You are trying to decide whether to buy Vanguard's Equity Fund and/ or its Bond Fund. For next year, you have identified several possible scenarios to which you have assigned probabilities. You have also estimated expected returns for the two funds for each scenario. Your spreadsheet looks like the following.

New Year's Possibillities	Probability	Stock Fund Return	Colummn D	Bond Fund Return	Colummn F
Recession	0.15	-13		15
Weak economy	0.05	5		3
Moderate economy	0.6	10		7
Strong economy	0.2	24		-9

A) Fill in the columns D and F and calculate the expected return for each fund

B) Given the expected value for each fund for next year, fill out the following spreadsheet to calculate the standard deviation of each fund. Note that you need to fill columns D, E, and F for the stock fund and columns H, I, and J for the bond fund. The first two columns in each set are labeled: you need to determine what goes in F and J, respectively, which will lead to the variance, and then the standard deviation.

C)

			Stock Fund				Bond Fund
Scenario	Probability	Return	Colummn D Deviation from Exp.	Column E Squared Deviation	Colummn F	Return	Colummn H Deviation from Exp.	Column I Squared Deviation	Colummn J
Recession	0.15	-13				15
Weak economy	0.05	5				3
Moderate economy	0.6	10				7
Strong economy	0.2	24				-9
				Variance =				Variance =
				Std Dev =				Std Dev =

D) Now calculate the covariance between the two funds and the correlation coefficient, using the following format.

Scenario	Probability	Deviation from Exp. Return for Stock fund	Deviation from Exp. Return for Bond Fund	Product of Deviation	Col B X Col E
Recession	0.15
Weak economy	0.05
Moderate economy	0.6
Strong economy	0.2

E) Using the formulas for the expected return and risk of a portfolio, calculate these values for each of the following portfolio weights.

w1 = Stock Fd % of Funds	w2 = Bonds Fd % of Funds	Portfolio Expected Return	Std Dev
0.1	0.9
0.2	0.8
0.3	0.7
0.4	0.6
0.5	0.5
0.6	0.4
0.7	0.3
0.8	0.2
0.9	0.1

F) Which of the portfolio in (e) is the minimum-variance portfolio?

G) Based on your analysis, should investors hold a portfolio of 100 percent bonds?