# First find the payment amount o ( ) o o o o

## Full text

(1)

Today is a day in July 2525 and a bond with annual coupon rate of 3.70% just yesterday paid a coupon. The bond matures in January 2539 and its quoted bond price is 84.71 percent of par (semiannual compounding). Find the current yield and capital gains yield.

  ( ) o ( ) o o o o 

(2)

BD9

The company today issues a 20-year \$1,000 bond that carries a 4.90% annual coupon rate

(semiannual coupons). Find the total interest that the company expects to pay over the lifetime of the bond.

2.2.

BD16b

Today is a day in August 2525 and a bond with annual yield-to-maturity of 8.80% just yesterday paid a coupon. The bond matures in August 2538 and its quoted bond price is 84.69 percent of par (semiannual compounding). Find the annual coupon rate and today's current yield.

 First find the payment amount o ( ) o o o o 

(3)

Today is a day in September 2525 and a bond with annual yield-to-maturity of 9.90% just yesterday paid a coupon. The bond matures in September 2545 and its quoted bond price today is 70.63 percent of par (semiannual compounding). Contrast the annual capital gains yield today with the annual capital gains yield for the six months that conclude with September 2545 (assume scientific amortization and constant YTM).

 First find the payment amount o ( ) o

o

o o

 Next find the current yield

o

 Then find the price when six months is left o

o

o o

o

 Then compute the future current yield

o

(4)

BD18

Bond X has annual coupon rate of 7.80%, 10 coupons remain until maturity, and its price is \$880. Premium bond Z with price of \$1,120 also has 10 coupons remaining. Which statement best describes whether the yield-to-maturity is larger for bond X or for Z?

a. If the coupon rate for Z is smaller than 11.7% then X definitely has the bigger YTM b. If the coupon rate for Z is smaller than 17.1% then X definitely has the smaller YTM c. If the coupon rate for Z equals 11.7% then X and Z have the same YTM

d. Two choices, B and C, are correct e. The three A-B-C choices are all correct

 First calculate the yield to maturity for bond X o

o o

o o

 Next, calculate the YTM for bond Z at different coupon rates

o

o

o

o

o

 Because at a coupon rate of 11.7% Z’s YTM is smaller then Z’s YTM will be smaller at any smaller coupon rate as well. A is correct.

(5)

A bond with annual coupon rate of 9.10% and price of \$830 just yesterday paid a coupon. A total of 30 coupons remain to be paid. Suppose you buy the bond at today's price, hold it and receive 10 coupons, and then sell the bond. When you sell the bond its yield-to-maturity has decreased a total of 25 basis points. Find the bond selling price and annual rate of return throughout the investment horizon.

 First calculate the yield to maturity for the bond over the full period o

o o

o o

 Then calculate the price after 10 coupons have been paid o

o o o o

 Finally, calculate the yield to maturity for the bond over the holding period o

o o

o o

(6)

BD5c

The yield-to-maturity for a zero coupon bond is 6.30% for a 1-year bond, 7.28% for a 2-year bond, and 7.68% for a 3-year bond. You think the yield curve will remain the same throughout the future. You wish to make a 1-year investment, that is, buy a bond today and sell it in one year. You can pursue three alternative strategies, call them S1, S2, and S3. For strategy S1, you buy the 1-year bond and hold it to maturity, in which case your annual rate of return obviously is 6.30%. For S2, buy a 2-year bond today and sell it when it has 1 year remaining to maturity. For S3, buy a 3-year bond today and sell it when it has 2 years remaining to maturity. What are your average annual rates of return for strategies S2 and S3? (Assume, if necessary, that you can buy fractions of bonds.)

 First calculate the price for all three bonds

o

o

o

o

o

 Then calculate the rate of return over the holding period from 2 to 1 and from 3 to 2

o

o

o

o

(7)

Which statement is the best description for a bond investment of the relation between the promised yield-to-maturity and the actual ex post rate of return?

 Accurate Statements

o The actual ex post ROR equals the promised yield-to-maturity when you own the bond until maturity and receive all expected cash flows.

o The actual ex post ROR equals the promised yield-to-maturity when you sell a bond before it matures and the YTM at time of sale is the same as when it was purchased. o The actual ex post ROR exceeds the promised yield-to-maturity when you sell a

bond before it matures and the YTM at time of sale is less than the YTM when it was purchased.

