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In this article the main features of portfolio theory will be outlined and illustrated by a simple numerical example. For purposes of clarity a few assumptions will be adopted. This is fol-lowed by the deduction of simple share investment strategies.
RESEARCHES & DISCUSSIONS In this article the main features of portfolio theory will be outlined and illustrated by a simple numerical example For purposes of clarity a few assumptions will be adopted This is fol-lowed by the deduction of simple share investment strategies Then it will be shown that, with the help of Return on Risk adjusted Capital (RoRaC), an improved evaluation of equity portfolios and investment strategies are more possible then with the Sharpe Ratio This will be illustrated by an example Finally, by means of the RoRaC, general recommendations for the handling of investments in Vietnam will be derived In doing so, the insights derived from the portfolio theory for shares can also be applied to real investments in Vietnam Keywords: Beta Factor, Component Value at Risk, Correlation Coefficient, Expected Return, Inefficient, Investment Strategies, Portfolio Theory, Return on Risk-adjusted Capital, Risk-averse, Risk-taking, Sharpe Ratio, Transformation Curves, Value at Risk, Vietnam Portfolio, Volatility Basics of the portfolio theory For a demonstration of the portfolio theory we shall assume an investment of only two Ger-man shares, those of the automobile manufacturer BMW and of MAN, the commercial vehicle manufacturer The insights from the portfolio theory for these two shares can be assigned to any number of different shares But, due to the necessary matrices, the calculation effort will be increased considerably and the deductions will no longer be quite so clear and easy to comprehend This would not be helpful for the aims of this article [for details on the following remarks see Elton et al., 2002] Historical share prices constitute the basic principles of the portfolio theory First, the corresponding share return is calculated from the historical share price rt: Thus the return is rt and the price is kt for the point in time t From the historical share returns the average share return r can now be calculated: * Berlin School of Economics and Law Where T is the number of historical share price returns On the basis of the average share price return r, the accompanying empirical variance s2 can now be calculated: In the portfolio theory volatility is computed instead of the variance Volatility s is the square root of the variance Finally, the empirical covariance s1,2 between the two price returns share and share is needed: With the help of the covariance the accompanying correlation coefficient k1,2 is calculated as follows: Compared to the covariance the correlation coefficient can be interpreted more easily and better Details of this will be handled later in this article At the heart of the portfolio theory are the socalled transformation curves These transfor-ma- Economic Development Review - April 2011 RESEARCHES & DISCUSSIONS tion curves specify the accompanying returns–risk combination for every possible portfolio combination of the two shares and The returns are measured by the average share return, the risk by the volatility The combination possibilities range from 100% in share and 0% in share to 50% in both shares and 2, to 100% in share and 0% in share In Figure the accompanying transformation curves are delineated for three different correlation coefficients In the process, the data from BMW and MAN are drawn upon, which is the aggregated portfolio level additional information and calculations are necessary It is assumed that an investor has purchased 10 BMW shares at a price of €37.00 and 10 MAN shares at €45.00 The portfolio weight for BMW amounts to 45.12 and 54.88% for MAN Its portfolio value comes to €820 (100%) The average daily share price returns for BMW amount to: rBMW = 0.042% and rMAN = 0.175% for MAN The calculation of the portfolio return is as follows: Figure 1: Basic principles of portfolio theory – transformation curves why we turn next to the explanation for the examples of the BMW and MAN shares Example of the portfolio theory For the calculation of the ratios the daily historical share prices from 2005 (257 trading days) for BMW and MAN were taken as the basis In order to be able to specify the essential values of 10 Economic Development Review - April 2011 Here wi is the weight of share i in the whole portfolio while ri is the accompanying return for share i The sum of all of the weights must always be The result for the BMW-MAN portfolio is rp = 0.115% RESEARCHES & DISCUSSIONS The volatilities s of the individual shares amount to sBMW = 1.031% and sMAN = 1.386% The portfolio volatility is calculated as: The correlation coefficient amounts to kBMW,MAN = +0.36 For the BMW-MAN portfolio the yield is sp = 1.025% Table shows the resulting key figures for 2005 Asset Risk Portfolio position exposure weights Average share Volatility return BMW €370.00 45.12% 0.04% 1.03% MAN €450.00 54.88% 0.18% 1.39% Portfolio €820.00 100.00% 0.11% 1.03% Table 1: Key figures for BMW and MAN shares for 2005 on the basis of daily trade data In Figure the average share returns and volatility are clearly visible in the transformation curve The above formulas can be used to calculate the accompanying returns and volatility for every other combination Now the transformation curves in Figure can be interpreted The blue transformation curve begins in the top right for the portfolio that consists of 100% MAN shares Portfolio returns and volatility reflect the individual MAN share Analogous to this, the other end of the dashed curve of transformation reflects the portfolio consisting only of BMW shares (see Figure and Table 1) Finally, the portfolio values of the above portfolio example (45.12% BMW and 54.88% MAN shares) are shown in Figure From Figure it is also clear that there is a portfolio combination in which the portfolio volatility is minimal This portfolio can be calculated as follows: The empirical covariance amounts to sBMW,MAN = 0.00005159 The accompanying portfolio proportion of the BMW shares amounts to wmvBMW = 71.98% while the accompanying minimal portfolio volatility is smvp = 0.954% The transformation curve exhibits another es- sential quality For transformation curves with a correlation coefficient smaller than one, there is a so-called inefficient area of portfolio combinations A portfolio is inefficient when there is another portfolio combination that has higher returns for the same risk For the dashed curve of transformation in Figure (kBMW,MAN = +0.36) the inefficient area extends from the portfolio with the minimal volatility (wmvBMW = 71.98%, see above) to a portfolio which consists only of BMW shares (wBMW = 100%) By selling BMW shares and purchasing MAN shares (restructuring), a portfolio manager who manages a portfolio of 80% BMW shares and 20% MAN shares could package a new portfolio that would have the same portfolio risk (portfolio volatility) but a higher portfolio return than the original portfolio Next, with the help of these important features of the transformation curves, a few simple investment strategies can be deduced Derivative of simple investment strategies The first general purpose strategy can be derived directly from the above-mentioned inefficiency and is “Inefficiency portfolios are to be avoided.” But in this context the transformation costs that are accrued by the restructuring of an inefficient portfolio need to be considered A restructuring only makes sense when the necessary transaction costs are not higher than the achieved advantage in profit For a risk-averse investor the strategy is: “Choose the portfolio combination with the minimal portfolio volatility!” For the example in Figure with correlation coefficients of k = + 0.36 this would mean se-lecting the portfolio with the minimal volatility, i.e wmvBMW = 71.98% and with smvp = 0.954% With a (assumed theoretically) correlation coefficient of k = +1 (black transformation curves in Figure 1) this means investing completely in the portfolio which consists of the share with the least risk (volatility) In the above example the investor would therefore only keep BMW shares (i.e wBMW = 100%) For a risk-taking investor the strategy is “Choose the portfolio which consists only of a share with the highest individual returns.” For every theoretical correlation coefficient the Economic Development Review - April 2011 11 RESEARCHES & DISCUSSIONS investor would therefore purchase MAN shares (wMAN = 100%) exclusively He would achieve the highest portfolio returns (rMAN = rP = 0.175%) At the same time the portfolio risk would also be the highest (sMAN = sP = 1.386%) Now it is obvious that an extreme risk-averse or extreme risk-taking investor would be the exception The question of which portfolio an investor who is willing to take an average amount of risk (between extreme risk-aversion and extreme risk-taking) should choose, is much more interesting The answer to this question cannot be derived directly from the transformation curves This is because the risks increase along with higher returns So the application of additional key figures is now necessary in order to derive appropriate strategies The Return of Risk-Adjusted Capital (RoRaC) For the evaluation of share portfolios and individual positions with respect to returns and risks, the Sharpe Ratio is often