Question 1:
30% Tesla (TSLA): 15/9: 303.75
22/9: 288.59
70% Google (GOOG): 15/9: 103.90
22/9: 100.57
Q2a. The weekly simple returns
Tesla (TSLA): (288.59-303.75)/ 303.75 = -4.99%
Google (GOOG): (100.57-103.90)/ 103.90 = -3.21%
Q2b. The weekly log-returns
Tesla (TSLA): ln(288.59/303.75) = -5.12%
Google (GOOG): ln(100.57/103.90) = -3.26%
Q2c. The weekly simple return of the portfolio
30%*-4.99% + 70%* -3.21% = -3.74%
Q2d. The weekly simple return of the portfolio
geometric mean daily returns = (1-3.74%)^(1/5)-1 = -0.76%
Q3a. Expected monthly simple returns of two stocks
Stock 1: 2.76% Stock 2: 1.48%
SR Stock 1 SR Stock 2 Probability Stock 1
Stock 2
Very Good
26%
14%
12%
3.1200%
1.6800%
Good
16%
10%
18%
2.8800%
1.8000%
1%
2%
48%
0.4800%
0.9600%
Bad
-14%
-12%
14% -1.9600%
-1.6800%
Very bad
-22%
-16%
8% -1.7600%
-1.2800%
2.7600%
1.4800%
Normal
Q3b. Expected monthly simple returns of the portfolio
30%*2.76%+70%*1.48%= 1.86%
Q3c. Variance of the two stocks returns
Stock 1: 1.86% Stock 2: 0.82%
2.76%
1.48%
SR Stock 1 SR Stock 2 Probability Varience 1 Varience 2
Very Good
26%
14%
12%
0.6481%
0.1881%
Good
16%
10%
18%
0.3155%
0.1307%
1%
2%
48%
0.0149%
0.0013%
Bad
-14%
-12%
14%
0.3933%
0.2544%
Very bad
-22%
-16%
8%
0.4904%
0.2444%
1.8622%
0.8189%
Normal
Q3d. Variance of the portfolio returns
Cov(1,2) = 0.0121
Variance(1,2) = (0.3^2)*1.86% + (0.7^2)* 0.82% + 2*(0.3)*(0.7)*0.0121 = 0.0108
Q3e. Sharpe ratio of the portfolio
(1.86%-0.5%)/(0.0108)^(1/2) = 0.1309
Q3f. Correlation between Stock 1 and Stock 2
0.0121/ (1.86%*0.82%)^(1/2) = 0.9798
Q3g. 30%-VaR of Stock 1
l {2.76% - (-0.524)*( 1.86%)^(1/2)} l
= 9.91%
Q3h. 30%-ES of Stock 1
-22%*8% + (-14%)*14% + 1%*8% = -3.64%
Q5a. Cash in at 9am
5.9*50+5.7*100+5.3*50 = 1130
Q5a. Saved: Cash in at 1am
6*200-1130 = 70
Q6a. Initial shorting margin
(1200+300-1200)/1200 =300/1200 = 25%
Q6b. Maintenance shorting margin
(6*200+300-7*200)/(7*200) = 7.14%