The runners Redeeming Vices and Gwendolyn and Ernest are in a race. The Odds (net returns for a winning unit bet) on offer for these runners are 1,2, and 4, respectively, and the respective 'true' probabilities are 0.6, 0.3, and 0.1.

1. Find the optimum allocation for the 3-asset portfolio of bets, from the Optimal growth perspective

2. Show that the expected returns for the 3 runners are (respectively) 0.2, -0.1, and -0.5.

3. Show that the variances are (respectively) 0.96,1.89,2.25 and the covariances are (1 with 2) -1.08, (1 with 3) -0.6, and (2 with 3) -0.45.

4. Find the Minimum Variance Portfolio for the 3-asset portfolio of bets.

5. For each of the possible values of Expected Return -0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2 find the portfolio of minimum variance and plot the corresponding Minimum Variance Set in the Mean-SD plane.