Answer:
The Jensen's alpha of a portfolio comprised of 45 percent portfolio A and 55 percent of portfolio B = 2.04 %
Step-by-step explanation:
Solution
Given that:
Now,
The Jensen’s alpha of a Portfolio is computed by applying the formula below:
Jensen's alpha = Portfolio Return − [Risk Free Rate of Return + ( Portfolio Beta * (Market Rate of Return − Risk Free Rate of Return ) ) ]
For the information given in the question we have the following,
The Risk free rate of return = 3. 1%
In order to find the Jensen’s alpha we have to first get the following from the information given in the question :
1. Portfolio Return
2. Portfolio Beta
3.Market Rate of Return
Thus,
(A)Calculation of Portfolio Return :
The formula for calculation of Portfolio Return is given as:
E(RP) = ( RA * WA )+ ( RB * WB )
Where
E(RP) = Portfolio Return
RA = Average Return of Portfolio A ; WA = Weight of Investment in Portfolio A
RB = Average Return of Portfolio B ; WB = Weight of Investment in Portfolio B
For the information given in the question we have the following:
RA = 18.9 %, WA = 45 % = 0.45, RB = 13.2 %, WB = 55 % = 0.55
By applying the values in the formula we have
= ( 18.9 % * 0.45 ) + ( 13.2 % * 0.55 )
= 8.5050 % + 7.2600 % = 15.7650 %
(B). Calculation of Portfolio Beta:
Now,
The formula for calculating the Portfolio Beta is
ΒP = [ ( WA * βA ) + ( WB * βB ) ]
Where,
βP = Portfolio Beta
WA = Weight of Investment in Portfolio A = 45 % = 0.45 ; βA = Beta of Portfolio A = 1.92
WB = Weight of Investment in Portfolio B = 55 % = 0.55 ; βB = Beta of Portfolio B = 1.27
By Applying the above vales in the formula we have
= ( 0.45 * 1.92 ) + ( 0.55 * 1.27 )
= 0.8640 + 0.6985
= 1.5625
(C). Calculation of Market rate of return :
Now,
The Market Risk Premium = Market rate of return - Risk free rate
From the Information given in the Question we have
The Market Risk Premium = 6.8 %
Risk free rate = 3. 1 %
Market rate of return = To find
Then
By applying the above information in the Market Risk Premium formula we have
6.8 % = Market rate of Return - 3.1 %
Thus Market rate of return = 6.8 % + 3.1 % = 9.9 %
So,
From the following information, we gave
Risk free rate of return = 3.1% ; Portfolio Return = 15.7650 %
The Portfolio Beta = 1.5625 ; Market Rate of Return = 9.9 %
Now
Applying the above values in the Jensen’s Alpha formula we have
The Jensen's alpha = Portfolio Return − [Risk Free Rate of Return + ( Portfolio Beta * (Market Rate of Return − Risk Free Rate of Return )) ]
= 15.7650 % - [ 3.1 % + ( 1.5625 * ( 9.9 % - 3.1 % ) ) ]
= 15.7650 % - [ 3.1 % + ( 1.5625 * 6.8 % ) ]
= 15.7650 % - [ 3.1 % + 10.6250 % ]
= 15.7650 % - 13.7250 %
= 2.0400 %
= 2.04 % ( when rounded off to two decimal places )
Therefore, the Jensen's alpha of a portfolio comprised of 45 percent portfolio A and 55 percent of portfolio B = 2.04 %