Retirement portfolio construction for Beatrix and Karl

Investment Strategy Report

Index

Beatrix and Karl are breaking even and have little savings. Their expenses in retirement, depending on estimates, could leave them with a deficit as their only source of non-investment income is Karl's pension. Therefore, the portfolio will be constructed with income generation in mind. The couple has a low risk tolerance and a short time horizon. They have three years until retirement that they can use to build the portfolio before they may have to start taking out. Their income needs may range from zero to €7000 per annum. Their budget does not include any abnormal expenses, but those will be included in our calculations, and we are seeking a portfolio that can generate €10,000 a year for the couple.

Because there is a strong need for liquidity, 10% of the portfolio will be in money market. The couple has the option to reduce this to 5% (€10,000) but it is advised that they do not. The couple has a low risk tolerance, but needs to make some long-term gains in order to meet financial needs closer to the end of their retirement. Thus, 20% of the portfolio will be in equities. This will come in the form of a highly regarded index fund, giving non-systemic risk at a fair price.

The remaining portfolio will be 30% corporate bonds and 40% government bonds, so mix safety with returns. These will be staggered such that the couple is always within a year of another maturity. No initial maturities will be less than 3 years. Once the couple retires, the proceeds of their home sale will be added to the portfolio and duration of the bond portfolios will tighten. The portfolio will generate in the range of €10,900 per year in retirement, sufficient even to meet the worst-case estimates of spending.

Chapter 1

Beatrix is fifty-seven years old and lives in Munich with her husband Karl. She works part-time as an administrative assistant. Her husband is a purchasing manager. Karl will retire from his position in three years' time with a full pension. Beatrix is expected to retire at this time as well, since they are selling their home in Munich and relocating to a small village. While there are villages on the Munich metro line, we will assume that Hans does not live within commuting distance. Beatrix is unlikely to find meaningful part-time work in the village so should expect to retire when they sell their house. Demand for housing in Munich is relatively strong so they can probably move their house quickly upon Karl's retirement.

The couple have limited financial resources but also limited needs. They have £20,000 remaining on a variable rate mortgage in the UK. They also need income for their cost of living. Their children have grown, so there is no immediate need to support any of the family. The couple intends to visit Paris in three years at a cost of €8000 but have few other major travel plans.

In terms of resources, Beatrix and Karl have just the remaining three years of income and modest savings of €10,000 cash. Neither has any stocks and therefore cannot be considered sophisticated investors. With their age and lack of investment knowledge, Beatrix and Karl can be expected to have a low risk tolerance. When they retire, they will sell their Munich house and purchase a house in the village, generating approximately €60,000 in free cash flow, net of sales fees.

Between the income earned over the next three years, Karl's pension and the profit on the swap of the houses, Beatrix and Karl can reasonably expect to have some savings stockpiled for their retirement. They have only modest ambitions for travel and expect to live an inexpensive Bavarian village life. Dinner for two with beer in such a village costs less than €15, for example. Aside from the occasional return to Munich for cultural events, month-to-month expenses for the couple can reasonably be covered by the pension. The savings, therefore, is to be used mainly for exceptional expenses.

That Beatrix and Karl are expected to have a sound financial footing for their retirement, they can view their inheritance in one of two ways. They can view it as a backup fund, in case of emergency. For example, to help out family members such as their relatives in Texas who could lose their health care benefits or have their home destroyed by a hurricane. They could use it as backup for themselves, in case retirement expenses are greater than expected. The other way to view the inheritance money is as money that if managed properly can flow through to their children.

The couple could also view the money as both -- financial backup for themselves or their family members in the case of crisis, but if it is not needed then it would become inheritance. In either case, Beatrix and Karl are in an advantageous position. Although they are not wealthy, their spending ambitions match their spending capabilities. This money is not needed immediately, but could prove valuable. With limited financial knowledge, Beatrix and Karl will not want to take great risks with this money, so the investment strategy must be drawn up with that in mind as well.

Chapter Two: Executive Summary

Beatrix and Karl have adequate cash flow. They have a minor shortfall at present owing to their mortgage in the UK. Using fairly conservative estimates, they will face a shortfall in their first two years of retirement as well. When the mortgage is finished, they will have a modest surplus. Sensitivity analysis shows that if their spending levels are higher than anticipated, they will run a deficit. However, the inheritance provides them with enough money to last the remainder of their lives. These estimates do not include large expenses, such as additional vacations beyond Paris, nor do they take into consideration the inheritance the couple may wish to leave their children. Although the couple has a relatively healthy financial position, they will need to find suitable investments for the inheritance money in order to meet their needs and reduce their financial risk.

