Dr. P.V. Viswanath

 

pviswanath@pace.edu

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  Courses/ FIN 652  
   
 
 
 

Fall 2012 Exams, FIN 652

  
   

 

Midterm

  • The midterm is closed book. However, you are allowed to bring in one 8.5"x11" sheet, containing only formulas.
  • Time allowed is 2 hours.
  • Explain all your steps; correct answers without explanations may not be given any credit at all.
  • Show all your computations and formulae. Make all your assumptions explicit. If your approach is correct, you will get some credit, even if your arithmetic answer is wrong. So concentrate on getting your logic right.
  • If you answer a question, I have the discretion to award you some points, even if you are completely wrong. If you don't attempt the question at all, I can give you no points! So attempt every question.
  1. You can invest in two different risky portfolios:
    2.  

    		Expected Return

    		Standard Dev of Returns

    Evergreen

    		9%

    		12%

    Fallcolor

    		16%

    		20%

    The correlation of returns between the two portfolios is 0.4.  Assume A = 4.

    1. (10 points) If you had $10000 to invest, how much would you invest in each portfolio, if you could also borrow and lend at 4% p.a.? 
    2. (5 points) How much would you invest in the risk-free asset?

  2. Dupont stock (DD) closed on October 15, 2012 at $49.01.  Suppose you had bought 500 shares at the close and financed it partly by using your margin privileges with your broker, who allows you to buy at 50% initial margin. 
    1. (10 points) If his maintenance margin is 30%, how much would the price have to change before you would have to put up margin?
    2. (10 points)Suppose you had sold short instead of buying on margin.  Assume, again, that initial margin on short sales is 50%.  If the maintenance margin on short sales is 30%, at what price would you have to put up fresh margin?
    3. (5 points)Suppose brokers decided on their own policies regarding maintenance margins.  If you discovered that your broker’s maintenance margins were higher for stock A than for stock B, what information would you glean (obtain) from that about the two stocks?

  3. Probabilities for three states of the economy and probabilities for the returns on a particular stock in each state are shown in the table below:
    4. State of the Economy Probability of economic state Stock Performance Probability of Stock Performance in Given Economic State
    Good 0.3 Good .6
        Poor .4
    Neutral 0.4 Good .5
        Poor .5
    Poor 0.3 Good .2
        Poor .8
    1. (5 points)What is the probability that the economy will be neutral and the stock will experience poor performance?
    2. (5 points)Is the stock performance independent of the state of the economy?
    3. (5 points)What is the expected return on the stock, assuming that the state of the economy is good?
    4. (5 points)If a good stock return is 15% and a bad stock return is 5%, what is the expected return on the stock?

  4. Answer any five of the following questions (25 points):
    1. How is the DJIA constructed?
    2. What is the role of specialists?  
    3. What is the problem with fragmentation?
    4. Define the Sharpe ratio? What is its function?
    5. What are the advantages of ETFs?
    6. If the Fisher Hypothesis is correct, what should be the correlation between inflation rates and nominal real rates?  Explain.
    7. What is the separation property?  What is the importance of the separation property?

  5. Read the article below from the NY Times of August 17, 2008 (http://www.nytimes.com/2008/08/17/business/economy/17stra.html?_r=0) by Mark Hulbert and answer the following questions:
    1. (10 points) The author claims that investors have wrongly believed that higher inflation is bad for stocks and thus have undervalued stocks.  Explain what the misconception of investors is that, according to the author, has led to this undervaluation.
    2. (10 points) According to the author, what is the correlation between nominal returns on equities and inflation? Explain with reference to the specific statement of the author.

Illusions About Inflation

THERE is widespread concern that high inflation — running at a 5.6 percent annual rate in the 12 months through July — could hurt the stock market. But this investor worry may be yet another example of money illusion: the confusion of nominal prices with their inflation-adjusted equivalent.

The notion that inflation is bad for stocks appears to make a good deal of sense. What’s more, there is reason to believe that this perception — mistaken though it may be — has sometimes driven down stock prices.

With inflation at 6 percent, for example, a dollar of profit that a company will earn a year from now is worth only 94 cents in today’s dollars. But if inflation were just 1 percent, as it was in early 2002, that dollar earned a year from now would be worth 99 cents today. Such differences add up, especially as investors consider a company’s earning power over many years.

