Question

Given the following data: market rate = 12%, risk-free rate= 3%, beta of Stock A = 2, beta of stock B= 0.5.

Part 1: Draw the SML and mark the dots for stock A and stock B on the graph. Hint: note that we only need the risk-free rate and the market rate to draw the SML. SML is the graph that depicts what required rates (appropriate rates) should be based on CAPM.

Part 2: Assume that the actual return (historical returns) on stock A has been 24% and on stock B has been 10%. Mark the actual Stock A and Stock B on the graph (not the line.) Is stock A undervalued or overvalued? Is stock B undervalued or overvalued? Show the stocks on the SML graph. You may copy and paste the graph from part 1 and add the new info on the same graph.

(hint: first see if alpha is + or -. + alpha indicates undervalued, - alpha indicates overvalued)

Answer 1

Part 1. For Stock A, expected rate of return is calculated below

E(RA) = Rf + beta(Rm-Rf)
= 3%+2.0(12%-3%)
      = 3%+2*9%
      =21% (plotted as stock A on graph)

For Stock B,
E(RB) = 3%+0.5(12%-3%)
   =3%+4.5%
   = 7.5% (plotted as stock B on graph)


  
Part 2. Stock A has been giving a return of 24% against the expected return of 21% as above, Hence the alpha for the stock is positive by 3% (24-21=3%). Therefore, the stock is undervalued.

Similarly Stock B has been giving historical return of 10% which is 2.5% more than expected return. Hence, even stock B is undervalued with alpha being 2.5% positive.

The below graph depicts the additional information of Stock A and Stock b's historical returns. Ideally any return which is above the SML line is undervalued and stocks below the SML line is overvalued.