2012 Investments syllabus by JBbAUr6

VIEWS: 9 PAGES: 13

									                                Investment Management, Fall 2012
                                 School of Business Administration
                                  Hebrew University of Jerusalem
Name: Doron E. Avramov, Ph.D, Professor of Finance                          ‫דורון אברמוב; פרופסור למימון‬
Office: 5132 Mount Scopus, Jerusalem
Web: http://pluto.huji.ac.il/~davramov/
Class Hours: Sunday 15:30-18:15
Office Hour: Wednesday 15:30-16:30
Room: 2113

Course Description:

        In this course you will study the theory and practice of investment management in domestic and
        global financial markets. I will cover the following topical issues:

              Understanding the risk-return tradeoff: Basic concepts and the empirical evidence;
              Constructing price weighted equity indexes (such as the Dow Jones) and value weighted
               equity indexes (such as TA100 and the S&P500);
              Understanding the concept of market efficiency;
              Analyzing performance of investment vehicles such as mutual funds;
              Examining evidence on apparently profitable trading strategies in global and domestic
               markets;
              Forming optimal portfolios with and without portfolio constraints;
              Investing in public and private equities, commodities, as well as nominal and indexed bonds;
              Understanding derivatives securities (options and futures contracts);

        Familiarity with statistics should extend through concepts of mean, standard deviation, covariance,
        correlation, and regression analysis. A good grounding in Excel is essential.

Resources:

       Textbook: In general, the class notes adequately cover the material to be taught. If you wish to
        enhance your knowledge, however, I would recommend the following two textbooks:

             o Fundamentals of Investments Valuation and Management (Fifth Edition) by Jordan &
               Miller.

             o Investments, Sixth Edition by Bodie, Kane, and Marcus

       Instructor: I welcome students to see me during the office hour and class breaks to discuss any
        aspect of the course. I welcome your feedbacks regarding any aspect of the teaching process.

Assignments (30%): There will be three case studies. You can form groups of up to four students to
submit all assignments. To purchase electronic versions of the three case studies please visit the web site
below           Estimated cost is $3.95 per case. Assignments' due dates will be announced in class.



                                                      1
Final Exam (70%): The exam will be based on the material and examples covered in class, class handouts,
assignments, and reading. The exam is closed books and closed notes. However, you will be allowed to
bring in one piece of paper with handwritten notes (double-sided, A4 size). You are not allowed to use any
other notes. I will allow the use of non-programmable calculators during the exam. You will find in the end
of this syllabus questions taken from past year exams. It would be beneficial to solve those questions as a
means of preparation for the final.

Class Participation: It is mandatory to attend all sessions. If you miss a session for good reason, make
sure you catch up on all missed material. In general, you are responsible for class lectures as well as any
announcements, discussions, or remarks.




                                                    2
Case 1: The dimensional fund advisors (DFA)

In June 2002, the time when the case study was written, DFA was a $30 billion investment fund. Check out
http://www.dfaus.com/dimensional/about/ -- I believe you will be surprised to notice the phenomenal
growth in assets managed by DFA. Indeed, a number of features make DFA an unusual fund:

   1.   DFA apparently believes that the capital markets are efficient.
   2.   DFA relies on passive strategies undertaking a buy-and-hold investment approach.
   3.   DFA uses academic research to form investments and assess their performance.
   4.   DFA has specialized in the purchase of large blocks of small stocks at discount prices.

The case covers several topical subjects including efficient markets, models of capital market equilibrium
(e.g., CAPM and the Fama-French three-factor model), financial instruments, investment management, tax
management, liquidity, and stock trading.

Questions:

   1. What is DFA’s business strategy? Are the DFA people really believers in efficient markets?
   2. What are the Fama-French findings? Should we expect small stocks to outperform large stocks in
      the future? Value stocks to outperform growth stocks? Does the Fama-French model have some
      value from either academic or practitioner perspective?
   3. Visit the web page http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
      Download returns on 25 size and book to market portfolios and then replicate the table in the class
      notes (the one in the value anomaly section) based on:

             a. the entire sample starting from 1/70
             b. the 1/1/90-31/12/00 period
             c. the period starting from 1/1/2001.

