Please provide excel spreadsheet detailing how you got to the multiple choice answer. I am trying to get ahead and understand each of the practiceproblems in prep for a exam so it would be very helpful to see not only numbers but mini explanation to each of the answers

Practice Problems Chapter 2 - BDY, BEY, TEY, Indices An investor buys a 180 day T-bill at a bank discount quote of 5 .25. The investor's actual annual rate of return on this investment was ______. a. 5.25% b. 5.39% C. 5.47% d. 5.52% What is the tax exempt equivalent yield on a 9% bond yield give n a marginal tax rate of 28%? A . 6.48% b. 7.25% c. 8.02% d. 9.00% A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 s hares, and 553,000 shares, res pectively. If the market value weighted index was 970 yesterday and th e prices changed to $23, $41, and $58, what is the new index value? a. 960 b. 970 C. 975 d. 985 Chapter 3 - Buying on Margin, Short Sales, Margin Calls, Orders Assume you purchased 500 shares of XYZ common stock on margin a t $40 per share from your broker. If the initial margin is 60%, the amount you borrowed from the bro ker is __________. a. $20,000 b. $12,000 C. $ 8,000 d. $15,000 You short-sell 200 shares of Rock Creek Fly Fishing Co., now se lling for $50 per share. If you wish to limit your loss to $2,500, you should place a stop-buy order at _____. a. $37.50 B . $62.50 c. $56.25 d. $59.75 An investor buys $8,000 worth of a stock priced at $40 per shar e using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance ma rgin. In one year the investor gets a margin call. At the time of the margin call the stock's price m ust have been _____. a. $20.00 b. $29.52 C. $30.29 d. $32.45 An investor buys $16,000 worth of a stock priced at $20 per sha re using 60% initial margin. The broker charges 8% on the margin loan and requires a 35% maintenance ma rgin. The stock pays a $0.50 per share dividend in one year and then the stock is sold at $23 per shar e. What was the investor's rate of return? a. 17.50% b. 19.67% C. 23.83% d. None of these answers are correct Chapter 4 - Mutual Funds Returns and NAV Consider a mutual fund with $300 million in assets at the start of the year, and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 0.75% of the year end value, what is the rate of re turn on the fund? a. 18.75% B. 17.12% c. 17.25% d. 17.45% Consider a mutual fund with $300 million in assets at the start of the year, and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 0.75% of the year end value, what is the rate of re turn on the fund? a. 18.75% B. 17.12% c. 17.25% d. 17.45% You pay $21,600 to the Laramie Fund which has a NAV of $18.00 p er share at the beginning of the year. The fund deducted a front-end lo ad of 4%. The securities in the fund increased in value by 10% during the year. The fund's expense ratio is 1.3% and is deducted from year end asset values. What is your rate of return on the fund if you sell your shares at the end of the ye ar? a. 4.35% B. 4.23% c. 6.45% d. 5.63% Chapter 5 - HPR, AM, GM, Real vs Nominal Returns, Portfolio Ret urn and St. Deviation, APR and EAR You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was a. 4.00% b. 3.50% c. 7.50% D. 11.00% The arithmetic average of -12%, 15% and 20% is _________. a. 15.67% B. 7.67% c. 11.22% d. 6.45% The geometric average of -12%, 20% and 25% is __________. a. 8.42% b. 11.00% C. 9.70% d. 18.88% An investment earns 10% the first year, 15% the second year and loses 12% the third year. Your total compound return over the three years was _______. a. 41.68% B. 11.32% c. 3.64% d. 13.00% If you are promised a nominal return of 12% on a one year inves tment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn? a. 5.48% B . 8.74% c. 9.00% d. 12.00% An investor invests 70% of her w ealth in a risky asset with an expected rate of return of 15% and a variance of 5% and she puts 30% in a Treasury bill that pays 5% . Her portfolio's expected rate of return and standard deviation are __________ and __________ respective ly. a. 10.0%, 6.7% b. 12.0%, 22.4% C . 12.0%, 15.7% d. 10.0%, 35.0% The buyer of a new home is quoted a mortgage rate of 0.5% per m onth. What is the APR on the loan? a. 0.50% b. 5.0% C. 6.0% d. 6.5% A loan for a new car costs the borrower 0.8% per month. What is the EAR? a. 0.80% b. 6.87% c. 9.60% D. 10.03% Chapter 7 - CAPM Consider the CAPM. The expected return on the market is 18%. Th e expected return on a stock with a beta of 1.2 is 20%. What is the risk-free rate? a. 2% b. 6% C. 8% d. 12% You have a $50,000 portfolio cons isting of Intel, GE and Con Ed ison. You put $20,000 in Intel, $12,000 in GE and the rest in Con Edis on. Intel, GE and Con Edison have betas of 1.3, 1.0 and 0.8 respectively. What is your portfolio beta? A. 1.048 b. 1.033 c. 1.000 d. 1.037 The risk-free rate and the expect ed market rate of return are 5 % and 15% respectively. According to the capital asset pricing model, the expected rate of return on sec urity X with a beta