Question

S&P 500 9.38% Gold 7.40% Average Annual Return Standard Deviation of Annual Returns 16.41% 23.70% Return Correlation(S&P.Gold) 1.10%

The annual risk free rate is 4%

USE FORMULAS

$Rule 2: E(rp)= wg E(re)+ ws E(rs) • Rule 3: 0% =(W60%) +(wos) +2(wx0p\w;05)ps$

1. What are the portfolio weights in the Tangency Portfolio? What are the mean and standard deviation of the Tangency Portfolio?      

2. What are the portfolio weights in the Minimum Variance Portfolio? What are the mean and standard deviation of the Minimum Variance Portfolio?

c. What are the portfolio weights in the Equal-Weighted Portfolio? What are the mean and standard deviation of the Equal-Weighted Portfolio?

Answer 1

a) Minimum Variance Portfolio
  Weight of S&P 500 = 0.68
Weight of Gold = 0.32
Mean Return = 8.74%
Std Dev = 13.56%
  

	S&P 500	Gold
Average Annual return	9.38%	7.40%
Std Dev	16.41%	23.7%
Correlation	1.10%
Variance	2.69%	5.62%
Weight	0.68	0.32
Weigh ^2	0.46	0.10
Mean Return	8.74%
Variance	1.84%
Std Dev	13.56%

b) Equal Weighted Portfolio
  Weight of S&P 500 = 0.5
Weight of Gold = 0.5
Mean Return = 8.39%
Std Dev = 14.49%

	S&P 500	Gold
Average Annual return	9.38%	7.40%
Std Dev	16.41%	23.7%
Correlation	1.10%
Variance	2.69%	5.62%
Weight	0.50	0.50
Weigh ^2	0.25	0.25
Mean Return	8.39%
Variance	2.10%
Std Dev	14.49%