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essentials of investments

Questions and Answers of Essentials of Investments

A share of stock sells for $50 today. It will pay a dividend of $6 per share at the end of the year.Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?
Consider the following table, which gives a security analyst’s expected return on two stocks for two particular market returns:Market Return Aggressive Stock Defensive Stock 5% 2% 6%25 38 12a.
Can you sort out the nuances of the following maze of models?a. CAPMb. Single-factor modelc. Single-index modeld. Market model
Data from the last eight decades (see Table 5.3) for the S&P 500 index yield the following statistics: average excess return, 7.9%; standard deviation, 23.2%.a. To the extent that these averages
When the annualized monthly percentage rates of return for a stock market index were regressed against the returns for ABC and XYZ stocks over a 5-year period ending in 2010, using an ordinary least
Suppose that the alpha forecasts in row 44 of Spreadsheet 8.1 are doubled. All the other data remain the same. Recalculate the optimal risky portfolio. Before you do any calculations, however, use
Suppose that on the basis of the analyst’s past record, you estimate that the relationship between forecast and actual alpha is:Actual abnormal return 5 .3 3 Forecast of alpha Use the alphas from
Recalculate Problem 17 for a portfolio manager who is not allowed to short sell securities.a. What is the cost of the restriction in terms of Sharpe’s measure?b. What is the utility loss to the
Based on current dividend yields and expected growth rates, the expected rates of return on stocks A and B are 11% and 14%, respectively. The beta of stock A is .8, while that of stock B is 1.5. The
A stock recently has been estimated to have a beta of 1.24:a. What will a beta book compute as the “adjusted beta” of this stock?b. Suppose that you estimate the following regression describing
Rework Problem 13 for portfolio Q with investment proportions of .50 in P, .30 in the market index, and .20 in T-bills.
What are the covariance and correlation coefficient between the two stocks?
Break down the variance of each stock to the systematic and firm-specific components.
Consider the two (excess return) index model regression results for A and B:R A 1% 1.2 R M R -square .576 Residual standard deviation 10.3%R B 2% .8 R M R -square .436 Residual
Why do we call alpha a “nonmarket” return premium? Why are high-alpha stocks desirable investments for active portfolio managers? With all other parameters held fixed, what would happen to a
Compare the first five and last four industries in Table 8.4 . What characteristic seems to determine whether the adjustment factor is positive or negative?
What was Intel’s index-model per month during the period covered by the Table 8.3 regression if during this period the average monthly rate of return on T-bills was .2%?
Reconsider the two stocks in Concept Check 2.Suppose we form an equally weighted portfolio of A and B. What will be the nonsystematic standard deviation of that portfolio?
Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth $100,000. Her financial adviser provided her with the following forecast
George Stephenson’s current portfolio of $2 million is invested as follows:Summary of Stephenson’s Current Portfolio Value Percent of Total Expected Annual Return Annual Standard Deviation
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?Portfolio Expected Return (%) Standard Deviation (%)a. W 15 36b. X 12 15c. Z 5 7d. Y 9 21
Another committee member suggested that, rather than evaluate each managed portfolio independently of other portfolios, it might be better to consider the effects of a change in the Hennessy
One committee member was particularly enthusiastic concerning Jones’s proposal. He suggested that Hennessy’s perfoxrmance might benefit further from reduction in the number of issues to 10.If the
If you were to use only the two risky funds, and still require an expected return of 14%, what would be the investment proportions of your portfolio? Compare its standard deviation to that of the
What is the reward-to-volatility ratio of the best feasible CAL?
Tabulate and draw the investment opportunity set of the two risky funds. Use investment proportions for the stock fund of zero to 100% in increments of 20%.
Suppose that the universe of available risky securities consists of a large number of stocks, identically distributed with E ( r ) 15%, 60%, and a common correlation coefficient of .5.a.
Suppose that two portfolio managers who work for competing investment management houses each employ a group of security analysts to prepare the input list for the Markowitz algorithm. When all is
Compute and draw the portfolio opportunity set for the debt and equity funds when the correlation coefficient between them is p = .25.
An analyst estimates that a stock has the following probabilities of return depending on the state of the economy:State of Economy Probability Return Good .1 15%Normal .6 13 Poor .3 7 What is the
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.State of Economy Probability of Economic State Stock
Based on the scenarios below, what is the expected return for a portfolio with the following return profile?Market Condition Bear Normal Bull Probability .2 .3 .5 Rate of return 25% 10% 24%Use the
Given $100,000 to invest, what is the expected risk premium in dollars of investing in equities versus risk-free T-bills (U.S. Treasury bills) based on the following table?Action Probability Expected
Compute the means, standard deviations, skewness, and kurtosis of the annual HPR of large stocks and long-term Treasury bonds using only the 30 years of data between 1980 and 2009. How do these
You can find annual holding-period returns for several asset classes at our Web site ( www.mhhe.com/bkm ); look for links to Chapter
Using historical risk premiums over the 1926–2009 period as your guide, what would be your estimate of the expected annual HPR on the S&P 500 stock portfolio if the current risk-free interest rate
What is the standard deviation of a random variable q with the following probability distribution:Value of q Probability 0 .25 1 .25 2 .50
Estimate the skew and kurtosis of the five rates in Spreadsheet 5.2 .
