Investment Fundamentals Exam 2
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 _________.
$2 .25 = (18-16+x)/16 x = $2
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 _________.
$7,000 E(r) = (.6*.20) + (.4*.05) = 14% Ending value: $50,000*1.14 = $57,000 profit: $57,000 - $50,000 = $7,000
Holding Period Return (HPR)
(End price - Beg Price + Div) / Beg Price
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 _________.
.32 = (x - 25 + 1.50) / 25 x= $31.50
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 ____.
.42 (15-4.5)/25
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?
.6 (16-4)/20 = .6
A loan for a new car costs the borrower .8% per month. What is the EAR?
10.03%
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?
11.24%
Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in 6 months. What is the effective annual rate of return for this investment?
13.17 % [10,000-9,400]^(12/6) - 1 = .1317 ~ 13.17%
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.
19% .11 = Wf(.05) + (1-Wf)[(.6)(.14) + (.4)(.10)] Wf= .19
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 ____.
4% + $3.50 / $50 = 11%
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 _________.
4.31% 28 + 2.25 - 29 / 29 = 4.31%
What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?
4.74%
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?
5.14% E(rp)=(.4)(.15)+(.5)(.10)+(.10)(-.03) = 10.7% std dev=.4(.15-.107)^2+.5(.10-.107)^2+.10(-.03-.107)^2 = 5.14%
You have an APR of 7.5% with continuous compounding. The EAR is _____.
7.79% EAR = e^.075 - 1 = 7.79%
The geometric average of -12%, 20%, and 25% is _________.
9.7%
The ______ measure of returns ignores compounding.
Arithmetic average
E(HPR): boom or normal or recession, all equally likely
Boom: (End price - Beg Price + Div) / Beg Price Normal: (End price - Beg Price + Div) / Beg Price Recession: (End price - Beg Price + Div) / Beg Price E(HPR) = [(1/3 * boom HPR) + [(1/3 * normal HPR) + [(1/3 * recession HPR)]
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?
Dollar weighted return
Which one of the following measures time-weighted returns and allows for compounding?
Geometric average return
Historical returns have generally been __________ for stocks of small firms as (than) for stocks of large firms.
Higher
at 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.
Higher
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
I, III, II, IV
The dollar-weighted return is the _________.
Internal rate or return (IRR)
The excess return is the _________.
Rate of return in excess of the Treasury bill rate
The market risk premium is defined as __________.
The difference between the return on an index fund and the return on Treasury bills
Geometric average (time-weighted average return)
The single per-period return that gives the same cumulative performance as the sequence of actual returns.
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 __________.
dollar weighted return
Both investors and gamblers take on risk. The difference between an investor and a gambler is that an investor _______.
requires a risk premium to take on the risk
The holding period return on a stock is equal to _________.
the capital gain yield over the period plus the dividend yield
The complete portfolio refers to the investment in _________.
the risk-free asset and the risky portfolio combined
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?
8.74% Real rate = (1.12/1.03) - 1
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?
9.2% E(r) = (.2)(30%) + (.5)(10%) + (.3)(-6%) = 9.2%
You have the following rates of return for a risky portfolio for several recent years: 2008: 35.23% 2009: 18.67% 2010: -9.87% 2011: 23.45% If you invested $1,000 at the beginning of 2008, your investment at the end of 2011 would be worth ___________.
$1785.56 1000(1.3523)(1.1867)(1-.0987)(1.2345)=1785.56
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?
3.09%
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?
3.92% (1+n) = (1+r)(1+π)
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 __________ and _________.
$150; $100 X = 1000(.25)(.6) = $150 Y = 1000(.25)(.4) = $100
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?
-6.44 HPR = (50-55+3)/55 => -3.64% - must account for π of 3% Fisher equation: (1-.0364) = (1+r)(1+.03) r = -6.44%
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 ______.
11.32%
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?
12.24% [(10,000-9.800)/9,800] * (12/2) = 12.24%
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 _________.
16.25%
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 _________.
3%
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%.
45% 9% = y * 20% y = 45%
The arithmetic average of -11%, 15%, and 20% is ________.
8 (-11 + 15 + 20) / 3 = 8
Dollar weighted average
The internal rate of return (IRR) on an investment. The IRR is the interest rate that sets the present value of the cash flows realized on the portfolio equal to the initial cost of establishing the portfolio
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 _________.
borrow $375,000 y*.16+(1-y)*.08 = .22 .16y-.08y+.08 = .22 .08y = .14 y = 1.75 1.75*500,000 = 875,000 --> invest 875,000 in risky asset by borrowing $375,000
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%?
$6,000 15y + 5(1-y) = 11 y=60% $10,000(.60) = $6,000
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?
0.71 reward to volatility ratio= Portfolio risk premium - std dev of portfolio excess return = 10%/14% = 0.71
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.
12% ; 15.7% E(r) = .7(.15) + .3(.05) = .12 std dev = .7(.05)^1/2 = 15.7%
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?
14.47%
The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?
6.17% which is roughly 6%
What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?
8.47% Return = (1.05 × 1.08 × 1.09 × 1.12).25 - 1 = .0847
You have an EAR of 9%. The equivalent APR with continuous compounding is _____.
8.62% continuous compounding = 1 + EAR = e^APR 1 + .09 = e^APR ln(1.09) = APR .08617 = APR
Capital Market Line
The capital allocation line provided by one month T-bills and a broad index of common stocks. A passive strategy using the broad stock market index as the risky portfolio generates an investment opportunity set that is represented by the CML
Effective Annual Return
The rate at which your invested funds actually grow. Takes into account compounding
Arithmetic average
The sum of the returns in each period divided by the number of periods.
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 _________.
place 40% of your money in the risky portfolio and the rest in the risk-free asset $1,100 = y × (1,000)(1.16) + (1 - y)1,000(1.06), so y =.4
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.
I and II only
Historically, small-firm stocks have earned higher returns than large-firm stocks. When viewed in the context of an efficient market, this suggests that ___________.
small firms are riskier than large firms