Investments HW and Quiz
A portfolio is composed of two stocks, A and B. Stock A has a standard deviation of return of 22%, while stock B has a standard deviation of return of 16%. Stock A comprises 60% of the portfolio, while stock B comprises 40% of the portfolio. If the variance of return on the portfolio is 0.033, the correlation coefficient between the returns on A and B is __________.
0.033 = (0.6^2)(0.22^2) + (0.42)(0.162) + 2(0.6)(0.4)(0.22)(0.16) ρ; ρ = 0.679
You purchased 1,000 shares of the New Fund at a price of $20 per share at the beginning of the year. You paid a front-end load of 4%. The securities in which the fund invests increase in value by 12% during the year. The fund's expense ratio is 1.2%. What is your rate of return on the fund if you sell your shares at the end of the year?
1 + r = 0.96 × (1 + 0.12 − 0.012) = 1.0637 → r = 0.0637 = 6.37%
An investor puts up $7,000 but borrows an equal amount of money from his broker to double the amount invested to $14,000. The broker charges 5% on the loan. The stock was originally purchased at $35 per share, and in 1 year the investor sells the stock for $42. The investor's rate of return was ____.
14,000/35=400 (42-35)400-(0.05*7000)/7000= 35%
Assume you purchased 500 shares of XYZ common stock on margin at $70 per share from your broker. If the initial margin is 70%, the amount you borrowed from the broker is _________.
500*70*(1-0.7)= $10,500
A mutual fund has total assets outstanding of $79 million. During the year the fund bought and sold assets equal to $19.75 million. This fund's turnover rate was _____.
=19.75/79 =25%
Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 4 should invest entirely in a risky portfolio with a standard deviation of 28% only if the risky portfolio's expected return is at least
A = (Expected return on the risky portfolio-Risk free rate of return)/(Standard deviation^2) Risk free rate of return is the return on treasury bills=4% Standard deviation= 28% or .28 4 = (Expected return on the risky portfolio - 4%)/.28^2 =Expected return on the risky portfolio =4*.28^2 + 4% =0.3136+0.04 =0.3536 or 35.36%
Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in A=E(rM)−rfσ2M is A = 4: a. What would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? c. What will happen to the risk premium if investors become more risk tolerant?
A) Market Risk Premium = (4*(20%^2)) = 16% B) Consistent value of A = (9%/(20%^2)) = 2.25 C) increased risk tolerance means decreased risk aversion (A), which results in a DECREASE in risk premiums.
Suppose that XTel currently is selling at $40 per share. You buy 500 shares using $15,000 of your own money, borrowing the remainder of the purchase price from your broker. The rate on the margin loan is 8%. a. What is the percentage increase in the net worth of your brokerage account if the price of XTel immediately changes to (i) $44; (ii) $40; (iii) $36? b. If the maintenance margin is 25%, how low can XTel's price fall before you get a margin call? c. How would your answer to requirement b change if you had financed the initial purchase with only $17,500 of your own money? d. What is the rate of return on your margined position (assuming again that you invest $15,000 of your own money) if XTel is selling after one year at (i) $44; (ii) $40; (iii) $36? e. Continue to assume that a year has passed. How low can XTel's price fall before you get a margin call? Note: Assume maintenance margin of 25%
A) share value = 40 * 500 = 20,000 equity = 15,000 debt = 5000 net worth = current share value - debt i. (44*500) - 5000 = 17,000 (17,000 - 15,000)/15,000 = 13.33% increase in net worth ii. (40*500) - 5000 = 15,000 0% increase iii. (36*500) - 5000 = 13,000 (13,000 - 15,000)/15,000 = -13.33% B) .25 = (500P - 5000)/500P = $13.33 C) .25 = (500P - 10000)/500P = $26.67 D) have to pay back 5000 + interest interest = 5000 * .08 = 400 i. ((44 * 500) - 5400)/15000 = 1.1067 - 1 = 10.67% ii. ((40 * 500) - 5400)/15000 = .9733 - 1 = -2.67% iii. ((36 * 500) - 5400)/15000 = .84 - 1 = -16% E) .25 = (500P - 5400)/500P P = 14.40
The standard deviation of return on investment A is 16%, while the standard deviation of return on investment B is 11%. If the covariance of returns on A and B is 0.009, the correlation coefficient between the returns on A and B is
Correlation = 0.009/[0.16(0.11)] =0.511
The standard deviation of return on investment A is 15%, while the standard deviation of return on investment B is 10%. If the correlation coefficient between the returns on A and B is −0.200, the covariance of returns on A and B is __________.
Covariance = −0.200(0.15)(0.10) = −0.003
The standard deviation of return on investment A is 24%, while the standard deviation of return on investment B is 19%. If the correlation coefficient between the returns on A and B is −0.263, the covariance of returns on A and B is __________.
