Investments Exam 1 Questions and Problems
Your grandfather invested $1,000 in a stock 50 years ago. Currently the value of his account is $324,000. What is his geometric return over this period?
($324,000 / $1,000)^1/50 - 1 = .1226, or 12.26%
You invested $10,000 in a mutual fund at the beginning of the year when the NAV was $32.24. At the end of the year the fund paid $0.24 in short-term distributions and $0.41 in long-term distributions. If the NAV of the fund at the end of the year was $35.23, what was your return for the year?
($35.23 - 32.24 + .24 + .41) / $32.24 = 11.29%
You are going to invest in a stock mutual fund with a 6% front-end load and a 1.75% expense ratio. You also can invest in a money market mutual fund with a 3.30% return and an expense ratio of 0.10%. If you plan to keep your investment for two years, what annual return must the stock mutual fund earn to exceed an investment in the money market fund? What if your investment horizon is 10 years?
(1 + .033 - .001)2 = (1 - .06)(1 + R - .0175)2; 1.065 = .94(1 + R - .0175)2; R = 8.19% (1 + .033 - .001)10 = (1 - .06)(1 + R - .0175)10; 1.370 = .94(1 + R - .0175)10; R = 5.59%
You've just opened a margin account with $20,000 at your local brokerage firm. You instruct your broker to purchase 500 shares of Landon Golf stock, which currently sells for $60 per share. What is your initial margin? Construct the equity account balance sheet of this position.
500 shares × $60 per share = $30,000 Initial margin = $20,000 / $30,000 = 66.67% Assets 500 shares $30,000 Total $30,000 Liabilities and account equity Margin loan $10,000 Account equity 20,000 Total $30,000
The Bruin Stock Fund sells Class A shares that have a front-end load of 5.75%, a 12b-1 fee of 0.23%, and other fees of 0.73%. There are also Class B shares with a 5% CDSC that declines 1% per year, a 12b-1 fee of 1.00%, and other fees of 0.73%. If the portfolio return is 10% per year and you plan to sell after the third year, should you invest in Class A or Class B shares? What if your investment horizon is 20 years?
After 3 years: (For every dollar invested) Class A: $0.9425(1 + .10 - .0023 - .0073)3 = $1.22191 Class B: [$1.00(1 + .10 - .01 - .0073)3](1 - .02) = $1.24380 You should invest in Class B shares. After 20 years: Class A: $0.9425(1 + .10 - .0023 - .0073)20 = $5.32106 Class B: $1.00(1 + .10 - .01 - .0073)20 = $4.89962 You should invest in Class A shares.
You decide to buy 1,200 shares of stock at a price of $34 and an initial margin of 55%. What is the maximum percentage decline in the stock before you will receive a margin call if the maintenance margin is 35%?
Amount borrowed = (1,200 × $34)(1 - .55) = $18,360 Margin call price = ($18,360 / 1,200) / (1 -.35) = $23.54 Stock price decline = ($23.54 - $34) / $34 = -30.77%
You buy 500 shares of stock at a price of $38 and an initial margin of 60%. If the maintenance margin is 30%, at what price will you receive a margin call?
Amount borrowed = (500 × $38) - (500 × $38)(.60) = $7,600 Margin call price = ($7,600 / 500) / (1 -.3) = $21.71
Suppose you bought 100 shares of stock at an initial price of $37 per share. The stock paid a dividend of $0.28 per share during the following year, and the share price at the end of the year was $41. What is the capital gains yield? The dividend yield? What is the total rate of return on the investment?
Capital gains yield = ($41 - 37)/$37 = 10.81% Dividend yield = $0.28/$37 = 0.76% Total rate of return = 10.81% + 0.76% = 11.57%
The rate of return on Cherry Jalopies, Inc., stock over the last five years was 17%, 11%, -2%, 3 %, and 14%. Over the same period, the return on Straw Construction Company's stock was 16%, 18%, -6%, 1 %, and 22%. What was the arithmetic average return on each stock over this period?
Cherry average return = (0.17 + 0.11 - 0.02 + 0.03 + 0.14)/5 = 8.60% Straw average return = (0.16 + 0.18 - 0.06 + 0.01 + 0.22)/5 = 10.20%
The rate of return on Cherry Jalopies, Inc., stock over the last five years was 17%, 11%, -2%, 3 %, and 14%. Over the same period, the return on Straw Construction Company's stock was 16%, 18%, -6%, 1 %, and 22%. Calculate the variances and the standard deviations for Cherry and Straw.
