Consider the following five stocks with their returns for the period 1991-1996:
 
 

	1991	1992	1993	1994	1995	1996
LemonCar Corp.	12%	12%	9%	11%	7%	3%
MonkeyInvest Inc.	14%	6%	-28%	25%	31%	30%
Dartboard Corp.	16%	18%	11%	5%	15%	-5%
Pitt Portfolio Inc.	-3%	-7%	-15%	19%	22%	50%
Steeler Invest Inc.	8%	9%	9%	10%	9%	3%

 
Calculate the cross-sectional average or expected return for each year.

        Example: For 1991, we have (12% + 14% + 16% - 3% + 8%) / 5 = 9.4%
 
Calculate the time-series average or expected return for each year.

        Example: For Pitt Portfolio Inc. we have (-3% - 7% - 15% + 19% + 22% + 50%) / 6 = 11%
 
If the inflation rate has been 1.9% during 1995, what is the average real return for 1995 on your investment if you own 12 stocks of LemonCar Corp. and 3 stocks of Dartboard Corp?

        Average nominal return = (12 * 7% + 3 * 15%) / (12 + 3) = 10.75%. Average real return = (1.1075 / 1.019) - 1 = 8.68%
        (see Fisher equation)

If the stock price of MonkeyInvest Inc. is $80 at the beginning of 1994 and it lists at $98 at the end of 1994, what is the amount of dividend
     that the firm has paid out during 1994?

        Return₁₉₉₄ = 25%  = ($98 - $80 + Dividend₁₉₉₄) / $80  => Dividend₁₉₉₄ = $2

If the expected return on a treasury-bill is 2.8% in 1992, what is the average risk-premium in 1992?

        Average return for 1992 equals 7.6%, hence the average risk-premium equals 7.6% - 2.8% = 4.8%
 
Calculate the variance and standard deviation for each of the 5 stocks.

        Example: For Pitt Portfolio Inc, we have E[R] = 11%, and hence,

        VAR[R] = ([-3% - 11%]² + [-7% - 11%]² + [-15% - 11%]² + [19% - 11%]² + [22% - 11%]² + [50% - 11%]²) / (6 - 1) = 0.058

        Standard Deviation = s = squared root of 0.058 = 0.2409 = 24.09%

Which stock is the most risky and why?

        For now, we define risk as the standard deviation or variance. Pitt Portfolio has the highest variance (or standard deviation) and is therefore considered to be the most risky.
 
If we assume that investors are risk-averse, which stock would they never be interested in, and why?

        If we assume that investors are risk-averse, it means that they require a compensation, in the form of a higher expected return, on their investment if this investment is more risky. One of the stocks offers a lower expected return, while being more risky than another stock in this example. Investors would never buy this stock. (Which one is it?)

If markets are efficient (in its generic form), what return would you expect to receive when you buy stocks in MonkeyInvest Inc.?

        You would expect to earn a 'normal' rate of return, which is the expected return for this stock: E[R] = 13%
 
If markets are weak-form efficient, semi-strong efficient, but not strong-form efficient, would it be possible to realize a higher return than 8%
      if  you invest your money in Steeler Invest Inc. based on a careful analysis of the Wall Street Journal, the firm's annual report and other
      publicly available information?

        Two things. First, if a market is only strong-form inefficient, it means that it is possible to earn an above-normal return if you base your investments on inside or private information. Second, in this example, you use publicly available information. Even though it looks like we violate weak form and semi-strong form efficiency, we have to realize that it is always possible, even in an efficient market, to realize an abnormal return. As long as this is not happening consistently. Hence, the answer is yes, this is possible.
 
If markets are weak-form efficient, semi-strong efficient, but not strong-form efficient, would it be possible to consistently realize a higher
     return than 8% if you invest your money in Steeler Invest Inc.based on a careful analysis of the Wall Street Journal, the firm's annual report
     and other publicly available information?

