Question

(b) The data relating to market portfolio and an investor ‘P’ portfolio is indicated as below: The treasury bill rate prevailing in the market is 11%

 

Metric	Investor P’s Portfolio	Market Portfolio (M)
Average   Return	28%	18%
Beta   (β)	1.4	1.0
Standard   deviation (α)	30%	20%

 

Required. Calculate the following performance evaluation ratios

i.                    Sharpe Ratio (4 marks)

 

ii.                   Treynor Ratio (4 marks)

 

 Comment on the risk profile of investor P’s portfolio in relation to the market. 

Answer 1

 

Required. Calculate the following performance evaluation ratios

i.                    Sharpe Ratio (4 marks)

S_p =ER_p- R_F

                     δ_P   

where by

1.      ER_p = Average return

2.    δ_{P =} standard deviation

3.     R_F = market rate

For investor P’s portfolio

ð  

ð  

ð  

 

For market portfolio M

S_m= ER_m-R_F

          δ_m

whereby

1.      ER_m   = Average return

2.     R_F      = market rate

3.      δ_m     = standard deviation

 

ð  

ð  

ð  0.35

 

 

ii.                   Treynor Ratio (4 marks)

is given by

T_p=ER_p-R_F

           B_p

whereby

1.      ER_p       = Average return

2.      R_F           = market rate

3.       B_{p          =} Beta (β)

For investor P’s portfolio

ð  

ð  

ð  12.14

 

 

For market portfolio M

Is given by

T_m=ER_m-R_F  

            B_p

Whereby

1.      ER_m        = Average return

2.       R_F       = market rate

3.        B_p          = Beta (β)

 

ð  

ð  

ð  7

 

 

iii.                 Comment on the risk profile of investor P’s portfolio in relation to the market. (2 marks

For the ratios calculated in Sharpe Ratio Sp is greater than Sm where it can be written as Sp>Sm which indicates superior portfolio performance for investor P’s portfolio compared to the market M portfolio.

for the ratios calculated in Treynor Ratio Tp is greater than Tm where it can be written as Tp>Tm. this indicates superior portfolio performance for investor P’s portfolio compared to the market M portfolio