- Direct real estate outperformed other asset classes on a risk-adjusted basis based on summary statistics of returns from 1987-1999 in the UK. Bonds also outperformed equities during this period. - Direct real estate had a negative correlation with other asset classes, providing diversification benefits, while indirect real estate was strongly positively correlated with equities. - During an economic downturn from 1993-1995 in the UK, direct real estate increased while other asset classes declined, demonstrating its diversification properties. - A mean variance analysis found that an optimal portfolio allocated 57% to direct real estate, 41% to bonds, 2% to equities, and 0% to indirect real estate, achieving the highest risk

1. CASE 6A – Real Estate
Maastricht University
School of Business & Economics
Place & date: Maastricht
September 27, 2017
Name, initials: Hodjeff, TCB , Busch, RS,
Hüttenrauch, N,
Falchetti, EF
Fassmer, SJ
For assessor only
ID number: I6112082, I6112235, I6112390,
I6112826,
I6170814
1. Content
Tutorial group
number
10 2. Language structure
Course code: EBC2054 3. Language accuracy
Sub-group
number:
2 4. Language: Format &
citing/referencing
Writing tutor
name:
Juan Overall:
Writing
assignment:
6A Advisory grade
Assessor’s initials
Our UM email address: t.tatiana@student.maastrichtuniversity.nl,
r.busch@student.maastrichtuniversity.nl​, ​e.falchetti@student.maastrichtuniversity.nl​;
s.fassmer@student.maastrichtuniversity.nl​, n.huttenrauch@student.maastrichtuniversity.nl

2. 01 Introduction
The Modern Portfolio Theory (MTP) suggests that investors should allocate investments
within and across asset classes in order to reduce exposure to risk. The most commonly used
are equity and bonds but there other major asset classes one can choose from. Commercial
real estate, for example, is such and in fact accounts for around one-third of all assets. What
makes allocating capital to real estate investments attractive are not their large expected
return, nor their low risk but rather their weak correlation with other asset classes that allows
for diversification (Geltner et al,. 2013). This diversification effect stems from lower
correlation with the market and is due to the nature of the asset class, which is its physicality.
According to Dr. Eichholtz (1996), returns of real estate markets are rather influenced
through local events than national and therefore follow largely different developments. The
asset class itself can be further separated into direct and indirect real estate investment. Direct
investment is acquiring the actual property whereas indirect investment is buying shares of
real estate investments through Real Estate Investment Trust (REIT).
That being said, the purpose of this paper is to examine how real estate (direct or indirect)
effects a mixed-asset portfolio, regarding risk, return and efficiency. In addition, the
diversification possibilities will be highlighted, as well as the potentials to reduce downside
risk of portfolios during economic distress. As a benchmark, modern portfolio theory will be
used to allocate investors funds effectively.
02 Summary Statistics
The following section of the paper will describe the summary statistics of four asset classes:
equity, bonds, direct and indirect real estate (see Appendix A). For convenience, the U.K.
data used has been annualized and it ranges from February 1987 until December 1999. When
comparing the statistics of the different asset classes, it becomes clear that the returns of
direct real estate outperformed all other investment possibilities on a risk-adjusted basis.
Moreover, bonds outperformed equity with a Sharpe ratio of 2.88, a return of 10.43 percent
and standard deviation of 3.61 percent. This result is unusual, implying that a decent bond
performance characterized this period. It can partly be explained by the weak economy
during the 1990s, where investors asked for higher returns, considering the higher risk of
repayment failure from the government. Moreover, many UK companies were urged to
increase the return of their corporate bonds. Nonetheless, equity is characterized by the

