation can have an effect on the movements of the exchange rates, as well as regulate the purchasing power of the local currencies.
2.4 International diversification
When allocating scarce capital, investors usually make use of diversification as this is a tool used to reduce risks. The two most frequently asked questions are: How many securities do you require in your portfolio to achieve a reasonable risk reduction? Does diversifying internationally reduce risk more rather than holding domestic securities?
Husain and Saidi (2000) say that when there are many markets, and there are low correlations between the returns, then International Diversification will present with increased benefits. In a groundbreaking article, Solnik (1974) found that in a portfolio of 10- 15 randomly selected securities, the benefits from diversification are maximised. By, having a small portfolio, large benefits can be gained through diversification. Table 2.1, shows the potential from international diversification for each country. Solnik found that within each country there was a level that could not be diversified, regardless of how many securities held. This is known as non- diversifiable risk. The table below also depicts that if a US investor diversified internationally, (portfolio fully hedged against exchange rate risk) then their risk could be reduced to 11.7%.
Table 2.1. Solnik (1974)
Potential from International Diversification
Country Non- diversifiable Risk
Switzerland 44%
Germany 43.8%
Italy about 39%
UK 34.5%
France 32.7%
USA 27%
Holland 24.1%
Belgium about 19%
International (USA) 11.7%
Solnik found out that there were larger gains from international diversification for smaller countries. Furthermore, the risk of a portfolio diversified across countries carried a smaller risk than a portfolio diversified across industries. However, diversifying in industries gave better returns. Cavaglia, Melas, Miyashita (1994) found that selecting industrial portfolios across countries rather than within countries would benefit from higher returns and lower correlations of assets.
Odier and Solnik (1993) found that correlations were lower for the bond markets than the stock markets between 1980- 1990. They used stocks and bonds as their assets. They showed that risk and return advantages of international diversification were significant in the major countries, such as the United Kingdom, Germany and Japan.
In the bond market, Levy and Lerman (1998) focused particularly on whether there were any benefits from international diversification in bonds. Samples of foreign countries between the period 1960- 1980 were used. It was found that over the time period, specialising in bonds would have improved the portfolio performance by 3-5% a year rather than just diversifying in domestic bonds. This was due to the low correlations between the bond markets in different countries. Larger gains were found diversifying both in stocks and bonds. Solnik and Noetzlin (1982) find similar results, between the data period 1770- 1980.
Diversifying in real estate is better than diversifying in stocks and bonds Eichholtz (1996). This was due to the significantly lower correlations between national real estate returns and common stock or bond returns. As a result, international diversification can reduce the risk of a real estate portfolio more than diversifying in common stock and bond portfolios across countries. Eichholtz (1996) used the data period from 1985-1994.
Diversifying an investor's portfolio in the emerging markets can reduce risk, Divecha, Drach, Stefek (1992). Their 5- year study between 1986- 1991 showed that, had 20% been involved in to the emerging market it would have outperformed the developed markets. This was because emerging markets had low correlations with the developed markets. Jorion (1985) showed in his study that the gains from international diversification in earlier studies were exaggerated. However, it also demonstrates that there is still some gain from diversifying internationally.
An interesting article by Sinquefield (1996) suggests that in the period 1970- 1994 (from the US perspective), diversifying in the international equity market would give greater expected returns than in the US equity market. This suggests it may be a good reason for the US investor to diversify their portfolios. The evidence suggests that two risk factors; value (high book- to- market) and size, influence the different expected returns across equity portfolios. Sinquefield (1996) also argues that a good reason to diversify would be to ''load'' up on the value stocks and on small stocks in different countries. Otherwise, it may not be worth diversifying internationally at all.
Overall, international diversification depends on the correlation coefficient across the markets, the risk in each market, and the returns in these markets. When holding a small portfolio of 10- 15 securities, large benefits can be gained through diversification. The studies outlined have shown that diversifying internationally can reduce risk more significantly than holding domestic securities.
Exchange Risk
There is a possibility of further risk from exchange rates when foreign stocks are held in an investor's portfolio. It is also important to find out if the correlations between stock returns compensate the risk from exchange rates. This will depend on the volatility of exchange rates, how stock returns and exchange rates are inter- related, and also the number exposure to foreign currencies within the overall portfolio. The possibility of further risk from exchange rates can be verified by comparing the volatility of stock values measured in local currencies to the volatility of stock values in foreign currencies. Eun and Resnick (1997) demonstrated that the exchange rate risk is the smaller of the two factors. Eun and Resnick (1988) also looked at the issue of the number of foreign countries invested in a portfolio of domestic stocks. They break down the volatility of returns on foreign stocks in to the volatility of exchange rates, the volatility of stock returns in terms of local currency and the covariance of stock returns in local currency and the exchange rates.
