The assessment of share investments portfolio theory and the return on risk-adjusted capital

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.

1 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

manu-facturer The insights from the portfolio theory for

these two shares can be assigned to any number

of different shares But, due to the necessary

ma-trices, the calculation effort will be increased

con-siderably 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

de-tails on the following remarks see Elton et al.,

2002]

Historical share prices constitute the basic

principles of the portfolio theory First, the

corre-sponding share return is calculated from the

his-torical share price rt:

Thus the return is rt and the price is kt for

the point in time t From the historical share

re-turns the average share return r can now be

cal-culated:

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 covari-ance s1,2 between the two price returns share 1 and share 2 is needed:

With the help of the covariance the accompa-nying correlation coefficient k1,2 is calculated as follows:

Compared to the covariance the correlation co-efficient can be interpreted more easily and bet-ter Details of this will be handled later in this article

At the heart of the portfolio theory are the so-called transformation curves These

transfor-ma-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

eval-uation 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,

Invest-ment Strategies, Portfolio Theory, Return on Risk-adjusted Capital, Risk-averse, Risk-taking, Sharpe Ratio,

Trans-formation Curves, Value at Risk, Vietnam Portfolio, Volatility

tion curves specify the accompanying returns–risk

combination for every possible portfolio

combina-tion of the two shares 1 and 2 The returns are

measured by the average share return, the risk by

the volatility The combination possibilities range

from 100% in share 1 and 0% in share 2 to 50%

in both shares 1 and 2, to 100% in share 2 and 0%

in share 1 In Figure 1 the accompanying

trans-formation curves are delineated for three different

correlation coefficients In the process, the data

from BMW and MAN are drawn upon, which is

why we turn next to the explanation for the

ex-amples of the BMW and MAN shares

2 Example of the portfolio theory

For the calculation of the ratios the daily

his-torical 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

the aggregated portfolio level additional informa-tion and calculainforma-tions 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 portfo-lio 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:

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 1 The result for the BMW-MAN portfolio is rp

= 0.115%

Figure 1: Basic principles of portfolio theory – transformation curves

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 1 shows the resulting key figures for

2005

Table 1: Key figures for BMW and MAN shares for

2005 on the basis of daily trade data.

In Figure 1 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 1 can

be interpreted The blue transformation curve

be-gins in the top right for the portfolio that consists

of 100% MAN shares Portfolio returns and

volatility reflect the individual MAN share

Anal-ogous to this, the other end of the dashed curve

of transformation reflects the portfolio consisting

only of BMW shares (see Figure 1 and Table 1)

Finally, the portfolio values of the above portfolio

example (45.12% BMW and 54.88% MAN shares)

are shown in Figure 1

From Figure 1 it is also clear that there is a

portfolio combination in which the portfolio

vola-tility is minimal This portfolio can be calculated

as follows:

The empirical covariance amounts to sBMW,MAN

= 0.00005159 The accompanying portfolio

propor-tion of the BMW shares amounts to wmv BMW =

71.98% while the accompanying minimal portfolio

volatility is smv p= 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 combina-tions A portfolio is inefficient when there is an-other portfolio combination that has higher returns for the same risk For the dashed curve of transformation in Figure 1 (kBMW,MAN= +0.36) the inefficient area extends from the portfolio with the minimal volatility (wmv

BMW = 71.98%, see above)

to a portfolio which consists only of BMW shares (wBMW= 100%) By selling BMW shares and pur-chasing 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 invest-ment strategies can be deduced

3 Derivative of simple investment strategies The first general purpose strategy can be de-rived directly from the above-mentioned ineffi-ciency and is “Ineffiineffi-ciency portfolios are to be avoided.”

But in this context the transformation costs that are accrued by the restructuring of an ineffi-cient portfolio need to be considered A restructur-ing 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 min-imal portfolio volatility!”