What is the probability that the return on the index in Example 5.10 will be below -15%?
Using the annual returns for years 2003–2005 in Spreadsheet 5.2 ,a. Compute the arithmetic average return.b. Compute the geometric average return.c. Compute the standard deviation of returns.d.
You invested $1 million at the beginning of 2008 in an S&P 500 stock-index fund. Given the rate of return for 2008, 38.6%, what rate of return in 2009 would have been necessary for your portfolio to
A bank offers you two alternative interest schedules for a savings account of $100,000 locked in for 3 years: ( a ) a monthly rate of 1%; ( b ) an annually, continuously compounded rate ( r cc ) of
A closed-end fund starts the year with a net asset value of $12.00. By year-end, NAV equals$12.10. At the beginning of the year, the fund was selling at a 2% premium to NAV. By the end of the year,
Suppose you observe the investment performance of 400 portfolio managers and rank them by investment returns during the year. Twenty percent of all managers are truly skilled, and therefore always
An investor’s portfolio currently is worth $1 million. During the year, the investor sells 1,000 shares of FedEx at a price of $80 per share and 4,000 shares of Cisco at a price of $20 per share.
Consider these data from the March 2009 balance sheet of Vanguard’s Global Equity Fund.What was the net asset value of the fund?Assets: $3,035.74 million Liabilities: $ 83.08 million Shares: 281.69
When Freddie Mac and Fannie Mae pooled mortgages into securities, they guaranteed the underlying mortgage loans against homeowner defaults. In contrast, there were no guarantees on the mortgages
Examine the balance sheet of commercial banks in Table 1.3 . What is the ratio of real assets to total assets? What is that ratio for nonfinancial firms( Table 1.4 )? Why should this difference be
What were the bid price, asked price, and yield to maturity of the 4.25% May 2039 Treasury bond displayed in Figure 2.3 ? What was its asked price the previous day?
Suppose your tax bracket is 30%. Would you prefer to earn a 6% taxable return or a 4% tax-free return? What is the equivalent taxable yield of the 4% tax-free yield?
a. If you buy 100 shares of IBM stock, to what are you entitled?b. What is the most money you can make on this investment over the next year?c. If you pay $80 per share, what is the most money you
Suppose XYZ in Table 2.3 increases in price to $110, while ABC falls to $20. Find the percentage change in the price-weighted average of these two stocks. Compare that to the percentage return of a
Reconsider companies XYZ and ABC from Concept Check
Calculate the percentage change in the market-value-weighted index. Compare that to the rate of return of a portfolio that holds $500 of ABC stock for every $100 of XYZ stock (i.e., an index
What would be the profit or loss per share of stock to an investor who bought the January 2010 expiration Intel call option with exercise price $20 if the stock price at the expiration date is $22?
Consider the three stocks in the following table. P t represents price at time t, and Q t represents shares outstanding at time t. Stock C splits two for one in the last period.a. Calculate the rate
Suppose that in this margin example, the investor borrows only $5,000 at the same interest rate of 9% per year. What will the rate of return be if the price of IBM goes up by 30%? If it goes down by
a. Construct the balance sheet if Dot Bomb in Example 3.4 goes up to $110.b. If the short position maintenance margin in the Dot Bomb example is 40%, how far can the stock price rise before the
1. (A nice inheritance) Suppose $1 were invested in 1776 at 3.3% interest compounded yearly (a) Approximately how much would that investment be worth today: $1,000, $10,000, $100,000, or $1,000,000?
2. (The 72 rule) The number of years required for an investment at interest rate, to double in value must satisfy (1+r)" 2. Using In 2 = 69 and the approximation In(1+r)*7 69/i, where i is the
3. (Effective rates) Find the corresponding effective rates for: (a) 3% compounded monthly (b) 18% compounded monthly (c) 18% compounded quarterly
4. (Newton's method) The IRR is generally calculated using an iterative procedure Sup- pose that we define / () = -ao+a+azd + +2", where alla, 's are positive and > Here is an iterative technique
5. (A prize) A major lottery advertises that it pays the winner $10 million However, this prize money is paid at the rate of $500,000 each year (with the first payment being imme- diate) for a total
6. (Sunk costs) A young couple has made a nonrefundable deposit of the first month's rent (equal to $1,000) on a 6-month apartment lease The next day they find a different apartment that they like
7. (Shortcut) Gavin Jones is inquisitive and determined to learn both the theory and the application of investment theory He pressed the tree farmer for additional information and learned that it was
8. (Copy machinesa) Two copy machines are available Both have useful lives of 5 years One machine can be either leased or purchased outright; the other mus: be purchased. Hence there are a total of
9. (An appraisal) You are considering the purchase of a nice home It is in every way perfect for you and in excellent condition, except for the roof The roof has only 5 years of life remaining A new
10. (Oil depletion allowance) A wealthy investor spends $1 million to drill and develop an oil well that has estimated reserves of 200,000 barrels The well is to be operated over 5 years, producing
11. (Conflicting recommendations +) Consider the two projects whose cash flows are shown in Table 2.8 Find the IRRS of the two projects and the NPVs at 5% Show that the IRR and NPV figures yield
12. (Domination) Suppose two competing projects have cash flows of the form (-A, B, B. B) and (-A By, By, . B), both with the same length and A1, A2, B1, B all positive Suppose B/A B/A Show that
13. (Crossing ) In general, we say that two projects with cash flows x, and y,,i = 0, 1, 2,... n, cross if xo yo and oo. Let P,(d) and Py(d) denote the present values of these two projects when the
14. (Depreciation choice) In the United States the accelerated cost recovery system (ACRS) must be used for depreciation of assets placed into service after December 1980. In this system, assets are
15. (An erroneous analysis) A division of ABBOX Corporation has developed the concept of a new product. Production of the product would require $10 million in initial capital expenditure. It is
1. (Amortization) A debt of $25,000 is to be amortized over 7 years at 7% interest. What value of monthly payments will achieve this?