Covariance = −0.263(0.24)(0.19) = −0.0120
The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend Stock Price Boom $ 2.00 $ 50 Normal economy 1.00 43 Recession 0.50 34 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%
HPR = (Ending Price − Beginning Price + Cash Dividend)/Beginning Price A) The holding period returns for the three scenarios are: Boom: ($50 − $40 + $2)/40 = 0.30 = 30% Normal: ($43 − $40 + $1)/40 = 0.10 = 10% Recession: ($34 − $40 + $0.50)/40 = −0.1375 = −13.75% E(HPR) = ∑Ss=1p(s) r(s) = [(1/3) × 0.30] + [(1/3) × 0.10] + [(1/3) × (−0.1375)] = 0.0875 or 8.75% Var(HPR) = ∑Ss=1p (s)[r(s) − E(r)]2 = [(1/ 3) × (0.30 − 0.0875)^2] + [(1/3) × (0.10 − 0.0875)^2] + [(1/3) × (−0.1375 − 0.0875)^2] = 0.031979 SD(r)≡σ=sqrt of Var(r) = sqrt of 319.79 = 0.1788 or 17.88% B) E(r) = (0.5 × 8.75%) + (0.5 × 4%) = 6.375% σ = 0.5 × 17.88% = 8.94%
Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 4% A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 25%. a. What is the investment proportion, y? b. What is the expected rate of return on the overall portfolio?
IN EXCEL NOTES
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. Required: a. What is the investment proportion, y? b. What is the expected rate of return on the overall portfolio?
IN EXCEL NOTES
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. You estimate that a passive portfolio invested to mimic the S&P 500 stock index provides an expected rate of return of 13% with a standard deviation of 25%. b. What is the slope of the CML?
IN EXCEL NOTES
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your risky portfolio includes the following investments in the given proportions: Stock A 27% Stock B 33 Stock C 40 Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 15%. a. What is the proportion y? b. What are your client's investment proportions in your three stocks and in T-bills? c. What is the standard deviation of the rate of return on your client's portfolio?
IN EXCEL NOTES
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. a. What are the expected return and standard deviation of your client's portfolio? b. What are the investment proportions of your client's overall portfolio, including the position in T-bills? c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio?
IN EXCEL NOTES
XYZ stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2018 $ 100 $ 4 2019 110 4 2020 90 4 2021 95 4 An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaining shares at the beginning of 2021. a. What are the arithmetic and geometric average time-weighted rates of return for the investor? b-1. Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2018, to January 1, 2021. b-2. What is the dollar-weighted rate of return? (Hint: If your calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and error.)
IN EXCEL NOTES
You invest $2,800 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 13% and a standard deviation of 20% and a Treasury bill with a rate of return of 8%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 12%.
Let the % of investment in Treasury Bill be X. It is important to note that treasury bill is a risk free investment, hence standard deviation would be 0. % invested in Risky Asset = 1-X Expected Standard Deviation = X*Standard Deviation of X + (1-X)*Standard Deviation of Risky Asset 12% = X*0 + (1-X)*20% 12% = 20% - 20%X X = (20% - 12%)/20% = 40% % Investment in Risky Asset = 1-40% = 60%
The Stone Harbor Fund is a closed-end investment company with a portfolio currently worth $500 million. It has liabilities of $6 million and 10 million shares outstanding. If the fund sells for $46 a share, what is its premium or discount as a percent of NAV?
NAV = ($500,000,000 - $6,000,000)/10,000,000 = $49.4 Discount = $49.4 - $46 = $3.4 Discount as % = $3.4/$49.4 = .0688 = 6.88%
Assume that you have just purchased some shares in an investment company reporting $660 million in assets, $30 million in liabilities, and 30 million shares outstanding. What is the net asset value (NAV) of these shares?
NAV = ($660,000,000 - $30,000,000)/30,000,000 = $21
Consider a no-load mutual fund with $528 million in assets and 16 million shares at the start of the year and with $578 million in assets and 17 million shares at the end of the year. During the year investors have received income distributions of $5 per share and capital gain distributions of $0.30 per share. Assuming that the fund carries no debt, and that the total expense ratio is 1%, what is the rate of return on the fund?
NAV0 = $528/16 = $33 NAV1 = [$578 - ($578 × 0.01)]/17 = $33.66 Gross return = ($33.66 - $33 + $5 + $0.3)/$33 = 18.06%
The composition of the Fingroup Fund portfolio is as follows: StockShares Price: A 200,000 shares $35 B 300,000 shares $40 C 400,000 shares $20 D 600,000 shares $25 The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $30,000. There are 4 million shares outstanding. What is the net asset value of the fund?
NAV= market value of assets - liabilities / shares outstanding (35 x 200,000 + 40 x 300,000 + 20 x 400,000 + 25 x 600,000) = Total market value TMV = 42,000,000 liabilities/fees= 30,000 shares outstanding= 4,000,000 NAV= (42,000,000 - 30,000) / (4,000,000) NAV= $10.49
The composition of the Fingroup Fund portfolio is as follows: Stock Shares Price A 220,000 $ 35 B 320,000 40 C 420,000 15 D 620,000 20 The fund has not borrowed any funds, but its accrued management fee with the portfolio manager currently totals $25,000. There are 4 million shares outstanding. What is the net asset value of the fund?
