The maximum diversification investment strategy: A portfolio performance comparison

Figures & data

Table 1. Weight calculation summary for the four approaches

Investment strategy	Weight formula	Equation number
Equally weighted	$w_{\text{EW}}=\frac{1}{n}$	1
Minimum variance	$w_{\text{MV}}=\frac{{\mathrm{\Omega }}^{-1}1}{1^{\prime }{\mathrm{\Omega }}^{-1}1}$	2
Tangent	$w_{\text{TG}}=\frac{{\mathrm{\Omega }}^{-1}\left(E-r_f·1\right)}{1^{\prime }{\mathrm{\Omega }}^{-1}\left(E-r_f·1\right)}$	4
Maximum diversification	$w_{\text{MD}}=\frac{{\mathrm{\Omega }}^{-1}\sigma }{{\sigma }^{\prime }{\mathrm{\Omega }}^{-1}\sigma }$	7

Figure 1. Diversification ratio of the constrained MD portfolio overtime.

Figure 2. Comparison of DRs using constrained and unconstrained portfolio weights.

Figure 3. Comparison of Cs using constrained and unconstrained portfolio weights.

Figure 4. Comparison of diversification correlations using constrained and unconstrained portfolio weights.

Figure 5. Portfolio weights for the maximum diversification portfolio overtime.

Note: The increasing popularity of real estate (via REITs) after the crisis.

Figure 6. Sharpe ratio for the various investment strategies.

Table 2. Vector of portfolio volatilities

	Bonds	Banks	Industrials	Biotech	REITS	NYSE TMT	Gold
σ	2.79%	21.47%	15.18%	31.59%	16.88%	13.87%	49.24%

Figure 7. Daily volatility for the various investment strategies. TG portfolio weights are constrained to be >0.

Table 3. Correlation matrix

	Bonds	Banks	Industrials	Biotech	REITs	NYSE TMT	Gold
Bonds	1	−0.58	−0.27	−0.38	0.08	−0.23	0.29
Banks	−0.58	1	0.67	0.57	0.32	0.64	−0.13
Industrials	−0.27	0.67	1	0.58	0.59	0.88	0.04
Biotech	−0.38	0.57	0.58	1	0.27	0.52	0.01
REITs	0.08	0.32	0.59	0.27	1	0.62	0.10
NYSE TMT	−0.23	0.64	0.88	0.52	0.62	1	0.14
Gold	0.29	−0.13	0.04	0.01	0.10	0.14	1

Figure 8. Cumulative returns for various investment strategies with constraints applied.

Figure 9. Cumulative returns for the various investment strategies.

Figure 10. Sharpe ratio for the various investment strategies.

Figure 11. Daily volatility for investment strategies. TG portfolio weights are unconstrained.