2. (Cycles and annual worth o) Given a cash flow stream X = (xo, X1, X2, X), a new stream X of infinite length is made by successively repeating the corresponding finite stream. The interest rate is
3. (Uncertain annuity o) Gavin's grandfather, Mr. Jones, has just turned 90 years old and is applying for a lifetime annuity that will pay $10,000 per year, starting 1 year from now, until he dies.
4. (APR) For the mortgage listed second in Table 3 I what are the total fees?
5. (Callable bond) The Z Corporation issues a 10%, 20-year bond at a time when yields are 10% The bond has a call provision that allows the corporation to force a bond holder to redeem his or her
6. (The biweekly mortgagee) Here is a proposal that has been advanced as a way for homeowners to save thousands of dollars on mortgage payments: pay biweekly instead of monthly Specifically, if
7. (Annual worth) One advantage of the annual worth method is that it simplifies the com- parison of investment projects that are repetitive but have different cycle times Consider the automobile
8. (Variable-rate mortgage ) The Smith family just took out a variable-rate mortgage on their new home. The mortgage value is $100,000, the term is 30 years, and initially the interest rate is 8% The
9. (Bond price) An 8% bond with 18 years to maturity has a yield of 9% What is the price of this bond?
10. (Duration) Find the price and duration of a 10-year, 8% bond that is trading at a yield of 10%
11. (Annuity duration o) Find the duration D and the modified duration D, of a perpetual annuity that pays an amount A at the beginning of each year, with the first such payment being 1 year from
12. (Bond selection) Consider the four bonds having annual payments as shown in Table 3.9 They are traded to produce a 15% yield (a) Determine the price of each bond (b) Determine the duration of
13. (Continuous compounding o) Under continuous compounding the Macaulay duration be- comes D = P where is the yield and P == e -JACK k=0 Find dP/dx in terms of D and P
14. (Duration limit) Show that the limiting value of duration as maturity is increased to infinity is 1+(A/m) D A. 2) we obtain D 20.5. Note that for For the bonds in Table 36 (where = 05 and large
15. (Convexity value) Find the convexity of a zero-coupon bond maturing at time I under continuous compounding (that is, when m 00)
16. (Convexity theorem o) Suppose that an obligation occurring at a single time period is immunized against interest rate changes with bonds that have only nonnegative cash flows (as in the X
1. (One forward rate) If the spot rates for 1 and 2 years are s = 6.3% and s = 69%, what is the forward rate 12?
2. (Spot update) Given the (yearly) spot rate curve s = (5.0, 5.3, 5.6. 58, 60, 61), find the spot rate curve for next year.
3. (Construction of a zero) Consider two 5-year bonds: one has a 9% coupon and sells for 101.00; the other has a 7% coupon and sells for 93.20 Find the price of a 5-year zero-coupon bond
4. (Spot rate projecte) It is November 5 in the year 2011 The bond quotations of Table 4 6 are available. Assume that all bonds make semiannual coupon payments on the 15th of the month. The
5. (Instantaneous rates o) Let s(1). 000, denote a spot rate curve; that is, the present value of a dollar to be received at time is ex For
6. (Discount conversion) At time zero the one-period discount rates dod 2, d 3.1 are known to be 0 950, 0.940, 0932, 0.925, 0.919, 0913 Find the time zero discount factors de 1. do 2. .do.6,d5.6
7. (Bond taxes) An investor is considering the purchase of 10-year US Treasury bonds and plans to hold them to maturity Federal taxes on coupons must be paid during the year they are received, and
8. (Real zeros) Actual zero-coupon bonds are taxed as if implied coupon payments were made each year (or really every 6 months), so tax payments are made each year, even though no coupon payments are
9. (Flat forwards) Show explicitly that if the spot rate curve is flat [with s(k) =r for all k], then all forward rates also equal
10. (Orange County blues) Orange County managed an investment pool into which several municipalities made short-term investments A total of $7.5 billion was invested in this pool, and this money was
11. (Running PV example) A (yearly) cash flow stream is x = (-40, 10, 10, 10, 10, 10, 10). The spot rates are those of Exercise 2. (a) Find the current discount factors do and use them to determine

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