of 1.2 is equal to __________. a. 12% B. 17% c. 18% d. 23% Chapter 18 - DDM, Earnings Model, PVGO A preferred share of Coquihalla C orporation will pay a dividend of $8.00 in the upcoming year, and every year thereafter, i.e., dividends are not expected to grow. You require a return of 7% on this stock. Using the constant growth DDM to calculate the intrinsic value, a pre ferred share of Coquihalla Corporation is worth __________. a. $13.50 b. $45.50 c. $91.00 D. $114.29 A firm is planning on paying its first dividend of $2 in three years. After that dividends are expected to grow at 6% per year indefinitely . The stock's required return i s 14%. What is the intrinsic value of a share today? a. $25.00 b. $16.87 C. $19.24 d. $20.99 Rose Hill Trading Company is expected to have EPS in the upcomi ng year of $8.00. The expected ROE is 18.0%. An appropriate require d return on the stock is 14%. I f the firm has a plowback ratio of 70%, its dividend in the upcoming year should be __________. a. $1.12 b. $1.44 C. $2.40 d. $5.60 Annie's Donut Shops, Inc. has expected earnings of $3.00 per sh are for next year. The firm's ROE is 18% and its earnings retention ratio is 60%. If the firm's market c apitalization rate is 12%, what is the value of the firm excluding any growth opportunities? A. $25.00 b. $50.00 c. $83.33 d. $208 Westsyde Tool Company is expected to pay a dividend of $2.00 in the upcoming year. The risk-free rate of return is 6% and the expected return on the market portfolio is 12%. Analysts expect the price of Westsyde Tool Company shares to be $29 a year from now. The bet a of Westsyde Tool Company's stock is 1.20. Using a one-period valu ation model, the intrinsic valu e of Westsyde Tool Company stock today is __________. a. $24.29 B. $27.39 c. $31.13 d. $34.52 Lifecycle Motorcycle Company is expected to pay a dividend in y ear 1 of $2.00, a dividend in year 2 of $3.00, and a dividend in year 3 of $4.00. After year 3, dividen ds are expected to grow at the rate of 7% per year. An appropriate require d return for the stock is 12%. Using the multistage DDM, the stock should be worth __________ today. a. $63.80 b. $65.13 C. $67.98 d. $85.60 ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock. At what price would you expect ART to sell? a. $25.00 B. $34.29 c. $42.86 d. $45.67 At what P/E ratio would you expect ART to sell? a. 8.33 B. 11.43 c. 14.29 d. 15.25 Chapter 14 & 16 - Bond Pricing, YTM, YTC, Price Sensitivity, Du ration A coupon bond which pays interest of $60 annually, has a par va lue of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The approxi mate yield on this bond is __________. a. 6% b. 7% C. 8% d. 9% A zero-coupon bond has a yield to maturity of 5% and a par valu e of $1,000. If the bond matures in 16 years, it should sell for a price of __________ today. A. $458.00 b. $641.00 c. $789.00 d. $1,100.00 The yield to maturity of an 8-year zero coupon bond, with a par value of $1,000 and a market price of $623.20, is ______. A. 6.1% b. 8.8% c. 10.1% d. 13.4% A callable bond pays annual interest of $60, has a par value of $1,000, matures in 20 years but is callable in 10 years at a price of $1,100, and has a value today of $105 5.84. The yield to call on this bond is __________. A. 6.00% b. 6.58% c. 7.20% d. 8.00% A 1% decline in yield will have the least effect on the price o f the bond with a __________. a. 10-year maturity, selling at 80 B. 10-year maturity, selling at 100 c. 20-year maturity, selling at 80 d. 20-year maturity, selling at 100 Assuming semiannual compounding, a 20-year zero coupon bond wit h a par value of $1,000 and a required return of 12% would be priced at __________. A. $97 b. $104 c. $364 d. $732 All other things equal, which of the following has the shortest duration? a. A 30 year bond with a 10% coupon b. A 20 year bond with a 9% coupon c. A 20 year bond with a 7% coupon D. A 10 year zero coupon bond A bond currently has a price of $1,050. The yield on the bond i s 6.00%. If the yield increases 25 basis points, the price of the bond w ill go down to $1,030. The durat ion of this bond is ____ years. a. 7.46 B. 8.08 c. 9.02 d. 10.11 You own a bond that has a duration of 6 years. Interest rates a re currently 7% but you believe the Fed is about to increase interest rates by 25 basis points. Your predi cted price change on this bond is _________. a. +1.40% B. -1.40% c. -2.51% d. +2.51% The duration of a par value bon d with a coupon rate of 6% and a remaining time to maturity of 10 years is __________. a. 9.29 b. 8.50 C. 7.80 d. 6.69 You have a 25 year maturity 10% coupon, 10% yield bond with a d uration of 9.98 years and a convexity of 139.59. If interest rate were to fall 125 basis points your predicted new price for the bond (including convexity) is __________. a. $1098.45 b. $1104.56 c. $1113.41 D. $1124.31 Practice Problems Chapter 2 - BDY, BEY, TEY, Indices An investor buys a 180 day T-bill at a bank discount quote of 5 .25. The investor's actual annual rate of return on this investment was ______. a. 5.25% b. 5.39% C. 5.47% d. 5.52% What is the tax exempt equivalent yield on a 9% bond yield give n a marginal tax rate of 28%? A . 