Chapter Two: Future values and risk

Beatrix and Karl's cash flow situation is adequate. It is assumed that they have been, more or less, breaking even with their inflows and outflows. To be conservative, it will be assumed that Beatrix will only earn €15,000 for each of the next three years. This hedges against economic downturn and it also assumes she will wish to slow down, in order to transition into retirement. The couples combined income for the next three years will then be €70,000 per year.

In terms of outflows, they have their living expenses, their mortgage in the UK and savings. Their living expenses are expected to decline, now that their last dependent child has moved out. If we assume this child cost them an average of €400 a month in food, extra utilities, gasoline and sundry school expenses, that money can be put towards savings.

The UK mortgage is worth £20,000 and is variable rate. Interest rates in the UK are low, and expected to remain there for some time in order to spur economic growth. The rate we will conservatively estimate at 5%. The time frame for this mortgage is unknown at present. If we assume that they would not have taken on a mortgage for more than a few years past retirement, then five years remaining can be assumed. This gives a mortgage payment of £378 per month, or £4529 per year. That equates to €5077 at current exchange rates.

To estimate post-retirement living expenses, their current expenses must be analyzed and then adjustments made to reflect the realities of post-retirement life. The couple broke even on €70,000 per year. It is estimated that post-retirement cash flow needs are between 60-80% of pre-retirement needs. At the lower end of the income scale, the lower figure can be used, since government benefits make up a greater portion of post-retirement cash flow (Ibbitson, et al., 2007). The cost of living in rural Bavaria is also much lower than the cost of living in Munich, by 20-30% on many key consumables such as food. Transportation costs are also lower in the villages due to their small size and complex bicycle networks. Therefore, it is a reasonable expectation that 60% of pre-retirement income will be required by Beatrix and Karl in order to survive. The couple will also benefit from the presence of their son and his family, who will be able to help them in their later years, further reducing costs. However, since 60% is at the very low end of the range, it is more conservative to utilize an estimate of 65% or 70%.

Germany's inflation rate is currently hovering around historic lows. The statistics for recent years are the most accurate guide, as they reveal the inflation rate in the post-unification, globalized, and expanded-EU environment. The German inflation rates have averaged, on a compounded basis, just over 1.9% for the past seven years (Index Mundi, 2009). An inflation rate of 2% per annum shall be assumed for our future cash flows model, the additional 0.1% reflecting a desire for conservativeness in our estimates.

Karl's pension pays him 80% of his current salary, which is not expected to increase in the final three years. The pension benefit is indexed to inflation. We will assume a 30% tax rate for both pre- and post-retirement income.

The couple is breaking even at present, with a surplus of €264 expected for 2010. This assumes minimal work for Beatrix, so anything she works above and beyond the €15,000 threshold will allow the couple to save more money for their retirement. With no raises and no additional work from Beatrix, the couple will run a small deficit for their last two working years.

In retirement, the couple will not make enough money to support themselves. Their income will be reduced considerably, given that Beatrix' income will disappear entirely and Karl's will be reduced by 20%. The expected reduction in living expenses will just barely accommodate for the reduced earning power. The couple's future cash flow statement looks as follows:

T

30%

I

2%

PRCF

65%

Future Values

Working

Retirement

2010

2011

2012

2013

2014

2015

2016

Income

70000

70000

70000

44,000

44,880

45,778

46,693

Taxes

21000

21000

21000

13200

13464

13733

14008

Net Income

49000

49000

49000

30800

31416

32044

32685

Mortgage

0

0

Living Exp

44200

45084

45986

30489

31098

31720

32355

Surplus (shortfall)

-277

-1161

-2063

-4766

-4759

When the couple enters retirement, they will face an annual shortfall of around €4700-€4800. This chart clearly illustrates the most pressing financial problem for the couple -- their UK mortgage. This is a drain in excess of €5000 per year for the next five years. This hampers their ability to add to their retirement savings. In their first two years of retirement, they will face a shortfall in excess of €4700, which is entirely attributable to the UK mortgage. Without that mortgage on their books, they would be in a much stronger financial position.