NAV= market value of assets - liabilities / shares outstanding (35 x 220,000 + 40 x 320,000 + 15 x 420,000 + 20 x 620,000) = Total market value TMV = 39,200,000 liabilities/fees= 25,000 shares outstanding= 4,000,000 NAV= (39,200,000 - 25,000) / (4,000,000) NAV= $9.79
An open-end fund has a net asset value of $10.70 per share. It is sold with a front-end load of 6%. What is the offering price?
Offering price= NAV / (1-load) NAV= 10.70 Load= 6% =10.70 / (1-0.06) = $11.38
You purchased a share of stock for $45. One year later you received $2.80 as dividend and sold the share for $44. Your holding-period return was
Purchase price of stock=$45 Dividend amount received= $2.80 Sale price of stock=$44 [2.80+(44-45)]/45 =1.80/45 HPR = 0.04 or 4%
You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio for the equity fund?
Reward to volatility ratio = Portfolio risk premium/Standard deviation of portfolio excess return = 10%/14% = 0.7143
A portfolio with a 20% standard deviation generated a return of 14% last year when T-bills were paying 3.0%. This portfolio had a Sharpe ratio of
Sharpe Ratio = (Return of the Portfolio - Risk free rate of return) / Standard deviation of Portfolio Return of the Portfolio = 14% Risk free rate of return or T-bill rate = 3% Standard deviation of Portfolio = 20% Sharpe Ratio = (14 - 3) / 20 = 11 / 20 = 0.55
Look at the futures listings for corn in Figure 2.11. Suppose you buy one contract for December 2020 delivery at the closing price. Required: If the contract closes in December at a price of $4.00 per bushel, what will be your profit or loss? (Each contract calls for delivery of 5,000 bushels.)
The December maturity futures price today is $3.9725 per bushel. If the contract closes at $4 per bushel in December, your profit / loss on each bushel will be the closing price you receive in December less the futures purchase you contracted for today, multiplied by the number of bushels per contract (for delivery of 5,000 bushels of corn) or: (4-3.9725)*5000= $137.5 gain
Look at the futures listings for corn in Figure 2.11. Suppose you buy one contract for September 2019 delivery at the closing price. Required: If the contract closes in September at a price of $3.68 per bushel, what will be your profit or loss? (Each contract calls for delivery of 5,000 bushels.)
The September maturity futures price today is $3.45 per bushel. If the contract closes at $3.68 per bushel in September, your profit / loss on each bushel will be the closing price you receive in September less the futures purchase you contracted for today, multiplied by the number of bushels per contract (for delivery of 5,000 bushels of corn) or: (3.68-3.45)*5000= $1150 gain
You are considering investing $3,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 6% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 9%. To form a complete portfolio with an expected rate of return of 8%, you should invest approximately __________ in the risky portfolio. This will mean you will also invest approximately __________ and __________ of your complete portfolio in security X and Y, respectively.
The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 9% Expected return from risky portfolio = 60% * 14% + 40% * 9% = 12% Return on Treasury bills = 6% Let us assume proportion of risky portfolio in investment = X Then: 12% * X + 6% * (1 - X) = 8% => 12%X - 6%X = 8% - 6% = 2% => X = 2% / 6 = 33.33% Hence: You should invest approximately 33% in the risky portfolio Investment in X =33.33% * 60% = 20% Investment in Y = 33.33% * 40% = 13%
An investment earns 15% the first year, earns 20% the second year, and loses 19% the third year. The total compound return over the 3 years was __________.
Total compounded rate of return over three years will be- = ((1-.19)(1+.15)(1+.2)-1) =0.1178 or 11.78%
Barnegat Light sold 120,000 shares in an initial public offering. The underwriter's explicit fees were $54,000. The offering price for the shares was $24, but immediately upon issue, the share price jumped to $30. What is the best estimate of the total cost to Barnegat Light of the equity issue?
Total cost = 54,000 + (30 - 24)120,000 = $774,000
The New Fund had average daily assets of $2.2 billion in the past year. The fund sold $400 million and purchased $500 million worth of stock during the year. What was its turnover ratio?
Turnover rate = Value of stocks sold or replaced/Value of assets = $400,000,000/$2,200,000,000 = 0.1818 = 18.18%
The New Fund had average daily assets of $3.5 billion in the past year. The fund sold $413 million and purchased $513 million worth of stock during the year. What was its turnover ratio?
Turnover rate = Value of stocks sold or replaced/Value of assets = $413,000,000/$3,500,000,000 = 0.118 = 11.8%
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 9.0%. Stock B has an expected return of 12% and a standard deviation of return of 3%. The correlation coefficient between the returns of A and B is 0.60. The risk-free rate of return is 7%. The proportion of the optimal risky portfolio that should be invested in stock A is __________.