For the example in Figure 1 with correlation coefficients of k = + 0.36 this would mean se-lect-ing the portfolio with the minimal volatility, i.e

wmv BMW = 71.98% and with smv

p= 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 (volatil-ity) 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

Asset

position exposure Risk Portfolio weights

Average share return Volatility

Portfolio €820.00 100.00% 0.11% 1.03%

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

ex-ception The question of which portfolio an

in-vestor who is willing to take an average amount

of risk (between extreme risk-aversion and

ex-treme risk-taking) should choose, is much more

in-teresting 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

ap-propriate strategies

4 The Return of Risk-Adjusted Capital (RoRaC)

For the evaluation of share portfolios and

indi-vidual 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

in-vestor who does not invest his capital in

invest-ments fraught with risk can invest the capital in

risk-free bonds, e.g German government bonds

[see Wolke (2011a)] The risk-free interest rate

re-flects opportunity costs that arise from an

invest-ment 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

ac-companying Sharpe Ratios (Table 2) can be

calcu-lated:

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

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 partic-ular 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 con-sideration 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 nec-essary 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-Ad-justed 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 in-fluencing 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 secu-rities The other earnings are e.g dividend pay-ments or coupon interest paypay-ments 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 dif-fers from the Sharpe Ratio by consideration of

Asset position

Risk-free interest rate (rrf)

Average share return (ri)

Volatility (si)

Sharpe Ratio (SRi)

Portfolio 0.01172% 0.115% 1.025% 0.10076

Table 2: Sharpe Ratios for BMW and MAN shares for

2005 on the basis of daily trade data.

other earnings instead of merely the average price

returns and the currency data The decisive

differ-ence 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

posi-tion 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,

ri: average return (expected value)

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

follow-ing 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

se-lects 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

diversifi-cation effect Now the diversifidiversifi-cation effect can be

quantified on the portfolio level, albeit not the

pro-portionate diversification effect for the individual

risk positions BMW and MAN The individual po-sitions 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 fol-lows:

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 in-fluence of the individual risk positions and the en-tire 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 accom-panying CoVaR can now be calculated:

The sum of the CoVaR must yield the VaR of the portfolio exactly The proportionate diversifi-cation effect is then €8.73 - €6.11 = €2.62 for BMW and €13.74 - €12.53 = €1.21 for MAN The propor-tionate 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 for-mula 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 be-tween 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 port-folio VaR can be lowered considerably when the MAN shares are disposed Both of these features

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

5 RoRaC Example for the BMW-MAN Portfolio

To begin with, in taking

dividend payments into

ac-count, assumptions about

the estimated amount of

distributions can be made

In this way the annual

div-idend payment will amount

to 2% p a for BMW and

1% for MAN with respect

to the risk position The

risk-free interest rate will

again be 3% p.a For the

final calculation of the

RoRaC all amounts will

have to be converted in

cur-rencies and be fixed within

a specific timeframe The

time frame of one year has

been chosen for this

exam-ple (the timeframe selected

will be insignificant for the RoRaC

result) The following total p.a

earn-ings for BMW and MAN are:

BMW: 0.042%.€370.256 days

(price return) + 2%.€370 (dividend) –

3%.€370 = €36.08

MAN: 0.175%.€450.256 days

(price return) + 1%.€450 (dividend) –

3%.€450 = €192.61

Finally, the Component Value at

Risk needs to be calculated for a full

year:

The result is now reflected in the

following RoRaC values:

BMW: €36.08 / €97.76 = 0.369

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 var-ious portfolio weights in the tables that follow In Table 3 the individual VaR, the Component Value

at Risk and the accompanying RoRaC values for BMW and MAN are shown In Table 4 the VaR and RoRaC values are shown for the portfolio With the help of the results from Table 3 and

Weight BMW = 1-Weight MAN CoVaR BMW VaR BMW Single CoVaR MAN VaR MAN Single RoRaC BMW RoRaC MAN

45.12% €6.11 €8.73 €12.53 €13.75 0.369 0.96

Weight BMW = 1-Weight MAN

Total portfo-lio profit p.

y.