6.48% b. 7.25% c. 8.02% d. 9.00% A benchmark index has three stocks priced at $23, $43, and $56. The number of outstanding shares for each is 350,000 shares, 405,000 s hares, and 553,000 shares, res pectively. If the market value weighted index was 970 yesterday and th e prices changed to $23, $41, and $58, what is the new index value? a. 960 b. 970 C. 975 d. 985 Chapter 3 - Buying on Margin, Short Sales, Margin Calls, Orders Assume you purchased 500 shares of XYZ common stock on margin a t $40 per share from your broker. If the initial margin is 60%, the amount you borrowed from the bro ker is __________. a. $20,000 b. $12,000 C. $ 8,000 d. $15,000 You short-sell 200 shares of Rock Creek Fly Fishing Co., now se lling for $50 per share. If you wish to limit your loss to $2,500, you should place a stop-buy order at _____. a. $37.50 B . $62.50 = 50 + (2500/200) = $62.50 c. $56.25 d. $59.75 An investor buys $8,000 worth of a stock priced at $40 per shar e using 50% initial margin. The broker charges 6% on the margin loan and requires a 30% maintenance ma rgin. In one year the investor gets a margin call. At the time of the margin call the stock's price m ust have been _____. a. $20.00 b. $29.52 C. $30.29 d. $32.45 An investor buys $16,000 worth of a stock priced at $20 per sha re using 60% initial margin. The broker charges 8% on the margin loan and requires a 35% maintenance ma rgin. The stock pays a $0.50 per share dividend in one year and then the stock is sold at $23 per shar e. What was the investor's rate of return? a. 17.50% b. 19.67% C. 23.83% d. None of these answers are correct Chapter 4 - Mutual Funds Returns and NAV Consider a mutual fund with $300 million in assets at the start of the year, and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 0.75% of the year end value, what is the rate of re turn on the fund? a. 18.75% B. 17.12% c. 17.25% d. 17.45% $300m *(1.18)= $354m .02* $354m = 7,080,000 ($354m- 7,080,000- 300m)/300m= 15.64% Consider a mutual fund with $300 million in assets at the start of the year, and 12 million shares outstanding. If the gross return on assets is 18% and the total expense ratio is 0.75% of the year end value, what is the rate of re turn on the fund? a. 18.75% B. 17.12% c. 17.25% d. 17.45% $300m *(1.18)= $354m .02* $354m = 7,080,000 ($354m- 7,080,000- 300m)/300m= 15.64% You pay $21,600 to the Laramie Fund which has a NAV of $18.00 p er share at the beginning of the year. The fund deducted a front-end lo ad of 4%. The securities in the fund increased in value by 10% during the year. The fund's expense ratio is 1.3% and is deducted from year end asset values. What is your rate of return on the fund if you sell your shares at the end of the ye ar? a. 4.35% B. 4.23% c. 6.45% d. 5.63% [((21600.96 )1.10*(1-.013))/21600]-1= 4.23% Chapter 5 - HPR, AM, GM, Real vs Nominal Returns, Portfolio Ret urn and St. Deviation, APR and EAR You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was a. 4.00% b. 3.50% c. 7.50% D. 11.00% The arithmetic average of -12%, 15% and 20% is _______8%__. a. 15.67% B. 7.67% c. 11.22% d. 6.45% The geometric average of -12%, 20% and 25% is _____5.2%_____. a. 8.42% b. 11.00% C. 9.70% d. 18.88% An investment earns 10% the first year, 15% the second year and loses 12% the third year. Your total compound return over the three years was _______. a. 41.68% B. 11.32% (1.10)(1.15)(1 - .12) - 1 = 11.32% c. 3.64% d. 13.00% If you are promised a nominal return of 12% on a one year inves tment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn? a. 5.48% B . 8.74% 1 + nom rate) = (1+real rate)(1+inflation rate) (1.12) = (1+real rate)(1.03) solving for real rate yields 8.74% c. 9.00% d. 12.00% An investor invests 70% of her w ealth in a risky asset with an expected rate of return of 15% and a variance of 5% and she puts 30% in a Treasury bill that pays 5% . Her portfolio's expected rate of return and standard deviation are __________ and __________ respective ly. a. 10.0%, 6.7% b. 12.0%, 22.4% C . 12.0%, 15.7% d. 10.0%, 35.0% The buyer of a new home is quoted a mortgage rate of 0.5% per m onth. What is the APR on the loan? a. 0.50% b. 5.0% C. 6.0% d. 6.5% A loan for a new car costs the borrower 0.8% per month. What is the EAR? a. 0.80% b. 6.87% c. 9.60% D. 10.03% Chapter 7 - CAPM Consider the CAPM. The expected return on the market is 18%. Th e expected return on a stock with a beta of 1.2 is 20%. What is the risk-free rate? a. 2% b. 6% C. 8% d. 12% You have a $50,000 portfolio cons isting of Intel, GE and Con Ed ison. You put $20,000 in Intel, $12,000 in GE and the rest in Con Edis on. Intel, GE and Con Edison have betas of 1.3, 1.0 and 0.8 respectively. What is your portfolio beta? A. 1.048 b. 1.033 c. 1.000 d. 1.037 The risk-free rate and the expect ed market rate of return