WA = ((0.16 − 0.07)(0.03)^2 − (0.12 − 0.07)(0.03)(0.090)(0.60)) / ((0.16 − 0.07)(0.60)^2 + (0.12 − 0.07)(0.090)^2 − (0.16 − 0.07 + 0.12 − 0.07)(0.03)(0.09)(0.60)) WA = 0 Since the numerator equals zero, WA = 0 without any further calculations.
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 20% and a standard deviation of return of 23%. Stock B has an expected return of 15% and a standard deviation of return of 12%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate of return is 7%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately __________.
WB = ((0.15 − 0.07)(0.23^2) − (0.20 − 0.07)(0.12)(0.23)(0.4))/((0.15 − 0.07)(0.23^2) + (0.20 − 0.07)(0.12^2) − (0.15 − 0.07 + 0.20 − 0.07)(0.12)(0.23)(0.4)) WB = 74%
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 30%. Stock B has an expected return of 11% and a standard deviation of return of 15%. The correlation coefficient between the returns of A and B is 0.5. The risk-free rate of return is 5%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately
Wb=1-((16%-5%)*(15%)^2-(11%-5%)*(30%*15%*0.5))/((16%-5%)*(15%)^2+(11%-5%)*(30%)^2-(16%-5%+11%-5%)*30%*15%*0.5) =0.7222 = 72%
You pay $22,200 to the Laramie Fund, which has a NAV of $22 per share at the beginning of the year. The fund deducted a front-end load of 4%. The securities in the fund increased in value by 10% during the year. The fund's expense ratio is 1.2% 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 year?
[((22,200)(0.96)(1.10)(1-.012))/22,200]-1=4.33%
City Street Fund has a portfolio of $450 million and liabilities of $10 million. a. If there are 44 million shares outstanding, what is the net asset value? b-1. If a large investor redeems 1 million shares, what happens to the portfolio value? b-2. If a large investor redeems 1 million shares, what happens to shares outstanding? b-3. If a large investor redeems 1 million shares, what is the net asset value?
a) NAV = (Market value of assets − Market value of liabilities)/Shares outstanding = ($450,000,000 − $10,000,000)/44,000,000 = $10 b-1) Because 1,000,000 shares are redeemed at NAV = $10, the value of the portfolio decreases to: Portfolio value = $450,000,000 − ($10 × 1,000,000) = $440,000,000 b-2) The number of shares outstanding will be the current shares outstanding minus the number of shares redeemed: 44,000,000 − 1,000,000 = 43,000,000 b-3) Thus, net asset value after the redemption will be: NAV = (Market value of assets − Market value of liabilities)/Shares outstanding = ($440,000,000 − $10,000,000)/43,000,000 = $10
The Closed Fund is a closed-end investment company with a portfolio currently worth $200 million. It has liabilities of $3 million and 5 million shares outstanding. a. What is the NAV of the fund? b. If the fund sells for $36 per share, what is its premium or discount as a percent of NAV?
a. NAV = (Market value of assets − Market value of liabilities)/Shares outstanding = ($200,000,000 − $3,000,000)/5,000,000 = $39.40 b. Premium (or discount) = (Price − NAV)/NAV = ($36 − $39.40)/$39.40 = −0.0863 = −8.63% The fund sells at an 8.63% discount from NAV.
Old Economy Traders opened an account to short-sell 1,000 shares of Internet Dreams at $110 per share. The initial margin requirement was 50%. (The margin account pays no interest.) A year later, the price of Internet Dreams has risen from $110 to $117.00, and the stock has paid a dividend of $18.00 per share. a. What is the remaining margin in the account? b-1. What is the margin on the short position? b-2. If the maintenance margin requirement is 30%, will Old Economy receive a margin call? c. What is the rate of return on the investment?
a. $30,000 b1. 25.6% b2. yes c. -60% a. Initial margin was: 110 x 1,000 x .5 = 55,000 As a result of the $7 increase, Old Economy Traders lose: $7 x 1,000 = 7,000 Old Economy Traders must pay the dividend of $18 per share to the lender of the shares: $18 x 1000 = 18,000. Remaining margin = 55,000-7,000-18,000 = 30,000 b. Margin on short position = equity in account/value of shares owed --> 30,000/117,000 = 25.64% Because percentage margin falls below maintenance level of 30%, will be a margin call. C. Rate of return = Ending equity - initial equity / initial equity. --> 30,000 - 55,000 / 55,000 = -.45.45
DRK, Incorporated, has just sold 100,000 shares in an initial public offering. The underwriter's explicit fees were $60,000. The offering price for the shares was $40, but immediately upon issue, the share price jumped to $44. a. What is the total cost to DRK of the equity issue?
a. $460,000 b. No a. In addition to the explicit fees of $60,000, we should also take into account the implicit cost incurred to DRK from the underpricing in the IPO. The underpricing is $4 (44-40) per share, or a total of $400,000 (4*100,000), implying total costs of $460,000 (400,000+60,000). b. No. The underwriters do not capture the part of the costs corresponding to the underpricing. However, the underpricing may be a rational marketing strategy to attract and retain long-term relationships with their investors. Without it, the underwriters would need to spend more resources in order to place the issue with the public. The underwriters would then need to charge higher explicit fees to the issuing firm. The issuing firm may be just as well off paying the implicit issuance cost represented by the underpricing.