5.2. MB7

Which statement about bond prices is most accurate?  Accurate Statements

o For a premium bond the yield-to-maturity is less than the coupon rate

o With an interest rate decline the price rises more for long-term bonds than for short-term bonds

o When a bond is sold at an interest rate less than the initial yield to maturity then the actual rate of return exceeds the promised yield

o For a discount bond the coupon rate is less than the yield to maturity 5.3.

MB19

Which characteristic best describes the Treasury yield curve?  Accurate Statement

o The curve normally begins with a steep upward slope that flattens toward the right 5.4.

MB24

The largest financial markets in the U.S.A. include the bond market and the stock market. One of these markets, however, is significantly larger than the other market. Decide whether this statement is true or false:

 On an average day the dollar trading volume of all stocks traded in the U.S.A. is significantly greater than the dollar trading volume of all bonds in the U.S.A.

o False

 On an average day the dollar trading volume of all stocks traded in the U.S.A. is significantly less than the dollar trading volume of all bonds in the U.S.A.

(8)

TK4

At the close of market yesterday the 10-day and 2-day moving average share prices for the company stock were \$22.75 and \$24.75, respectively. The share prices 10 and 2 days ago were \$18.25 and \$24.50, respectively. According to a trading rule that generates a signal when the 2-day moving average crosses the 10-day moving average, what would be today's cross-over stock price that generates a signal reversal?

To answer the question set the new 10 day moving average equal to the new 2 day moving average and solve for P algebraically

( ) ( )

(9)

The stock for a start-up company probably will pay no dividends until exactly 6 years from today. At that time it will pay \$5.20 per year forever. You assess the intrinsic value of the stock with a 8.9% discount rate. Find the stock's intrinsic value today.

First find the intrinsic value 5 years from now

Then discount that price back to its present value

     Answer = 38.15

(10)

ST12

A stock you are buying today promises no dividends for a long time. In exactly 7 years you expect the stock will pay its first annual dividend of \$3.90. At that time, you also believe that the stock could be sold for \$37.00. If today you can buy the stock for \$13.23, what is the expected annual rate of return on the stock investment?

     8.2. ST21

A stock you are buying today promises no dividends for a long time. In exactly 6 years you expect the stock will pay its first annual dividend of \$6.80, which you expect will be paid annually forever. If today you can buy the stock for \$35.23, what is the expected annual rate of return on the stock investment?

Solve this using the CF function      Compute IRR = 11.3 8.3. ST22

The company preferred stock pays a \$6.00 annual dividend. The local bank pays 3.9% interest (compounded annually) on 5-year CDs. You consider the preferred stock an attractive investment if its ROR is 350 basis points more than the CD rate. Find your assessment of the preferred stock intrinsic value.

(11)

The company preferred stock yesterday paid \$5.20 annual dividend and today's stock price is \$102.10. The local bank pays 4.1% interest on CDs. You consider the preferred stock an attractive investment if its ROR is 150 basis points more than the CD rate. Find the actual risk premium and is this stock a buy or a sell?

(12)

ST8

The company just paid its annual dividend of \$3.75. You believe the dividend will grow perpetually at 8.0% per annum. Today's price-to-earnings ratio is 18.2 and the payout ratio always equals 60%. You assess intrinsic value with a 13.2% discount rate. Find the one-year rate of return from buying the stock today and holding it one year, given that next year's share price converges to next year's intrinsic value.  o  o o ( ) ( ) o ( )

(13)

The company preferred stock just yesterday paid its annual dividend of \$2.00 per share. Today's share price is \$18.70. You believe the dividend yield is abnormally high but that it will revert to its normal value of 8.40%. Your strategy is to buy the stock today and receive annual dividends for 3 years. Upon receiving the last dividend you expect the dividend yield will be normal. Your strategy is to sell the stock at that time. Compute the expected annual rate of return for the strategy.

    

(14)

TR18

The dividend growth valuation model equates intrinsic value to the discounted sum of the

perpetual and smoothly growing dividend stream. When the dividend growth rate (g) exceeds the discount rate (r) the formula gives an intrinsic value that is a negative number. Determine whether the following interpretation of the preceding fact is TRUE or FALSE: the stock has an infinite intrinsic value.