applied in connection with the portfolio theory For the share position i, the Sharpe Ratio (SRi) is defined as follows: Here rrf is the risk-free interest rate An investor who does not invest his capital in investments fraught with risk can invest the capital in risk-free bonds, e.g German government bonds [see Wolke (2011a)] The risk-free interest rate reflects opportunity costs that arise from an investment fraught with risks These must be deducted from the returns (here: ri) fraught with risks If a risk-free interest rate of 3% p.a is assumed [see Wolke (2011a)], one must consider that the most influential factors of the Sharpe Ratio all refer to the same period of time Returns and risk in the above example represent daily trade data This is the reason why risk-free interest must be spread across 256 trading days (3% / 256 days = 0.01172%) Now the portfolio example of the accompanying Sharpe Ratios (Table 2) can be calculated: The investment in MAN shares is therefore much more attractive than an investment in BMW shares as the Sharpe Ratio is about three times as high In other words: With MAN shares at the same level of risk, an investor achieves a return 12 Economic Development Review - April 2011 Table 2: Sharpe Ratios for BMW and MAN shares for 2005 on the basis of daily trade data Asset position Risk-free Average Volatility share interest (si) rate (rrf) return (ri) Sharpe Ratio (SRi) BMW 0.01172% 0.042% 1.031% 0.02937 MAN 0.01172% 0.175% 1.386% 0.11781 Portfolio 0.01172% 0.115% 1.025% 0.10076 that is three times higher Or, in other words: he achieves the same profit with one third of the risk However, the Sharpe Ratio reflects a few grave weaknesses [for details see Wolke, 2008] - The return consists of average price returns only Other possible profit components, in particular dividend payments, are disregarded - Among other things the risk attitude of the investor is not explicitly considered - The consideration of the diversification effect emerges only on the portfolio level Partial consideration of the diversification effect on the level of individual share positions is not undertaken - Finally, the Sharpe Ratio refers to relative (percentage) factors of influence But this does not however mean that there is a connection to a necessary equity capital burden of the investors (for his investment fraught with risks) These weaknesses of the Sharpe Ratio were the reason why a ratio was developed in the 1990s which more or less corrects these weaknesses This involves the so-called Return on Risk-Adjusted Capital (RoRaC) The RoRaC can be defined as follows: Average price return + other income – risk-free interest payments Component Value at Risk In contrast to the Sharpe Ratio, all of the influencing variables of the RoRaC are expressed in currencies (e.g €) The average gain in capital in the example of an average daily investment return corresponds with ri The average price return can however apply to profits of bonds and other securities The other earnings are e.g dividend payments or coupon interest payments As in the above example, the risk-free interest payments are 3% p.a., but they will have to be converted into currencies The numerator of the RoRaC only differs from the Sharpe Ratio by consideration of RESEARCHES & DISCUSSIONS other earnings instead of merely the average price returns and the currency data The decisive difference is in the application of the Component Value at Risk (CoVaR) instead of volatility In this way the RoRaC becomes much more significant than the Sharpe Ratio For this reason the Component Value at Risk is explained in greater detail below [for specific details of the CoVaR see Jorion, 2007 and Wolke, 2008] The basis of the Component Value at Risk stems from the Value at Risk (VaR) for the position i, which is calculated as follows [for an outline see also Wolke (2011b), for greater detail see also Jorion (2007) and Wolke (2008)]: with: RPi: amount of risk position of i in euro, a: number of standard deviations (from the standard normal quantile), si: volatility of i, T: liquidation period in days, average return (expected value) ri: For the liquidation period of one trading day and a level of confidence of 99%, which is the equivalent of 2.33 standard deviations, the following VaR for the sample portfolio would result in: The VaR for e.g BMW can be interpreted as follows: With a probability of 99% the expected loss in BMW shares from one trading day to the next would not be greater than €8.73 The investor’s risk propensity is reflected in the confidence level A risk-averse investor selects a high level of confidence (e.g 99%) and a risk-taking investor chooses a lower level (e.g 95%) The higher the level of confidence, the higher the VaR will be If