Question

Suppose we observe two stocks with the following characteristics:                  
                                                                                                                             

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

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).                                                                                           

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).                                                    

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

An asset is overvalued if it is giving less return per unit of risk taken. If it is providing less return per unit of risk as compared to other asset, then it is overvalued relative to other asset. So, for finding which asset is overvalued and which one is undervalued on a relative basis we can find out Treynor Ratio of both the assets and compare that.

Treynor Ratio provides the excess return earned over the risk free rate per unit of systematic risk taken which is measured by Beta. So, higher the Treynor Ratio, it means that asset is providing better return per unit of Beta than other assets, means undervalued relatively.

Treynor Ratio =

So,

(a)

Treynor Ratio of Asset K = (20% - 6%) / 1.6 = 8.75%

Treynor Ratio of Asset L = (12% - 6%) / 0.9 = 6.67%

So, Treynor Ratio of Asset K > Treynor Ratio of Asset L,

Thus, Asset L is relatively overvalued and Asset K is relatively undervalued. The reason is it is providing less return as compared to Asset K. Though Asset K is also having high systematic risk, excess return is more than enough to compensate for it.

(b)

Treynor Ratio of Asset M = (20% - 6%) / 1.6 = 8.75%

Treynor Ratio of Asset N = (12% - 6%) / 0.9 = 6.67%

So, Treynor Ratio of Asset M > Treynor Ratio of Asset N,

Thus, Asset N is relatively overvalued and Asset M is relatively undervalued. The reason is it is providing less return as compared to Asset M. Though Asset M is also having high systematic risk, excess return is more than enough to compensate for it.

(c)

Generally, it is very unlikely that a stock remains relatively overvalued or undervalued than general market for a very long period of time. Because as a participant see that one stock is overvalued relatively to general market, they would short that stock while going long on overall market. So, in this way price of overvalued security will fall while overall market will rise. Thus, overvaluation will automatically disappear.

Similarly, with undervalued stock as well, which more and more investor would buy when they come to know about undervaluation. They would buy undervalued stock and short the overall market. Thus, undervalued security will rise while overall market falling upto a point that both are relatively fairly priced. This way equilibirium is established whenever such undervaluation or overvaluation happens.