To meet these needs, the couple will have approximately €60,000 in profit from the swap of houses, and the inheritance. The current savings of €10,000 is likely to be spent on the Paris vacation and therefore should not be considered as funds available for retirement. The above calculation indicates that the couple is actually unlikely to save any more money prior to retirement under their current situation.

However, their expected annual surplus is only €300. This cuts a fine line. For example, using the same spreadsheet if the savings required jumped to 70% instead of 65%, the couple would face a shortfall in the first two years in excess of €7000 and in the remaining years the shortfall will be over €2000. If the couple's costs are much higher than expected, at 80%, they will face a shortfall of nearly €12,000 for the first two years and around €7000 thereafter. These figures do not include major expenses such as travel, vehicles, gifts to children/grandchildren and other potentially sizeable outlays that are not a part of the couple's current spending patterns but could be as retirees.

Germans live, on average, to be. £200,000 is worth €223,896. If the inheritance is not invested, and the couple's will easily have enough to last their retirement. However, they may wish to consider the amount of money they would like to leave their children and grandchildren.

It is determined then that the couple needs to invest the inheritance money in a manner that allows them to meet their income needs. The couple is in a good position, whereby it can probably earn enough with the returns on the inheritance to leave the principle for large expenditures and to leave behind.

The couple does need to consider the financial risk that they have. Their retirement income is going to be fixed, which means that their budget is going to be highly sensitive to spending. If their spending levels are higher than they expect, they will not likely spend all of the inheritance money, but with a few big ticket items they may find themselves with nothing to leave behind.

The average life expectancy for Germans is 79 years at birth, which equates more to 83 or 84 for a couple in their late 50s. They will therefore need the inheritance money to last at least the next twenty-five years, if not more. Taking the view that some of this money is expected to be passed down to their heirs, their investment horizon is even longer. However, given their level of sensitivity to retirement costs, they should focus their investment plan on using this money to meet their own retirement needs, and not worry about passing it down.

Chapter 3 Executive Summary

Beatrix and Karl are not savvy investors and therefore will only be offered the most basic of securities -- money market instruments, bonds, stocks and mutual funds. Money market instruments give the lowest return but bear the least risk. They are short-term in nature. Bonds are riskier, but most types of bonds are relatively safe investments. Equity can be risky, but proper diversification can eliminate firm-specific risk. Mutual fund risk and returns depend on the fund.

The couple has a short time horizon, since they will need their inheritance money to help finance their retirement. They have a low risk tolerance, owing to their lack of investment sophistication. The portfolio chosen should reflect a low-risk orientation and short time horizon above all else.

Chapter 4 Executive Summary

The first component of the investment strategy is that the couple should pay off the mortgage in the UK. They will want to generate from free cash flow in the three years that until they retire, which allows them to build out a bond portfolio with a medium-range duration. With a cash cushion of €10,000 in money market funds, they can maintain the longer duration on their bond portfolio, allowing them to capture higher returns.

An ideal figure to cover even the highest expected post-retirement living costs plus incidental expenses is around €10,000 per annum. The couple can achieve this with 50% equities, but that figure is too high. Instead, the couple should have only around 20% equity in their portfolio, and use mid-range corporate bonds to increase the returns without increasing risk significantly, since all of the bonds will still be investment grade.

Chapter 4 Investment Strategy and Benchmarks

The investment strategy is predicated on a few assumptions. We have determined that Beatrix and Karl have a low risk tolerance and a short time horizon. The portfolio needs to have some degree of liquidity to meet both potential ongoing needs plus any large or unforeseen expenses that may arise. Potential inheritance to children and grandchildren will be addressed in subsequent years and therefore will not play a large role in the current investment strategy. These factors will underpin the investment strategy that is devised.

Beatrix and Karl are facing two distinct components to their future. One is the remaining work years and the other is the retirement years. The first component of the strategy therefore deals with the immediate strategy to get the couple through the next three years until they reach their retirement. The numbers show minor shortfalls in the next three years, of €277 in 2010, €1161 in 2011 and €2063 in 2012. The couple does not make enough money to cover their current living expenses. The primary cause of this shortfall is the mortgage in England.

It is assumed that the couple's current €10,000 savings will go to the planned vacation to Paris. The first component of the strategy therefore will be to get the couple to retirement and allow them to take that trip. At their current burn rate the couple's savings would drop from €10,000 to €6499 by retirement. This will not be enough to cover the estimated €8000 cost of the trip (especially considering that inexperienced travelers always underestimate how much they will spend on when they vacation). The Paris trip thus becomes the first challenge that the strategy needs to address.

