Please use excel to solve the questions.......,,,,,

INVESTMENT MANAGEMENT AND PORTFOLIO THEORY Fall 2013 Homework 7 LAW OF LARGE NUMBERS, CENTRAL LIMIT THEOREM, NORMAL DISTRIBUTION 1. Suppose the annual return of an investment is determined by the roll of a die with faces 1%,2%,3%,4%,5%,6% a. What is the mean () and standard deviation () of the annual return b. How can you simulate the outcome of this investment? c. LAW OF LARGE NUMBERS: Let Ri be the outcome of one simulation. Simulate the investment 500 time and calculate (Ri )/500 and - (Ri )/500 d. Consider the simulation of return for 25 years and the quantity ( Ri - 25)/ (5). Calculate this quantity for 1000 simulations of 25 years and plot the histogram of this quantity. CENTRAL LIMIT THEOREM e. Repeat the above for the following values of the faces of the die and their probabilities Outcome: -3% -1% 0% 2.5% 3% 4% Probability: 1/12 3/12 2/12 2/12 3/12 1/12 2. consider the daily (excluding weekend) performance of the team's portfolio during the investment exercise. (check the attached excel file to solve it) a. What is the arithmetic average return of your portfolio? b. What is the geometric average return of your portfolio? c. What is the dollar weighted average return of your portfolio? d. What is the Sharpe Ratio of your investment strategy? FIRST TRADE Sept. 11, 2015 Friday, September 11, 2015 Friday, October 02, 2015 1.1335 1.5428 44.75 1106.9 38.13 134.67 114.21 51.1 1.121 1.5178 45.61 1137.3 40.39 132.56 110.38 5% ` 49.88 Sunday, September 13, 2015 CASH TEAMS AMSA Capital CURRENCIES EUR $33,000.00 $0.00 GBP $30,000.00 COMMODITIES WTI $0.00 GOLD $15,000.00 EQUITIES KO BA $0.00 $15,000.00 AAPL $7,000.00 Absolute C Interest $0.00 -$291.67 P&L -$835.60 Annualized Return Return -0.8356% -14.52% Absolute P&L -$27.78 Annualized Return Return Monday -0.0278% -5.07% P&L -$6.99 1.1273 1.5569 1.1299 1.5569 1.1189 1.5507 1104.4 47.16 1119 46.74 1127.7 44.79 1138.1 46.96 1133.39 136.6 39.15 137.2 39.38 137.45 39.98 136.09 39.19 136.02 52 116.41 52.59 113.92 51.65 113.45 50.29 115.21 50.71 Tuesday, September 15, 2015 Annualized Return 1.1408 116.28 Return 1.5488 38.5 Absolute 1.1285 44.66 ay, September 14, 2015 1.534 -0.0070% -0.85% Absolute -$6.99 Annualized Return P&L Return Wednesday, September 16, 2015 -0.0070% -0.85% Absolute P&L $627.84 Annualized Return Return Thursday, September 17, 2015 0.6278% 45.83% Absolute P&L $764.58 Annualized Return Return Friday, September 18, 2015 0.7646% 46.51% Absolute P&L $585.36 Annualized Return Return Monday, September 21, 2015 0.5854% 21.37% Absolute P&L $585.36 Annualized Return Return 0.5854% 21.37% 1.112 1.5365 1.1186 1.5246 1.1234 1.5244 1.1198 1.5182 1.1245 1.5174 1.1235 1.5156 46.36 1124.7 44.48 1130.32 44.91 1153.97 45.7 1146.4 44.43 1131.97 44.88 1126.4 38.79 133.99 38.76 131.67 39.15 129.75 39.62 131.01 39.53 128.13 39.66 128.75 113.4 50.38 114.32 50.12 115 49.13 114.71 50.55 112.44 49.03 109.06 49 Tuesday, September 22, 2015 Absolute P&L $585.36 Annualized Return Return Wednesday, September 23, 2015 0.5854% 21.37% Absolute P&L -$530.60 Annualized Return Return Thursday, September 24, 2015 -0.5306% -16.14% Absolute P&L -$400.07 Annualized Return Return Friday, September 25, 2015 -0.4001% -11.23% Absolute P&L -$400.07 Annualized Return Return Monday, September 28, 2015 -0.4001% -11.23% Absolute P&L -$400.07 Annualized Return Return Tuesday, September 29 -0.4001% -11.23% Absolute P&L -$1,489.69 Return -1.4897% 1.1174 1.1189 1.513 44.88 1114.5 44.99 1113.5 40.12 130.95 39.8 130.61 110.3 mber 29, 2015 1.5121 49.61 109.58 49.89 Wednesday, September 30, 2015 Annualized Return -30.21% Absolute P&L -$1,489.69 Annualized Return Return Thursday, October 01, 2015 -1.4897% -30.21% Absolute P&L -$1,489.69 Annualized Return Return -1.4897% -30.21%