Question

You are given the following information concerning three portfolios, the market portfolio, and the risk-free asset: Portfolio RP σP βP X 14.0 % 20 % 1.80 Y 13.0 15 1.30 Z 9.2 5 0.85 Market 11.1 10 1.00 Risk-free 6.6 0 0 What is the Sharpe ratio, Treynor ratio, and Jensen’s alpha for each portfolio?

Answer 1

The table is attached in screenshot:

Task 1

Sharp ratio:

X = 0.37

Y = 0.42666

Z = 0.52

Market = 0.45

Risk free = 0.00

Task 2

Treynor ratio:

X = 4.11

Y = 4.92307

Z = 3.05582

Market = 4.4

Risk free = 0.00

Task 3:

Jensen’s alpha:

X = (0.7)

Y = 0.55

Z = (1.225)

Market = 0.0

Risk free = 0.0

Step-by-step explanation:

Task 1

Sharp ratio= RP-Rf / σP

X= 14%-6.6% / 20% = 0.37

Y=13%-6.6% / 15% = 0.42666

Z= 9.2%-6.6% / 5% = 0.52

Market = 11.1%-6.6% / 10% = 0.45

Risk free = 6.6%-6.6% / 0% = 0.00

Task 2:

Treynor ratio= RP-Rf / βP

X= 14%-6.6% / 1.8 = 4.11

Y=13%-6.6% / 1.3 = 4.92307

Z= 9.2%-6.6% / 0.85 = 3.05582

Market = 11.1%-6.6% / 1 = 4.4

Risk free = 6.6%-6.6% / 0% = 0.00

Task 3:

Jensen’s alpha = RP-Rf - (βP*(Rm-Rf))

X= 14%-6.6% -( 1.8*(11.1-6.6))=7.4-(8.1)= (0.7)

Y=13%-6.6% -( 1.3*(11.1-6.6))=6.4-(5.85)= 0.55

Z= 9.2%-6.6% -( 0.85*(11.1-6.6))=2.6-(3.825)= (1.225)

Market = 11.1%-6.6% -( 1*(11.1-6.6))=4.5-(4.5)=0.00

Risk free = 6.6%-6.6% -( 0*(11.1-6.6))=7.4-(8.1)=0.00