      What do you learn?
   4. Discuss DFA’s liquidity providing strategy. How does it work, and what are the costs and benefits?
   5. Would you invest in DFA?
   6. What should be the firm strategy going forward? Does the company need to modify its basic
      strategy if it wants to grow assets and/or profits?
   7. Look at DFA web site – how would you explain the impressive progress DFA has made over time
      in attracting new money relative to its competitors.

Guidelines

Question 1: The business strategy section is pretty much open ended. In addition, DFA has been closely
affiliated with a prominent academic from the University of Chicago (the advisor of my own advisor)
called Eugene Fama. Fama has been a strong believer that markets are efficient starting from a paper he had
written in the 60s. He has not changed his views all along. In his view, if high book-to-market small-cap
stocks earn more – these stocks are essentially more risky and moreover the famous CAPM is unable to
capture these additional risk sources. DFA claims to have adopted these beliefs as well. Do you agree that
the DFA folks are believes in market efficiency?

Question 2 is about describing the Fama-French findings based on past evidence and future prospects. Here
is some background. The Fama-French three-factor model (which extends the one-factor CAPM) has
                                                       3
become a standard in the industry and academia. Its prominence has to do with the fact that the Fama-
French three factors are available to the public at the web site of Ken French, which you are going to visit
in question 3. Of course it does not hurt that Fama and French are both prominent scholars.

Some folks dislike the Fama-French model, to say the least. What could be the objections here? First, as
noted in class, the value and size premiums appeared, disappeared, and then reappeared (you will also
examine such time variation in question 3). Second, even when the value and size premiums were there
during the sample period selected by the Fama and French study, some disagree with the notion that high
book to market small stocks are more risky.

For example, there are behavioral (non risk) explanations for the value premium. Here is one. Investors
classify stocks to growth or value categories based on past performance. These investors are willing to pay
high prices for growth stocks believing that the previously observed phenomenal growth rates will be there
also in the future. But in reality, high growth rates don’t last for long – past high growth rate firms become
low growth rate firms in the future. Therefore, growth stocks earn less in the future once investors realize
that growth firms perform poorly relative to prior expectations. Thus, the value premium reflects investors’
incorrect extrapolation of past growth rates. There are other behavioral explanations.

Question 3 is self-explanatory. Simply download the data and compute statistics similar to those displayed
in the class notes.

Question 4: DFA has established an excellent reputation in the niche in liquidity providing. They do very
nice stuff as the case describes. What do they do? Describe your own thoughts about pros and cons. If you
have anything else to say about the important concept of liquidity please feel free to detail it in your papers.

Question 5 – open ended – there is no right or wrong here. Write an executive summary describing why
you would (or would not) invest in DFA. Of course, it makes sense to compare DFA to other investment
corporations, private brokers, hedge funds, mutual funds, etc.

Question 6 – DFA has objectives and strategy to accomplish those objectives. Would you change their
strategy? Based on what we know today have they been able to accomplish their objectives?

Question 7 requires some thinking regarding the impressive ability of DFA to attract new investors.




                                                       4
Case 2: The Harvard Management Company (2010)

   The central issue in this case is to propose an asset allocation policy for Harvard Management
   Company using concepts of mean variance optimization and portfolio constraints studied in class.

   Let us start with the policy portfolio displayed in Exhibit 4. The policy portfolio is the long run asset
   mix of Harvard. It specifies the “neutral weighting” for each asset class. HMC was given a minimum
   and maximum range for each asset class within which they could trade. HMC made tactical asset
   allocation bets from time to time attempting to beat the policy portfolio in anticipation for short-term
   market moves. Some of the questions below involve using the Excel Solver for forming optimal
   portfolios under constraints for each of the asset classes under consideration.

