In the following table, find rate-of-return data over a 60-month period for Alphabet, the parent company of Google; the T-bill rate; and the S&P 500, which we will use as the market index portfolio. Please use Microsoft Excel to answer the questions below.

	GOOG	S&P 500	3-month T-bills
201501	0.015426	-0.03104	0.03%
201502	0.044676	0.05489	0.02%
201503	-0.018625	-0.01740	0.03%
201504	-0.01676	0.00852	0.02%
201505	-0.009733	0.01049	0.02%
201506	-0.0218	-0.02101	0.02%
201507	0.201917	0.01974	0.03%
201508	-0.011764	-0.06258	0.07%
201509	-0.0159	-0.02644	0.02%
201510	0.168288	0.08298	0.02%
201511	0.044724	0.00051	0.12%
201512	0.021923	-0.01753	0.23%
201601	-0.020991	-0.05074	0.26%
201602	-0.060812	-0.00413	0.31%
201603	0.067615	0.06599	0.29%
201604	-0.069723	0.00270	0.23%
201605	0.06163	0.01533	0.27%
201606	-0.059289	0.00091	0.27%
201607	0.110808	0.03561	0.30%
201608	-0.002263	-0.00122	0.30%
201609	0.01335	-0.00123	0.29%
201610	0.009327	-0.01943	0.33%
201611	-0.033778	0.03417	0.45%
201612	0.018179	0.01820	0.51%
201701	0.032352	0.01788	0.51%
201702	0.033158	0.03720	0.52%
201703	0.007714	-0.00039	0.74%
201704	0.092097	0.00909	0.80%
201705	0.065014	0.01158	0.89%
201706	-0.058174	0.00481	0.98%
201707	0.023957	0.01935	1.07%
201708	0.00949	0.00055	1.01%
201709	0.021058	0.01930	1.03%
201710	0.059983	0.02219	1.07%
201711	0.004692	0.02808	1.23%
201712	0.024466	0.00983	1.32%
201801	0.118062	0.05618	1.41%
201802	-0.055738	-0.03895	1.57%
201803	-0.066025	-0.02689	1.70%
201804	-0.014015	0.00272	1.76%
201805	0.066507	0.02161	1.86%
201806	0.028258	0.00484	1.90%
201807	0.091077	0.03602	1.96%
201808	0.000764	0.03026	2.03%
201809	-0.020292	0.00429	2.13%
201810	-0.097782	-0.06940	2.25%
201811	0.016401	0.01786	2.33%
201812	-0.053745	-0.09178	2.37%
201901	0.077983	0.07868	2.37%
201902	0.00318	0.02973	2.39%
201903	0.047673	0.01792	2.40%
201904	0.012929	0.03931	2.38%
201905	-0.071394	-0.06578	2.35%
201906	-0.020587	0.06893	2.17%
201907	0.125607	0.01313	2.10%
201908	-0.02349	-0.01809	1.95%
201909	0.026008	0.01718	1.89%
201910	0.033724	0.02043	1.65%
201911	0.035592	0.03405	1.54%
201912	0.024568	0.02859	1.54%

1. Use these data and Excels regression function to compute Googles excess return in each month as well as its alpha, beta, and residual standard deviation, (e), over the entire period.
2. What was the Sharpe ratio of the S&P 500 over this period?
3. What was Googles information ratio over this period?
4. If someone whose risky portfolio is currently invested in an index portfolio such as the S&P 500 wishes to take a position in Google based on the estimates from parts (1)-(3), what would be the optimal fraction of the risky portfolio to invest in Google? Use Equations 6.16 and 6.17.
5. Based on Equation 6.18 and your answer to part (4), by how much would the Sharpe ratio of the optimal risky portfolio increase given the incremental position in Google?

wG0=RM/M2G/2(eG) wG=1+wG0(1G)wG0;wM=1wG SO2SM2=[(eG)G]2