a. Is portfolio invested 100% in gold efficient? Why yes or why not?

b. What proportion of the funds need to be invested in individual assets to obtain minimum variance portfolio? What is the average return of the minimum variance portfolio?

c. What proportion of the funds need to be invested in individual assets to obtain a portfolio that has a standard deviation 6% higher than the minimum variance portfolio? What is the average return of such portfolio?

d. Is gold a part of any of the portfolios? Why do you think this is the case?

e. How does the proportion invested in bonds change when the volatility of the portfolio increases? Why do you think this is the case?

Equally-weighted Portfolio Weights Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 Average Variance Std. dev 0.25 Aggregate Bond 7.40% 9.75% -2.92% 18.46% 3.64% 9.64% 8.70% -0.82% 11.63% 8.43% 10.26% 4.10% 4.34% 2.43% 4.33% 6.97% 5.24% 5.93% 6.54% 7.84% 4.22% -2.02% 5.97% 0.55% 2.65% 5.73% 0.002137121 4.62% 0.25 0.25 0.25 Total US Stock REITs Gold Portfolio 9.06% 12.18% -5.80% 5.71% 11.59% 18.55% 17.35% 14.31% -0.76% 0.81% -2.09% -1.24% 35.67% 18.31% 1.10% 18.38% 21.18% 35.75% -4.43% 14.03% 30.35% 18.86% -21.74% 9.28% 22.26% -18.82% -0.61% 2.88% 25.26% -6.48% 1.18% 4.79% -11.16% 25.89% -6.26% 5.03% -11.27% 15.50% 1.41% 3.52% -20.84% 5.22% 23.96% 4.65% 33.14% 38.47% 21.74% 24.36% 12.99% 30.41% 4.97% 13.18% 7.31% 8.29% 17.12% 8.79% 16.21% 34.35% 23.92% 19.70% 7.28% -17.83% 31.59% 7.00% -38.21% -37.34% 3.41% -16.73% 31.29% 27.45% 27.63% 23.07% 17.71% 27.58% 27.74% 19.89% -1.07% 7.28% 11.65% 6.42% 15.76% 20.14% 5.68% 11.45% 30.45% 3.21% -27.79% 0.96% 10.50% 27.15% -0.19% 10.86% -1.68% 2.29% -11.42% -2.57% 12.67% 9.28% 9.12% 8.43% 10.63% 12.26% 5.97% 8.65% 0.032060112 0.034230552 0.023407015 0.008081 17.91% 18.50% 15.30% 8.99% Average Return (Re Each column in the table below is a different portfolio Weights (Optimization) Aggregate Bond Total US Stock REITS Gold Variance Std. Dev. Average 0.886592757 0.069073379 0 0.044333864 0.001930609 4.39% 6.08% target std. deviation Target Average MAX 0 0.4250569602 0.230957115 0.2147909141 0.27278331 0.3340539469 0.478606903 0.0260981788 0.017652673 0.0082433257 0.014590886 9.08% 12.08% 8.97% 10.20% 9.08% 12.08% 0.044867782 0 0.328325059 0.042118 0.617440092 0.957882 0.009367067 0 0.022738467 0.032686 15.08% 18.08% 11.37% 12.19% 15.08% 18.08% Correlation Matrix Aggregate Bond Total US stock REITS Gold Aggregate Bond Total US stock REITS 1 -0.0270344496 1 0.1434088242 0.4569127668 1 0.1636360206 -0.0703977281 0.1188388291 Variance-Covariance Matrix Aggregate Bond Total US Stock REITS Aggregate Bond 0.0021 -0.0002 Total US Stock -0.0002 0.0321 REITS 0.0012 0.0151 Gold 0.0012 -0.0019 Portfolio Average 8.65% Variance 0.008081 St. dev. 8.99% Gold 1 Gold 0.0012 0.0151 0.0342 0.0034 0.0012 -0.0019 0.0034 0.0234 Each column in the table below is a different portfolio Weights (Randomly Assigned) Aggregate Bond 0.3 0.1 0.4 0.2 0.1 Total US Stock 0.1 0.5 0 0.2 0.6 REITS 0.2 0.2 0.2 0.3 0.1 Gold 0.4 0.2 0.4 0.3 0.2 Average 7.62% 9.53% 7.13% 8.74% 9.37% Variance 0.0070282115 0.0133255769 0.006561109 0.0090138879 0.014374 Std. Dev. 8.38% 11.54% 8.10% 9.49% 11.99% Portfolio of Four Assets 14.00% 12.00% 10.00% Average Return (Reward) 8.00% 6.00% 4.00% 2.00% 0.00% 0.00% 5.00% 10.00% 15.00% Standard Deviation (Risk) Random Portfolios Individual Assets Efficient Portfolio 20.00% weights 0.25 0.25 0.25 0.25 0.2 0.4 0.1 0.3 8.41% 0.008766 9.36% Answers: 3. The correlations range between -.07 to .16. The correlation between REITS and Total US Stock have the greatest diversifi