       1. Given figures in Exhibits 4 and 17 what is the expected return and volatility of the policy
          portfolio?
       2. Find an efficient portfolio having the same expected return as the policy portfolio but lower
          volatility based on portfolio constraints displayed in Exhibit 18.
       3. Find an efficient portfolio having the same volatility as the policy portfolio but higher expected
          return based on the same portfolio constraints.
       4. Repeat questions 2 and 3 using the new set of constraints in Exhibit 19.
       5. Plot on one space two efficient frontiers – the first one pertains to the constraints in Exhibit 18
          along with the inputs in Exhibit 4; the second one pertains to the constraints displayed in
          Exhibit 19 along with the inputs in Exhibit 4. Start the frontier from the Global Minimum
          Variance Portfolio (GMVP); end the frontier with the maximum expected return portfolio. Pick
          three other intermediate portfolios.
       6. Look at the Historical Asset Mix in Exhibit 3 – how would you explain the vast change in the
          asset mix for the periods 1992 through 2010 (e.g., equities versus bonds versus commodities)?
          In your opinion, does the asset mix simply follow past changing market conditions or does it
          predict future market conditions?
       7. Look at the percentage of assets invested with internal and external managers in Exhibit 5 –
          how would you explain the change in that percentage over time?
       8. Explain the pros and cons of the mean variance paradigm and describe whether you would use
          it in practice.
       9. Would you invest in HMC?

      Hints: Let me propose some guidelines for solving some of the questions. There is no need to
      attach excel files. The first question is merely a computational one. The objective here is to examine
      your ability to compute expected return and volatility of a portfolio accommodating multiple asset
      classes. Moreover, inputs from the first question will be used to solve the three questions that
      follow. In particular, the second (third) question requires displaying the weights of an efficient
      portfolio dominating the policy portfolio along the volatility (expected return) dimension. Of
      course, you are also required to exhibit the mean and volatility of these two dominating portfolios.
      So far everything is just computations. But questions (2) and (3) suggest that the policy portfolio is
      inefficient. Hence, why does HMC spend tremendous efforts on establishing the policy portfolio?
      Do your best efforts to answer this important question. Question4 (4) and (5) call for some new
      computations. You will see that with a tighter set of portfolio constraints the investment
      opportunities appear less attractive. Then explain: why imposing constraints to begin with? The
      fifth question is an open-ended question.



                                                      5
Case 3: The Harvard Management Company and Inflation Protected Bonds (2001)

This case examines the decision of the Harvard Management Company to recommend Harvard University
to invest part of its endowment in a new asset class - Treasury Inflation Protected Bonds (TIPS). The TIPS
principal and coupons grow with the general level of prices as measured by the Consumer Price Index
(CPI).

   1. When would TIPS outperform/underperform regular Treasuries (on a real basis)?
   2. From a conceptual perspective, should TIPS be considered an additional asset class in Harvard’s
      policy portfolio?
   3. Re-form the optimal portfolios in Exhibit 5 assuming that TIPS are unavailable for investment.
   4. Why did HMC ultimately recommend only 7% investment in TIPS?
   5. Do TIPS have advantages or disadvantages beyond their mean-variance properties that make them
      an attractive asset class for investors with long horizons such as Harvard?
   6. Should the Harvard Board accept the HMC proposal? (Did the Board accept the proposal?)


   Hints: TIPS have only recently been introduced in the US but such bonds have long been traded in UK
   as well as other high inflation economies. Indeed TIPS are intended to protect investors from Inflation.
   However, we have to be careful and distinguish between expected and unexpected inflation. In
   particular, when regular bonds and TIPS are issued, inflation expectations are already accounted for in
   determining the coupon paid on these bonds as well as setting the market price of the bonds. To gain
   some more essential knowledge on the important differences between regular bonds and TIPS please
   read the case study carefully and feel free to Google search the properties of inflation-indexed bonds.
   The information in the web is invaluable. I use the web on multiple occasions. Your answer to question
   1 should contain terminologies like expected and unexpected inflation as well as inflation risk premium.
   Question 2 is straightforward, as we did discuss in class three qualitative indicators of an additional
   asset class (the fourth one is quantitative). Do TIPS satisfy those requirements? Please be explicit.
   Question 3 is self-explanatory! It would be useful, as I noted in class, to contain some quantitative
   analysis here. For instance, for a given volatility what is the maximal expected return with versus
   without TIPS? Then report the expected return differential. You can consider several volatility levels.
   You can also compute Sharpe ratios and certainty equivalent rate of returns with versus without TIPS
   (for several volatility targets). In Question 4 you will find out that TIPS account for a large fraction of
   the optimal portfolio. Nevertheless the recommendation is to invest in TIPS only 7%. Why? Question 5:
   There are several other aspects of investment management beyond mean variance (e.g., hedging,
   skewness, liquidity, horizon effect, to name a few) that could be considered here. Question 6: Apart
   from making your recommendation I would like you to tell the fraction of investment in TIPS based on
   the most updated release (information is on the web).