Portfolio volatility Portfolio VaR Portfolio RoRaC

45.12% €228.69 1.03% €18.64 0.767

Table 4: VaR, and RoRaC for different portfolio weights for

the entire portfolio Table 3: Component Value at Risk and the accompanying RoRaC values for

BMW and MAN

4, a few mechanisms can now be observed From

Table 3 it becomes apparent that the

proportion-ate 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 –

depend-ing on the amount - be greater (and analogous

with high numbers of MAN shares)

From Table 3 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

de-creasing 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

vola-tility 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

in-vestor 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

eq-uity capital should only invest in the number of

MAN shares that maintains the portfolio VaR which is lower than his/her equity If the inves-tor 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 disposi-tion, if he has much more than €18 in equity cap-ital, 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 in-crease in equity capital, or (2) A reduction of the portfolio VaR

An increase in equity capital is usually not im-mediately feasible and has something to do with aspects that are not within the scope of this arti-cle 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 free or almost risk-free investments

Next, the previous explanations can be applied

to real investments in Vietnam

6 Applications and implications for real invest-ments in Vietnam

For the previously mentioned deductions, it will be necessary to make a number of assump-tions which are not achieved in real investments

Here are the most important assumptions as fol-lows:

- 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 recommenda-tions for real investments, returns, beta factors, Value at Risk values and correlations must all be estimated from plausible assumptions or compa-rable investments

The first key assumption concerns the risk

propensity of the investors For the most part

in-vestments in Vietnam can be undertaken by:

- Foreign private investors (firms, investment

companies),

- Vietnamese private investors (firms,

individ-uals) and

- The Vietnamese government (state

institu-tions)

The deduction or assumption in terms of a

con-sistent risk attitude of all three investor types is

not possible The conditions under which the

var-ious investors evaluate their possible real

invest-ments are much too different to find a common

denominator amongst them Another possible

ap-proach consists of forming or analysing portfolios

of real investments on different aggregation

lev-els In this way one can try to apply the portfolio

theory on the company level The different

prod-ucts 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

atti-tudes This is only possible at the highest

aggre-gation level

If one looks at the portfolio at the highest

ag-gregation 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,

in-dustrial 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

possi-ble bursting of the real-estate bubpossi-ble; (2) a

sub-stantial 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

eco-nomic see Herr/Stachuletz, 2010]

With the help of portfolio theory, beta factors

and the RoRaC, a few basic recommendations can

now be made

In Figure 1 it has become clear that a high risk reduction is possible when the correlations be-tween the individual positions are very negative where possible A highly diversified Vietnam port-folio should also be aimed for In Figure 1 it has also become apparent that with a correlation co-efficient 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 re-turns

A stronger diversification in Vietnam can, for example, be achieved by means of more invest-ments in highly developed technological produc-tion 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 metrol-ogy With its high-tech products, this company plays a leading role in the world With the con-struction of a production site in Vietnam, a state-of-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 cor-related 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 3 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 diffi-cult in the medium term to carry substantial state-of-the-art technology from foreign companies to Vietnam This is why several additional recom-mendations 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 ex-ample for this can be seen in the touristic devel-opments 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 con-siderable destruction of wealth and far-reaching

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

fac-tor 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

ef-fect, 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

ex-ample of Spain Consequences include a steep

in-crease in unemployment and public debt as well

as a massive destruction of wealth The

conse-quences 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

struc-tures (numerous large villas with golf courses and

luxury hotels) as in Spain have unfortunately

al-ready 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

prob-ably impossible, a more cautious development,

ac-companied 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

eq-uity 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

de-velop a sustainable eco-tourism in Vietnam These

measures could lead to the lowering of both fields

in Vietnam’s portfolio, which would allow the di-versification 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 re-turns 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 can-not 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

1 Elton, Edwin J et al (2002), Modern Portfolio

The-ory and Investment Analysis, Wiley

2 Herr, Hansjörg & R Stachuletz (2010), Vietnam am

Scheideweg – Analysen einer Ökonomie auf dem Draht-seil, German, Friedrich Ebert Stiftung, Internationale

En-twicklungszusammenarbeit, Referat Asien und Pazifik, Dezember 2010

3 Jorion, Philippe (2007), Value at Risk – The New

Benchmark for Managing Financial Risk, 3rd Edition,

Mc-Graw-Hill.

4 Wolke, Thomas (2008), Risikomanagement, 2nd

Edition, German, Oldenbourg, München, Wien

5 Wolke, Thomas (2011a), “The Functioning of Gov-ernment Bonds - The Example of Greece and Vietnam”,

Economic Development Review, Vietnam, HCMC,

Janu-ary, 2011

6 Wolke, Thomas (2011b), “Towards a Better Under-standing 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