 True 11.2.

TR22

According to the constant growth dividend valuation model, the total rate of return partitions into the expected dividend yield and the capital gains yield. Which statement is the most accurate description of the partition?

Accurate Statements

 the long-run average dividend yield is smaller than the capital gains yield  the dividend yield is more predictable and less risky than the capital gains yield

 usually the dividend component is a realized cash flow whereas the capital gains yield is an accrued cash flow

 the total rate of return minus the expected dividend yield equals the capital gains yield  the dividends are usually taxable in the year received whereas capital gains are tax deferred 11.3.

TR34

A mainstay of technical analysis is comparison of moving averages with different lengths. Is the following statement of the moving average trading strategy

True or False: A sell signal results when the short-run moving average becomes bigger than the long-run moving average.

o False

True or False: A buy signal results when the short-run moving average becomes smaller than the long-run moving average.

o False

True or False: A sell signal results when the short-run moving average becomes smaller than the long-run moving average.

(15)

The dividend growth valuation model equates a stock's intrinsic value to the discounted sum of the perpetual and smoothly growing dividend stream. The relation between the dividend growth rate (g) and the discount rate (r) is very important. Which statement accurately describes that relation? Accurate Statements

 When g equals zero percent then the stock's intrinsic value computes as the present value of a perpetuity, div/r.

 When g exceeds r then the stock's intrinsic value tends to infinity, meaning the stock is priceless.

(16)

ST1e

Yesterday the Company paid its annual dividend of \$2.60 per share, its payout ratio always is 30% (= dividendst / net incomet), and today you wish to purchase the stock while its price-to-earnings ratio (= sharepricet / earnings per sharet) is 4.69. You believe that the dividend growth rate is 4.3%. You believe that a fair total rate of return for this stock is 9.8%. If also you believe the stock is valued according to the dividend growth model, which statement is most consistent with your beliefs?

a. Intrinsic value is \$56.70 and the share is undervalued b. Intrinsic value is \$42.87 and the share is overvalued c. Intrinsic value is \$49.31 and the share is undervalued d. Intrinsic value is \$49.31 and the share is overvalued e. Intrinsic value is \$56.70 and the share is overvalued  ( )  o   12.2. ST2a

The Company is expected to announce their annual dividend tomorrow. One year ago they paid a dividend of \$2.90, and 5 years ago they paid \$2.15. You believe that future dividends will grow by the same rate as past ones. You are aware that riskless government securities are yielding 4.8%, and you make an offer to purchase the stock so that you earn 9.8% above the riskless rate. How much is your offer price?

First, calculate the dividend growth rate.  N = 5 – 1 = 4

 I/Y = CPT = 7.768  PV = 2.15

 PMT = 0  FV = 2.90

Second, calculate the intrinsic value to figure out your offer price. 

( )

(17)

A share of company stock just paid its annual dividend of \$2.70. Exactly 6 years ago the dividend was \$2.04. Your analyst tells you the stock's expected dividend yield is 2.7%. You believe the constant growth dividend valuation model applies perfectly to this properly valued stock. Find (i) the expected total rate of return and (ii) the stock's current intrinsic value.

First, calculate the dividend growth rate.  N = 6

 I/Y = CPT = 4.783  PV = 2.04

 PMT = 0  FV = 2.70

Next, calculate the stocks total rate of return, .

 Finally, calculate intrinsic value.

 ( ) 12.4. ST17

You pick up the Wall Street Journal and see that riskless government securities are offering 5.1%. You read that the Company just increased their annual dividend by \$0.68 cents so that today it is paying a \$7.55 dividend per share. You also read that its share price is \$192.96. You believe the constant growth dividend valuation model applies perfectly to this properly valued stock. What is the implied risk premium that is earned from owning the stock; that is, by how much does the expected return on the stock exceed the riskless interest rate?

First find the dividend growth rate, . 

Then, find the stocks return, .

