Suppose you are considering two investments, stock A and stock B. The beta of A is 1.20, and the beta of B is 0.80. Stock A has an expected return of 12% and Treasury Bills are yielding 3%.
If the two stocks are fairly prices, what's the expected return on the Market Index?
Someone said the answer was:
(.12-.03)/1.2)+.03 = .105
Can someone please explain why??
To understand why the formula (.12 - .03)/1.2 + .03 is used to calculate the expected return on the Market Index, let's break it down step by step:
1. The expected return on a stock (in this case, Stock A) can be calculated using the Capital Asset Pricing Model (CAPM) formula:
Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
2. In this scenario, the risk-free rate is given as 3% (the yield on Treasury Bills).
3. Stock A's beta is given as 1.20.
4. The expected return of Stock A is given as 12%.
Now, to find the expected return on the Market Index, we need to rearrange the CAPM formula to solve for the Market Return:
Market Return = (Expected Return - Risk-Free Rate) / Beta + Risk-Free Rate
Let's plug in the given values:
Expected Return = 12%
Risk-Free Rate = 3%
Beta = 1.20
Market Return = (12% - 3%) / 1.20 + 3%
Simplifying the equation:
Market Return = 9% / 1.20 + 3%
Market Return = 0.075 + 0.03
Market Return = 0.105
Therefore, the expected return on the Market Index is 10.5% or 0.105 when expressed in decimal form.
So, to summarize, the formula (.12 - .03)/1.2 + .03 is used to calculate the expected return on the Market Index by rearranging the Capital Asset Pricing Model (CAPM) formula and plugging in the given values.