are 5 % and 15% respectively. According to the capital asset pricing model, the expected rate of return on sec urity X with a beta of 1.2 is equal to __________. a. 12% B. 17% c. 18% d. 23% Chapter 18 - DDM, Earnings Model, PVGO A preferred share of Coquihalla C orporation will pay a dividend of $8.00 in the upcoming year, and every year thereafter, i.e., dividends are not expected to grow. You require a return of 7% on this stock. Using the constant growth DDM to calculate the intrinsic value, a pre ferred share of Coquihalla Corporation is worth __________. a. $13.50 b. $45.50 c. $91.00 D. $114.29 A firm is planning on paying its first dividend of $2 in three years. After that dividends are expected to grow at 6% per year indefinitely . The stock's required return i s 14%. What is the intrinsic value of a share today? a. $25.00 b. $16.87 C. $19.24 d. $20.99 This is an easy two-stage DDM problem. First, you need to calculate the expected price of a share at the end of year 2: P 2 = D 3 k g = 2 0.14 0.06 = 25. Then calculate the present price. Since in the first two years, the firm doesn't pay out any dividend, the price is just given by: P0 = P 2 ( 1 + k ) 2 = 25 ( 1 + 0.14 ) 2 = 19.24 Rose Hill Trading Company is expected to have EPS in the upcomi ng year of $8.00. The expected ROE is 18.0%. An appropriate require d return on the stock is 14%. I f the firm has a plowback ratio of 70%, its dividend in the upcoming year should be __________. a. $1.12 b. $1.44 C. $2.40 d. $5.60 Annie's Donut Shops, Inc. has expected earnings of $3.00 per sh are for next year. The firm's ROE is 18% and its earnings retention ratio is 60%. If the firm's market c apitalization rate is 12%, what is the value of the firm excluding any growth opportunities? A. $25.00 b. $50.00 c. $83.33 d. $208 Westsyde Tool Company is expected to pay a dividend of $2.00 in the upcoming year. The risk-free rate of return is 6% and the expected return on the market portfolio is 12%. Analysts expect the price of Westsyde Tool Company shares to be $29 a year from now. The bet a of Westsyde Tool Company's stock is 1.20. Using a one-period valu ation model, the intrinsic valu e of Westsyde Tool Company stock today is __________. a. $24.29 B. $27.39 c. $31.13 d. $34.52 Lifecycle Motorcycle Company is expected to pay a dividend in y ear 1 of $2.00, a dividend in year 2 of $3.00, and a dividend in year 3 of $4.00. After year 3, dividen ds are expected to grow at the rate of 7% per year. An appropriate require d return for the stock is 12%. Using the multistage DDM, the stock should be worth __________ today. a. $63.80 b. $65.13 C. $67.98 d. $85.60 D1 = $2; D2 = $3; D3 = $4 We can use the dividend growth model to calculate P3 = D4/(r-g) D4 = D3 x (1+g) = 4 x (1.07) r = 0.12 and g = 0.07 so P3 = $85.60 Calculate the present value of D1, D2, D3+P3 to get the price today (use r=0.12) And P = $67.98 ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock. At what price would you expect ART to sell? a. $25.00 B. $34.29 c. $42.86 d. $45.67 At what P/E ratio would you expect ART to sell? a. 8.33 B. 11.43 c. 14.29 d. 15.25 Chapter 14 & 16 - Bond Pricing, YTM, YTC, Price Sensitivity, Du ration A coupon bond which pays interest of $60 annually, has a par va lue of $1,000, matures in 5 years, and is selling today at an $84.52 discount from par value. The approxi mate yield on this bond is __________. a. 6% b. 7% C. 8% d. 9% Approx YTM = Interest amount + (par value price) (price + par value)/2 = 60 + 84.52/5 957.74 = 0.08 A zero-coupon bond has a yield to maturity of 5% and a par valu e of $1,000. If the bond matures in 16 years, it should sell for a price of __________ today. A. $458.00 b. $641.00 c. $789.00 d. $1,100.00 Price of the bond = 1000 1.0516 The yield to maturity of an 8-year zero coupon bond, with a par value of $1,000 and a market price of $623.20, is ______. A. 6.1% b. 8.8% c. 10.1% d. 13.4% A callable bond pays annual interest of $60, has a par value of $1,000, matures in 20 years but is callable in 10 years at a price of $1,100, and has a value today of $105 5.84. The yield to call on this bond is __________. A. 6.00% b. 6.58% c. 7.20% d. 8.00% A 1% decline in yield will have the least effect on the price o f the bond with a __________. a. 10-year maturity, selling at 80 B. 10-year maturity, selling at 100 c. 20-year maturity, selling at 80 d. 20-year maturity, selling at 100 Assuming semiannual compounding, a 20-year zero coupon bond wit h a par value of $1,000 and a required return of 12% would be priced at __________. A. $97 b. $104 c. $364 d. $732 All other things equal, which of the following has the shortest duration? a. A 30 year bond with a 10% coupon b. A 20 year bond with a 9% coupon c. A 20 year bond with a 7% coupon D. A 10 year zero coupon bond A bond currently has a price of $1,050. The yield on the bond i s 6.00%. If the yield increases 25 basis points, the price of the bond w ill go down to $1,030. The durat ion of this bond is ____ years. a. 7.46 B. 8.08 c. 9.02 d. 10.11 You own a bond that has a duration of 6 years. Interest rates a re currently 7% but you believe the Fed is about to increase interest rates by 25 basis points. Your predi cted price change on this bond is _________. a. +1.40% B. -1.40% c. -2.51% d. +2.51% D* = 6/1.07 = 5.61P/P= -D*(y) = -5.61(.25%) = -1.4 The duration of a par value bon d with a coupon rate of 6% and a remaining time to maturity of 10 years is __________. a. 9.29 b. 8.50 C. 7.80 d. 6.69 You have a 25 year maturity 10% coupon, 10% yield bond with a d uration of 9.98 years and a convexity of 139.59. If interest rate were to fall 125 basis points your predicted new price for the bond (including convexity) is __________. a. $1098.45 b. $1104.56 c. $1113.41 D. $1124.31 Tutorial Work Sheet: Module 5 Part A Solutions Question 1 What is the duration of a par value bond with a coupon rate of 8% and a remaining time to maturity of 5 years? Solution: CF Time PV of CF@08% Time * PV of CF $80 1 $80/1.08 = $74.07 74.07 * 1 = 74.07 $80 2 $80/(1.08)2 = $68.59 68.59 * 2 = 137.18 $80 3 $80/(1.08)3 = $63.51 63.51 * 3 = 190.53 4 $80 4 $80/(1.08) = $58.80 58.80 * 4 = 235.20 $1,080 5 $1,080/(1.08)5 = $735.03 735.03 * 5 = 3675.15 Price=$1000.00 4312.13 Duration = 4312.12 / 1000 = 4.312 Question 2 Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. What is the duration if the yield to maturity is 10%? Solution: a. YTM = 6% (1) (2) Cash Flow Time $60.00 $60.00 $1,060.00 1 2 3 (3) PV of CF (Discount rate = 6%) $56.60 $53.40 $890.00 Price=$1,000. (4) Time * PV of CF 56.60 106.80 2670.00 2833.40 00 Duration = 2833.40/1000 = 2.833 years b. YTM = 10% (1) Time until Payment (years) 1 2 3 (2) Cash Flow $60.00 $60.00 $1,060.00 (3) PV of CF (Discount rate = 10%) $54.55 $49.40 $796.39 1 (4) (5) Weight Column (1) Column (4) 0.0606 0.0551 0.8844 0.0606 0.1102 2.6532 Column Sums $900.53 1.0000 2.8240 Duration = 2.824 years, which is less than the duration at the YTM of 6%. Question 3 You own a fixed-income asset with a duration of five years. If the level of interest rates, which is currently 8%, goes up by 10 basis points, how much do you expect the price of the asset to go down (in percentage terms)? Solution: DM = 5/(1.08) = 4.63 When interest rate goes up by 100 basis points, price goes down by 4.63%. When interest rates go up by 10 basis points, price goes down by 0.463%. Question 4 Rank the following bonds in order of descending duration. Bond A B C D E Coupon 15% 15 0 8 15 Time to Maturity 20 years 15 20 20 15 Yield to Maturity 10% 10 10 10 15 Solution: The ranking of bonds in descending order of Duration: C Higher the time to maturity higher the duration D Lower the coupon higher the duration A B Lower the YTM higher the Duration E Question 5 You are managing a portfolio of $1 million. Your target duration is 10 years. You can choose from 2 bonds: a zero coupon bond with 5 years to maturity and a perpetuity each currently yielding 5%. a) How much of each bond will you hold in the portfolio? b) How will these fractions change next year if the target duration is now 9 years? 2 Solution: a. The duration of the perpetuity is: 1.05/0.05 = 21 years Call w the weight of the zero-coupon bond. Then: (w 5) + [(1 - w) 21] = 10 w = 11/16 = 0.6875 Therefore, the portfolio weights would be as follows: 11/16 invested in the zero and 5/16 in the perpetuity. b. Next year, the zero-coupon bond will have a duration of 4 years and the perpetuity will still have a 21-year duration. To obtain the target duration of nine years, which is now the duration of the obligation, we again solve for w: (w 4) + [(1 - w) 21] = 9 w = 12/17 = 0.7059 So, the proportion of the portfolio invested in the zero increases to 12/17 and the proportion invested in the perpetuity falls to 5/17. 3 Problem Set #6 Solutions 1. You put up $50 at the beginning of the year for an investment. The value of the investment grows 4% and you earn a dividend of $3.50. Your HPR was ____. A. 4.00% B. 3.50% C. 7.00% D. 11.00% Dividend yield = HPR = .04+.07 = .11 2. The holding period return on a stock is equal to _________. A. the capital gain yield over the period plus the inflation rate B. the capital gain yield over the period plus the dividend yield C. the current yield plus the dividend yield D. the dividend yield plus the risk premium 3. The market risk premium is defined as __________. A. the difference between the return on an index fund and the return on Treasury bills B. the difference between the return on a small firm mutual fund and the return on the Standard and Poor's 500 index C. the difference between the return on the risky asset with the lowest returns and the return on Treasury bills D. the difference between the return on the highest yielding asset and the lowest yielding asset 4. Treasury bills are paying a 4% rate of return. A risk averse investor with a risk aversion of A = 3 should invest in a risky portfolio with a standard deviation of 24% only if the risky