DATE

S&P 500 Index

Gold Prices

S&P returns

Gold returns

1975

90.19

139.30

1976

107.46

133.80

19.15%

-3.95%

1977

95.10

160.45

-11.50%

19.92%

1978

96.11

207.83

1.06%

29.53%

1979

107.94

455.08

12.31%

118.97%

1980

135.76

594.92

25.77%

30.73%

1981

122.55

410.09

-9.73%

-31.07%

1982

140.64

444.30

14.76%

8.34%

1983

164.93

389.36

17.27%

-12.37%

1984

167.24

320.14

1.40%

-17.78%

1985

211.28

320.81

26.33%

0.21%

1986

242.17

391.23

14.62%

21.95%

1987

247.08

486.31

2.03%

24.30%

1988

277.72

418.49

12.40%

-13.95%

1989

353.40

409.39

27.25%

-2.17%

1990

330.22

378.16

-6.56%

-7.63%

1991

417.09

361.06

26.31%

-4.52%

1992

435.71

334.80

4.46%

-7.27%

1993

466.45

383.35

7.06%

14.50%

1994

459.27

379.29

-1.54%

-1.06%

1995

615.93

387.44

34.11%

2.15%

1996

740.74

369.00

20.26%

-4.76%

1997

970.43

288.74

31.01%

-21.75%

1998

1229.23

291.62

26.67%

1.00%

1999

1469.25

282.37

19.53%

-3.17%

2000

1320.28

271.45

-10.14%

-3.87%

2001

1148.08

275.45

-13.04%

1.47%

2002

798.55

321.18

-30.44%

16.60%

2003

1111.92

417.25

39.24%

29.91%

2004

1211.92

435.60

8.99%

4.40%

2005

1248.29

513.00

3.00%

17.77%

2006

1418.30

635.70

13.62%

23.92%

2007

1468.36

836.50

3.53%

31.59%

2008

903.25

869.75

-38.49%

3.97%

2009

1115.10

1087.50

23.45%

25.04%

2010

1257.64

1420.25

12.78%

30.60%

2011

1257.60

1531.00

0.00%

7.80%

2012

1426.19

1664.00

13.41%

8.69%

2013

1848.36

1204.50

29.60%

-27.61%

2014

2058.90

1135.80

11.39%

-5.70%

2015

2043.94

1060.30

-0.73%

-6.65%

2016

2238.83

1061.19

9.54%

0.08%

Data: This project makes use of annual data for two risky securities: the S&P 500 Index and Gold. Annual values for each of these securities during the period from 1975-2016 are provided in a spreadsheet.

You should use an annual risk-free rate of 4% for this project.

Return Calculations: Calculate annual returns for each of the two securities from 1976 through 2015. Calculate the average annual return, the standard deviation of annual returns, and the correlation between the returns of the two securities during this period and fill in the table provided. (Note: all of these calculations are based on annual security % returns NOT index values). Attach the spreadsheet showing all of the relevant calculations as Exhibit 1.

	S&P 500	Gold
Average Annual Return
Standard Deviation of Annual Returns
Return Correlation(S&P,Gold)

Capital Allocation Lines: Assume that the mean return, standard deviation, and correlation estimates you calculated above provide a reasonable forecast of the expected returns and risks of these securities for the coming year. Based on these forecasts, plot the two risky securities on an expected return standard deviation graph. Also, plot the risk-free security. Be sure to label all three securities on the graph. Draw the Capital Allocation Line for each of the risky securities (S&P and Gold). Attach the graph as Exhibit 2.

Risky Portfolios: Calculate the expected returns and standard deviations of portfolios that combine the two risky securities (S&P and Gold), varying weights from 0% to 100% in increments of 5% (note: this should result in 21 portfolios). Attach the spreadsheet showing all relevant calculations as Exhibit 3.

The Opportunity Set and the Tangency Portfolio: Plot the risk-free security and the 21 portfolios described in question 4 on an expected return standard deviation graph. Be sure to clearly label the S&P 500, Gold, and the risk-free security on the graph. Identify and label the minimum variance portfolio on the graph. Identify and label the optimal risky portfolio (a.k.a. the tangency portfolio) on the graph and draw the Capital Allocation Line (CAL) for this portfolio. Attach the graph as Exhibit 4.

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

(b)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?