Investment Fundamentals Exam 2 – Flashcards
Unlock all answers in this set
Unlock answersquestion
If you are promised a nominal return of 12% on a 1-year investment, and you expect the rate of inflation to be 3%, what real rate do you expect to earn?
answer
Real rate = (1.12/1.03) - 1 = 8.74%
question
The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?
answer
6% (.5x12months)
question
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 yields an expected rate of return of 13% with a standard deviation of 25%. a. What is the slope of the CML?
answer
(13% - 7%)/25% = 0.24
question
Rank the following from highest average historical standard deviation to lowest average historical standard deviation from 1926 to 2010. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills
answer
I, III, II, IV
question
The excess return is the _________. rate of return that can be earned with certainty index return rate of return to risk aversion rate of return in excess of the Treasury-bill rate
answer
Rate of return in excess of the Treasury-bill rate
question
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 .50 34 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return % Standard deviation % 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%. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Expected return % Standard deviation %
answer
a. HPR(boom)= (50-40+2)/40 = 30% HPR(Normal)= (43-40+1)/40 = 10% HPR(Recession)= (34-40+.5)/40 = -13.75% (1/3 x 30%) + (1/3 x 10%) + (1/3 x -13.75%) = 8.75% 1/3*(30 - 8.75)^2 + 1/3*(10 - 8.75)^2 + 1/3*(-13.75 - 8.75)^2 = 319.79 variance Square Root of 319.79 = 17.88% Standard Deviation b. Expected Return of business venture 8.75% Return on Treasury Bill 4% W1 = .5 W2 = .5 (.5*8.75) + (.5*4) = 6.375% (.5*17.88) = 8.94%
question
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?
answer
4% + (3.5/50) = 11%
question
The geometric average of -12%, 20%, and 25% is
answer
[Square Root of (1 - .12) x (1 + .20) x (1 + .25) ] -1 [Square Root of (.88) x (1.2) x (1.25) ] - 1 = 9.7%
question
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? (Round your answer to 1 decimal place.) Proportion y b. What are your client's investment proportions in your three stocks and the T-bill fund? (Round your answers to 1 decimal place.) Security Investment Proportions T-Bills % Stock A % Stock B % Stock C % c. What is the standard deviation of the rate of return on your client's portfolio? (Round your answer to 1 decimal place.) Standard deviation % per year
answer
1. Mean = (0.30 * 7%) + (0.7 * 17%) = 14% per Year Standard Deviation = 0.70 * 27% = 18.9% per Year 2. Mean Return on Portfolio = Rf + (Rp - Rf)y = 7% + (17% - 7%)y = 7% + 10%y If the mean of the portfolio is equal to 15%, then solving for y we will get 15% = 7% + 10%y y = (15% - 7%) / 10% = 0.8 3. (a) Mean Return on Portfolio = Rf + (Rp - Rf)y = 7% + (17% - 7%)y = 7% + 10%y Thus in order to obtain a mean return of 15%, the client must invest 80% of total funds in the risky portfolio and 20% in treasure bills. (b). Investment proportions of the client's funds: 20% in T bills 0.8 *27% = 21.6% in stock A 0.8 * 33% = 26.4% in stock B 0.8 * 40% = 32.0% in Stock C c. 18.9
question
If you require a real growth in the purchasing power of your investment of 8%, and you expect the rate of inflation over the next year to be 3%, what is the lowest nominal return that you would be satisfied with?
answer
3% + 8%*(1+3%) = 11.24%
question
Suppose you pay $9,800 for a $10,000 par Treasury bill maturing in 2 months. What is the annual percentage rate of return for this investment?
answer
12.24%
question
The complete portfolio refers to the investment in?
answer
The risk free asset ; the risky portfolio combined
question
The arithmetic average of -11%, 15%, and 20% is
answer
(-11% + 15% + 20%)/3 = 8%
question
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% 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 10%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in Treasury bills.
answer
.11 = Wf(.05)+(1-Wf)*{(.6)(.14)+(.4)(.10 Wf=.19
question
The price of a stock is $38 at the beginning of the year and $41 at the end of the year. If the stock paid a $2.50 dividend, what is the holding-period return for the year?
answer
(41-38+2.5)/38 = 14.47%
question
You have the following rates of return for a risky portfolio for several recent years: The annualized (geometric) average return on this investment is
answer
15.60% (1.17856)1/4 - 1 = 15.60%
question
Historical returns have generally been __________ for stocks of small firms as (than) for stocks of large firms.