The mortgage in the UK should be paid off. The first £20,000 of the inheritance should be used to eliminate this mortgage burden. This strategy serves multiple purposes. First, it eliminates the risk of their variable rate mortgage increasing in the coming years as the UK rebounds from the economic downturn. Second, the early repayment penalty -- if there is one -- is likely less than the interest the couple will pay on this mortgage. The third benefit is that it frees up cash flow over the course of the next three years. The house has been sold and the mortgage is at least twenty years old. There is no need to carry this debt any longer. By applying £20,000 to pay off the mortgage, the couple will have piece of mind knowing that their remaining major debt has been eliminated and that they can get on with the business of saving for and enjoying their retirement. Without the mortgage debt, the couple will have a surplus for each of the next three years. That surplus will be €4800, €3916 and €3014. If the couple saves all of this, they will have a savings account worth €21,370, including the amount they already have saved. Instead of having a deficit in their first two years of retirement, they will carry a surplus there as well.

The alternative to this strategy is to carry the deficit and then tap the investment account when the Paris trip arrives. Alternately, the Paris trip could be paid for with the proceeds of the sale of the Munich house. The way to measure the effectiveness of the strategy is to compare the rate that the couple pays for its mortgage with the rate it can expect to earn if it invests that £20,000. The estimated the interest rate on the mortgage is around 5%; a low-risk, short time horizon investment will not best that. It is important to evaluate the opportunity cost of an investment decision. In this case, investing the £20,000 will not yield enough return to cover the cost of the mortgage interest over that period. The best use of that £20,000 therefore is to pay off the UK mortgage.

For the next three years, the couple will be saving money. This will give them a savings account with €21,370. Half of this will go to Paris. They will have approximately €200,000 remaining from the inheritance after the mortgage has been paid off. Although the couple expects to gain €60,000 on the sale of their Munch house and subsequent purchase of a village home, the timing of this cash flow is uncertain. Therefore, the investment strategy should assume that monthly income from the investment account will be required immediately upon retirement.

To guide investment strategy, the amount of income generated must be estimated. The original estimate of 65% of pre-retirement expenditures may be insufficiently conservative. Taking 70% as a more conservative number, the couple will need to generate approximately €2200 per year from its investment account in order to meet its ongoing needs in retirement. During the first three years, the investment account will be able to stockpile earnings in order to prepare for retirement.

The next step is to analyze the current rates of return. Given that the couple will not need to touch their investment account for the next three years, there is no reason to put any of it in cash or money market securities. It is assumed that interest rate parity holds, such that there is no need to differentiate between bonds denoted in different currencies. German government bonds currently offer yields of 1.66% on three-year bonds (Bloomberg, 2009). If the entire €200,000 was invested in such bonds for three years, compounding, the total return would be €10,126. This level of return is higher than the current inflation rate but lower than the long-term inflation rate in Germany. This level of return is acceptable, because the couple only expects a shortfall of around €2100 per year. The portfolio would earn approximately €3320 per year on a non-compounding basis. Clearly, a portfolio comprised entirely of German government bonds would meet the couple's cash needs under normal expenditure scenarios.

However, the possibility of abnormal expenditures makes it reasonable that the couple should seek higher returns. Risk tolerance is a two-way street, after all. The risk that such a portfolio would not meet the couple's needs must be given equal consideration with the risk that the portfolio will lose value.

The retirement period will be marked with the €60,000 infusion to the retirement account. At this point, the couple's retirement future looks much more certain. They will still want to earn more than the government bond rate, however, to hedge against their expenses being in the 80% range or against unexpected major spending requirements. A portfolio generating a 5% annual return would yield €10,000 per year to the couple pre-retirement and €13,000 post retirement. This would provide comfort level against an 80% spending level (which equates to an annual deficit of around €7000), plus unforeseen expenses. In other words, such a return would provide the couple with the income they need and build capital for future, unforeseen uses. The next step is to calculate the portfolio that will give the couple this level of return.