Table 2.2 Eun and Resnick (1988)
Variance of US Dollar, 1980- 1985
Country Exchange Rate Local Return 2 x covariance
Canada 4.26 84.91 10.83
France 29.66 61.79 8.55
Germany 38.92 41.51 19.57
Japan 31.85 47.65 20.5
Switzerland 55.17 30.01 14.81
UK 32.35 51.23 16.52
From table 2.2, it is shown that the volatility in the exchange rate can contribute from just over 4 percent to just fewer than 56 percent of the volatility of dollar returns. Furthermore, movements in local stock markets reflect movements in exchange rates. The volatility of exchange rates does not cancel the benefits of international diversification, because exchange rate volatility can be hedged. Hedging encompasses using futures, currency options, borrowing in the foreign currencies. Solnik (1974) finds the advantages of international diversification with and without exchange risk. The results in his study demonstrate it was better to be hedged to foreign currency exposure than be unhedged. Another factor that is important is political risk. This factor may affect gains from international diversification. A key problem is, however, how political risk can be quantified and thereby incorporated in to the analysis.
Hedging
When an investor diversifies internationally, there is exposure from future exchange rate movements on risk and return. The standard deviation of foreign investments generally increases due to exchange
rate risk. The issue of estimation risk (parameter uncertainty) is important and if it is not considered, the gains made from diversifying internationally are greatly overstated; Eun and Resnick (1988). From the various strategies used, they found that after controlling for exchange risk and estimation risk, considerable gains could be made. They also used hedged and unhedged strategies. It was found that the minimum variance portfolio (MVP) hedging strategy was the best performing strategy. The data period used was from 1980- 1985. Similarly, Jorian (1985) stated that estimation risk due to uncertain mean returns makes a substantial difference in selecting an optimal portfolio. Eun and Resnick (1988) and Jorian (1985) show that it is important to control estimation risk and foreign exchange, so investors can benefit from international diversification.
Two methods that can be used to hedge against exchange risk are forward contracts and protective puts. Comparing these passive hedging strategies, using parameter estimation techniques, Eun and Resnick (1997) found that forward hedging strategy was superior to protective put hedging strategy. These parameter estimation techniques include the equal- weighted (EQW) portfolio, MVP, the Bayes- Stein technique (BST) and the certainty equivalence portfolio technique (CET). In this study Eun and Resnick (1997), a strategy was said to dominate another strategy if it had a higher sharp measurement (i.e. 51 out of the 100 sample holding periods).
Table 2.3 Eun and Resnick (1997)
Dominance analysis comparing the ex ante performance of the passive forward and protective put strategies Protective put
EQW CET MVP BST
Passive forward EQW 68 59 55 65
CET 55 65 52 544
MVP 70 64 63 63
BST 65 66 61 64
From table 2.3, it was found that the MVP and BST parameter estimation techniques work the best. It also looked at alternative strategies comparing the option writing strategy with the other hedging strategies using the parameter estimation techniques. It was found that the option- writing strategy out- performed all the other hedging strategies, with the MVP and BST again performing the best. The data period used was from 1978 to 1994.
Filtov and Rapport (1992) consider whether complete hedging is optimal for international bond portfolios. They found that currency hedging has a significant role in international asset allocation. The correlations between asset and currency returns determine whether currency hedging contribute to diversification. They found that if the covariances were negative, it would be best to stay partially unhedged. If the covariances are positive or zero, it would be best to be offset from the benefits of diversification, so they should not be persuaded from being unhedged. The data period they used was from 1980 to 1989.
Odier and Solnik (1993) found that the optimal hedging policy depends on the nationality of the investor, the percentage of the foreign assets and with the asset classes included in the portfolio. The data period used was from 1980- 1990. In an emerging market, Akdogan (1996) states that by hedging against the exchange risk, the benefits from diversification cannot be improved. In the author's opinion, if an investor were to hedge, their best strategy would be to follow the MVP method, as this would control estimation and exchange risks combined.