Old Economy Traders opened an account to short-sell 1,000 shares of Internet Dreams at $40 per share. The initial margin requirement was 50%. (The margin account pays no interest.) A year later, the price of Internet Dreams has risen from $40 to $50, and the stock has paid a dividend of $2 per share. a. What is the remaining margin in the account? b-1. What is the margin on the short position? b-2. If the maintenance margin requirement is 30%, will Old Economy receive a margin call? c. What is the rate of return on the investment?
a. $8,000 b1. 16% b2. yes c. -60% a. Initial margin was: 40 x 1,000 x .5 = 20,000 As a result of the $10 increase, Old Economy Traders lose: $10 x 1,000 = 10,000 Old Economy Traders must pay the dividend of $2 per share to the lender of the shares: $2 x 1000 = 2,000. Remaining margin = 20,000-10,000-2,000 = 8,000 Margin on short position = equity in account/value of shares owed --> 8,000/50,000. Because percentage margin falls below maintenance level of 30%, will be a margin call. C. Rate of return = Ending equity - initial equity / initial equity. --> 8,000 - 20,000 / 20,000 = -.6
You are bearish on Telecom and decide to sell short 100 shares at the current market price of $41 per share. a. How much in cash or securities must you put into your brokerage account if the broker's initial margin requirement is 50% of the value of the short position? b. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?
a. Initial margin is 50% of $4,100 or $2,050. b. Total assets are $6,150 ($4,100 from the sale of the stock and $2,050 put up for margin). Liabilities are 100P. Therefore, equity is ($6,150 - 100P). A margin call will be issued when: ($6150 - 100P)/100P = 0.30 --> when P = $47.31 or higher
You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share. a. How much in cash or securities must you put into your brokerage account if the broker's initial margin requirement is 50% of the value of the short position? b. How high can the price of the stock go before you get a margin call if the maintenance margin is 30% of the value of the short position?
a. Initial margin is 50% of $5,000 or $2,500. b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin). Liabilities are 100P. Therefore, equity is ($7,500 - 100P). A margin call will be issued when: ($7500 - 100P)/100P = 0.30 --> when P = $57.69 or higher
On January 1, you sold short one round lot (that is, 100 shares) of Snow's stock at $21 per share. On March 1, a dividend of $3 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $15 per share. You paid 50 cents per share in commissions for each transaction. a. What is the proceeds from the short sale (net of commission)? b. What is the dividend payment? c. What is the total cost, including commission, if you have to cover the short sale by buying the stock at a price of $15 per share? d. What is the net gain from your transaction?
a. The proceeds from the short sale (net of commission) were: ($21 × 100) - $50 = $2,050. b. 100 shares x $3 a share = $300 c. A dividend payment of $300 was withdrawn from the account. Covering the short sale at $15 per share costs (including commission): $1,500 + $50 = $1,550 d. Therefore, the value of your account is equal to the net profit on the transaction: $2,050 - $300 - $1,550 = $200
On January 1, you sold short one round lot (that is, 100 shares) of Snow's stock at $27.50 per share. On March 1, a dividend of $1.10 per share was paid. On April 1, you covered the short sale by buying the stock at a price of $24.00 per share. You paid 45 cents per share in commissions for each transaction. a. What is the proceeds from the short sale (net of commission)? b. What is the dividend payment? c. What is the total cost, including commission, if you have to cover the short sale by buying the stock at a price of $24.00 per share? d. What is the net gain from your transaction?
a. The proceeds from the short sale (net of commission) were: ($27.50 × 100) - $45 = $2,705. b. 100 shares x $1.1 a share = $110 c. A dividend payment of $110 was withdrawn from the account. Covering the short sale at $24 per share costs (including commission): $2400 + $45 = $2,445 d. Therefore, the value of your account is equal to the net profit on the transaction: $2,705 - $110 - $2,445 = $150
Here is some price information on Fincorp stock. Suppose first that Fincorp trades in a dealer market. Bid Asked 55.25 55.50 a. Suppose you have submitted an order to your broker to buy at market. At what price will your trade be executed? b. Suppose you have submitted an order to sell at market. At what price will your trade be executed? c. What will happen suppose you have submitted a limit order to sell at $55.62? d. What will happen suppose you have submitted a limit order to buy at $55.37?
a. The trade will be executed at $55.50. b. The trade will be executed at $55.25. c. The trade will not be executed because the bid price is lower than the price specified in the limit-sell order. d. The trade will not be executed because the asked price is higher than the price specified in the limit-buy order.
