The expected return on the market (Rm) is 11.67%.
The Capital Asset Pricing Model (CAPM) allows us to calculate the expected return on a stock based on its beta, the expected return on the market, and the risk-free rate of return. The formula for the expected return on a stock (Re) using CAPM is:
Re = Rf + Beta (Rm - Rf)
Where:
- Re = Expected return on the stock
- Rf = Risk-free rate of return
- Beta = Beta of the stock
- Rm = Expected return on the market
We have the following information:
For Stock J:
- Beta (J) = 1.2
- Expected return (Rj) = 15.6%
For Stock K:
- Beta (K) = 0.8
- Expected return (Rk) = 12.4%
We need to find the expected return on the market (Rm) and the risk-free rate of return (Rf). To do this, we can use the information from Stock J and Stock K. We'll set up two equations:
1. For Stock J:
15.6% = Rf + 1.2 (Rm - Rf)
2. For Stock K:
12.4% = Rf + 0.8 (Rm - Rf)
Now, we'll solve this system of equations step by step:
First, isolate Rf in both equations:
From equation (1):
15.6% - 1.2 (Rm - Rf) = Rf
From equation (2):
12.4% - 0.8 (Rm - Rf) = Rf
Now, set these two equations equal to each other because they both equal Rf:
15.6% - 1.2 (Rm - Rf) = 12.4% - 0.8 (Rm - Rf)
Now, let's solve for Rf:
15.6% - 1.2Rm + 1.2Rf = 12.4% - 0.8Rm + 0.8Rf
Rearrange terms with Rf on one side and other terms on the other side:
1.2Rf - 0.8Rf = 12.4% - 0.8Rm + 1.2Rm - 15.6%
Combine like terms:
0.4Rf = -3.2%
Now, isolate Rf by dividing both sides by 0.4:
Rf = (-3.2%) / 0.4
Rf = -8%
So, the risk-free rate of return (Rf) is -8%.
Now that we have Rf, we can find Rm using equation (1):
15.6% = Rf + 1.2 (Rm - Rf)
15.6% = -8% + 1.2 (Rm + 8%)
Now, isolate Rm:
15.6% + 8% = 1.2 (Rm + 8%)
23.6% = 1.2 (Rm + 8%)
Divide both sides by 1.2:
Rm + 8% = 23.6% / 1.2
Rm + 8% = 19.67%
Now, subtract 8% from both sides to find Rm:
Rm = 19.67% - 8%
Rm = 11.67%
So, the expected return on the market (Rm) is 11.67%.
To summarize:
- The risk-free rate of return (Rf) is -8%.
- The expected return on the market (Rm) is 11.67%.