portfolio's expected return is at least ______. A. 8.67% B. 9.84% C. 12.64% D. 14.68% E(rp) - 0.04 = 0.5(3)(.24)2 E(rp) =.1264 5. The holding period return on a stock was 25%. Its ending price was $18 and its beginning price was $16. Its cash dividend must have been _________. A. $0.25 B. $1.00 C. $2.00 D. $4.00 16(0.25) = 2+Div Div = 2 6. Consider the following two investment alternatives. First, a risky portfolio that pays 15% rate of return with a probability of 40% or 5% with a probability of 60%. Second, a treasury bill that pays 6%. The risk premium on the risky investment is _________. A. 1% B. 3% C. 6% D. 9% E(Rrisky) = .4(.15) + .6(.05) = .09 Risk premium = .09 - .06 = .03 PRACTICE QUESTIONS AND ANSWERS 1 1. Derivative securities can be based on _________. a. currencies b. common stocks c. home mortgages d. all of the above 2. The material wealth of a society is determined by the economys __________, which is a function of the economys ___________. a. investment bankers; financial assets b. investment bankers; real assets c. productive capacity; financial assets d. productive capacity; real assets 3. Asset allocation refers to the _______________. a. allocation of the investment portfolio across broad asset classes b. analysis of the value of securities c. choice of specific assets within each asset class d. none of the above 4. _____________ portfolio management calls for holding diversified portfolios without spending effort or resources attempting to improve investment performance through security analysis. a. active b. idiotic c. passive d. none of the above 5. _____________ is not a true statement regarding municipal bonds. a. A municipal bond is a debt obligation issued by state or local governments. b. A municipal bond is a debt obligation issued by the Federal Government. c. The interest income from a municipal bond is exempt from federal income taxation. d. The interest income from a municipal bond is exempt from state and local taxation in the issuing state. 6. Money market securities are characterized by ______________. a. a very short term to maturity b. a medium term to maturity c. a long term to maturity d. none of the above 2 7. Mutual funds perform the function of __________ for their shareholders. a. diversification b. professional management c. record keeping and administration d. all of the above 8. When computing the bank discount yield in a leap year, you would use ________ days. a. 260 b. 360 c. 365 d. 366 9. The ask price of a treasury bill is ______________. a. the price at which the dealer in treasury bills is willing to sell the bill b. the price at which the dealer in treasury bills is willing to buy the bill c. greater than the ask price of the treasury bill expressed in dollar terms d. the price at which the investor can buy the treasury bill 10. In a futures contract, the short position is taken by the person who ____________. a. commits to delivering the commodity b. commits to purchasing the commodity c. plays between second base and third base d. uses his margin 11. A __________ gives its holder the right to sell an asset for a specified exercise price on or before a specified expiration date. a. call option b. futures contract c. put option d. none of the above 12. A treasury bill has a face value of $10,000 and is selling for $9,800. If the treasury bill matures in 80 days, its effective annual yield is ___________. a. 2.04% b. 9.46% c. 8.42% d. 9.66% 13. The asked discount yield on a treasury bill is 5%. The ask price of the bill is ______________ if it matures in 60 days and has a face value of $1,000. a. $950.00 b. $991.67 c. $952.38 d. none of the above 3 14. If the market prices of the 30 stocks in the Dow Jones Industrial Average all change by the same dollar amount on a given day (ignoring stock splits), which stock will have the greatest impact on the average? a. the one with the highest price b. the one with the lowest price c. all 30 stocks will have the same impact d. the answer cannot be determined by the information given 15. Which of the following are not characteristic of common stock ownership? a. residual claimant b. unlimited liability c. voting rights d. all of the above are characteristics of stock ownership 16. Assume that you have just purchased some shares in an investment company reporting $300 million in assets, $20 million in liabilities, and 30 million shares outstanding. What is the net asset value of these shares? a. $10 b. $9.33 c. $15 d. $1.50 17. Sponsors of unit investment trusts earn a profit by ______________. a. deducting a quarterly management fee from fund assets b. deducting a percentage of any gains in asset value c. selling shares in the trust at a premium to the cost of acquiring the underlying assets d. none of the above 18. Investors who wish to liquidate their holdings in a unit investment trust may _______________. a. sell their shares back to the trustee at a discount b. sell their shares back to the trustee at