What portfolio gives the highest possible sharpe ratio for

Question

1. You want to invest in these stocks:

Microsoft, µ: 0,15, standard deviation: 0,45

Apple: µ: 0,08, standard deviation: 0,20.

HP: µ: 0,12, standard deviation: 0,30

Correlation:

	Microsoft	Apple	HP
Microsoft	1
Apple	0,4	1
HP	0,6	0,5	1

The formula for this portfolio is:

µ = w₁µ₁ + w₂µ₂ + w₃µ₃

Standard deviation:

a) Draw the efficient frontier for these three stocks. Put the return on the y - axis and the standard deviation on the x - axis. Use Excel and Scatter - plot to draw the efficient frontier. Suppose that the interest rate is 4 %. You only invest in the stocks in whole 20 %, so 0 %, 20 %, 40 %, 60 %, 80 % and 100 % (0, 0, 1.0), then (0, 0.2, 0.8) and so on (21 rows). Then change the weight for Microsoft to 0,2: (0.2, 0, 0.8) etc.

Then change Microsoft weights to 0,4 (0.4, 0, 0.6). Keep on changing the weight of Microsoft to 0.6, 0.8 and 1. Finally you'll have 21 rows with 3 columns.

Then calculate the expected return and the standard deviations for the 21 portfolios.

b) Which portfolio gives the lowest standard deviation?

c) With only two assets all the weight combinations are effiecient, they are on the efficient frontier. But, with three assets or more, this is no longer true. Why?

d) Calculate the Sharpe ratio for the 21 portfolios:

S_p = (µp-rf)/op

e) What portfolio gives the highest possible Sharpe ratio for the 21 portfolios?

f) Finally draw the line between the risk free interest rate and the tangency portfolio in the efficient frontier. Explain what this line shows and what an investers choice of portfolio has to do with the line.

Attachment:- Lowest standard deviation.xlsx