 ( ) ( ) ( )

(18)

ST13

Yesterday (year-end 2525) the company paid its annual dividend of \$1.85. You believe that the stock merits a buy recommendation if it returns 8.5% per year. Your estimate of intrinsic value assumes that dividends grow smoothly in accordance with the constant exponential growth model. The annual dividend history is:

year, dividend 2521, \$1.62 2522, \$1.47 2523, \$1.57 2524, \$1.56

Find the best estimate of the dividend growth rate and intrinsic value.

First, use the “DATA” function on your calculator to enter the information from the last five years  X01 = 1 Y01 = 1.62

 X02 = 2 Y02 = 1.47  X03 = 3 Y03 = 1.57  X04 = 4 Y04 = 1.56  X05 = 5 Y05 = 1.85

Next, Use the “STAT” function to find the dividend growth rate, by looking up in the calculator. (Make sure the STAT function is set to EXP)

Then, use the “STAT” function to find what the next dividend will be.  X’ = 6

 Y’ = CPT = 1.77

Finally, use the next dividend and to find the intrinsic value. 

(19)

The Company just announced earnings per share of \$3.80, which means that their price to earnings ratio is 3.73. The Company has an asset turnover ratio (= Salest / Total assetst) of 2.21, a net profit

margin (= net income / sales) of 5.6%, a debt ratio (= total debt / total assets) of 35%, and a payout ratio (= dividends / net income) of 30%. The Company always operates at their sustainable growth rate and successfully holds constant all relevant financial ratios. You would like to invest in the stock such that you'll get a 23.1% total rate of return. What is your assessment of the stock's intrinsic value?

First, calculate the sustainable growth rate.  ( ) ( ) o  ( ) ( ) o ( )  ( ) ( ) ( ) (( ) ) Next, calculate the intrinsic value.

( )( )

(20)

ER5

Your analysis of common stocks for companies X and Y lead you to believe rates of return depend as follows on the future strength of the economy:

--- The probability for declining GNP is 40% in which case RORx = -0.3% and RORY = -5.4%.

--- The probability for flat GNP is 30% in which case RORx = 10.4% and RORY = 23.1%.

--- The probability for rising GNP is 30% in which case RORx = 14.2% and RORY = 15.4%.

Which statement is most accurate?

a. The standard deviation is 6.35% for X, 12.44% for Y, and X is dominant. b. The standard deviation is 6.35% for X, 12.44% for Y, and there is a trade-off. c. The standard deviation is 6.35% for X, 12.44% for Y, and Y is dominant. d. The standard deviation is 6.35% for X, 10.37% for Y, and X is dominant. e. The standard deviation is 6.35% for X, 10.37% for Y, and Y is dominant.  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) )  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) )

Since X has a smaller standard deviation and Y has a larger expected return there is a tradeoff and the correct answer is b.

15.2. ER16

Your analysis of a small company convinces you that future movements in their stock price depend on how many big clients adopt the small company's product innovations. Today's price for this non-dividend-paying small company stock is \$13. Your beliefs about future outcomes include:

--- The probability is 25% that one big client adopts the product in which case the resultant intrinsic value for the company stock price likely will be \$24.

--- The probability is 10% that two big clients adopt the product in which case the resultant intrinsic value for the company stock price likely will be \$37.

If no big clients adopt the product then the small company goes bankrupt and the stock is worthless. Compute this small company stock's measurements for risk [= sigma] and return [= E(ROR)].

   [ ] ∑ ( )( )  (∑ ( [ ]) ) ( ( ) ( ) ( )( ) )

(21)

Choose the most accurate statement about the NASDAQ stock exchange. Accurate Statements

 The NASD (National Association of Securities Dealers) created NASDAQ and every securities dealer in the USA that works with the public must belong to NASD

 NASDAQ is a complex telecommunications network composed of many market makers on many stocks

 NASDAQ lists stocks for between 3,000 and 5,500 companies 16.2.

BS26

Which statement about the NASDAQ market is most accurate? Accurate Statements

 NASDAQ is a market comprised of many market makers for between 3,000 and 5,500 stocks  All brokers and companies in the U.S.A. working with securities and the public are members

of NASD

 NASDAQ is a market that lacks a physical exchange floor but has a complex telecommunications network

16.3. BS36

The acquisition of equities in the U.S. financial markets occurs in a very competitive marketplace with many layers and alternative routes for trade execution. Which one of the following choices is a blatantly FALSE description about one of the routes.