net asset value c. sell their shares on the open market d. none of the above 19. ____________ is a false statement regarding open-end mutual funds. a. they offer investors a guaranteed rate of return b. they offer investors a well diversified portfolio c. they redeem their shares at their net asset value d. none of the above 4 20. Mutual funds that hold both equities and fixed-income securities in relatively stable proportions are called ______________. a. income funds b. balanced funds c. asset allocation funds d. index funds 21. In a recent study, Malkiel finds that evidence of persistence in the performance of mutual funds _______________ in the 1980s a. grows stronger b. remains about the same c. becomes slightly weaker d. virtually disappears 22. Empirical evidence suggests that investors become ____________ as they approach retirement. a. greedier b. less interested in investments c. more risk averse d. more risk tolerant 23. The ___________ average ignores compounding. a. geometric b. arithmetic c. both a and b above d. none of the above 24. Of the alternatives available, _____________ typically have the highest standard deviation of returns. a. commercial paper b. corporate bonds c. stocks d. treasury bills 25. If you purchase a stock for $50, receive dividends of $2, and sell the stock at the end of the year for $53, what is your holding period return? a. 5% b. 10% c. 14% d. 18% 26. The arithmetic average of 12%, 15%, and 20% is ________________. a. 15.7% b. 15% c. 17.2 d. 20% 5 27. The geometric average of 10%, 20% and 41% is ____________. a. 14.9% b. 18.2% c. 19.7% d. 23% 28. The dollar weighted return is the same as the _______________. a. difference between cash inflows and outflows b. arithmetic average return c. geometric average return d. internal rate of return 29. Suppose you pay $9,700 for a Treasury bill maturing in three months. What is the effective annual rate of return for this investment? a. 3.1% b. 13% c. 8.42% d. 10.66% 30. The reward/variability ratio is given by ________________. a. the slope of the capital allocation line b. the second derivative of the capital allocation line c. the point at which the second derivative of the investors indifference curve reaches zero. d. none of the above. 31. If you are promised a nominal return of 12% on a one year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn? (exact rate, not approximation) a. 5.48% b. 8.74% c. 9% d. 12% 32. A Treasury bill pays a 6% rate of return. A risk averse investor _____________ invest in a risky portfolio that pays 12% with a probability of 40% or 2% with a probability of 60% because ___________________. a. might; she is rewarded a risk premium b. would not; because she is not rewarded any risk premium c. would not; because the risk premium is small d. cannot be determined 6 33. Consider a treasury bill with a rate of return of 5% and the following risky securities: Expected Return Variance A 0.15 0.0400 B 0.10 0.0225 C 0.12 0.1000 D 0.13 0.0625 The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. The security the investor would choose as part of his complete portfolio would be _____________. a. security A b. security B c. security C d. security D 34. An investor invests 40% of his wealth in a risky asset with an expected rate of return of 15% and a variance of 4% and 60% in a treasury bill that pays 6%. The portfolios expected rate of return and standard deviation are _____________ and ______________. a. 8.0%; 12% b. 9.6%; 8% c. 9.6%; 10% d. 11.4%; 12% 35. Consider the following two investment alternatives. First, a risky portfolio that pays 15% rate of return with a probability of 60% or 5% with a probability of 40%. Second, a treasury bill that pays 6%. The risk premium on the risky investment is a. 1% b. 5% c. 9% d. 7% 36. You invest $100 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 12% and a standard deviation of 15% and a treasury bill with a rate of return of 5%. ____________ of your money should be invested in the risky asset to form a portfolio with an expected return of 9%. a. 28% b. 86% c. 57% d. 50% 7 37. A portfolio is composed to two stocks, A and B. Stock A has a standard deviation of return of 25% while stock B has a standard deviation of return of 5%. Stock A comprises 20% of the portfolio while stock B comprises 80% of the portfolio. If the variance of returns on the portfolio is 0.0050, the correlation coefficient between the returns on A and B is ____________. a. -0.225 b. -0.474 c. 0.474 d. 0.225 38. The standard deviation of return on investment A is 0.1 while the standard deviation of return on investment B is 0.05. If the covariance of returns on A and B is 0.0030, the correlation coefficient between the returns A and B is ____________. a. 0.12 b. 0.36 c. 0.60 d. 0.77 39. An investor can design a risky portfolio based on two stocks, A and B. The standard deviation of return on stock A is 20% while the standard deviation on stock stock B is 15%. The correlation