Questions About Aquira, Spring, 1996

Negative Price!

"In question 10, I find an expected return for DB less than the 
analysts' growth rate forecast for earnings.  This gives a 
negative price!"

Your calculations are correct.  You will find that there is
no guarantee when you apply the CAPM returns to observed 
earnings and growth forecasts that the answers come out
nicely.  One inferece to draw from this result is that the
earnings forecast are overly-optimistic, or pertain only
to next year's earnings, and not to a perpetual growth rate,
as require by the perpetuity formula with no uncertainty.

Lehigh Return Error

Dear Professor Goetzmann,

In reviewing your answer key to the Acquira Co. assignment I've come 
across a couple of items that I cannot figure out.

First, I believe your calculation of the quarterly mean for Lehigh is 
erroneous.  I had 0.008.  I'm pretty sure I entered the right numbers, 
but perhaps I missed something.

More importantly, I need some clarification on the answer to #5.  I do not 
understand why Rm is equal to the actual annualized mean for the S&P 500 
and not the 8% equity risk premium given to us in problem #4.  As I 
understand it, Jensen's alpha = actual return - CAPM expected return.
In #4 we calculated the CAPM expected returns using the 8% equity risk 
premium and not the 11.8% S&P500.  Why the switch?

Finally, could you elaborate on #5?  Is a negative alpha a violation of 
the CAPM?

-Troy Resch

Dear Troy --

Thank-you for bringing the quarterly calculation error to
my attention.  Yes, I typed in a number wrong on the case.
1992.1 should have been -.121.  In any case, I get a number 
closer to yours: my annualised Lehigh  return is: .032. 
This gives an alpha in #5 for Lehigh of -.130.  

It is true that Jensen's alpha = actual return - CAPM expected return
, but you would not expect a company with a beta of 1
to have a 13%% return last year if the market dropped
by 20%.   In evaluating PAST performance, you correct for the
actual market return.  In number 4 you are correct to use the
equity risk premium because you are estimating the future expected
returns, given that the market perform as expected as well.
Finally on number 5, the negative (or positive) alpha is not
a violation of the CAPM because the CAPM is a theory about
expected returns. Actual returns deviate from expected returns
by an error:

R = E[R] + e

the deviation from the CAPM line could be due to e