Question

1. Compare the following Actively Managed Equity Portfolios (A, B, & C) to the Market Portfolio (S&P 500). For each portfolio (A, B, C, & the Market Portfolio) Calculate 1) Treynor’s Ratio, 2) Sharpe’s Alpha and 3) Jensen’s Alpha. Using the calculated statistics determine which portfolio offers the most favorable risk adjusted results. Justify your choice. The Risk Free Rate of Return is 3%.

Portfolio, Annual Return , Beta , Standard Deviation of Returns

S&P =10% (.10), ? , 0.278

A = 10% (.10), 0.9 , 0.11

  B =14% (.14) , 1.03, 0.250

   C =15% (.15), 1.20 , 0.325

Answer 1

1) Treynor Ratio

Portfolio A= Portfolio return - Risk free rate / Beta

= 10% - 03% / 0.9

= 7% / 0.9

= 7.78

Portfolio B= Portfolio return - Risk free rate / Beta

= 14% - 3% / 1.03

= 11% / 1.03

= 10.68

Portfolio C= Portfolio return - risk free rate / beta

= 15% - 3% / 1.20

= 12% / 1.20

= 10

S&P= portfolio return - risk free rate / beta

= 10% - 3% / 1

= 7% / 1

= 7

Portfolio B has the highest Treynor ratio and offers the most favourable risk adjusted return. So, we should choose Portfolio B as per Treynor ratio.

B) Sharpe ratio

Portfolio A = portfolio return - risk free rate / std deviation

= 0.10 - 0.03/ 0.11

= 0.07/ 0.11

= 0.64

Portfolio B= Portfolio return - risk free rate / std deviation

= 0.14 - 0.03 / 0.25

= 0.11 / 0.25

= 0.44

Portfolio C= portfolio return - risk free rate / std deviation

= 0.15 - 0.03 / 0.325

= 0.12 / 0.325

= 0.37

S&P = portfolio return - risk free rate / std deviation

= 0.10 -0.03 / 0.278

= 0.07 / 0.278

= 0.25

Portfolio A has the highest Sharpe ratio, and provides the the most favourable risk adjusted return. So , we should choose portfolio A as per Sharpe ratio.

C) Jensen Alpha   

Portfolio A = Portfolio return- { Risk free rate + Beta ( market return - risk free rate)}

= 10% - { 3% + 0.9 ( 10% - 3%)}

= 10% - { 3% + 0.9 (7%)}

= 10% - {3% + 6.3%}

= 10% - 9.3%

= 0.07%

Portfolio B= Portfolio return - {Risk free rate + beta ( market return - risk free ratr)}

= 14% - {3% + 1.03 (10% - 3%)}

= 14% - { 3% + 1.03 (7%)}

= 14% - {3% + 7.21%}

= 14% - 10.21%

= 3.79%

Portfolio C= portfolio return - { risk free rate + beta ( market return - risk free rate) }

= 15% - { 3% + 1.2 (10% - 3%)}

= 15% - { 3% + 8.4%}

= 15% - 11.4%

= 3.6%

Portfolio B has the highest Jensen Alpha, and probides the highest favourable ridk adjusted return. So, we should choose portfolio B, as per Jensen alpha.