You are bullish on Telecom stock. The current market price is $50 per share, and you have $5,000 of your own to invest. You borrow an additional $5,000 from your broker at an interest rate of 8% per year and invest $10,000 in the stock. a. What will be your rate of return if the price of Telecom stock goes up by 10% during the next year? (Ignore the expected dividend.) b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.
a. You buy 200 shares of Telecom for $10,000. These shares increase in value by 10%, or $1,000. You pay interest of: 0.08 x $5,000 = $400 The rate of return will be: ($1000-$400)/$5000 = 0.12 = 12% b. The value of the 200 shares is 200P. Equity is (200P - $5,000). You will receive a margin call when: (200P - $5000)/200P = 0.30 --> when P = $35.71 or lower
You are bullish on Telecom stock. The current market price is $60 per share, and you have $12,000 of your own to invest. You borrow an additional $12,000 from your broker at an interest rate of 5.8% per year and invest $24,000 in the stock. a. What will be your rate of return if the price of Telecom stock goes up by 8% during the next year? b. How far does the price of Telecom stock have to fall for you to get a margin call if the maintenance margin is 30%? Assume the price fall happens immediately.
a. You buy 400 shares of Telecom for $24,000. These shares increase in value by 8%, or $1,920. You pay interest of: 0.058 x $12,000 = $696 The rate of return will be: ($1920-$696)/$12000 = 0.102 = 10.2% b. The value of the 400 shares is 400P. Equity is (400P - $12,000). You will receive a margin call when: (400P - $12000)/400P = 0.30 --> when P = $42.86 or lower
The New Fund had average daily assets of $2.2 billion in the past year. New Fund's expense ratio was 1.1%, and its management fee was 0.7%. a. What were the total fees paid to the fund's investment managers during the year? b. What were the other administrative expenses?
a.) Fees paid to investment managers were: 0.7% × $2.2 billion = $15.4 million. b.) Since the total expense ratio was 1.1% and the management fee was 0.7%, we conclude that 0.4% must be for other expenses. Therefore, other administrative expenses were: 0.004 × $2.2 billion = $8.8 million.
Which security should sell at a greater price? a. A 10-year Treasury bond with a 5% coupon rate or a 10-year Treasury bond with a 6% coupon. b. A three-month expiration call option with an exercise price of $40 or a three-month call on the same stock with an exercise price of $35. c. A put option on a stock selling at $50 or a put option on another stock selling at $60. (All other relevant features of the stocks and options are assumed to be identical.)
a.) A 10-year Treasury bond with a 6% coupon Correct b.) A three-month call on the same stock with an exercise price of $35 Correct c.) A put option on a stock selling at $50
Refer to Figure 2.3 and look at the Treasury bond maturing in February 2039. Required: a. How much would you have to pay to purchase one of these bonds? b. What is its coupon rate? c. What is the current yield (i.e., coupon income as a fraction of bond price) of the bond?
a.) Ask: 128.212-> purchase price= $1,282.12 b.) Coupon Rate= 3.5, implying coupon payments of $35 annually c.) Current yield = Annual coupon income/price =35/1282.12 =2.73%
A T-bill with face value $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4%. Required: a. What is the price of the bill? b. What is its bond equivalent yield?
a.) Bank discount of 87 days--> 0.034 × (87/360) = 0.008217 Price--> $10,000 × (1 - 0.008217) = $9,917.83 b.)𝑟_𝐵𝐸𝑌=(𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒−𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒)/(𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒)×365/(# 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦) =(10,000-9917.83)/9917.83*(365/87) =3.48%
A T-bill with face value $10,000 and 93 days to maturity is selling at a bank discount ask yield of 4.0%. Required: a. What is the price of the bill? b. What is its bond equivalent yield?
a.) Bank discount of 93 days--> 0.04 × (93/360) = 0.01033 Price--> $10,000 × (1 - 0.01033) = $9,896.67 b.)𝑟_𝐵𝐸𝑌=(𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒−𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒)/(𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑟𝑖𝑐𝑒)×365/(# 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦) =(10,000-9896.67)/9896.67*(365/93) =4.10%
Dée Trader opens a brokerage account and purchases 300 shares of Internet Dreams at $40 per share. She borrows $4,000 from her broker to help pay for the purchase. The interest rate on the loan is 8%. a. What is the margin in Dée's account when she first purchases the stock? b. If the share price falls to $30 per share by the end of the year, what is the remaining margin in her account? c. If the maintenance margin requirement is 30%, will she receive a margin call? d. What is the rate of return on her investment?
a.) initial purchase price= $12,000 (40*300) amt borrowed from broker= $4,000 beg. equity/margin= $8,000 (12,000-4,000) b.) value of shares after one year= $9,000 (30*300) less amount borrowed= $5,000 (9,000-4,000) less interest on amt borrowed = $4,680 (5000-(4000*.08)) remaining margin/equity in accounts= $4,680 c.) 4680/9000= 52% remaining margin no b/c 52% > 30% d.) Rate of Return= (Ending Equity Value-Interest Expense)/Initial Equity Value -1 end equity= 5000 (30*300-4000) beg equity= 8000 (300*40-4000) interest on amt borrowed = 320 (4000*.08) rate of return= -41.5% ((5000-320)/8000)-1
Dée Trader opens a brokerage account and purchases 200 shares of Internet Dreams at $44 per share. She borrows $4,150 from her broker to help pay for the purchase. The interest rate on the loan is 10%. a. What is the margin in Dée's account when she first purchases the stock? b. If the share price falls to $34 per share by the end of the year, what is the remaining margin in her account? c. If the maintenance margin requirement is 30%, will she receive a margin call? d. What is the rate of return on her investment?