                                                      6
Past Exam Questions - Class Notes Number 1
                                                 ?Dow Jones-‫1. איזה מהמשפטים הבאים הינו נכון ביחס למדד ה‬
                                                .‫א. המדד הוא ממוצע משוכלל ערך של 03 מניות אמריקאיות גדולות‬
                                              .‫ב. המדד הוא ממוצע משוכלל מחיר של 03 מניות אמריקאיות גדולות‬
                             .‫) צריך להיות מתואם לפיצול מניות וחלוקת דיבידנד במזומן‬the divisor( ‫ג. מחלק המדד‬
                                                    .‫ד. זהו מדד ממוצע שווה ערך של 03 מניות אמריקאיות גדולות‬


‫ בתאריכים 28 לאוקטובר 2828 ו-28 לאוקטובר 2828 הם %111 ו- %10- בהתאמה. מהו‬S&P -‫2. התשואות על מדד ה‬
    ‫) של שני תשואות אלו? איזו שיטת‬geometric average( ‫) והגיאומטרי‬arithmetic average ( ‫הממוצע האריתמטי‬
                                                      ?‫ממוצעים נראית יותר רלוונטית למדידת ביצועי השקעה‬
  02-‫ ל‬AAA ‫ הוא %25.2. מהי תשואת אג"ח‬yield spread -‫3. הנח כי תשואת אג"ח ממשלתי ל-20 שנים הינה %5, ה‬
                                                                                         ?‫שנים‬
4. Which of the following is true of the S&P500 index?

       A)   It is a value-weighted average of 500 stocks.
       B)   It is a price-weighted average of 500 stocks.
       C)   The divisor must be adjusted for stock splits and cash dividends.
       D)   It is an equal-weighted average of 500 stocks.
       E)   B and C.

5. What is the price-weighted index constructed with the three stocks below

  Stock       Price     Number of shares outstanding
 Stock A       $40                  200
 Stock B       $50                  500
 Stock C       $60                  600

6. The Value Line Index is a geometric average of the return of about 1,700 firms. Following that
       formulation what is the return on the index based on three stocks only with rates of return 10%, -
       7%, and 6%?

7. You have been given this probability distribution for the holding period return for XYZ stock:

 State of the Economy     Probability    HPR
          Boom               .30         8%
     Normal growth           .50         4%
       Recession             .20         - 5%

       What is the expected holding period return for XYZ stock? What is the standard deviation for XYZ
       stock?

  8. You purchase a share of Clal-Israel stock for $100. One year later, after receiving a dividend of $4,
                                                       7
       you sell the stock for $98. What was your holding period return?

   9. The geometric average for the five year period 2006-2011 is 10% per year. The geometric average
      for the three year period 2006-2007 is 11%. The geometric average for the period 2008-2009 is 8%.
      What is the geometric average for the two year period 2010-2011?

  10. You purchase a share of Google stock for $100. One year later, after receiving a dividend of $4,
you sell the stock for $92. What was your holding period return?

   11. The geometric average for the five year period 2006-2010 is 10% per year. The geometric average
for the three year period 2006-2008 is 11%. What is the geometric average for the two year period 2009-
2010?


