Question

Q15) The market risk premium for next period is 8.50% and the risk-free rate is 3.80%. Stock Z has a beta of 0.636 and an expected return of 13.40%. What is the: "

a) Market's reward-to-risk ratio? :

b) Stock Z's reward-to-risk ratio :

15b.) You are invested 30.10% in growth stocks with a beta of 1.785, 10.20% in value stocks with a beta of 1.444, and 59.70% in the market portfolio. What is the beta of your portfolio? (1 point)

Answer 1

Solution:

15a).

Calculation of Reward to Risk Ratio of the Market :

The formula for calculating the Reward to Risk ratio of the market is

= ( R_M – R_F ) / β_M

Where R_M = Market risk premium ;   R_F = Risk free rate    ;   β_P = Beta of the market

As per the Information given in the question we have :

R_M = 8.50 %    ;     R_F =   3.80 %    ;      β_M = 1        ( Since the Beta of the market is always 1 )

Applying the above values in the above formula we have

= ( 8.50 - 3.80 ) / 1

= 4.70 / 1 =

Thus the Treynor’s Ratio of the market = 4.7

Calculation of Reward to Risk Ratio of the Stock Z :

The formula for calculating the Reward to Risk ratio of the Stock Z is

= ( R_S – R_F ) / β_S

Where R_S = Expected Return of the stock ;   R_F = Risk free rate    ;   β_S = Beta of the Stock

As per the Information given in the question we have :

R_S = 13.40 %    ;     R_F =   3.80 %    ;      β_S = 0.636    

Applying the above values in the above formula we have

= ( 13.40 - 3.80 ) / 0.636

= 9.6 / 0.636

= 15.0943

Thus the Treynor’s Ratio for the Stock Z = 15.0943

15b)

Solution :

The formula for calculating the beta of the portfolio is

Β_P = [ ( W_A * β_A ) + ( W_B * β_B ) + ( W_C * β_C ) ]

where

β_P = Beta of the Portfolio

W_A = Weight of Investment in Growth Stocks = 30.10 % = 0.3010 ;     

β_A = Beta of the Growth Stock = 1.785    ;

W_B = Weight of Investment in Value Stock = 10.20 % = 0.1020   ;      

Β_B = Beta of the Value Stock = 1.444     ;

W_C = Weight of Investment in Market = 59.70 % = 0.5970   ;     

β_C = Beta of the Market = 1 ;

Applying the above vales in the formula we have

= ( 0.3010 * 1.785 )   + ( 0.1020 * 1.444 )   + ( 0.5970 * 1 )

= 0.537285 + 0.147288 + 0.5970

= 1.281573

Thus beta of the Portfolio is = 1.281573

= 1.28 ( when rounded off to two decimal places )