the VaR of the individual positions (€8.73 + €13.74 = €22.47) is added together, and if the VaR of the portfolio is then deducted, the outcome is a value of €3.83 This value quantifies the diversification effect Now the diversification effect can be quantified on the portfolio level, albeit not the proportionate diversification effect for the individual risk positions BMW and MAN The individual positions also cannot really be compared with each other With the help of the Component Value at Risk this diversification effect can be determined, which is calculated for the risk position i as follows: with The value si,p is the covariance between the daily return of position i and the daily return of the portfolio The beta factor (bi) measures the influence of the individual risk positions and the entire portfolio risk The higher the beta factor, the higher the influence will also be on the portfolio risk This aspect will play an important role later The beta factors for BMW and MAN are With the help of these beta factors the accompanying CoVaR can now be calculated: The sum of the CoVaR must yield the VaR of the portfolio exactly The proportionate diversification effect is then €8.73 - €6.11 = €2.62 for BMW and €13.74 - €12.53 = €1.21 for MAN The proportionate diversification effect of the MAN shares is much lower than those of BMW shares This may be a surprise initially, since the influence of the MAN shares on the portfolio risk is clearly higher (higher beta factor) However, if we look at the formula for the CoVaR more carefully, it becomes clear that a higher beta factor and a high portfolio weight will bring about a higher CoVaR A higher CoVaR means that the diversification effect will be lower proportionately (as the difference between the VaR of the individual positions and the CoVaR will be less)! In addition, the beta factor also has another important feature A higher beta factor means that the portfolio risk will be reduced dramatically if the accompanying share position is sold So if the portfolio risk is too high, the portfolio VaR can be lowered considerably when the MAN shares are disposed Both of these features Economic Development Review - April 2011 13 RESEARCHES & DISCUSSIONS play a role when ap-plied to real investments in Vietnam Now the four weaknesses of the Sharpe Ratio mentioned above (taking into account dividend payments, proportionate diversification effect, risk propensity of the investor, risk measurement in currencies through VaR) have been solved Next, with the help of the RoRaC or CoVaR, strategies for our portfolio example can be drawn RoRaC Example for the BMW-MAN Portfolio MAN: €192.61 / €200.48 = 0.96 Portfolio: (€36.08+€192.61) / €298.24 = 0.767 For the deduction of possible investment strategies it now makes sense to illustrate the various portfolio weights in the tables that follow In Table the individual VaR, the Component Value at Risk and the accompanying RoRaC values for BMW and MAN are shown In Table the VaR and RoRaC values are shown for the portfolio With the help of the results from Table and To begin with, in taking Weight BMW = CoVaR Single CoVaR Single RoRaC RoRaC dividend payments into ac- 1-Weight MAN BMW VaR BMW MAN VaR MAN BMW MAN count, assumptions about 0.00% €0.00 €0.00 €25.05 €25.05 n d 0.876 the estimated amount of 10.00% €0.80 €1.94 €22.49 €22.54 0.624 0.878 distributions can be made In this way the annual div20.00% €1.89 €3.87 €19.80 €20.04 0.53 0.886 idend payment will amount 30.00% €3.30 €5.81 €16.99 €17.53 0.454 0.904 to 2% p a for BMW and 40.00% €5.07 €7.74 €14.06 €15.03 0.395 0.936 1% for MAN with respect €13.75 €6.11 €8.73 €12.53 0.96 0.369 45.12% to the risk position The 50.00% €7.18 €9.68 €11.08 €12.52 0.348 0.99 risk-free interest rate will again be 3% p.a For the 60.00% €9.57 €11.61 €8.15 €10.02 0.313 1.077 final calculation of the 70.00% €12.13 €13.55 €5.42 €7.51 0.288 1.213 RoRaC all amounts will 80.00% €14.71 €15.48 €3.07 €5.01 0.272 1.427 have to be converted in cur90.00% €17.15 €17.42 €1.24 €2.50 0.262 1.768 rencies and be fixed within a specific timeframe The 100.00% €19.35 €19.35 €0.00 €0.00 0.258 n d time frame of one year has Table 3: Component Value at Risk and the accompanying RoRaC values for been chosen for this examBMW and MAN ple (the timeframe selected Total portfowill be insignificant for the RoRaC Weight BMW = Portfolio Portfolio RoRaC lio profit p result) The following total p.a earn1-Weight MAN volatility VaR Portfolio y ings for BMW and MAN are: 0.00% €350.96 1.39% €25.05 0.876 BMW: 0.042%.€370.256 days 10.00% €323.86 1.29% €23.29 0.869 (price return) + 2%.€370 (dividend) – 20.00% €296.76 1.20% €21.69 0.855 3%.€370 = €36.08 30.00% €269.66 1.12% €20.29 0.831 MAN: 0.175%.€450.256 days (price return) + 1%.