answer
Higher
question
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?
answer
{ (D1+18)/16 - 1 = .25 } = $2
question
The market risk premium is defined as
answer
the difference between the return on an index fund and the return on Treasury bills
question
Consider the following two investment alternatives: First, a risky portfolio that pays a 15% rate of return with a probability of 40% or a 5% rate of return with a probability of 60%. Second, a Treasury bill that pays 6%. The risk premium on the risky investment is
answer
(.4 x 15) - (.6 x 5) = 3
question
A portfolio with a 25% standard deviation generated a return of 15% last year when T-bills were paying 4.5%. This portfolio had a Sharpe ratio of
answer
( .15 - .045 / .25 ) = .42
question
Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of .5. The alternative risk less investment in T-bills pays 5%. a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.) Value of the portfolio $ b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) Rate of return % c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now? (Round your answer to the nearest dollar amount.) Value of the portfolio $
answer
http://www.chegg.com/homework-help/consider-risky-portfolio-end-year-cash-flow-derived-portfoli-chapter-5-problem-11p-solution-9780073382401-exc
question
If you want to measure the performance of your investment in a fund, including the timing of your purchases and redemptions, you should calculate the
answer
Dollar weighted return
question
Suppose your expectations regarding the stock market are as follows: State of the Economy Probability HPR Boom 0.3 44% Normal growth 0.4 14 Recession 0.3 -16 Picture Use above equations to compute the mean and standard deviation of the HPR on stocks. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
answer
E( r ) = 0.3*44 + 0.4*14+0.3*(-16)=14% Sigma^2=0.3*(44-14)^2+0.4*(14-14)^2+0.3*(-16-14)^2=540 Sigma=23.24%
question
Suppose you pay $9,700 for a $10,000 par Treasury bill maturing in 3 months. What is the holding-period return for this investment?
answer
10000-9700/9700 = 3.09%
question
The Manhawkin Fund has an expected return of 16% and a standard deviation of 20%. The risk-free rate is 4%. What is the reward-to-volatility ratio for the Manhawkin Fund?
answer
.6
question
Your timing was good last year. You invested more in your portfolio right before prices went up, and you sold right before prices went down. In calculating historical performance measures, which one of the following will be the largest?
answer
Dollar weighted return
question
Your investment has a 40% chance of earning a 15% rate of return, a 50% chance of earning a 10% rate of return, and a 10% chance of losing 3%. What is the standard deviation of this investment?
answer
E(rp)= (.4)(.15)+(.5)(.10)+(.10)(-.03)= 10.7% ?P= .4(.15-.107)^2 + .5(10-.107)^ 2 +.10(-.03-.107)^2 ?P= 5.14%
question
An investor invests 70% of her wealth 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 __________ respectively.
answer
12%; 15.7%
question
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. __________ of your complete portfolio should be invested in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.
answer
?C = y × ?p 9% = y × 20% y = 9/20 = 45%
question
You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% 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 10%. If you decide to hold 25% of your complete portfolio in the risky portfolio and 75% in the Treasury bills, then the dollar values of your positions in X and Y, respectively, would be
answer
.25 x 1000 = 250 250 x .6 = 150 250 x .4 = 100
question
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 ratio for the equity fund? (Round your answer to 2 decimal places.)
answer
10/14 = .71
question
Your investment has a 20% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return, and a 30% chance of losing 6%. What is your expected return on this investment?
answer
9.2%
question
You have an EAR of 9%. The equivalent APR with continuous compounding is
answer
1+.09 (LN) = 8.62%
question
You have the following rates of return for a risky portfolio for several recent years: If you invested $1,000 at the beginning of 2008, your investment at the end of 2011 would be worth
answer
$1,000(1.3523)(1.1867)(1 + -.0987)(1.2345) = $1,785.56
question
Rank the following from highest average historical return to lowest average historical return from 1926 to 2010. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills
answer
C. I, III, II, IV
question
Both investors and gamblers take on risk. The difference between an investor and a gambler is that an investor
answer
requires a risk premium to take on the risk
question
What do you think would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks? Assuming no change in tastes, that is, an unchanged risk aversion, investors perceiving higher risk will demand a higher risk premium to hold the same portfolio they held before. If we assume that the risk-free rate is unaffected, the increase in the risk premium would require a expected rate of return in the equity market.
