A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are:

Expected Return	Standard Deviation
Stock fund (S)	15%	32%
Bond fund (B)	9	23

The correlation between the fund returns is .15

1.Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of 0% to 100% in increments of 20%. What expected return and standard deviation does your graph show for the minimum-variance portfolio?

% in stocks	% in bonds	Exp. Return	Std. dev.	Sharpe Ratio
0.0000	1.0000	0.0900	0.2300	0.1522
0.2000	0.8000	0.1020	0.2037	0.2308
0.3142	0.6858	0.1089	0.1994	0.2701	Minimum Variance Portfolio
0.4000	0.6000	0.1140	0.2018	0.2924
0.6000	0.4000	0.1260	0.2250	0.3155
0.6466	0.3534	0.1288	0.2334	0.3162	Tangency Portfolio
0.8000	0.2000	0.1380	0.2668	0.3111
1.0000	0.0000	0.1500	0.3200	0.2969

Can you help me figure out how to get those numbers. My professor posted the table, but never explained it. That is why I need your help. I don't get how to find tangency portfolio, what is the formula or steps. Please help.