The risk-free rate of interest is 6% and the expected rate of return on the market is 12%. A stock has an expected rate of return of 3%.

What is this stock's beta? Is the following statement true or false? "No investors would buy this stock because it provides an expected return less than the risk-free rate." Explain.

1. Beta of Stock = -0.5

2. 2. Is the following statement true or false? "No investors would buy this stock because it provides an expected return less than the risk-free rate." Explain.

The statement is true.

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Step-by-step explanation

Risk Free Rate of  Return = 6%

Market Expected Return = 12%

Expected Return of of Stock = 3%

1. Calculation Beta of Stock

  As per CAPM Modal 

   E_r = R_f+B_s(R_m-R_f)

Where

E_r= Expected Return of Stock i.e. 3%

R_f= Risk Free Rate  of Return i.e. 6%

B_s = Beta of Security i.e. to be calculated

R_m= Market Expected Return i.e. 12%

Therefore 

Our calculation will be as follows

                 E_r = R_f+B_s(R_m-R_f)

              0.03 = 0.06+B_s(0.12-0.06)

              0.03 = 0.06+0.06B_s

   0.03-0.06 = 0.06B_s

            -0.03 = 0.06B_s

  -0.03/0.06=B_s

               -0.5 =B_s

Therefore

Beta of Stock =B_s= -0.5

2. Is the following statement true or false? "No investors would buy this stock because it provides an expected return less than the risk-free rate." Explain.

The statement is true.

Explanation:

Risk-free rate is the minimum return an investor should expect for any investment, as any amount of risk would not be accepted unless the expected rate of return was greater than the risk-free rate. Since the stock is  providing an expected return less than the risk-free rate, hence no investor would buy this stock.