Accurate Statements – (Note that the question asks for FALSE statements, so these statements are all incorrect answers)

 The Philadelphia Stock Exchange (PHLX) was founded in 1790 and is the nation's oldest. The PHLX has a strong market position trading 1,600 equity options, 19 sectors index options, and currency options and futures.

 The Pink sheets were founded in 1904 in New York and today quote stock prices for

companies that do not register with the SEC and are not required to file financial statements with the government.

 The National Stock Exchange (NSX) in Chicago is the third largest stock market in the U.S.A. NSX was founded in 1885 as the Cincinnati Stock Exchange.

 The Pacific Stock Exchange (PCX) in San Francisco was founded in 1862 and in 1999 PCX became the first U.S. stock exchange to demutualize, meaning switch from a member-owned organization and instead operate as a for-profit publicly traded company. In 2002 PCX closed its equities floors and migrated stock trading to the Archipelago Exchange (ArcaEx).  The OTC Bulletin Board (OTCBB) began operations in June 1990 to provide transparency in

the over-the-counter equities market. The OTCBB provides price quotes for stocks for companies that register and file financial statements with the SEC. Average share price for OTCBB stocks is about ten cents a share.

(22)

ER2c

Your analysis of outcomes for sales and the associated rate of return on common stocks for companies X and Y are shown below. You intend to form a portfolio by allocating 45% of your funds in Company X, and the remainder in Company Y.

--- The probability for declining Sales is 30% in which case RORx = -2.7% and RORY = 4.1%.

--- The probability for flat Sales is 35% in which case RORx = 9.5% and RORY = 20.1%.

--- The probability for rising Sales is 35% in which case RORx = 19.1% and RORY = -9.6%.

What is the expected return and standard deviation of portfolio returns?  ∑ o ( ) o o ( )  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) )

(23)

The rates of return listed below for securities X and Y are equally likely. Find the standard deviation and expected rates of return for securities X and Y, and also compare the two regarding dominance or tradeoff. ROR for X: -1.1%, 9.5%, 19.5%, 15.9% ROR for Y: 23.5%, 16.5%, 13.7%, -4.3%  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) ( ) )  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) ( ) )

(24)

ER9c

You form a portfolio that invests 60% of total funds in stock X and 40% in stock Z. Two possible outcomes exist. The probability is 45% that the first outcome occurs, in which case the rates of return equal 15% for X and 29% for Z. The probability is 55% that the second outcome occurs, in which case the rates of return equal 35% for X and 12% for Z. Find the diversification benefit, measured as the standard deviation reduction in basis points (BP), that the portfolio provides.

 [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) )  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) )   [ ] ∑ ∑ ( ) ( )  (∑ (∑ [ ]) ) ( (( ) ) (( ) ) ) 

(25)

The expected rate of return on common stock for company X equals 7.6%. For Company Y, the expected rate of return is 12.9%. You wish to form a portfolio by allocating some of your funds in Company X and the remainder in Company Y. In order to form a portfolio whose expected return equals 9.50%, what proportion of funds should be invested in Company X?

 [ ] ∑ [ ] o ( ) o o o 20.2. ER7

The standard deviation of returns equals 10.0% for stock X and 14.0% for stock Z. The correlation between the two stocks equals 0.00. You make a portfolio that allocates 70% of funds to stock X. The remainder is put in stock Z. Which statement correctly describes the risk of the resultant portfolio?

a. The portfolio standard deviation is 7.1% and represents diversification benefits of 304 basis points relative to average component risk

b. The portfolio standard deviation is 8.2% and represents diversification benefits of 349 basis points relative to average component risk

c. The portfolio standard deviation is 8.2% and represents diversification benefits of 304 basis points relative to average component risk

d. The portfolio standard deviation is 7.1% and represents diversification benefits of 349 basis points relative to average component risk

e. The portfolio standard deviation is 6.2% and represents diversification benefits of 304 basis points relative to average component risk

  (∑ ∑ ∑ ) ( )  Answer = C

(26)

ER8b

Investment risk, as measured by the standard deviation of returns, equals 17.8% for stock X and 24.3% for stock Y. The correlation between the securities is zero. You form a portfolio allocated 55% in X and 45% in Y. Find the diversification benefit, measured as percent reduction in risk, for the portfolio.   (∑ ∑ ∑ ) ( )  20.4. ER13

At the beginning of last month about 30% of your \$5,000 portfolio was in stock X; stock Y accounted for 30% and stock Z for the rest. Monthly rates of return equaled 16% for stock X, 15% for Y, and 12% for Z. Find last month's percentage change in total portfolio wealth.