        Same question, but now we are asked whether it is possible to realize an abnormal return, based on publicly available information, consistently. This is not possible if markets are semi-strong form efficient.
 
If markets are weak-form efficient, semi-strong efficient, but not strong-form efficient, would it be possible to consistently realize a higher
     return than 8% if  you invest your money in Steeler Invest Inc. based on a tip that you received from your aunt who sits on the board of
     directors of Steeler Invest?

        Since the market is not strong form efficient, you could easily make consistently better returns on your investments when you use your private information (in reality this 'insider trading' is illegal).

1. The semi-strong form of the efficient market hypothesis (EMH) states that:

a. Technical analysis cannot be used to consistently beat the market, but combining historical stock data with other fundamental publicly available information can.

b. Fundamental analysis cannot be used to consistently beat the market, but historical stock price data can.

c. Both technical and fundamental analysis is useless in trying to consistently beat the market.

d. Inside information is useless to predict future stock prices

e. Both a. and b.
 

2. Suppose you notice that every time when firms with unexpectedly high earnings generate abnormally high returns for several months after the announcement of the earnings.  This would be evidence of:

a. Inefficient markets in the weak form.

b. Efficient markets in the semi-strong form.

c. Efficient markets in the strong form.

d. Inefficient markets only in the semi-strong and strong form

e. Inefficient markets only in the weak and strong form.

What can you generally say about market efficiency if:

i) If you observe that after an earnings report came out, the actual return for Apple is 3% on that particular day.

    Even though the daily return is much higher than the expected or normal daily return, and hence we have an
abnormal return, there is no reason to question market efficiency. First of all, there is new information entering
the market (an earnings announcement) so we would expect to see a stock price reaction, making the new price reflect
all the information. Second, there is no consistency here, in other words, it doesn't say anything about this happening
each and every time.

ii) Same as i) but the report says that earnings are down by 38% from last year.

    It might be perceived as bad news if earnings are down, but we have to be careful here. A decrease in earnings is only
bad news to the extent that it was unexpected. If investors were expecting to see a drop in earnings, there is no bad news
associated with a drop in earnings, because that expectation should have been incorporated in the stock prices already.

iii) Same as i) but earnings are down by 38%, while analysts were expecting a drop of 10%

    This is an example of bad news since the actual drop in earnings was much more than people had anticipated. Therefore,
this comes as a surprise and the stock price will react to the news. It seems like a strange reaction to see the stock price go
up by 3%  in this case.

iv) Same as i) but earnings are up by 29%.

    It looks like good news if earnings are up, but similar as above, this is only true to the extent that the increase in earnings
is more than investors anticipated. The 3% therefore is very well possible, but you cannot say in general that an increase in
earnings is good news. It depends on the expected change in the earnings.

v) Same as i) but earnings are up by 29%, while investors were expecting 63%.

    This is an example of bad news, because the earnings have increased by less than investors were expecting.
Observing a 3% increase in the stock price seems strange here.

vi) You observe that the yearly return for Apple after the announcement of their earnings is 26%.

    While we are making an abnormal return of 26%-18%=8%, we do not now if we are able to do this on a consistent
basis. Therefore, this does not violate market efficiency.

vii) You observe that after each positive earnings report, Apple experiences an abnormal return of 12% per year.

    Here we are making a consistent, or on average abnormal return, based on publicly available information (earnings
announcements), which violates semi-strong form efficiency. If we could use even better information, our performance would
improve, so this is also a violation of strong form efficiency.

viii) You observe that after each earnings report, Apple has a semi-annual return of 22% during the first six months after the announcement.

    Similar as above.

ix) You observe that using the earnings information does not help you in realizing any abnormal performance, but every time you use the tips you get from your neighbor, who works at Apple, you do realize abnormal returns.
 
    This violated strong form efficiency only, because we know that we cannot beat the market (or realize an abnormal return) when
we only use all the publicly available information.  This means that using even worse information, like past stock price patterns, will
definitely not work.