Cherry: RA = 8.60% Var = 1/4[(.17 - .086)^2 + (.11 - .086)^2 + (-.02 - .086)^2 + (.03 - .086)^2 + (.14 - .086)^2] = .00623 Standard deviation = (0.00623)^1/2 = .0789, or 7.89% Straw: RA = 10.20% Var= 1/4[(.16 - .102)^2 + (.18 - .102)^2 + (-.06 - .102)^2 + (.01 - .102)^2 + (.22 - .102)^2] = .01452 Standard Deviation = (0.01452)^1/2 = 0.0789, or 7.89%
The contract size for platinum futures is 50 troy ounces. Suppose you need 300 troy ounces of platinum and the current futures price is $2,025 per ounce. How many contracts do you need to purchase? How much will you pay for your platinum? What is your dollar profit if platinum sells for $2,075 a troy ounces when the futures contract expires? What if the price is $1,975 at expiration?
Contract to buy = 300 / 50 = 6 Purchase price = 6 × 50 × $2,025 = $607,500 P = $2,075: Gain = ($2,075 - 2,025) × 6 × 50 = $15,000 P = $1,975: Gain = ($1,975 - 2,025) × 6 × 50 = -$15,000
You purchase 10 call option contracts with a strike price of $75 and a premium of $3.85. If the stock price at expiration is $82, what is your dollar profit? What if the stock price is $72?
Cost of contracts = $3.85 × 10 × 100 = $3,850 If the stock price is $82, the value is: ($82 - 75) × 10 × 100 = $7,000 Dollar return = $7,000 - 3,850 = $3,150 If the stock price is $72, the call is worthless, so the dollar return is -$3,850.
You find a stock selling for $74.20 that has a dividend yield of 3.4%. What was the last quarterly dividend paid?
Dividend yield is 3.4%, so annualized dividend is .034($74.20) = $2.52. This is just four times the last quarterly dividend, which is thus $2.52 / 4 = $0.63/share.
The rate of return on Cherry Jalopies, Inc., stock over the last five years was 17%, 11%, -2%, 3 %, and 14%. What is the geometric return for Cherry Jalopies, Inc.?
Geometric return = [(1 + .17)(1 + .11)(1 - .02)(1 + .03)(1 + .14)]^(1/5) - 1 = .0837, or 8.37%
You purchase 275 shares of 2nd Chance Co. stock on margin at a price of $53. Your broker requires you to deposit $8,000. What is your margin loan amount? What is the initial margin requirement?
Margin loan = ($53 × 275) - $8,000 = $6,575 Margin requirement = $8,000 / ($53 × 275) = .5489, or 54.89%
Carson Corporation stock sells for $17 per share, and you've decided to purchase as many shares as you possibly can. You have $31,000 available to invest. What is the maximum number of shares you can buy if the initial margin is 60%?
Maximum investment = $31,000/0.60 = $51,667 Number of shares = $51,667/$17 per share = 3,039.22 (or 3,039) shares
The World Income Appreciation Fund has current assets with a market value of $8.5 billion and has 410 million shares outstanding. What is the net asset value (NAV) for this mutual fund?
NAV = $8,500,000,000 / 410,000,000 = $20.73
A closed-end fund has total assets of $240 million and liabilities of $110,000. Currently, 11 million shares are outstanding. What is the NAV of the fund? If the shares currently sell for $19.25, what is the premium or discount on the fund?
NAV = ($240,000,000 - 110,000) / 11,000,000 = $21.81 ($19.25 - 21.81) / $21.81= -11.73%
You find a stock selling for $74.20 that has a dividend yield of 3.4%. If the company has a P/E ratio of 21.5, what is the earnings per share (EPS) for the company?
PE = 21.5; EPS = P0 / PE = $74.20 / 21.50 = $3.45
You believe that Rose, Inc., stock is going to fall and you've decided to sell 800 shares short. If the current share price is $47, construct the equity account balance sheet for this trade. Assume the initial margin is 60%.