3. highest average annual return of all asset classes, but also shows the second highest volatility
of 17.3 percent. Lastly, indirect real estate had the highest risk of 21.26 percent exposure with
a return of 8.28 percent, implying the lowest return-risk performance.
03 Correlation Analysis & Bear Markets
The Modern Portfolio Theory states that investors can diversify their risk by reducing the
correlation between the returns of the securities in their portfolio (Geltner et al,. 2013) This
section will thus analyse the correlation between the different asset classes. In particular, the
correlations of equity and bonds with real estate is of significant importance in this case.
Furthermore, the possibility of using real estate to hedge against economic downturns will be
outlined. The correlation table (see Appendix B) shows that the assets can be classified into
three distinct groups, assets with a strong positive correlation, low overall correlation, and a
negative correlation. Indirect real estate and equity tend to be strongly correlated with a
correlation coefficient of 0,74. Bonds only show a small positive correlation towards equity
and indirect real estate and is therefore generally uncorrelated towards all other asset classes.
Direct real estate, however, shows a small to medium strong negative correlation of -0,01 to
-0,13. The overall impact, of direct or indirect real estate, on diversification will be analysed
in the further readings.
One major critique of Markowitz’ original Modern Portfolio Theory was the assumption that
the correlation between assets is fixed (Geltner et al,. 2013). However, during times of
uncertainty, this is necessarily not always the case. From 1993 until 1995, the United
Kingdom has been characterized by a declining economy, to declining growth rates and
falling employment rates. Therefore, this period will be used as an illustration to highlight the
developments of the different asset classes. As depicted in the graph (see Appendix C),
indirect real estate, bonds, and equity decline and are relatively closely correlated. Indirect
real estate suffered from the most significant drop followed by the bond market. This implies
that the bond market is not as weakly correlated as the other asset classes during economic
downturns. Direct real estate instead shows a positive development during that times, which
is in alignment with the negative correlation towards the other asset classes.

4. 04 Mean Variance Analysis
The mean variance analysis builds upon the efficient market hypothesis that investors are
rational and only accept more risk for a higher expected return (Geltner et al,. 2013). The
mean variance analysis is therefore a quantitative model that aims to minimize the portfolio
risk exposure. Hence for every return there is an optimal combination of asset weights that
minimize the variance of the portfolio. These points connected result in the efficient frontier.
This analysis neglects the possibility to incorporate risk-free assets into the portfolio, since it
does not directly affect the efficient frontier.
Graph 2 (see Appendix D) shows the different combinations of the asset classes with one
another and the resulting efficient frontier. All the points on the frontier illustrate a
combination of the asset classes that minimize the variance given an expected return. Hence
the optimal portfolio lies on the efficient frontier that has the characteristics of the best
risk-return performance and thus the highest sharpe ratio. Table 3 (see Appendix E) shows
the optimal allocation of the different asset weights resulting in the optimal portfolio with the
highest sharpe ratio given the lowest portfolio variance. That portfolio has a standard
deviation of 2,16 percent with a return of 10,32 percent resulting in a risk-return ratio of 4,77.
The highest allocation of asset goes into direct real estate with around 57 percent, 41 percent
goes into Bonds, 2 percent into equity and 0 percent into indirect real estate. Considering the
summary statistics (section 01) which was described earlier, this allocation seems reasonable:
Recall that direct real estate and bonds were yielding high returns given the implied level of
risk. Indirect real estate on the other hand recorded high volatility and a strong correlation
with equity, whilst having a weak correlation with bonds. Thus the diversification impact of
indirect real estate is not present and therefore does not affect the optimal portfolio.
05 Incorporating Real Estate
The key points from the mean variance analysis (section 04) are that direct real estate makes
up 57 percent of the optimal portfolio, whereas indirect real estate does not play any role.
Consequently, this section of the paper will illustrate the effects of incorporating direct real
estate into the portfolio and what the resulting effects are on return, risk and the sharpe ratio.
Table 3 (see Appendix E) shows different portfolios that are optimized given the different
available investment classes. To illustrate the effect real estate has on the portfolio, it is
important to point out the relative return, risk and sharpe ratio of the initial portfolio. The

5. initial portfolio, the one without any real estate investment (top right in Appendix E) only
consists of bonds and equity, and results in a return of 10,50 percent, carrying an implied risk
of 3,59 and results in a sharpe ratio of 2,93.
In the following, direct and indirect real estate will be separately incorporated until finally all
asset classes are considered. Although adding direct real estate to the portfolio (bottom left in
Appendix E) yield to a lower expected return of 10,32 percent, it also lowers volatility to 2,16
percent, which is desirable. Only through including direct real estate to the portfolio, the
overall risk decreased by 39,83 percent and also yield to a higher sharpe ratio of 4,77. This
clearly demonstrates that direct real estate improves the efficiency of the portfolio. On the
other hand, by incorporating indirect real estate (bottom right in Appendix E), the portfolio is
not affected at all. Here, the optimal allocation of weights are still the same as from the
portfolio without any real estate (initial portfolio), since the allocation towards indirect real
estate is 0 percent. Indirect real estate does therefore neither increase return nor does it
positively affect diversification, and therefore the sharpe ratio stays the same. Hence, not all
real estate investments contribute positively toward diversification. The final step therefore is
to allocate the optimal portfolio with the lowest variance, which was already touched on
(section 03). Intuitively, it can already be derived that the mixed portfolio (the optimal
portfolio, top left in Appendix E) is ultimately the mirror of the portfolio that only
incorporated bonds, equity and direct real estate since the optimal portfolio weights of
indirect real estate is equal to zero. Incorporating indirect real estate thus would only worsen
any portfolios in terms of risk, return and sharpe ratio.It therefore can be concluded that not
all real estate investments improve diversification or the sharpe ratio. The analysis showed
that only direct real estate has an improving effect on the portfolio when added. This also
implies that the efficient frontier is only affected by direct real estate and not by indirect real
estate. The frontier shifts therefore, by incorporating direct real estate, into the north-west
corridor.
Nonetheless, there certain drawback in the analysis that have to be outlined. First the time
span is relatively short and may entail market anomalies, with special attention on the bond
market. Secondly, the allocation in the mixed portfolio is to some extent problematic: 57
percent of the fund are recommended to be allocated to direct real estate. Doing so however
may cause liquidity issues, and is amongst others, also only possible for wealthy private or
institutional investors. Private investors generally can not afford to purchase whole buildings

6. that then make up of 57 percent of their portfolio. An additional problem is that there will be
diversification considering the asset classes, however by investing in direct real estate it is not
possible to just buy the market index, thus investors have to set all of the fund allocated into
direct real estate into a few buildings. Macroeconomic risk may also raise some concerns,
when the real estate market sufferers from a crises (for example in 2008) then the portfolio's
exposure to that macroeconomic risk is large (​Adair, 2006)​. An additional issue with direct
real estate is, that it is relatively hard to measure the volatility of the underlying building.
Indirect real estate however brings certain advantages considering the liquidity and the
diversification within the real estate market. The optimization of the portfolio does not
consider these factors and thus the result may not reflect the true efficient allocation of funds.
Thus each investor may have to further develop the outcomes of the mean-variance results.
05 Conclusion
To conclude, adding direct real estate to one’s portfolio does bring additional diversification
and improved risk-return performance, however is mostly only feasible for wealthy or
institutional investors. The analysis clearly showed that direct real estate has an significant
impact on the sharpe ratio and the risk exposure of the portfolio. This however is not the
case for private investors with say less resources who may invest indirectly in real estate
property. Indirect real estate plays no significant role towards the portfolio optimization,
regarding the mean-variance optimization. The efficient frontier is therefore only affected by
direct real estate and not by indirect real estate, and shifts it to the north-west corridor.
Nonetheless, did our result also reveal one major drawback when using direct real estate for
diversification purpose.Direct real estate is an highly illiquid investment compared to indirect
real estate and thus certainly increases the liquidity risk exposure.
Last but not least, it should be noted that investors cannot fully rely on the mean-variance
theory but its result can be used as an underlying benchmark which then can be further
customized towards the investors needs.

7. 06 References List
Adair, A., McGreal, S,. Webb, James., (2006). Diversification Effects of Direct versus
Indirect Real Estate Investments in the U.K..​Journal of Real Estate Portfolio
Management,​ 12(9), 85-90.
Eichholtz, P. M. (1996). Does International Diversification Work Better for Real Estate than
for Stocks and Bonds?​ Financial Analysts Journal, ​52(1), 56-62.
Geltner, D., Eichholtz, P., Miller, J and N,. (2013). ​Commercial Real Estate Analysis and
Investment​. Cengage Learning Inc.

8. 07 Appendices
Appendix A
Table 1: Summary Statistics of U.K data set ranging from 1987-1999

9. Appendix B
Table 2: Correlation analysis of the asset classes

10. Appendix C
Graph 1: Performance During Bear Markets (U.K. Economy 1993- 1995)

11. Appendix D
Graph 2: Efficient Portfolio. The Combination of Different Asset Classes.

12. Appendix E
Table 3: Different Portfolios (Section 04)