Past Exam Questions -- Class Notes Number 2
 ,‫(). איזו צורת יעילות שוק, אם בכלל‬price momentum trading strategy ‫0 הסבר מהי אסטרטגית מסחר מומנטום מחיר‬
                                                                                   ?‫מפרה האסטרטגיה הנ"ל‬
     ‫8 הנח כי אסטרטגית מסחר שבה נרכשות מניות בעלות מחיר גבוה ונמכרות מניות בעלות מחיר נמוך, מניבה באופן עקבי‬
                                                                                        .‫תשואה עודפת על השוק‬
                                                   ?‫א. האם השווקים מקיימים את ההנחה החלשה של יעילות השוק‬
                                              ?‫האם השווקים מקיימים את ההנחה החצי - חזקה של יעילות השוק‬     .‫ב‬
                                                    ?‫ג. האם השווקים מקיימים את ההנחה החזקה של יעילות השוק‬


    3. The Sharpe ratios and Jensen’s alphas of five actively managed mutual funds and the S&P 500
       index are given by

    4. The accruals based trading strategy means that you can outperform the market by
       A. Taking long (short) position in firms with high (low) working capital
       B. Taking long (short) position in firms with high (low) profitability.
       C. Taking long (short) position in firms with high (low) non-cash based profits
       D. Taking long (short) position in firms with high (low) cash based profits
       E. None of the above

5 . Assume that a strategy that buys low volatility stocks and sells high volatility stocks consistently
outperforms the market. Does this evidence establish violation of market efficiency? If yes, what sorts of
market efficiency are being violated?


‫" מהווה הפרה של השוק היעיל? אם כן איזה צורה של שוק‬short-term reversal" ‫"? האם‬short-term reversal " ‫6. מהו‬
                                                                                          ?‫יעיל מופרת‬



                                                       8
7. Explain the relationship between the book-to-market ratio, value stocks, and growth stocks


Past Exam Questions - Class Notes Number 3
  ‫) הינו בעל תשואה צפויה של %80 וסטיית תקן של %10 והנכס‬A( ‫. הנכס הראשון‬B-‫ ו‬A ‫0. קיימים שני נכסים מסוכנים‬
A ‫) הינו בעל תשואה צפויה של %2 וסטיית תקן של %10. מקדם המתאם בין הנכסים הוא 1.2. מהו משקל נכס‬B( ‫השני‬
                                   )global minimum variance portfolio( ?‫בתיק בעל השונות המינימאלית‬
 ‫). ריבית חסרת הסיכון היא 52.2. איזה ערך של‬s=0.14( 2.01 ‫8. לתיק השקעות, תשואה צפויה של 50.2 וסטיית תקן של‬
                                                      E(r) - (A/2)s2 ‫ יגרום למשקיע בעל פונקצית התועלת‬A
       .‫, חישבת את תיק ההשקעות האופטימאלי כפוף לאילוצים‬Harvard Management Company ‫3. בניתוח אירוע של‬
                         .‫). הסבר מדוע‬commodities( ‫בפתרון מצאת כי מומלץ להשקיע שיעור גבוה מהכסף בסחורות‬
    4. A portfolio has an expected rate of return of 0.12 and a standard deviation of s=0.13. The risk-free
         rate is 6.085%. An investor has the following utility function: U = E(r) - (A/2)s2. Which value of
         A makes this investor indifferent between the risky portfolio and the risk-free asset?


     5. The Sharpe ratios and Jensen’s alphas of five actively managed mutual funds and the S&P 500
        index are given by

             Fund                       Sharpe ratio                  Jensen’s alpha
A                                           0.40                              0.01
B                                           0.50                              0.02
C                                           0.20                              0.01
D                                           0.10                          -0.02
E                                           0.25                          -0.01
S&P 500                                     0.30                              0.00



     You apply the following decision rule: an outperforming fund is one that dominates along both the
     Sharpe ratio and Jensen’s alpha criteria. Based upon that decision rule, which of the funds outperform
     the S&P index
6. Your utility function is U =µ - (A/2) σ2, where A is unknown. You can invest in ONLY ONE of the
following five assets:

                      Asset      Expected Return (µ)         Volatility (σ)
                       A                0.10                     0.15
                       B                0.11                     0.17
                       C                0.13                     0.20
                       D                0.17                     0.25
                       E                0.20                     0.32
                                                       9
Which value of A makes investment A the best investment? (There are many such values – pick only one).


      7. You have four portfolios W (15, 36), X (12, 15), Z (5, 7), and Y (9, 21) – which one cannot lie on the
      efficient frontier? Are the remaining three portfolios efficient?