The historic market premium for equity is around 7% above the risk free rate. The risk free rate in Germany is 0.44% at present, meaning that equity risk is 7.44%. Using the capital asset pricing model, this implies a risk level (beta) on 7-year German government bonds (yield 2.9%) of

0.33. The equity component of this portfolio will need to be fully diversified to remove non-systemic risk, giving it a beta of 1. At any given point, there should be around €10000 to meet the couple's known and potential emergency liquidity needs, with a beta of 0. These figures can then be solved for the desired return of 5 to determine the appropriate asset allocation of the portfolio. The resulting investment strategy is to have 51.6% in equities, 38.4% in bonds and 10% in money market.

Given the couple's low risk tolerance, age, time horizon and low knowledge of investments, such a high proportion of equities is likely unsuitable. It is tempting to load up on equities given that the markets are down a little bit at present, but marketing timing is not sound investment strategy for near-retirees. While this investment plan delivers adequate gains, it is too risky. An asset allocation of 20-30% equities in more in line with their risk tolerance. The expected return on a portfolio that is 20% equity, 70% fixed income and 10% money market is 3.562%, which would yield returns of €9261 after retirement. This figure is sufficient to meet even the most conservative estimates of the couple's cash flow needs.

One means for the couple to increase their return without sacrificing too much risk is to replace some of the government bonds with corporate bonds. The Bloomberg Investment Grade U.S. Corporate Bond Index, with an average duration of 4.58 years, has an average redemption yield of 5.05% (Bloomberg, 2009). If 30% of the portfolio was placed in investment grade corporate bonds the expected return on the portfolio would be as follows:

(.2)(7.44) + (0.1)(0.44)+(.3)(5.05)+(.4)(2.9) = 4.207%

This equates to €10,938 post-retirement. It leaves the couple with just 20% equity, which amounts to €52,000 post-retirement. It is difficult to build a fully diversified equity portfolio with that amount of money, the investment should be in an index fund. This will allow the couple to participate in market gains, have no non-systemic risk in their equity component, and will give them lower transaction costs than if they purchased individual stocks.

Chapter 5 Executive Summary

The money market will be chosen on the basis of the best available option. Because of the need for diversification at low cost, an equity mutual fund will be chosen rather than individual equity securities. The DWS Deutschland Fund is one of the best performing funds in the sector. The government bond portfolio will contain 5 bonds, with maturities staggered between 3-7 years initially, moving to 1-4 years when the couple retires, to provide steadily liquidity. The corporate bond portfolio will be structured in a similar manner, but with a variety of companies, credit ratings, nations and industries to provide the best possible diversification that a five security portfolio can have.

Chapter 5 Specific Securities

There are found components to our investment strategy -- money market, government bonds, corporate bonds and an equity mutual fund. The latter was chosen on the basis of cost reduction -- it is cheaper to absorb mutual fund management fees that the pay the transaction costs to build and maintain a diversified equity portfolio in the €50,000 range.

There are a number of equity mutual funds available to Beatrix and Karl. One highly regarded fund is the DWS Deutschland Fund, which has a five star rating from Morningstar (Morningstar.de, 2009). The benchmark for this fund is the DAX. For most years, this fund has performed in line with the DAX, give or take a few percentage points. During the past two years, however, the fund has drastically outperformed the DAX, by 8.3% and 14.1% respectively. This strong performance in the face of economic downturn is encouraging. While it should be noted that with mutual funds past performance is not an indicator of future performance, the Morningstar system is well regarded and this fund has performed well. It has a relatively low management expense ratio of 1.4%, which is in the appropriate range for an index fund. The fund is categorized as a large growth fund, so is not subject to the volatility that smaller funds or growth funds are.

The money market component to the investment strategy will be simple. The main objective of the money market portion of the portfolio is to provide liquidity for Beatrix and Karl. Purchases will be revolving, and based on availability. Potential components can be German government short-term securities (3 months) or bank issued money market instruments.

The most complex components of the portfolio will be the bond portfolios. Bond funds were considered for these, because of the benefits of professional management, but were ruled out for a couple of reasons. The first is that bond funds do not typically provide distributions the way that bonds do. Whereas a typical semi-bond will pay interest twice a year to the investor, which will fuel the money market account for Beatrix and Hans, bond funds may not; the interest may be plowed back into the fund. Thus, bond funds may serve to reduce portfolio risk, they do not provide the distributions that the couple needs. The second reason is that bond funds may lose value over time. Bonds may also lose value as a result in changes in interest rates, but that is irrelevant if the bonds are held to maturity. A bond fund, however, will see its value decrease with changes in the interest rates. In particular, increasing interest rates are bad for bond funds, as the value of the cash flows that they will receive goes down. For Beatrix and Karl, a bond held to maturity will give them the precise cash flows that they expected when they purchased it.