Proceeds from sale = 800 × $47 = $37,600 Initial margin = $37,600 × .60 = $22,560 Assets Proceeds from sale $37,600 Initial margin deposit 22,560 Total $60,160 Liabilities and account equity Short position $37,600 Account equity 22,560 Total $60,160
You believe that Rose, Inc., stock is going to fall and you've decided to sell 800 shares short. If the current share price is $47, construct the equity account balance sheet for this trade. Assume the initial margin is 100%.
Proceeds from sale = 800 × $47 = $37,600 Initial margin = $37,600 × 1.00 = $37,600 Assets Proceeds from sale $37,600 Initial margin deposit 37,600 Account equity 37,600 Total $75,200 Liabilities and account equity Short Position $37,600 Account equity 22,560 Total $75,200
A stock has had the following year-end prices and dividends: YEAR PRICE DIV 0 $13.25 - 1 15.61 $0.15 2 16.72 0.18 3 15.18 0.20 4 17.12 0.24 5 20.43 0.28 What are the arithmetic and geometric returns for the stock?
R1 = ($15.61 - 13.25 + 0.15) / $13.25 = 18.94% R2 = ($16.72 - 15.61 + 0.18) / $15.61 = 8.26% R3 = ($15.18 - 16.72 + 0.20) / $16.72 = -8.01% R4 = ($17.12 - 15.18 + 0.24) / $15.18 = 14.36% R5 = ($20.43 - 17.12 + 0.28) / $17.12 = 20.97% RA = (.1894 + .0826 - .0801 + .1436 + .2097) / 5 = .1090, or 10.90% RG = [(1 + .1894)(1 + .0826)(1 - .0801)(1 + .1436)(1 + .2097)]^(1/5) - 1 = .1038, or 10.38%
You purchase 275 shares of 2nd Chance Co. stock on margin at a price of $53. Your broker requires you to deposit $8,000. Suppose you now sell the stock at a price of $62. What is your return? What would your return have been had you purchased the stock without margin? What if the stock price is $46 when you sell the stock?
Terminal price = $62 Without margin = ($62 - 53) / $53 = 16.98% With margin = {($62 × 275) - ($53 × 275)} / $8,000 = 30.94% Terminal price = $46 Without margin = ($46 - 53) / $53 = -13.21% With margin = {($46 × 275) - ($53 × 275)} / $8,000 = -24.06%
An investment has an expected return of 11% per year with a standard deviation of 24%. Assuming that the returns on this investment are at least roughly normally distributed, how frequently do you expect to earn between -13% and 35%? How often do you expect to see 95% of the time? 99% of the time?
That's plus or minus one standard deviation, so about two-thirds of the time, or about two years out of three. In one year out of three, you will be outside this range, implying that you will be below it about one year out of six and above it about one year out of six.
An open-end mutual fund has the following stocks: Stock Shares Price A 6000 $98 B 33000 19 C 4600 89 D 82500 12 If there are 50,000 shares of the mutual fund, what is the NAV?
Total assets = (6,000 × $98) + (33,000 × $19) + (4,600 × $89) + (82,500 × $12) = $2,614,400 NAV = $2,614,400 / 50,000 = $52.29
Suppose you bought 100 shares of stock at an initial price of $37 per share. The stock paid a dividend of $0.28 per share during the following year, and the share price at the end of the year was $41. Compute your total dollar return on this investment. Does your answer change if you keep the stock instead of selling it? Why or why not?
Total dollar return = 100($41 - 37 + 0.28) = $428.00 *whether you choose to sell the stock or not, does not affect the gain or loss for the year; your stock is worth what it would bring if you sold it. Whether you choose to do so or not is irrelevant (ignoring commissions and taxes).
You invested $1,250,000 with a market-neutral hedge fund manager. The fee structure is 2/20, and the fund has a high-water-mark provision. Suppose the first year the fund manager loses 10%, and the second year she gains 20%. What are the management and performance fees paid each year? Assume management fees are paid at the beginning of each year and performance fees are taken at the end of each year.
Yr 1: There is no performance fee since the manager had a negative return. So, the only year 1 fee is the 2% management fee: $1,250,000 × .02=$25,000. Yr 2: The management fee is taken out at the beginning of the year on the new balance, so it is: [($1,250,000-25,000) × (1+(-.10))] × .02 = $1,102,500 × .02 = $22,050 The performance fee is 20% of everything over the $1,250,000 high water mark. ($1,102,500-22,050) × (1+.20) = $1,296,540 ($1,296,540-1,250,000) × .20 = $9,308