Put a different way, if other things are equal, the value of a company’s future earnings will be lower to the extent that inflation is higher. That would make the company’s stock less valuable, and if investors went no further in their analysis, stock prices would deserve to decline.
But other things are not equal when it comes to stocks and inflation. Over the last eight decades, corporate profits have tended to grow faster when inflation is higher. In such periods, companies have been able to pass along higher costs to their customers. As a result, even though higher inflation leads to a greater discounting of future years’ earnings, those earnings tend to be bigger than they would have been otherwise. The net result is that the current value of a company’s future earnings remains relatively stable in the face of rising inflation.

This was the strong conclusion of a study conducted five years ago by John Campbell and Tuomo Vuolteenaho, both economics professors at Harvard at the time. (Mr. Campbell is still at Harvard; Mr. Vuolteenaho is not. Both are now partners at Arrowstreet Capital, a money management firm based in Boston.) Their study, “Inflation Illusion and Stock Prices,” was in the May 2004 issue of the American Economic Review.
In an interview, Professor Campbell emphasized that their study does not mean investors are wrong to worry about developments like high oil prices, which may be damaging the economy in specific ways while also contributing to inflation. But, he said, “inflation should not be an additional source of concern above and beyond those other developments.”

Of course, investors suffering from money illusion could knock down stock prices further than they deserve to be. Historically, this has sometimes occurred as inflation has begun to heat up, as investors extrapolate too low a growth rate for corporate profits into the future.
ONE of the best-known illustrations occurred during the high-inflation 1970s. For the 10 years through 1979, the Standard & Poor’s 500-stock index had an annualized gain of just 1.6 percent, a far cry from the historical average of close to 10 percent. That dismal performance helped to lower the index’s price-to-earnings ratio to a low of 6.8 by the end of that decade, according to data from Robert J. Shiller, the Yale finance professor. The comparable ratio today is around 20.

Franco Modigliani, who in the late 1970s was a finance professor at the Massachusetts Institute of Technology, realized that money illusion was a major factor in the market’s dismal performance in that decade. In a 1979 article written with Richard A. Cohn, then also an M.I.T. professor, he argued that stocks, in fact, were a good long-term hedge against inflation and that the stock market was therefore significantly undervalued. The strong bull market of the 1980s and 1990s vindicated their argument, and in 1985 Professor Modigliani was the Nobel laureate in economics. (Both men are now deceased.)

There’s no way to know, of course, whether investors will make the same mistake in the next few years as they did in the 1970s, pushing stock prices down to unjustifiably low levels. But even if they did, it doesn’t necessarily mean stocks deserve to be cheaper when inflation is high.
As Clifford S. Asness, managing principal at AQR Capital Management, a hedge fund firm, put it in an e-mail message, “It is a strange leap to observe that investors consistently make an error, and then recommend that error to current investors based on precedent.”
In any case, if inflation keeps heating up and investors fall victim to money illusion, stocks may well decline for a while. But if history is any guide, such weakness would signal an excellent long-term buying opportunity.   

Solutions to Midterm


1.
Suppose we consider Evergreen to be asset D, and Fallcolor to be asset E, we can use the formula below:
formula
Plugging numbers into the formula, we get the tangent portfolio as:
wD = (9-4)(20)(20)-[(16-4)(12)(20)(0.4)] ÷ [(9-4)(20)(20)+(16-4)(12)(12)-(9-4+16-4)(12)(20)(0.4)] = 0.40458;
Hence wE = 1-0.40458 = 0.59542.

The expected return on this portfolio is (0.40458)(9)+(0.59542)(16) = 13.16794%
The variance is given by (0.40458*12)2+(0.59542*20)2+2(0.40458)(0.59542)(12)(20)(0.4) = 211.6324, so that the standard deviation is the square root or 14.54759%.

We can now use the formula y* = [E(Rport) – Rf]/(0.01AVar(Rtgtport)) to get y* = 9.16794/[(0.01)(4)(211.6324)] = 1.083; hence it would be necessary to borrow 8.3% of the investor’s total investment.
Hence you would borrow (0.083)(10000) = $830.  This would be invested as follows: (0.40458)(10830) = $4381.60 in the Evergreen fund and $6448.40 in the Fallcolor fund.

2. a. Total purchase is 49.01x500 = $24,505.  Initial margin is 50%, so the investor would have put up 50% of this amount, viz.  $12252.50; the loan would also be $12252.50. Actual margin is computed as Equity/Total Value of Assets.  Suppose the stock price is P, then actual margin would be (500P-12252.5)/500P. Setting this equal to 0.3 and solving for P, we get $35.01
b. In this case, the amount of the loan would be 500P; the total amount of assets would be (1.5)(24505), and the equity would be  (1.5)( 24505) - 500P.  The margin is computed as a fraction of the loan, viz. 500P, so we solve [(1.5)(24505) - 500P]/500P = 0.3.  The solution is P = $56.55.
c. This would imply that stock A is more volatile than stock B.