a.) initial purchase price= $8,800 (44*200) amt borrowed from broker= $4,150 beg. equity/margin= $4,650 (8,800-4,150) b.) value of shares after one year= $6,800 (34*200) less amount borrowed= $2,650 (6,800-4,150) less interest on amt borrowed = $2,235 (2650-(4150*.1)) remaining margin/equity in accounts= $2,235 c.) 2235/6800= 32.87% remaining margin no b/c 32.87% > 30% d.) Rate of Return= (Ending Equity Value-Interest Expense)/Initial Equity Value -1 end equity= 2650 (34*200-4150) beg equity= 4650 (200*40-4150) interest on amt borrowed = 415 (4150*.1) rate of return= -51.94% ((2650-415)/4650)-1
An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 16% and a standard deviation of return of 20.0%. Stock B has an expected return of 12% and a standard deviation of return of 5%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate of return is 8%. The proportion of the optimal risky portfolio that should be invested in stock A is
answer = 0?
Find the equivalent taxable yield of the municipal bond for tax brackets of zero, 10%, 20%, and 30%, if it offers a yield of 4%.
equivalent taxable yield=(rate on tax exempt bond)/((1-Tax Rate)) 0%=0.04/(1-0)= 4% 10%=0.04/(1-0.1)=4.44% 20%=0.04/(1-0.2)=5% 30%=0.04/(1-0.3)=5.71%
A municipal bond carries a coupon rate of 2.25% and is trading at par. Required: What would be the equivalent taxable yield of this bond to a taxpayer in a 35% combined tax bracket?
equivalent taxable yield=(rate on tax exempt bond)/((1-Tax Rate)) =0.0225/(1-0.35)=0.0346 3.46%
A municipal bond carries a coupon rate of 7.50% and is trading at par. Required: What would be the equivalent taxable yield of this bond to a taxpayer in a 40% combined tax bracket?
equivalent taxable yield=(rate on tax exempt bond)/((1-Tax Rate)) =0.075/(1-0.4)=0.125 12.5%
Suppose that you sell short 500 shares of XTel, currently selling for $40 per share, and give your broker $15,000 to establish your margin account. a. If you earn no interest on the funds in your margin account, Assume that XTel pays no dividends. So what will be your rate of return after one year if XTel stock is selling at: (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) (i) $44 Rate of return (ii) $40 Rate of return (iii) $36 Rate of return b. If the maintenance margin is 25%, how high can XTel's price rise before you get a margin call? P c. Redo parts (a) and (b), but now assume that XTel also has paid a year-end dividend of $1 per share. The prices in part (a) should be interpreted as ex-dividend, that is, prices after the dividend has been paid. (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.) (i) $44 Rate of return (ii) $40 Rate of return (iii) $36 Rate of return P
general -- share value (cash in) = 20,000 margin account (another asset/insurance) = 15,000 current debt = 20,000 current equity = 15,000 a) rate of return = (new equity - initial equity)/initial equity (i) new equity = 35,000 - (44*500) = 13,000 (13,000 - 15,000)/15,000 = -13.33% (ii) new equity = 35,000 - (40*500) = 15,000 0% (iii) new equity = 35,000 - (36*500) = 17,000 (17,000 - 15,000)/15,000 = 13.33% b) .25 = (35,000 - 500P)/500P P = $56 c) rate of return = (new equity - initial equity)/initial equity (i) new equity = 35,000 - (44*500) - 500 = 12500 (12500 - 15,000)/15000 = -16.67% (ii) new equity = 35000 - (40*500) - 500 = 14,500 (14500 - 15000)/15000 = -3.33% (iii) new equity = 35000 - (36*500) - 500 = 16,500 (16500 - 15000)/15000 = 10% Price at which you get margin call -- (35000 - 500P - 500)/500P = $55.20
Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period. P0 Q0 P1 Q1 P2 Q2 A 90 100 95 100 95 100 B 50 200 45 200 45 200 C 100 200 110 200 55 400 Required: a. Calculate the rate of return on a price-weighted index of the three stocks for the first period (t = 0 to t = 1). b. What will be the divisor for the price-weighted index in year 2? c. Calculate the rate of return of the price-weighted index for the second period (t = 1 to t = 2).
in excel Ch. 2 work
The composition of the Fingroup Fund portfolio is as follows: StockShares and Price : A: 200,000 shares $35 B: 300,000 shares $40 C: 400,000 shares $20 D: 600,000 shares $25 If during the year the portfolio manager sells all of the holdings of stock D and replaces it with 200,000 shares of stock E at $50 per share and 200,000 shares of stock F at $25 per share. What is the portfolio turnover rate?