(27)

The standard deviation of expected returns for investments X and Y equal 12.5% and 18.0%, respectively. The correlation between returns for X and Y is 0.50. How much risk reduction, that is diversification benefit in basis points, does the minimum risk portfolio provide?

 ( )  (∑ ∑ ∑ ) ( ( ) ( ) ) 

(28)

ER10

Suppose that you are able to perfectly measure expected return. Also, suppose that there exist two different kinds of risk that you can measure, call them Risk1 and Risk2. The amount of Risk1 an

investment possesses is totally unrelated to the amount of Risk2 that it possesses. Three possible

asset investments, call them X, Y, and Z, have measurements for (Risk1, Risk2, return) as follows: X:

(25,10,30); Y: (20,15,24); Z: (20,30,34). Compare the three with regards to dominance or tradeoff. a. X and Y coexist as tradeoffs

b. Z dominates Y c. X dominates Z

d. Two choices, A and C, are correct e. The three A-B-C choices are all correct Answer = A

22.2. ER11

Suppose that you are able to perfectly measure risk and expected return, and the bigger the number the bigger the risk or return. Measurements of (risk, return) for three possible asset investments, call them X, Y, and Z, are as follows: X: (10,10); Y: (10,24); Z: (25,27). Compare the three with regards to dominance or tradeoff.

a. X and Y coexist as tradeoffs b. Y and Z coexist as tradeoffs c. X dominates Z

d. Two choices, A and B, are correct e. None of the A-B-C choices are correct Answer = B

22.3. TR19

The most common statistic for measuring risk is the standard deviation of expected returns. Which statement best describes the standard deviation as a risk measure?

Accurate Statements

 the standard deviation gets larger as the likelihood of extreme outcomes increases  the standard deviation is equally sensitive to upside as well as downside extreme returns  when expected returns have a normal distribution then the 95% confidence interval for

next period's return approximately equals the mean return plus or minus two standard deviations

(29)

The minimum risk portfolio for two securities, call them X and Y, is easily found given the

component security risks (say sigma(X) and sigma(Y) ) and the correlation between returns (rho). Which statement accurately describes the minimum risk portfolio?

Accurate Statements

 The allocation in X increases as the risk of Y increases.

 The covariance equals the product of rho times sigma(X) times sigma(Y) and always the signs of covariance and rho are identical.

 When the correlation equals zero then the allocation to X equals the ratio of Y's variance to the sum of variances.

(30)

MR1d

Find the combination of Alpha and Zed that yield the minimum risk portfolio given that each of the paired-outcomes is equally likely:

Outcome 1: RORAlpha = -0.9% and RORZed = 17.3%.

Outcome 2: RORAlpha = 6.9% and RORZed = 9.2%.

Outcome 3: RORAlpha = 23.7% and RORZed = 18.0%.

Outcome 4: RORAlpha = 16.9% and RORZed = -6.0%.

Which statement about the minimum risk portfolio is most accurate? a. the expected return is 10.7% and the standard deviation is 5.2% b. the expected return is 12.3% and the standard deviation is 5.2% c. the expected return is 14.1% and the standard deviation is 6.0% d. the expected return is 14.1% and the standard deviation is 5.2% e. the expected return is 10.7% and the standard deviation is 6.0%

 [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) ( ) )  [ ] ∑  (∑ ( [ ]) ) ( ( ) ( ) ( ) ( ) )  ∑ ( [ ])( [ ]) ( )( ) ( )( ) ( )( ) ( )( )   [ ] ∑ [ ] ( )  (∑ ∑ ∑ ) ( ( ) ( ) )

(31)

The standard deviation of expected returns for investments X and Y equal 17.5% and 11.5%, respectively. The correlation between returns for X and Y is -0.40. Find the combination of X and Y that yield the minimum risk portfolio. If your objective is to form a portfolio with these two securities that is not dominated by any other combination, which one statement is supported best by your finding?