3. a. This is the joint event that the economy is neutral and that the stock performance will be poor.  This is the product (0.4)(0.5) = (0.2) or 20%.
b. The answer is no – since the conditional probabilities vary according to the state of the economy.
c. If the state of the economy is good, the expected return will be (0.6)(15) + (0.4)(5) = 11%.
d. We have to compute the expected return in the other two possibilities – these will be (0.5)(15) + (0.5)(5) = 10% and (0.2)(15) + (0.8)(5) = 7% for the neutral and poor states respectively.  The associated probabilities of the three states of the economy are 0.3, 0.4 and 0.3; so weighting the three expected returns by these probabilities, we get (0.3)(11)+(0.4)(10)+(0.3)(7) = 9.4%

4.
a. The DJIA is simply the average price of the 30 stocks in the index, divided by the divisor that is valid at the given time.
b. Specialists are charged with maintaining a fair and orderly market.  In particular, this means that if there is significant market movement in a particular direction, the specialist should be resisting the trend so as to make price changes smaller.  In addition to this role, the specialist makes a market by offering to buy and sell the stock at all times, and acts as a catalyst by bringing buyers and sellers together.
c. The problem with fragmentation is that it reduces liquidity in each market.  The number of traders in each market will be lower than if there were a centralized market; the bid-ask price in each market will be higher than if the market were centralized.
d. The Sharpe ratio is defined as [E(Rp)-Rf]/Std Dev(excess returns), where excess return= Rp-Rf.  Its function is to operate as a reward-risk ratio for portfolios.
e. ETFs can be traded at any time of the day, like a stock.  There are tax consequences to the investor only if s/he trades the ETF, unlike a share in a mutual fund, where the overall trading of the fund can result in capital gains realizations for the investor.
f. The correlation between inflation and nominal interest rates should be 1, since nominal rates should keep up with inflation.  There should be no correlation between inflation and the real rate because under the Fisher hypothesis, the real sector is independent of the monetary sector.
g. The separation property says that the choice of the risky portfolio is independent of the risk preference of the investor – this portfolio is the same for all investors.  However, the choice of how much to invest in this risky portfolio and how much to invest in the risk-free asset depends on the investor’s risk aversion.  The reason that this is important is that there can be a single mutual fund, replicating the single risky portfolio, that all investors can invest in; this would reduce trading costs.

5.
a. The author says that investors have incorrectly believed that higher inflation is bad for stocks and thus have undervalued stocks.  According to him, investors have taken future profits as being uncorrelated with inflation.  Hence the higher inflation is, the higher interest rates would be, and equity profits would be discounted at higher rates; hence stock prices would be lower.  In fact, when inflation is high, corporate profits rise, as well.  As he notes, “Over the last eight decades, corporate profits have tended to grow faster when inflation is higher.”
b. The author seems to believe that, in the long run, investors’ money illusion would be dispelled.  If this happens, then (as in the 1980s), equities would end up being a good hedge against inflation.  In this case, the correlation between nominal returns on equities and inflation should be high, close to 1. This can be understood from two statements that the author makes: one, "In a 1979 article written with Richard A. Cohn, then also an M.I.T. professor, he argued that stocks, in fact, were a good long-term hedge against inflation and that the stock market was therefore significantly undervalued. The strong bull market of the 1980s and 1990s vindicated their argument" and two, " if history is any guide, such weakness would signal an excellent long-term buying opportunity."

 

Final

Notes:

  • If your answers are not legible or are otherwise difficult to follow, I reserve the right not to give you any points.
  • If you cheat in any way, I reserve the right to give you no points for the exam, and to give you a failing grade for the course.
  • You may bring in sheets with formulas, but no worked-out examples, or definitions, or anything else.
  • You must explain all your answers. Answers without explanations may not receive any points.
  • For quantitative questions, you must write down the formula; then show what the numerical equivalents for the variables in the formula are, and then provide the numerical answer. You may use a calculator to obtain the answer, but you still have to follow the requirements stated here.
  • All questions must be answered on the sheets provided only.
  • Question 1 from Part A is compulsory; answer any two other questions from Part A; three questions from part B and three questions from part C.
  • You may substitute the media article question for any other question. 


Solutions to Final

  
 

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