Question

Stock	Expected return	Beta
K	20%	1.6
L	12%	0.9

6.      Suppose we observe two stocks with the following characteristics:    
                                                                                                                                      

a. An asset is said to be overvalued if its price is too high given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks overvalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not overvalued).                                        (3.5 marks)                                            

Stock	Expected return	Beta
M	20%	1.6
N	12%	0.9

b. Suppose we observe two stocks with the following characteristics:

     An asset is said to be undervalued if its price is too low given its expected return and risk. The risk-free rate is currently 6%. Is one of the two stocks undervalued relative to the other? Explain your answer fully (i.e., provide reasons why you think the stock is or is not undervalued).                                      (3.5 marks)

c. In a well-functioning, well-organized, active market, can a stock be persistently over- or undervalued relative to an average asset in the market? Explain why or why not. How and when is equilibrium achieved?    

Answer 1

1.
Let market return be x%

In equilibrium,
expected return=required return=risk free rate+beta*(market return-risk free rate)

From K: 6%+1.6*(x%-6%)=20%
=>x=(20%-6%)/1.6+6%
=>x=14.7500%

From L: 6%+0.9*(x%-6%)=12%
=>x=(12%-6%)/0.9+6%
=>x=12.6667%

As market return gotten using L is less than that gotten using K, we see that Stock L is overvalued relative to Stock K

2.
Let market return be x%

In equilibrium,
expected return=required return=risk free rate+beta*(market return-risk free rate)

From K: 6%+1.6*(x%-6%)=20%
=>x=(20%-6%)/1.6+6%
=>x=14.7500%

From L: 6%+0.9*(x%-6%)=12%
=>x=(12%-6%)/0.9+6%
=>x=12.6667%

As market return gotten using K is more than that gotten using L, we see that Stock K is undervalued relative to Stock L

3.
No in an well functioning market, no stock can be persistently under or overvalued as arbitrage will occur i.e., investors will start exploiting arbitrage and buy undervalued stocks thus raising price and lowering return till it reaches required return. Similarly, they will start selling overvalued stocks and thus lowering price and increasing return till it reaches required return. Equilibrium is achieved when expected return is same as required return.