In table 1.1 below, information on three stocks (X, Y and Z) in the next period is stated. The stocks are traded on a financial market, where the usual assumptions for a normal market are satisfied. It is assumed, that a risk-free asset is traded on the financial market as well, which has a return of 5% (rf) in the next period. Problem: Determine the tangent portfolio of the three stocks (i.e. determine the weights that the three stocks have in the portfolio) Hint 1: Recall, that the tangency portfolio (T) is given as the portfolio that has the largest Sharpe Ratio. To find T, you therefore have to write up the expression for Sharpe Ratio and maximize this in Excel or another program. Hint 2: Recall (cf. formula 11.11), that the variance of a portfolios return is given by: Var( RP ~ )= = N i 1 = N j 1 xixjCov( ir ~ , j r ~ ) Where xi and xj denotes de respective portfolio weights, i,j = 1,2...N.

Stock	Std. Deviation Of the return	Expected return	Correlation with return on Y	Correlation with return on Z
X	0,2	0,15	0,8	-0,1
Y	0,3	0,1	1	0,2
Z	0,25	0,12	0,2	1
R(f)	5%
	Covariances	X	Y	Z
Problem 1.1 + 1.2	X	0,04	0,048	-0,005
	Y	0,048	0,09	0,015
	Z	-0,005	0,015	0,0625