There are two bond portfolios are that are being constructed. The first is the government bond portfolio. The couple has a short time horizon, so should not purchase long-term bonds. Long-term bonds may lose value in a rising interest rate environment. If the couple has emergency funding needs, they will be forced to sell such bonds at a loss. The best strategy for this bond portfolio is to build a staggered set of maturities going out to the midrange.

The benefit of a staggered set of maturities is that a bond will mature every year or two, providing liquidity to the portfolio beyond the interest flows. This will help the couple to meet large needs. Even if the need is sudden, there will be a bond within a year of maturity that can be sold without taking too large a loss. The number of bonds and the length of the stagger are determined by two further factors. One is the size of the portfolio; the other is the desired duration. The government bond portfolio is 40% of the total portfolio, which initially is €80,000, expanding to €104,000 post retirement. The couple does not need any money during the first three years of the investment period. Thus, it is recommended that the bond portfolio contain five bonds, €16,000 each, with maturities from 3-7 years. The bond portfolio would therefore have the following bonds:

10/12/2012, yield 1.67%

10/11/13, yield 2.08%

10/10/14, yield 2.39%

1/4/16, yield 2.7%

1/4/17, yield 2.9%

This portfolio has a modest duration and a relatively low yield. The first bond will mature just prior to Karl's retirement, which will allow the couple to make a decision as to whether or not they need the money or wish to reinvest it. Duration is an important consideration for the bond portfolio because the duration should match, more or less, the time horizon of the investment. By avoiding long-term bonds, the duration is kept in the short to medium term range. The portfolio's duration will be longer at this stage of the investment because they do not need any of the money for at least three years. When the first maturity is reinvested, it will likely be in the 1/4/18 bond. This will result in a much lower duration for the government bond portfolio, because the time horizon for the investment is much shorter at that point due to the couple's more immediate liquidity needs.

The corporate bond portfolio will be constructed along much the same lines. The income from the corporate bonds will be needed by the couple just as much as the income from the government bonds. Therefore, the duration will be kept shorter once the couple reaches retirement than when the portfolio is first formed.

There are a wide range of corporate bonds available. They should all be investment grade, but beyond that a mix of industries and firms would help to diversify the corporate bond portfolio a little. It will not be complete diversification, of course, but some is better than none. Bonds are not traded on open markets, but rather traded through brokers. As such, the use of a specific bond in a portfolio is subject to its availability. The following portfolio is therefore an example of the type of maturities, yield and diversification that the corporate bond portfolio should have. Each of these would be purchased in increments of €12,000 initially, since corporate bonds are 30% of the €200,000 initial investment.

HSBC 12-12-12, yield 4.867%, rated A

Daimler Chrysler 11-15-13, yield 5.465%, rated A

Credit Suisse 1-15-15, yield 4.453%, rated AA

Time Warner 1-15-16, yield 6.26%, rated BBB

Landwirtschaftliche Rentebank 2-1-17, yield 3.553%, rated AAA

This portfolio mixes firms from a wide range of countries, most with global operations. There are a variety of different credit ratings as well -- the riskier firms like Time Warner must be balanced with AAA corporate bonds. The portfolio is otherwise structured in a manner similar to the government bonds.

In summation, the portfolio will consist of:

10% money market

20% DWS Deutschland Fund

40% Government bond portfolio

30% Corporate bond portfolio

Works Cited:

Ibbitson, R.; Xiong, J.; Kreitler, R.; Kreitler, C. & Chen, P. (2007). National savings rates guidelines for individuals. Journal of Financial Planning. April 2007.

Index Mundi. (2009). Germany Inflation Rates. Index Mundi. Retrieved November 16, 2009 from http://www.indexmundi.com/germany/inflation_rate_%28consumer_prices%29.html

McClure, B. (2009). Modern portfolio theory: An overview. Investopedia. Retrieved November 16, 2009 from http://www.investopedia.com/articles/06/MPT.asp

No author. (2009). German government bonds. Bloomberg. Retrieved November 16, 2009 from http://www.bloomberg.com/markets/rates/germany.html

Morningstar. (2009). DWS Deutschland. Morningstar.de. Retrieved November 16, 2009 from http://www.morningstar.de/de/snapshot/snapshot.aspx?id=F0GBR04COC&lang=de-DE