€450 (dividend) – 40.00% €242.56 1.05% €19.13 0.793 3%.€450 = €192.61 €228.69 1.03% €18.64 0.767 45.12% Finally, the Component Value at 50.00% €215.46 1.00% €18.26 0.738 Risk needs to be calculated for a full 60.00% €188.36 0.97% €17.72 0.664 year: The result is now reflected in the following RoRaC values: BMW: €36.08 / €97.76 = 0.369 14 70.00% €161.26 0.95% €17.56 0.574 80.00% €134.17 0.96% €17.79 0.471 90.00% €107.07 0.99% €18.39 0.364 100.00% €79.97 1.03% €19.35 0.258 Table 4: VaR, and RoRaC for different portfolio weights for Economic Development Review - April 2011 the entire portfolio RESEARCHES & DISCUSSIONS 4, a few mechanisms can now be observed From Table it becomes apparent that the proportionate diversification effect for BMW shares is much higher than for the MAN shares This is due to the respective weighting in the portfolio and the beta factor Only with a very high number of BMW shares in the portfolio (above 70%) will the diversification effect of the MAN shares – depending on the amount - be greater (and analogous with high numbers of MAN shares) From Table a much more significant feature can be deduced from the RoRaC values In this way the RoRaC values sink with increasing weighting in the portfolio This is based on a decreasing proportionate diversification effect The lower the proportionate diversification ef-fect, the higher the CoVaR is, which means that the RoRaC will decrease Due to the above average gain compared to the risk, the RoRaC of the MAN shares will be higher than that of the BMW shares This could lead to the assumption that it only makes sense to buy MAN shares But this would mean neglecting the respective risk of MAN shares and the lower (or no) diversification effect associated with them So, in the next step the risk can be taken into account at the portfolio level The RoRaC of the portfolio always lies between the two RoRaC values of the individual positions (a weighted average) The RoRaC is the highest for 100% MAN shares and the lowest for 100% BMW shares This is due to the above average gains of the MAN shares For amounts of more than 70% BMW shares the portfolio is inefficient, i.e the portfolio volatility begins to increase again, while the portfolio returns decline (due to the high weighting of the BMW shares) Next, the question is which weighting an investor should choose between 0% and 70% This question can be answered according to: (1) the risk propensity of the investor; and (2) the amount of available equity capital A risk-taking investor who can finance the portfolio with much more than €25 equity capital should invest in 100% MAN shares, although in doing so he will not realize a diversification effect (see above discussion) A risk-taking investor with less than €25 equity capital should only invest in the number of MAN shares that maintains the portfolio VaR which is lower than his/her equity If the investor only has €19 in equity capital, he should not have more than 50 MAN shares A risk-averse investor should choose a portfolio with a minimal amount of volatility (71.98% BMW shares, see above) Depending on his risk disposition, if he has much more than €18 in equity capital, he can invest in a portfolio with less than 70% BMW shares to achieve a higher RoRaC For the application of the portfolio theory and the RoRaC in real investments in Vietnam, it should be kept in mind that the amount of equity capital is much lower than the portfolio VaR In this case there are two possibilities: (1) An increase in equity capital, or (2) A reduction of the portfolio VaR An increase in equity capital is usually not immediately feasible and has something to with aspects that are not within the scope of this article What is left is the reduction of the portfolio VaR Here again, the beta factor comes into play If the portfolio VaR should be reduced as much as possible, this can be achieved by the sale of shares with a high beta factor In our example this would mean the sale of MAN shares and the investment of this return of sale in risk-free or almost riskfree investments Next, the previous explanations can be applied to real investments in Vietnam Applications and implications for real investments in Vietnam For the previously mentioned deductions, it will be necessary to make a number of assumptions which are not achieved in real investments Here are the most important assumptions as follows: - The calculation of covariances, returns and volatilities by means of historical data, - The permanence of returns and volatilities, or the restructuring of portfolios, - The realization of random portfolio weights, etc Nevertheless, in order to derive recommendations for real investments, returns, beta factors, Value at Risk values and correlations must all