Investments Problem Set 1-3
You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills? $240; $360 $360; $240 $100; $240 $240; $160 Cannot be determined.
$240; $160 $400(0.6) = $240 in X; $400(0.4) = $160 in Y.
An investor invests 60% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 40% in a T-bill that pays 5%. His portfolio's expected return and standard deviation are __________ and __________, respectively. 0.110; 0.12 0.087; 0.06 0.295; 0.12 0.087; 0.12
0.110; 0.12 E(rP) = 0.6(15%) + 0.4(5%) = 11.0%; sP = 0.6(0.04)1/2 = 12%.
If a portfolio had a return of 8%, the risk-free asset return was 3%, and the standard deviation of the portfolio's excess returns was 20%, the Sharpe measure would be 0.08. 0.03. 0.20. 0.11. 0.25.
0.25 (8 − 3)/20 = 0.25
Over the past year, you earned a nominal rate of interest of 3.6% on your money. The inflation rate was 3.1% over the same period. The exact actual growth rate of your purchasing power was 3.6%. 3.1%. 0.48%. 6.7%.
0.48% r = (1 + R)/(1 + I) − 1; 1.036/1.031 − 1 = 0.484%.
You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 -5% What is the expected holding-period return for KMP stock? 10.40% 9.32% 11.63% 11.54% 10.88%
10.40% HPR = 0.30 (18%) + 0.50 (12%) + 0.20 (−5%) = 10.4%.
If a portfolio had a return of 18%, the risk-free asset return was 5%, and the standard deviation of the portfolio's excess returns was 34%, the risk premium would be 13%. 18%. 49%. 12%. 29%.
13% 18%- 5% = 13%
You purchased a share of stock for $68. One year later, you received $5.00 as a dividend and sold the share for $74.50. What was your holding-period return? 12.5% 16.9% 13.6% 11.8%
16.9% ($5.00 + $74.50 − $68.00)/$68.00 = 0.1691, or 16.91%.
Coca Cola stock has the following probability distribution of expected prices one year from now: State Probability Price 1 25% $50 2 40% $60 3 35% $70 If you buy Coca Cola today for $55 and it will pay a dividend during the year of $4 per share, what is your expected holding-period return on Coca Cola? 17.72% 18.89% 17.91% 18.18%
18.18% E(P1) = 0.25 (54/55 − 1) + 0.40 (64/55 − 1) + 0.35 (74/55 − 1) = 18.18%.
Consider the following probability distribution for stocks A and B: The variances of stocks A and B are _____ and _____, respectively.
2.2%; 1.2%
An investor purchased a bond 63 days ago for $980. He received $17 in interest and sold the bond for $987. What is the holding-period return on his investment? 1.52% 2.45% 1.92% 2.68%
2.45% HPR = ($17 + $987 − $980)/$980 = 0.0244898 = approximately 2.45%.
In order for you to be indifferent between the after-tax returns on a corporate bond paying 8.5% and a tax-exempt municipal bond paying 6.12%, what would your tax bracket need to be? 33% 72% 15% 28% Cannot be determined from the information given.
28% 0.0612 = 0.085(1 − t) (1 − t) = 0.72 t = 0.28.
Your portfolio returns over three consecutive periods were 10%, 20%, and 5%. What was the overall three month return on your portfolio? 35% 38.6% 1000% 11.67%
38.6% (1+0.1)*(1+0.2)*(1+0.05) - 1 = 0.386
Use the below information to answer the following question. Expected Return E(r)Standard Deviation 1 - 0.12 - 0.13 2 - 0.15 - 0.15 3 - 0.21 - 0.16 4 - 0.24 - 0.21 Which investment would you select if you were risk neutral? 1 2 3 4 Cannot be determined from the information given
4 If you are risk neutral, your only concern is with return, not risk.
Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets. Standard Deviation of P 7.20% Proportion of Complete Portfolio in P 80% Proportion of Complete Portfolio in T-Bills 20% What is the standard deviation of Bo's complete portfolio?