coefficient between the return on A and B is 0.The expected return on stock A is 20% while on stock B is 10%. The proportion of the minimum variance portfolio that would be invested in stock B is ________. a. 6% b. 50% c. 64% d. 100% 40. A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 5% while stock B has a standard deviation of return of 15%. The correlation coefficient between the returns on A and B is 0.5. Stock A comprises 40% of the portfolio while stock B comprises 60% of the portfolio. The variance of return on the portfolio is ___________. a. 0.0056 b. 0.0067 c. 0.0114 d. 0.0103 8 41. According to Tobins separation property, portfolio choice can be separated into two independent tasks consisting of ___________ and ___________. a. identifying all investor imposed constraints; identifying the set of securities that conform to the investors constraints and offer the best riskreturn tradeoff b. identifying the investors degree of risk aversion; choosing securities from industry groups that are consistent with the investors risk profile c. identifying the optimal risky portfolio; constructing a complete portfolio from the T-bills and the optimal risky portfolio based on the investors degree of risk aversion d. none of the above answers is correct. 42. The values of beta coefficients of securities are ___________. a. always positive b. always negative c. always between +1 and 1 d. usually positive, but not restricted in any particular way 43. Rational risk-averse investors will always prefer portfolios ____________. a. located on the efficient frontier to those located on the capital market line b. located on the capital market line to those located on the efficient frontier c. at or near the minimum variance point on the efficient frontier d. rational risk-averse investors prefer the risk-free asset to all other asset classes 44. Risk that can be eliminated through diversification is called _____________ risk. a. firm-specific b. unique c. both of the above d. none of the above 45. The term excess returns refers to ______________. a. returns earned illegally by means of insider trading b. the difference between the rate of return earned and the risk-free rate c. the difference between the rate of return earned on a particular security and the rate of return earned on other securities of equivalent risk d. the portion of the return on a security which represents tax liability and therefore cannot be reinvested 9 Answers to Quiz 1 (Since the correct answers are circled in red pen on your returned quizzes, only the work for computational questions are provided here.) 12. Holding period return = (face value price)/price = 0.02041 Effective annual yield = (1.02041)(365/80) - 1 = 0.0966 I also accepted 9.46% since if you use 360/80 rather than 365/80, your answer is closer to 9.46%. 13. Ask discount yield = (face value price)/face value x 360/60 0.05 = (1000-P)/1000 x 360/60 solving for P yields $991.67 16. NAV = (assets-liabs)/shares outstanding = (300m-20m)/30m = $9.33 25. Return = (selling price +dividend)/purch price - 1 = (53+2)/50 - 1 = 10% 26. Arithmetric average = (0.12 + 0.15 + 0.20)/3 = 0.157 = 15.7% 27. Geometric average = ((1.1)(1.2)(1.41))1/3 1 = 23% 29. Holding period return = (10,000-9,700)/9,700 = 0.0309278 EAR = (1.0309278)4 - 1 = 0.1296 = 13% 31. (1 + nom rate) = (1+real rate)(1+inflation rate) (1.12) = (1+real rate)(1.03) solving for real rate yields 8.74% 32. Expected return on the risky portfolio = (0.4)(0.12) + (0.6)(0.02) = 0.06 No point in investing in the risky portfolio since you can get the same rate of return from the risk free asset (there is no risk premium) 33. Calculate the slope of the CAL between the risk free asset and each of the risky securities. Slope of the CAL = (Expected return on risky asset risk free rate)/std dev of risky asset For A: (0.15-0.05)/sqr root of 0.0400 = 0.5 For B: = 0.33 For C: = 0.22 For D: = 0.32 Security A is best since it allows for a CAL with the highest slope. 34. Expected return on portfolio = (0.4)(0.15) + (0.6)(0.06) = 0.096 Standard deviation = (0.4)(sqr root of 0.04) = 0.08 10 35. Expected return on risky portfolio = (0.6)(0.15)+(0.4)(0.05) = 0.11 The risk premium = 0.11 risk free rate = 0.11-0.06 = 0.05 36. Expected return on portfolio = x(0.12) + (1-x)(0.05) We want the expected return to equal 0.09 so 0.09 = x(0.12) + (1-x)(0.05) solving for x yields 57% 37. using the equation for variance of returns on a portfolio: 0.0050 = (0.2)2(0.25)2 + (0.8)2(0.05)2 + 2(0.2)(0.8)(0.25)(0.05)(corr) solving for correlation yields 0.225 38. correlation coeff = covariance/(std dev of A x std dev of B) = 0.003/(0.1*0.05) = 0.6 39. using the equation for solving the weight of asset B in the minimum variance portfolio = (0.2)2 - (0.2)(0.15)(0) (0.15)2 + (0.2)2 - 2(0.2)(0.15)(0) = 0.64 = 64% 40. using the equation for variance of returns on a portfolio = (0.4)2(0.05)2 + (0.6)2(0.15)2 + 2(0.4)(0.6)(0.05)(0.15)(0.5) = 0.0004 + 0.0081 + (0.0018) = 0.0103 11