      8.    A portfolio consists of the following two securities

                                             A                   B
                  Expected return           16%                  10%
                  Standard deviation        25%                  15%
                  Portfolio market value    $25,000             $15,000
                  Correlation (RA, RB)                   0.30
                  Risk-free rate                         4%

            What is the Sharpe ratio of the portfolio?


 9.    Stocks offer Ex=18% and Vol=22%. Gold offers Ex=10% and Vol=30%. Would you invest in gold?
       Use plot to explain!

10. Your utility function is U =µ - (A/2) σ2, where A =2. You can invest in ONLY ONE of                 the
following five assets:

                     Asset          Expected Return (µ)              Volatility (σ)
                         A                  0.10                              0.15
                         B                  0.11                              0.17
                         C                  0.13                              0.20
                         D                  0.17                              0.25
                         E                  0.20                              0.32


Which asset is your best choice? Explain!

11.        Which one of the following portfolios cannot lie on the efficient frontier as described by
           Markowitz? Explain!

             Portfolio Expected Return Standard Deviation
                W            9%               10%
                X            5%                7%
                Y           15%               30%
                Z           12%               30%

                .2.25 ‫). ריבית חסרת הסיכון היא‬s=0.14( 2.01 ‫80. לתיק השקעות, תשואה צפויה של 50.2 וסטיית תקן של‬
       ‫איזה ערך של‬A ‫ יגרום למשקיע בעל פונקצית התועלת‬E(r) - (A/2)s2 U = ‫להיות אדיש בין התיק המסוכן המפורט לעיל‬
      ?‫לנכס חסר סיכון‬
                                                                10
Questions for Class Notes Number 4
1. High Tech Chip Company is expected to have EPS in the coming year of $2.50. The expected ROE is
       14%. An appropriate required return on the stock is 11%. If the firm has a dividend payout ratio of
       40%, what is the intrinsic value of the stock?

    2. A stock has a required return of 16%, a constant perpetual growth rate of 10%, and a dividend
       payout ratio of 45%. What is the P/E ratio?

    3. A stock pays a current dividend of $2.80. The dividend will grow at 5% rate per year. If the
       required return is 8%, what is the capital gain for this stock over the next year? What is the
       expected dividend yield?

   4 . Consider the constant dividend growth model studied in class. Firm A has a required rate return
   (cost of equity) of 10% and growth rate of 6% - what is the expected capital gain on that stock?



Questions for Class Notes Number 5

   ‫) לפי מודלים מקובלים לתמחור אופציות ומצאנו שמחיר האופציה בשוק גבוה‬CALL( ‫0. אם חישבנו את אופציית הרכש‬
                                                                         :‫יותר, הסיבה לכך יכולה להיות‬
                                                                              .‫א. הערכת יתר של התנודתיות‬
                                                                            .‫ב. אי התחשבות בדיבידנד במודל‬
                                            .‫ג. אי התחשבות במודל בקשר האפשרי בין שער הריבית למחיר המניה‬
                                                                                       .‫ד. כל הסיבות לעיל‬
                                                                                 .‫ה. אף אחת מהסיבות לעיל‬


 32% ‫8. להערכתך, שוק המניות צפוי לעלות יותר מהר משיעור הריבית חסרת הסיכון. מנגד הינך מוכן להסתכן בהפסד של‬
                                                                           :‫לכל היותר מערך השקעתך. אזי‬
                                    .‫ על מדד המעו"ף‬CALL ‫א. תקנה ב-%23 מכספך מק"מ ובשאר הכסף אופציות‬
                                          .PUT ‫ ובשאר הכסף אופציות‬CALL ‫ב. תקנה ב-%20 מכספך אופציות‬
                                          .PUT ‫ ובשאר הכסף אופציות‬CALL ‫ג. תקנה ב-%23 מכספך אופציות‬
                                                  .‫ ובשאר הכסף מק"מ‬CALL ‫ד. תקנה ב-%23 מכספך אופציות‬
                          .‫ה. תקנה ב-%220 מכספך מק"מ שכן זו הדרך היחידה להבטיח לא להפסיד %23 מהשקעתך‬