5.76% Std. Dev. of C = 0.8 × 7.20% = 5.76%.
You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.06? 30% and 70% 50% and 50% 60% and 40% 40% and 60% Cannot be determined.
60% and 40% 0.06 = x(0.15) x = 40% in risky asset.
A year ago, you invested $1,000 in a savings account that pays an annual interest rate of 9%. What is your approximate annual real rate of return if the rate of inflation was 2% over the year? 5% 10% 7% 3%
7% 9% - 2% = 7%
You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 -5% What is the volatility for KMP stock returns? 66% 17.1% 8.1% 6.6%
8.1% The variance is 66.04. The volatility is the square root of that.
You have been given this probability distribution for the holding-period return for KMP stock: Stock of the Economy Probability HPR Boom 0.30 18% Normal growth 0.50 12% Recession 0.20 -5% What is the expected standard deviation for KMP stock? 6.91% 8.13% 7.79% 7.25% 8.85%
8.13% s = [0.30 (18 − 10.4)^2 + 0.50 (12 − 10.4)^2 + 0.20 (−5 − 10.4)2 = (66.09)^1/2 = 8.13%.
Which of the following statements is true regarding a corporate bond? A corporate callable bond gives the holder the right to exchange it for a specified number of the company's common shares. A corporate debenture is a secured bond. A corporate indenture is a secured bond. A corporate convertible bond gives the holder the right to exchange the bond for a specified number of the company's common shares. Holders of corporate bonds have voting rights in the company.
A corporate convertible bond gives the holder the right to exchange the bond for a specified number of the company's common shares.
Money market securities are short term are highly marketable are generally very low risk are highly marketable and generally very low risk All of the options
All of the options
_______ are examples of financial intermediaries. Commercial banks Insurance companies Investment companies Credit unions All of the options
All of the options All are institutions that bring borrowers and lenders together.
Investment bankers perform which of the following role(s)? Market new stock and bond issues for firms Provide advice to the firms as to market conditions, price, etc. Design securities with desirable properties All of the options None of the options
All of the options Investment bankers perform all of the roles described above for their clients.
Financial intermediaries exist because small investors cannot efficiently diversify their portfolios. assess credit risk of borrowers. advertise for needed investments. diversify their portfolios and assess credit risk of borrowers. All of the options
All of the options The individual investor cannot efficiently and effectively perform any of the tasks above without more time and knowledge than that available to most individual investors.
A portfolio generates a Sharpe ratio of 0.83. Which of the following benchmark Sharpe ratios show the portfolio outperformed? 0.81 0.79 0.65 0.62 All of them
All of them A higher Sharpe ratio indicates over performance.
Which of the following securities is a money market instrument? Treasury note Treasury bond Municipal bond Commercial paper Mortgage security
Commercial Paper Only commercial paper is a money market security. The others are capital market instruments.
________ are, in essence, an insurance contract against the default of one or more borrowers. Credit default swaps CMOs ETFs Collateralized debt obligations All of the options
Credit default swaps Credit default swaps are in essence an insurance contract against the default of one or more borrowers.
Consider a risky portfolio, X, with an expected rate of return of 0.15 and a standard deviation of 0.15, that lies on a given indifference curve. Which one of the following portfolios might lie on the same indifference curve for a risk averse investor? E(r) = 0.15; Standard deviation = 0.20 E(r) = 0.15; Standard deviation = 0.10 E(r) = 0.10; Standard deviation = 0.10 E(r) = 0.20; Standard deviation = 0.15 E(r) = 0.10; Standard deviation = 0.20
E(r) = 0.10; Standard deviation = 0.10 Portfolio X has a reward to risk ratio of 1.0; portfolio C is the only choice with the same risk-return trade-off.
All financial assets are issued in a primary market and publicly traded in a secondary market. True False
False Not all financial assets are issued in primary markets (derivatives are not) and not all are able tradable in public markets.
Steve is more risk-averse than Edie. On a graph that shows Steve and Edie's indifference curves, which of the following is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis. I) