Real Estate ETNs in Strategic Asset Allocation

Figures & data

Table 1. Market size in billions of euros as of the end of 2012.

	(in % of the world)
Country	Stocks	Bonds	Real estate
United States	10,524	6,608	6,414
	(31.9%)	(27.7)	(28.8%)
United Kingdom	1,952	830	1,239
	(5.7%)	(3.5%)	(5.5%)
France	1,377	1,182	1,211
	(4.0%)	(5.0%)	(5.4%)
Germany	906	1,080	1,483
	(2.7%)	(4.5%)	(6.7%)
World	34,002	23,829	22,257

Note: This table reports the invested market size in billions of euros for stocks, bonds, and real estate market at the end of 2012. Figures in parentheses show the country’s share of the world market. The data for stocks were obtained from the Databank of the World Bank, for bonds from the Quarterly Review of the Bank for International Settlements, and for real estate from Prudential Real Estate Investors.

Table 2. Real estate derivatives market in millions of euros as of Q2 2010.

	UK	FRA	GER
Total outstanding notional value (in m. euro)	8,377.3	318	319.3
Outstanding number of trades	928	49	57
Average outstanding deal size (in m. euro)	8.6	8.6	6.1

Note: This table reports the total outstanding notional value, number of trades, and the average deal size of all derivative products on Investment Property Databank (IPD) Indices in the UK, France, and Germany until Q2 2010. m. stands for million. The data are obtained from IPD.

Table 3. Descriptive statistics (1996–2009).

	USA	UK	FRA	GER
Stocks
Mean p.a.	8.01	7.44	11.37	11.12
Std. dev. p.a.	18.32	16.31	23.87	27.59
Skewness	−0.32	−0.18	−0.34	−0.41
Kurtosis	0.19	0.37	0.44	0.71
p value (LJB)	0.59	0.73	0.47	0.25
p value (KSL)	0.59	0.38	0.39	0.37
Bonds
Mean p.a.	4.84	5.13	4.61	4.50
Std. dev. p.a.	0.51	0.55	0.42	0.43
Skewness	−0.03	1.03	0.49	0.35
Kurtosis	−0.38	0.94	−0.40	−0.57
p value (LJB)	0.84	0.00	0.27	0.39
p value (KSL)	0.94	0.04	0.47	0.52
Real estate ETNs
Mean p.a.	6.70	5.56	5.64	1.34
Std. dev. p.a.	5.39	7.31	3.74	0.78
Skewness	−2.40	−2.16	−0.16	−0.47
Kurtosis	6.41	6.64	−0.63	−0.83
p value (LJB)	0.00	0.00	0.56	0.16
p value (KSL)	0.00	0.00	0.21	0.50

Note: This table shows descriptive statistics for the asset classes used in our optimization. The sample period is from 1996 to 2009 for stocks, bonds, and real estate exchange traded notes (ETN). Std. dev. refers to standard deviation. The p values for testing normality are calculated by using the Lomnicki-Jarque-Bera test (LJB) and the Kolmogorow-Smirnow-Lilliefors test (KSL).

Figure 1. Efficient sets in a mean/LPM framework.

Note: This figure shows the efficient frontiers of four different portfolios in a risk-return spectrum. These are (1) stocks and bonds, (2) stocks, bonds, and real estate ETNs, (3) previous assets within a 130/30 long-short portfolio, and (4) previous portfolio in a currency hedged setting. The expected return is represented by the mean per quarter of each portfolio and risk by LPM. The lines are the interpolation of estimated data by a second-degree polynomial.

Figure 2. Composition of a hedged 130/30 long-short portfolio.

Note: This figure shows the weights of all 12 assets in the efficiently hedged 130/30 long-short portfolios along the efficient frontier. Stocks are shown horizontally, bonds are shown vertically, and real estate exchange traded notes (ETNs) are in the dotted areas.

Table 4. Return/risk characteristics for the in-sample optimization.

	Mean	LPM	SR
Unhedged
Stocks and bonds
EWP	1.60	3.90	0.20
MRP	1.27	0.02	19.53
TP	1.27	0.02	19.53
Stocks, bonds, and ETNs
EWP	1.32	2.84	0.17
MRP	1.27	0.02	19.53
TP	1.27	0.02	19.53
Unhedged 130/30 Structure
Stocks and bonds
EWP	–	–	–
MRP	1.22	0.01	29.40
TP	1.23	0.01	30.13
Stocks, bonds and ETNs
EWP -	–		–
MRP	1.22	0.01	31.98
TP	1.22	0.01	31.98
Hedged 130/30 structure
Stocks and bonds
EWP	–	–	–
MRP	1.20	0.004	92.87
TP	1.20	0.003	126.44
Stocks, bonds, and ETNs
EWP -	–		–
MRP	1.28	0.002	214.52
TP	1.30	0.002	276.84

Note: This table shows the mean (in %), lower partial moment (LPM, in %), and Sortino ratios (SR) of in-sample optimizations for equally weighted portfolios (EWP), minimum-risk portfolios (MRP), and tangency portfolios (TP). The EWP weights for all 130/30 portfolios are not displayed because they would be the same as in the long-only portfolios.

Table 5. Optimal weights for the in-sample optimization.

	Stocks				Stocks				Real estate ETNs
	USA	UK	FRA	GER	USA	UK	FRA	GER	USA	UK	FRA	GER
Unhedged
Stocks and bonds
MRP	0.00	0.00	0.00	0.00	0.0	100.00	0.00	0.00	–	–	–	–
TP	0.00	0.00	0.00	0.00	0.0	100.00	0.00	0.00	–	–	–	–
Stocks, bonds, and ETNs
MRP	0.00	0.00	0.00	0.00	0.0	100.00	0.00	0.00	0.00	0.00	0.00	0.00
TP	0.00	0.00	0.00	0.00	0.0	100.00	0.00	0.00	0.00	0.00	0.00	0.00
Unhedged 130/30 structure
Stocks and bonds
MRP	0.02	−0.10	−0.07	0.07	−29.83	88.94	40.96	0.00	–	–	–	–
TP	0.02	−0.10	−0.05	0.06	−29.85	91.72	38.20	0.00	–	–	–	–
Stocks, bonds, and ETNs
MRP	0.01	0.10	−0.07	−0.03	−29.24	85.41	44.23	0.00	0.26	−0.34	−0.20	−0.13
TP	0.01	0.10	−0.07	−0.03	−29.23	85.37	44.27	0.00	0.26	−0.34	−0.20	−0.14
Hedged 130/30 structure
Stocks and bonds
MRP	0.00	0.00	−1.23	−0.33	−28.08	85.46	44.06	0.47	–	–	–	–
TP	0.44	0.44	−2.17	−0.03	−27.80	85.52	44.01	0.36	–	–	–	–
Stocks, bonds, and ETNs
MRP	2.26	−2.38	3.46	−2.91	27.65	31.46	26.49	25.23	6.10	−17.96	7.35	−6.74
TP	5.36	−0.71	−2.08	−0.33	26.50	29.47	27.90	27.09	−2.00	−11.98	13.68	−12.89

Note: This table shows the optimal weights (in %) of stocks, bonds, and real estate ETNs for the minimum-risk portfolio (MRP) and the tangency portfolios (TP) for different asset combinations and in different hedged or long-short portfolios.

Table 6. Return/risk characteristics for the out-of-sample optimization.

	Q1 2000–Q4 2009			Q12000–Q4 2004			Q12005–Q4 2009
	Mean	LPM	LPM	Mean	LPM	LPM	Mean	LPM	LPM
Unhedged
Stocks and bonds
EWP	0.42	4.22	−0.08	−0.14	4.73	−0.20	0.98	3.65	0.06
MRP	0.91	0.57	0.24	1.11	0.04	8.71	0.71	0.80	−0.05
Stocks, bonds, and ETNs
EWP	0.65	3.05	−0.04	0.45	3.07	−0.11	0.85	3.02	0.03
MRP	1.72	0.64	1.47	1.75	0.12	8.05	1.69	0.90	1.04
Unhedged 130/30 structure
Stocks and bonds
EWP	–	–	–	–	–	–	–	–	–
MRP	1.52	0.39	1.91	1.86	0.55	1.94	1.17	0.03	12.16
Stocks, bonds, and ETNs
EWP	–	–	–	–	–	–	–	–	–
MRP	1.18	0.64	0.63	1.66	0.01	60.64	0.70	0.91	−0.06
Hedged 130/30 structure
Stocks and bonds
EWP	–	–	–	–	–	–	–	–	–
MRP	0.92	0.80	0.18	1.19	0.20	1.94	0.65	1.12	−0.10
Stocks, bonds, and ETNs
EWP	–	–	–	–	–	–	–	–	–
MRP	1.50	0.50	1.46	1.61	0.20	4.14	1.40	0.68	0.95

Note: This table shows the mean (in %), lower partial moment (LPM, in %) and Sortino ratios (SR) of out-of-sample optimizations for equally weighted portfolios (EWP) and minimum-risk portfolios (MRP). The EWP’s weights for all 130/30 portfolios are not displayed because they would be the same as in the long-only portfolios. The out-of-sample optimizations are split in three different periods: Q1 2000–Q4 2009 and two subperiods Q1 2000–Q4 2004 and Q1 2005–Q4 2009.