be estimated from plausible assumptions or comparable investments The first key assumption concerns the risk Economic Development Review - April 2011 15 RESEARCHES & DISCUSSIONS propensity of the investors For the most part investments in Vietnam can be undertaken by: - Foreign private investors (firms, investment companies), - Vietnamese private investors (firms, individuals) and - The Vietnamese government (state institutions) The deduction or assumption in terms of a consistent risk attitude of all three investor types is not possible The conditions under which the various investors evaluate their possible real investments are much too different to find a common denominator amongst them Another possible approach consists of forming or analysing portfolios of real investments on different aggregation levels In this way one can try to apply the portfolio theory on the company level The different products and business areas of a firm are considered as investments that, all together, make up the portfolio of the company The equity capital of the company then forms the ceiling for the portfolio VaR of the company But this does not solve the problem of de-ducing assumptions about risk attitudes This is only possible at the highest aggregation level If one looks at the portfolio at the highest aggregation level, this is the portfolio of the entire Vietnamese economy This is an overview of all real investments of the entire Vietnamese state Various fields (tourism, real estate, services, industrial production, and agriculture, etc.) reflect the individual positions of the “Vietnam Portfolio” If one now looks at the develop-mental risks of the Vietnamese economy, as for example: (1) a possible bursting of the real-estate bubble; (2) a substantial sinking of US$ reserves (currently only US$14 billion) of the Vietnamese state bank; (3) a high import dependency and accompanying high trade deficit; and (4) a flat value chain, there can be in my opinion only one recommendation: for current and future real investments in Vietnam, risks should be avoided at all costs! In other words investors should follow a risk-averse attitude with respect to Vietnam portfolios [for details on the risks and problems of the entire Vietnamese economic see Herr/Stachuletz, 2010] With the help of portfolio theory, beta factors and the RoRaC, a few basic recommendations can now be made 16 Economic Development Review - April 2011 In Figure it has become clear that a high risk reduction is possible when the correlations between the individual positions are very negative where possible A highly diversified Vietnam portfolio should also be aimed for In Figure it has also become apparent that with a correlation coefficient of -1, the portfolio return will be about as high as in risk-averse portfolios with much higher correlation coefficients (e.g for k=+0.36, see Fig 1) A stronger diversification therefore does not add up to significant losses with respect to returns A stronger diversification in Vietnam can, for example, be achieved by means of more investments in highly developed technological production sites In this way and at the same time, a deeper value chain can be developed An excellent example for this is the investment of “Pepperle&Fuchs” in HCMC Pepperle&Fuchs is a German company for ultrasound and laser metrology With its high-tech products, this company plays a leading role in the world With the construction of a production site in Vietnam, a stateof-the-art technology is carried to Vietnam and at the same time it creates highly-skilled jobs There is also the advantage that this branch can be correlated negatively with other heavy weights of the Vietnamese portfolio Since the proportion of this type of investment in the portfolio is probably still small, the proportionate diversification effect (see Table above) will be very high This means that for this type of investment a higher RoRaC can be achieved However, it will probably be quite difficult in the medium term to carry substantial stateof-the-art technology from foreign companies to Vietnam This is why several additional recommendations are needed If one looks at the current developments in the Vietnam portfolio, two main streams are striking: The tourism field and the real-estate sector Both sectors have, to a certain extent, a strong positive correlation to each other (due to real-estate in tourism) and reflect high levels of growth One example for this can be seen in the touristic developments in Nha Trang and the construction of numerous new commercial high-rise buildings in HCMC Both fields promise high returns in future, albeit significant risks as well The real-estate bubble could burst, which would bring about a considerable destruction of wealth