a. If the expected return is greater for Y than for X, then dominant portfolios comprise exclusively positions that allocate between 35.5% and 100% in X

b. If the expected return is greater for Y than for X, then dominant portfolios comprise exclusively positions that allocate between 35.5% and 100% in Y

c. If the expected return is greater for Y than for X, then dominant portfolios comprise exclusively positions that allocate between 35.5% and 0% in Y

d. If the expected return is less for Y than for X, then dominant portfolios comprise exclusively positions that allocate between 64.5% and 100% in Y

e. If the expected return is less for X than for Y, then dominant portfolios comprise exclusively positions that allocate between 64.5% and 100% in Y

( )

( )

The dominant portfolio is the combination that gives you a higher return for adding risk. Since the lowest risk happens when 35.5% of the portfolio is invested in stock X then the dominant portfolio is between that allocation and 100% in whichever stock has the highest return.

(32)

MR2a

Throughout the past, the return for Large Cap Stocks has averaged 11.8% and the standard deviation has been 34.7%. For Growth Stocks, the return has averaged 15.1% and the standard deviation 27.8%. The correlation between the returns for these two assets has been -0.08. What is the percentage allocation of funds in Large Cap Stocks that results in a portfolio with the lowest possible risk; the remaining funds are to be invested in the other asset.

( ) ( ) 25.2. MR5

Throughout the past, the return for type X stocks has averaged 12.2% and the standard deviation has been 31.0%. For type Y stocks the return has averaged 8.9% and the standard deviation 24.0%. The correlation between the returns for these two assets has been 0.33. You expect these

tendencies to persist into the future. What is the most comprehensive allocation rule that correctly describes all portfolios in the feasible allocation set?

a. Always invest 74.7% or more in asset Y b. Always invest 74.7% or less in asset X c. Always invest 25.3% or less in asset X d. Always invest 31.7% or more in asset X e. Always invest 25.3% or more in asset Y 

( )

( ) Since X has a higher return the answer is D.

(33)

Throughout the past, the standard deviation for type X stocks has averaged 10.5%. For type Y stocks the standard deviation has averaged 11.5%. These two asset return series also always seem to be in uncorrelated parts of the business cycle - the correlation coefficient for returns is

indistinguishable from zero. You expect these tendencies to persist into the future. You also expect that Y is so different from X that X correlates more positively with almost every other stock. What is the most likely statement that correctly compares the minimum risk portfolio containing X and Y with the portfolio containing X and any other stock?

a. Allocating 72.1% of a portfolio to type X stocks and the rest in almost any other stock besides Y will result in a portfolio with greater diversification benefits.

b. Allocating 62.7% of a portfolio to type X stocks and the rest in almost any other stock besides Y will result in a portfolio with greater diversification benefits.

c. Allocating 54.5% of a portfolio to type X stocks and the rest in almost any other stock besides Y will result in a portfolio with greater diversification benefits.

d. Allocating 54.5% of a portfolio to type X stocks and the rest in almost any other stock besides Y will result in a portfolio with fewer diversification benefits.

e. Allocating 62.7% of a portfolio to type X stocks and the rest in almost any other stock besides Y will result in a portfolio with fewer diversification benefits.

( ) ( ) Answer = D 25.4. MR7

Throughout the past, the return for type X stocks has averaged 11.2% and the standard deviation has been 26.6%. For type Y stocks the return has averaged 8.1% and the standard deviation 35.9%. The correlation between the returns for these two assets has been 0.03. You expect these

tendencies to persist into the future. For the minimum risk portfolio comprising X and Y what is the allocation and average portfolio risk?

a. The minimum risk portfolio allocates 65.0% to X; average component risk is 34.3%. b. The minimum risk portfolio allocates 65.0% to X; average component risk is 29.9%. c. The minimum risk portfolio allocates 65.0% to X; average component risk is 39.5%. d. The minimum risk portfolio allocates 74.8% to X; average component risk is 34.3%. e. The minimum risk portfolio allocates 74.8% to X; average component risk is 29.9%.  ( ) ( )  ( ) Answer = B

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