 .‫3. הנח כי רכשת דירה בבניה בניו יורק ואתה אמור לשלם בגינה בתוך 3 חודשים. אתה חושש מתנודתיות של שער הדולר‬
                                                ?‫כיצד תוכל להשתמש בשוק ההון כדי לגדר את הפוזיציה שלך‬


                                                     11
‫4. חוזה עתידי בשם ”%001 ‪ .“Treasury Bonds (CBT)-$100,000; pts 32nds of‬המחיר העתידי (‪ (future price‬של‬
  ‫החוזה ביום 2228280203 הינו 68-22. שנה לאחר מכן ביום 2228280203, המחיר העתידי (‪ (future price‬של החוזה‬
                                                       ‫הינו 23-22. מהו הרווח או ההפסד שלך מהחזקת החוזה.‬


‫5. הנח כי מחיר יצור של מוצר מסוים ביום 22282220 הינו 2220$. התוצרת תימכר ב-22282220. כדי להתגונן מתנודתיות‬
   ‫במחיר המוצר, נרכשת אופציית ‪ put‬לשנה על מחיר המוצר. מחיר האופציה הינו 50$, מחיר המימוש (‪)strike price‬‬
‫הינו 2200$ ושיעור הריבית הינו אפס. הצג את גרף הרווח של החברה ביום 22282220 כפונקציה של מחיר המוצר ביום‬
                                                                                                     ‫זה.‬
                                                                          ‫איזה מהמשפטים הבאים הינו נכון:‬   ‫6.‬
                                                ‫א. ה- ‪ call price‬מתואם שלילית עם מחיר המימוש (‪.)strike price‬‬
                                                ‫ב. ה- ‪ put price‬מתואם שלילית עם מחיר המימוש (‪.)strike price‬‬
                                            ‫ג. ה- ‪ call price‬מתואם שלילית עם מועד הפדיון (‪.)time to maturity‬‬
                                                                 ‫ד. ה- ‪ put price‬מתואם חיובית עם מחיר המניה.‬
                                                              ‫ה. חוזה רכש (‪ )call contract‬הינו חוזה חסר סיכון.‬


‫0. אתה בונה תיק השקעות משתי אופציות. אתה קונה אופציית ‪ call‬במחיר של 0$ ומוכר אופציית ‪ put‬במחיר של 5$. שתי‬
   ‫האופציות הינן על אותה המניה, אותה תקופת מימוש ואותו מחיר מימוש. מייד לאחר בניית התיק, התנודתיות בשווקים‬
        ‫הפיננסים ירדה מ-%21 ל-%28. מחיר המניה וריבית חסרת הסיכון לא השתנו. תאר מה קרה לערך התיק שלך?‬


  ‫2. ביום 202826268, מחיר של אופציית ‪ call‬הינו 80$ ומחיר של אופציית ‪ put‬הינו 20$. הנח כי שתי האופציות הינן על‬
      ‫אותה מניה, בעלות אותו מועד לפדיון (שנה) ואותו מחיר מימוש (‪ .)strike price‬מחיר המניה 220$, מחיר המימוש‬
          ‫(‪ )strike price‬הינו 200$ והריבית השנתית חסרת הסיכון הינה %20. הצע אסטרטגיית ארביטראז' כך שביום‬
  ‫202826268 סך תזרים המזומנים הינו אפס, וביום 002826228 סך תזרים המזומנים הינו חיובי ללא קשר למחיר המניה.‬


‫‪To solve the next three questions, consider the three-period Binomial Tree framework when the stock price‬‬
‫:‪at time zero is 40, U=1.5, D=0.6, and R=1.1. Based upon these inputs answer the following four questions‬‬


    ‫?001 ‪9. What is the price of a European put option with a strike price of‬‬

   ‫‪10. What is the price of a European call option with a strike price of 100? (Hint: If you feel strongly‬‬
       ‫).‪about your answer for the put price you can implement the put-call parity‬‬

   ‫?001 ‪11. What is the price of an American Put option with a strike price of‬‬


   ‫.‪12. Assume that the prices of the underlying stock, call, and put options are 110, 17, and 8, respectively‬‬
       ‫‪In addition, the strike price is 105, the time to maturity is 0.5 years, and the annual risk free rate is‬‬
       ‫?‪10.25%. Which of the following statements is correct‬‬