portfolio analysis= (200,000 x 35 + 300,000 x 40 + 400,000 x 20 + 600,000 x 25) portfolio analysis = 42,000,000 The value of stocks sold = $15,000,000 = (200,000 × $50 + 200,000 × $25) Turnover rate = Value of stocks sold or replaced/Value of assets = $15,000,000/$42,000,000 = 0.3571 = 35.71%
The composition of the Fingroup Fund portfolio is as follows: Stock Shares Price A 330,000 $ 30 B 430,000 35 C 530,000 15 D 730,000 20 If during the year the portfolio manager sells all of the holdings of stock D and replaces it with 200,000 shares of stock E at $40 per share and 200,000 shares of stock F at $33 per share, what is the portfolio turnover rate?
portfolio analysis= (330,000 x 30 + 430,000 x 35 + 530,000 x 15 + 730,000 x 20) portfolio analysis = 47,500,000 value of stock sold= $14,600,000 (200,000*40+200,000*33) Turnover rate = Value of stocks sold or replaced/Value of assets = $14,600,000/$47,500,000 = 0.3074 = 30.74%
Corporate Fund started the year with a net asset value of $12.50. By year-end, its NAV equaled $12.10. The fund paid year-end distributions of income and capital gains of $1.50. What was the rate of return to an investor in the fund?
rate of return = (Δ(NAV) + Distributions)/Start of year NAV = ($12.10 − $12.50 + $1.50)/$12.50 = 0.0880 = 8.80%
Market orders entail greater price uncertainty than limit orders.
True
The offer price of an open-end fund is $15 and the fund is sold with a front-end load of 8%. What is the fund's NAV?
(15)(1-0.08) = $13.8
An open-end fund has a NAV of $19.00 per share. The fund charges a 7% load. What is the offering price?
(19)/(1-0.07%) = $20.43
You sell short 600 shares of Microsoft that are currently selling at $25 per share. You post the 40% margin required on the short sale. If you earn no interest on the funds in your margin account, what will be your rate of return after 1 year if Microsoft is selling at $24? (Ignore any dividends.)
(25 - 24)/.4(25) = .1 = 10%
An investor is in a 35% combined federal plus state tax bracket. If corporate bonds offer 8.25% yields, what yield must municipals offer for the investor to prefer them to corporate bonds?
.0825 x (1-0.35)=0.1269 12.69%
The arithmetic average of -30%, 53%, and 58% is __________.
27% (average fxn in excel)
The geometric average of −15%, 20%, and 25% is __________.
8.44% On EXCEL ((1+-15%)*(1+20%)*(1+25%))^(1/3)-1
The standard deviation of return on investment A is 11%, while the standard deviation of return on investment B is 6%. If the covariance of returns on A and B is 0.004, the correlation coefficient between the returns on A and B is __________.
Correlation = 0.004/[0.11(0.06)] = 0.606
You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What are the expected return and standard deviation of your client's portfolio?
Expected return for your fund = T-bill rate + risk premium = 6% + 10% = 16% Expected return of client's overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Standard deviation of client's overall portfolio = 0.6 × 14% = 8.4%
The expected return of a portfolio is 10.8%, and the risk-free rate is 2%. If the portfolio standard deviation is 13%, what is the reward-to-variability ratio of the portfolio?
Expected return of a portfolio = RP = 10.8% Risk free rate= RF = 2% Standard deviation of the portfolio = σP = 13% Reward is the excess return of the portfolio over the risk-free rate Reward = RP - RF = 10.8% - 2% = 8.8% Standard deviation is the measure of variability Reward-to-variability ratio of portfolio = (RP - RF)/σP = 8.8%/13% = 0.676923 Answer -> 0.68
Market orders entail greater time-of-execution uncertainty than limit orders.
False
Suppose your expectations regarding the stock market are as follows: State of the Economy Probability HPR Boom 0.3 42% Normal growth 0.4 15 Recession 0.3 −18 Use above equations to compute the mean and standard deviation of the HPR on stocks.
IN EXCEL NOTES
Consider the three stocks in the following table. Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period. P0 Q0 P1 Q1 P2 Q2 A 90 100 95 100 95 100 B 50 200 45 200 45 200 C 100 200 110 200 55 400 Required: Calculate the first-period rates of return on the following indexes of the three stocks: a. A market value-weighted index b. An equally weighted index
in excel Ch. 2 work
If the offering price of an open-end fund is $12.30 per share and the fund is sold with a front-end load of 5%, what is its net asset value?
offering price= NAV / (1-load) 12.30=NAV / (1-0.05) 12.30=NAV / (0.95) (12.30)(0.95) = NAV NAV= $11.69
An investor is in a 30% combined federal plus state tax bracket. Required: If corporate bonds offer 9% yields, what yield must municipals offer for the investor to prefer them to corporate bonds?
.09 x (1-0.3)=0.063 6.3%
