fina 4320 chapter 5

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%

What is the geometric average return of the following quarterly returns: 3%, 5%, 4%, and 7%?

4.74%

A security with normally distributed returns has an annual expected return of 18% and standard deviation of 23%. The probability of getting a return between -28% and 64% in any one year is ________.

95.44%

Rank the following from highest average historical return to lowest average historical return from 1926 to 2017. I. Small stocks II. Long-term bonds III. Large stocks IV. T-bills

I, III, II, IV

In the mean standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called the ________.

capital allocation line

According to historical data, over the long run which of the following assets has the best chance to provide the best after-inflation, after-tax rate of return?

common stocks

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%

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

The geometric average of -12%, 20%, and 25% is ________.

9.7%

You have the following rates of return for a risky portfolio for several recent years: 2013 35.23% 2014 18.67% 2015 −9.87% 2016 23.45% If you invested $1,000 at the beginning of 2013, your investment at the end of 2016 would be worth ________.

$1,785.56

What is the VaR of a $10 million portfolio with normally distributed returns at the 5% VaR? Assume the expected return is 13% and the standard deviation is 20%.

-19.90%

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

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%. The dollar values of your positions in X, Y, and Treasury bills would be ________, ________, and ________, respectively, if you decide to hold a complete portfolio that has an expected return of 8%.

$243; $162; $595

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 ________.

$31.50

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

Your great aunt Zella invested $100 in 1925 in a portfolio of large U.S. stocks that earned a compound return of 10% annually.If she left that money to you, how much would be in the account 92 years later in 2017?

$642,875.74

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 after one year would be ________.

$7,000

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%

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

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%. The slope of the capital allocation line formed with the risky asset and the risk-free asset is approximately ________.

.5

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?

.60

A loan for a new car costs the borrower .8% per month. What is the EAR?

10.03%

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 ________.

11%

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%

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%

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%

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%

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%

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%

You have the following rates of return for a risky portfolio for several recent years: 2013 35.23% 2014 18.67% 2015 −9.87% 2016 23.45% The annualized (geometric) average return on this investment is ________.

15.60%

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%

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%

Treasury bills are paying a 4% rate of return. A risk-averse investor with a risk aversion of A = 3 should invest entirely in a risky portfolio with a standard deviation of 24% only if the risky portfolio's expected return is at least ________.

21.28%

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%

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%

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 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.

40%; 24%; 16%

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%

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%

If you believe you have a 60% chance of doubling your money, a 30% chance of gaining 15%, and a 10% chance of losing your entire investment, what is your expected return?

54.5%

The buyer of a new home is quoted a mortgage rate of .5% per month. What is the APR on the loan?

6%

You have an APR of 7.5% with continuous compounding. The EAR is ________.

7.79 %

The arithmetic average of -11%, 15%, and 20% is ________.

8%

What is the geometric average return over 1 year if the quarterly returns are 8%, 9%, 5%, and 12%?

8.47%

You have an EAR of 9%. The equivalent APR with continuous compounding is ________.

8.62%

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%

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%

The CAL provided by combinations of 1-month T-bills and a broad index of common stocks is called the ________.

CML

In calculating the variance of a portfolio's returns, squaring the deviations from the mean results in: I. Preventing the sum of the deviations from always equaling zero II. Exaggerating the effects of large positive and negative deviations III. A number for which the unit is percentage of returns

I and II only

The rate of return on ________ is known at the beginning of the holding period, while the rate of return on ________ is not known until the end of the holding period.

Treasury bills; risky assets

Which one of the following would be considered a risk-free asset in real terms as opposed to nominal?

U.S. T-bill whose return was indexed to inflation

Annual percentage rates can be converted to effective annual rates by means of the following formula:

[1 + (APR/n)]n - 1

The ________ measure of returns ignores compounding.

arithmetic average

You have calculated the historical dollar-weighted return, annual geometric average return, and annual arithmetic average return. If you desire to forecast performance for next year, the best forecast will be given by the ________.

arithmetic average return

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

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

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

You have calculated the historical dollar-weighted return, annual geometric average return, and annual arithmetic average return. You always reinvest your dividends and interest earned on the portfolio. Which method provides the best measure of the actual average historical performance of the investments you have chosen?

geometric average return

Published data on past returns earned by mutual funds are required to be ________.

geometric returns

Historical returns have generally been ________ for stocks of small firms as (than) for stocks of large firms.

higher

Which of the following arguments supporting passive investment strategies is (are) correct? I. Active trading strategies may not guarantee higher returns but guarantee higher costs. II. Passive investors can free-ride on the activity of knowledge investors whose trades force prices to reflect currently available information. III. Passive investors are guaranteed to earn higher rates of return than active investors over sufficiently long time horizons.

i and ii only

You invest all of your money in 1-year T-bills. Which of the following statements is (are) correct? I. Your nominal return on the T-bills is riskless. II. Your real return on the T-bills is riskless. III. Your nominal Sharpe ratio is zero.

i and ii only

Security A has a higher standard deviation of returns than security B. We would expect that: I. Security A would have a risk premium equal to 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.

ii only

The dollar-weighted return is the ________.

internal rate of return

From 1926 to 2013 the world stock portfolio offered ________ return and ________ volatility than the portfolio of large U.S. stocks.

lower, lower

The normal distribution is completely described by its ________.

mean and standard deviation

Two assets have the following expected returns and standard deviations when the risk-free rate is 5%: Asset A E(rA) = 10% σA = 20% Asset B E(rB) = 15% σB = 27% An investor with a risk aversion of A = 3 would find that ________ on a risk-return basis.

neither

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

The excess return is the ________.

rate of return in excess of the Treasury-bill rate

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

Consider a Treasury bill with a rate of return of 5% and the following risky securities: Security A: E(r) = .15; variance = .0400 Security B: E(r) = .10; variance = .0225 Security C: E(r) = .12; variance = .1000 Security D: E(r) = .13; variance = .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 should choose as part of her complete portfolio to achieve the best CAL would be ________.

security a

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

Historically, the best asset for the long-term investor wanting to fend off the threats of inflation and taxes while making his money grow has been ________.

stocks

The holding period return on a stock is equal to ________.

the capital gain yield over the period plus the dividend yield

The market risk premium is defined as ________.

the difference between the return on an index fund and the return on Treasury bills

The complete portfolio refers to the investment in ________.

the risk-free asset and the risky portfolio combined

The reward-to-volatility ratio is given by ________.

the slope of the capital allocation line

Which measure of downside risk predicts the worst loss that will be suffered with a given probability?

value at risk