and far-reaching RESEARCHES & DISCUSSIONS consequences for Vietnam But tourism also has significant risks (e.g environmental pollution, changing preferences of tourists, and new trends in tourism, etc.) All of this leads to the legitimate assumption that both sectors have a high beta factor and therefore a strong influence on the level of risk in the whole portfolio At the same time the two fields only have a low diversification effect, which is also a disadvantage (lower RoRaC, see the previous explanations) What will happen if the real-estate bubble bursts can currently be seen very clearly in the example of Spain Consequences include a steep increase in unemployment and public debt as well as a massive destruction of wealth The consequences for Spanish tourism are substantial No tourist wants to stay in unoccupied housing estates and the capital for operating tourist facilities has been reduced significantly, or totally destroyed Similar developments with almost identical structures (numerous large villas with golf courses and luxury hotels) as in Spain have unfortunately already been observed in Vietnam One example for this is “Sealinkscity“ in Phan Thieát I sincerely hope that the real-estate bubble in Vietnam will not burst, as in contrast with Spain, Vietnam has no European Union to help out in times of crisis So, what can be recommended? The portfolio risk of Vietnam can be lowered quickest in the positions that exhibit the highest beta factor and a high portfolio proportion, i.e the tourism and real-estate branches Although probably impossible, a more cautious development, accompanied by a few precautionary measures, could help In foreign investments great care should be taken in both fields to determine whether foreign investors have sufficient equity base In times of crisis, only when an investor possesses ample equity capital, which clearly exceeds that of the Value at Risk of the investment or the portfolio, can the far-reaching negative consequences for the whole country be held in check Investments of foreign investors with an equity base of less than 5% should be avoided For the development in tourism I recommend following a cautious development which is linked first and foremost to the natural resources of this country, i.e no luxury hotels or golf courses One possible perspective would be to foster and develop a sustainable eco-tourism in Vietnam These measures could lead to the lowering of both fields in Vietnam’s portfolio, which would allow the diversification effect to increase (see above) If at the same time it were possible to attract foreign state-of-the-art technology (especially, for example, in renewable power generation, e.g wind power generation), a well-diversified Vietnam portfolio that would yield satisfactory portfolio returns could be put in place It is of course clear to me that these recommendations presuppose quite a number of assumptions which for the moment are not very realistic for Vietnam However, I see no reason why the potential risk in Vietnam cannot be limited in the medium-to-long term, so that a well-diversified Vietnam portfolio will be able to achieve positive development and prosperity in Vietnamn References Elton, Edwin J et al (2002), Modern Portfolio Theory and Investment Analysis, Wiley Herr, Hansjörg & R Stachuletz (2010), Vietnam am Scheideweg – Analysen einer Ökonomie auf dem Drahtseil, German, Friedrich Ebert Stiftung, Internationale Entwicklungszusammenarbeit, Referat Asien und Pazifik, Dezember 2010 Jorion, Philippe (2007), Value at Risk – The New Benchmark for Managing Financial Risk, 3rd Edition, McGraw-Hill Wolke, Thomas (2008), Risikomanagement, 2nd Edition, German, Oldenbourg, München, Wien Wolke, Thomas (2011a), “The Functioning of Government Bonds - The Example of Greece and Vietnam”, Economic Development Review, Vietnam, HCMC, January, 2011 Wolke, Thomas (2011b), “Towards a Better Understanding of the Current Financial Crisis: The Problems of Measuring Credit Default Risk and the Corresponding Equity Requirements for Banks”, Economic Development Review, Vietnam, HCMC, February, 2011 Economic Development Review - April 2011 17 ... explicitly considered - The consideration of the diversification effect emerges only on the portfolio level Partial consideration of the diversification effect on the level of individual share positions... the daily return of position i and the daily return of the portfolio The beta factor (bi) measures the influence of the individual risk positions and the entire portfolio risk The higher the beta... curves why we turn next to the explanation for the examples of the BMW and MAN shares Example of the portfolio theory For the calculation of the ratios the daily historical share prices from 2005