answer
Higher
question
The holding-period return on a stock was 32%. Its beginning price was $25, and its cash dividend was $1.50. Its ending price must have been
answer
.32 x 25 - 1.5 = $31.50
question
You have an APR of 7.5% with continuous compounding. The EAR is
answer
EAR = (e^(.075)) - 1 = 7.79%
question
Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in six months. What is the effective annual rate of return for this investment?
answer
13.17%
question
If the nominal rate of return on investment is 6% and inflation is 2% over a holding period, what is the real rate of return on this investment?
answer
r=R-i 1+i = .06-.02 1+.02 = .04 1.02 =3.922%
question
A loan for a new car costs the borrower .8% per month. What is the EAR?
answer
0.8*12=9.6% 2nd 2 NOM=9.6 I/Y=12 EFF=10.03387
question
The holding period return on a stock is equal to
answer
Capital Gain Yield over the period plus the dividend yield
question
The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year?
answer
Nominal return on stock: (50 + 3)/55 - 1 = ?3.64% Real return: (1 + R) = (1 + r)(1 + i) 1 + r = (1 - .0364)/(1.03) = .935 R = .935 - 1 = -.0644
question
Historically, small-firm stocks have earned higher returns than large-firm stocks. When viewed in the context of an efficient market, this suggests that
answer
small firms are riskier than large firms
question
You purchased a share of stock for $29. One year later you received $2.25 as dividend and sold the share for $28. Your holding-period return was
answer
(28-29+2.25)/29 = 4.31%
question
The ______ measure of returns ignores compounding.
answer
Arithmetic Average
question
The formula is used to calculate the
answer
Sharpe measure
question
An investment earns 10% the first year, earns 15% the second year, and loses 12% the third year. The total compound return over the 3 years was
answer
11.32%
question
Security A has a higher standard deviation of returns than security B. We would expect that: I. Security A would have a higher risk premium than security B. II. The likely range of returns for security A in any given year would be higher than the likely range of returns for security B. III. The Sharpe ratio of A will be higher than the Sharpe ratio of B.
answer
I and II only
question
The dollar-weighted return is the
answer
Internal Rate of Return
question
You have $500,000 available to invest. The risk-free rate, as well as your borrowing rate, is 8%. The return on the risky portfolio is 16%. If you wish to earn a 22% return, you should
answer
If W is the portfolio weight on riskfree security, then E(rp) = 22% = W * 8% + (1-W) * 16% Î W = -75% A negative portfolio weight in riskfree security means you need to borrow for 500,000*W = - 375,000
question
What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?
answer
4.74%
question
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 expected return and standard deviation of return on your client's portfolio? (Do not round intermediate calculations. Round your answers to 1 decimal place.)
answer
10 + 6 = 16% 60000/100000 = 60% 40000/100000 = 40% .4 x 6% + .6 x 16% = 12% Expected Rate of Return .6 x 14% = 8.4% Standard Deviation
question
The return on the risky portfolio is 15%. The risk-free rate, as well as the investor's borrowing rate, is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, the expected return on the complete portfolio is
answer
If W is the portfolio weight on the risky portfolio, then Std Dev of complete portfolio = W*20% = 25% Î W = 125% E(rc) = (1-W) * 10% + W * 15% = 16.25%
question
What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?
answer
8.47%
question
Which one of the following measures time-weighted returns and allows for compounding?
answer
Geometric average return
question
You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. A portfolio that has an expected value in 1 year of $1,100 could be formed if you
answer
$1,100 = y × (1,000)(1.16) + (1 - y)1,000(1.06), so y =.4 place 40% of your money in the risky portfolio and the rest in the risk-free asset
question
Consider the following two investment alternatives: First, a risky portfolio that pays a 20% rate of return with a probability of 60% or a 5% rate of return with a probability of 40%. Second, a Treasury bill that pays 6%. If you invest $50,000 in the risky portfolio, your expected profit would be
answer
E(rp) = 0.6*20% + 0.4*5% = 14%. Expected Profit = 50,000 * 14% = 7,000
question
You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 15% and a standard deviation of 21% and a Treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 11%?
answer
15y + 5(1 - y) = 11; y = 60%; .60(10,000) = $6,000
