A Portfolio Manager (PM) has three mutual funds in has portfolio. Following the details of these three mutual funds: Particulars Growth fund…

(a) (i) Variance of different Funds can be calculated by using Sharpe Ratio as follows: (a) Growth Fund Let σ G be the Standard Deviation of Growth Fund. Accordingly - 0.15 = (7.50-9.00) / σ G σ G = 10 Hence the variance of Growth Fund (σ G ) 2 = 100 (b) Balanced Fund Let σ B be the Standard Deviation of Balanced Fund. Accordingly - 0.36 = (6.30-9.00) / σ B σ B = 7.50 Hence the variance of Growth Fund (σ B ) 2 = 56.25 (c) Regular Fund Let σ R be the Standard Deviation of Regular Fund. Accordingly - 0.48 = (5.40-9.00) / σ R σ R = 7.50 Hence the variance of Growth Fund (σ R ) 2 = 56.25 (ii) To determine the Coefficient of Determination we need the Coefficient of Correlation which can be determined by computing β using the Treynor Ratio as follows: (a) Growth Fund Let β G be the Beta of Growth Fund. Accordingly - 2 = (7.50-9.00) / β G β G = 0.75 Since Beta = Corr G,M × σ G / σ M and σ G = 10 and σ M = √50.41 = 7.1 Hence 0.75 = (10 Corr G,M ) / 7.10 Corr G,M = 0.5325 or 0.53 and Coefficient of Determination of Growth Fund = (0.5325) 2 = 0.2836 or (0.53) 2 = 0.28 (b) Balanced Fund Let β B be the Beta of Balanced Fund. Accordingly - 3 = (6.30-9.00) / β B β B = 0.90 Since Beta = Corr B,M × σ B / σ M and σ B = 7.50 and σ M = √50.41 = 7.1 Hence 0.90 = (7.50Corr B,M ) / 7.10 Corr B,M = 0.852 or 0.85 and Coefficient of Determination of Balanced Fund = (0.852) 2 = 0.7259 or (0.85) 2 = 0.73 (c) Regular Fund Let β R be the Beta of Regular Fund. Accordingly - 4.80 = (5.40-9.00) / β R β R = 0.75 Since Beta = Corr R,M × σ R / σ M and σ R = 7.50 and σ R = √50.41 = 7.1 Hence 0.75 = (7.50Corr R,M ) / 7.10 Corr R,M = 0.71 and Coefficient of Determination of Regular Fund = (0.71) 2 = 0.5041 or 0.50