                                                       ‫21‬
          ‫.‪a‬‬   ‫‪The call price must be too expensive‬‬
          ‫.‪b‬‬   ‫‪The put price must be too expensive‬‬
          ‫.‪c‬‬   ‫‪The put and call are properly priced‬‬
          ‫.‪d‬‬   ‫‪The leveraged equity is correctly priced‬‬
          ‫.‪e‬‬   ‫.‪By buying the call and selling the put you make an arbitrage profit‬‬


   ‫30. אתה קורא את עיתון ה- ‪ ,Wall Street Journal‬במוסף המתאר את ה- ‪ . future prices‬אתה רואה שהמחיר העתידי‬
   ‫(‪ (future price‬של ‪ future contract‬בשם ”%001 ‪ “Treasury Bonds (CBT)-$100,000; pts 32nds of‬הוא‬
 ‫68-22. באמצעות רכישה של ה- ‪ future contract‬הזה, אתה מתחייב לשלם בעתיד סכום של ___________$ בגין‬
                                                                           ‫‪.$100,000 Treasury bonds‬‬


  ‫44. הנח כי אתה מגדל פרי הדר בפלורידה ואתה מתכנן למכור את תוצרתך תוך 6 חודשים. אתה חושש מתנודתיות במחיר‬
                                        ‫התוצרת. כיצד תוכל להשתמש בשוק ההון כדי לגדר את הפוזיציה שלך?‬
                                                                         ‫50. איזה מהמשפטים הבאים אינו נכון:‬
                                              ‫ו. ה- ‪ call price‬מתואם שלילית עם מחיר המימוש (‪.)strike price‬‬
                                               ‫ז. ה- ‪ put price‬מתואם חיובית עם מחיר המימוש (‪.)strike price‬‬
                                           ‫ח. ה- ‪ call price‬מתואם חיובית עם מועד הפדיון (‪.)time to maturity‬‬
                                                               ‫ט. ה- ‪ put price‬מתואם חיובית עם מחיר המניה.‬
                                                                ‫י. חוזה רכש (‪ )call contract‬הינו חוזה מסוכן.‬
‫60. אתה בונה תיק השקעות משתי אופציות. אתה קונה אופציית ‪ call‬במחיר של 0$ ומוכר אופציית ‪ put‬במחיר של 5$. שתי‬
  ‫האופציות הינן על אותה המניה, אותה תקופת מימוש ואותו מחיר מימוש. מייד לאחר בניית התיק, התנודתיות בשווקים‬
       ‫הפיננסים עלתה מ-%28 ל-%21. מחיר המניה וריבית חסרת הסיכון לא השתנו. תאר מה קרה לערך התיק שלך?‬


 ‫00. מחיר של אופציית ‪ call‬הינו 80$ ומחיר של אופציית ‪ put‬הינו 20$. הנח כי שתי האופציות הם על אותה מניה, בעלות‬
  ‫אותו מועד לפדיון (שנה) ואותו מחיר מימוש (‪ .)strike price‬מחיר המניה כיום 220$, מחיר המימוש (‪)strike price‬‬
                               ‫הינו 200$ והריבית השנתית חסרת הסיכון הינה %20. הצע אסטרטגיית ארביטראז'‬



  ‫20. אם חישבנו את אופציית הרכש (‪ )CALL‬לפי מודלים מקובלים לתמחור אופציות ומצאנו שמחיר האופציה בשוק גבוה‬
                                                                         ‫יותר, הסיבה לכך יכולה להיות:‬
                                                                               ‫ו. הערכת יתר של התנודתיות.‬
                                                                             ‫ז. אי התחשבות בדיבידנד במודל.‬
                                            ‫ח. אי התחשבות במודל בקשר האפשרי בין שער הריבית למחיר המניה.‬
                                                                                         ‫ט. כל הסיבות לעיל.‬
                                                                                   ‫י. אף אחת מהסיבות לעיל.‬


                                                     ‫31‬

								
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