Suppose you want to construct a minimum variance portfolio with the following stocks Apple Inc. (AAPL), Amazon.com Inc.(AMZN), Alphabet Inc. (GOOG), and Facebook, Inc. (FB). The expected rate of return of the portfolio you want to construct should be the average of the expected rates of return of these stocks. The daily expected rates of return, standard deviations, and covariancesof these stocks are raapl=0.008771662, ramzn=0.03385526, rfb =0.012982714, rgoog=0.015362285, saapl =0.075290371, samzn =0.086245607, sfb =0.06266357, sgoog =0.06167237, cov(aapl,amzn) =0.002156755, cov(aapl,fb) =0.001721943, cov(aapl, goog) =0.001618178, cov(amzn,fb) =0.002464478, cov(amzn, goog)=0.003620894, and cov(fb, goog) =0.002012736. Moreover, the amount you want to invest is $1,000,000, and the initial share prices of these stocks are: AAPL=141.04, AMZN = 1,500.28, FB =131.74, and GOOG =1,016.06. Let r= (ramzn + raapl + rfb +rgoog)/4 be the average of the expected rates of return of these stocks. Find the weights of the minimum variance portfolio with the expected rate of return r.

1. w_aapl=0.165388,w_amzn=0.329212,w_fb=0.322789,w_goog=0.182612.
2. w_aapl=0.165388,w_amzn=0.129212,w_fb=0.322789,w_goog=0.382611.
3. w_aapl=0.165388,w_amzn=0.129212,w_fb=0.422789,w_goog=0.282612.
4. w_aapl=0.265388,w_amzn=0.229212,w_fb=0.322789,w_goog=0.182611
5. w_aapl=0.165388,w_amzn=0.229212,w_fb=0.422789,w_goog=0.182611.
6. w_aapl=0.165388,w_amzn=0.229212,w_fb=0.322789,w_goog=0.282612.