According to the monthly returns of the following Fama French 3 factors, which are long-short portfolios of stocks. Answer the following questions.

1. Using the full time series, estimate the average (expected) returns, volatility and correlations for each of the three factors. What do you observe?

2. First, consider only the MKT factor. Using the additional information on the latest risk-free rate which the dataset provides, sketch the Capital Allocation Line (CAL) in the standard-deviation/expected return space. What are the weights of the optimal portfolio when investors have mean variance preferences and their risk-aversion is = 2?

3. What is the correlation between the MVP and the MKJT factor?

Mkt-RF SMB HML RF

201501 -3.11 -0.55 -3.58 0.00

201502 6.13 0.61 -1.86 0.00

201503 -1.12 3.04 -0.37 0.00

201504 0.59 -3.03 1.82 0.00

201505 1.36 0.92 -1.14 0.00

201506 -1.53 2.90 -0.79 0.00

201507 1.54 -4.19 -4.13 0.00

201508 -6.04 0.33 2.77 0.00

201509 -3.07 -2.63 0.56 0.00

201510 7.75 -1.87 -0.46 0.00

201511 0.56 3.59 -0.42 0.00

201512 -2.17 -2.82 -2.61 0.01

201601 -5.77 -3.43 2.09 0.01

201602 -0.07 0.71 -0.57 0.02

201603 6.96 0.82 1.19 0.02

201604 0.91 0.74 3.28 0.01

201605 1.78 -0.18 -1.66 0.01

201606 -0.05 0.60 -1.48 0.02

201607 3.95 2.51 -1.27 0.02

201608 0.49 1.18 3.13 0.02

201609 0.25 2.13 -1.23 0.02

201610 -2.02 -4.42 4.12 0.02

201611 4.86 5.67 8.19 0.01

201612 1.81 0.08 3.56 0.03

201701 1.94 -1.14 -2.76 0.04

201702 3.57 -2.02 -1.68 0.04

201703 0.17 1.14 -3.32 0.03

201704 1.09 0.72 -2.10 0.05

201705 1.06 -2.52 -3.78 0.06

201706 0.78 2.23 1.48 0.06

201707 1.87 -1.46 -0.24 0.07

201708 0.16 -1.67 -2.09 0.09

201709 2.51 4.46 3.12 0.09

201710 2.25 -1.93 0.21 0.09

201711 3.12 -0.58 -0.08 0.08

201712 1.06 -1.32 0.05 0.09

201801 5.57 -3.15 -1.33 0.12

201802 -3.65 0.23 -1.07 0.11

201803 -2.35 4.05 -0.23 0.11

201804 0.28 1.14 0.54 0.14

201805 2.65 5.26 -3.18 0.14

201806 0.48 1.15 -2.33 0.14

201807 3.19 -2.22 0.47 0.16

201808 3.44 1.12 -3.99 0.16

201809 0.06 -2.28 -1.69 0.15

201810 -7.68 -4.77 3.44 0.19

201811 1.69 -0.68 0.27 0.18

201812 -9.57 -2.38 -1.86 0.20

201901 8.40 2.90 -0.45 0.21

201902 3.40 2.05 -2.68 0.18

201903 1.10 -3.03 -4.10 0.19

201904 3.97 -1.74 2.14 0.21

201905 -6.94 -1.31 -2.34 0.21

201906 6.93 0.28 -0.72 0.18

201907 1.19 -1.93 0.47 0.19

201908 -2.58 -2.36 -4.76 0.16

201909 1.43 -0.97 6.74 0.18

201910 2.06 0.29 -1.92 0.16

201911 3.87 0.78 -2.01 0.12

201912 2.77 0.73 1.76 0.14

202001 -0.11 -3.10 -6.22 0.13

202002 -8.13 1.07 -3.79 0.12

202003 -13.39 -4.88 -13.97 0.13

202004 13.65 2.49 -1.23 0.00

202005 5.58 2.48 -4.89 0.01

202006 2.46 2.70 -2.17 0.01

202007 5.77 -2.32 -1.38 0.01

202008 7.63 -0.22 -2.95 0.01

202009 -3.63 0.04 -2.68 0.01

202010 -2.10 4.36 4.21 0.01

202011 12.47 5.82 2.14 0.01

202012 4.63 4.89 -1.51 0.01

202101 -0.03 7.34 2.96 0.01

202102 2.78 2.06 7.18 0.00

202103 3.08 -2.37 7.40 0.00

202104 4.93 -3.19 -0.94 0.00

202105 0.29 -0.25 7.08 0.00

202106 2.75 1.70 -7.82 0.00

202107 1.27 -3.99 -1.76 0.00

202108 2.91 -0.43 -0.16 0.00

202109 -4.37 0.72 5.08 0.00

202110 6.65 -2.35 -0.48 0.00

202111 -1.55 -1.32 -0.44 0.00

202112 3.10 -1.66 3.28 0.01

202201 -6.25 -5.94 12.75 0.00

202202 -2.29 2.23 3.04 0.00

202203 3.05 -1.60 -1.80 0.01

202204 -9.46 -1.41 6.19 0.01

202205 -0.34 -1.85 8.41 0.03

202206 -8.43 2.09 -5.97 0.06

202207 9.57 2.81 -4.10 0.08

202208 -3.77 1.39 0.31 0.19

202209 -9.35 -0.82 0.03 0.19

202210 7.83 0.10 8.05 0.23

202211 4.60 -3.40 1.39 0.29

202212 -6.41 -0.64 1.36 0.33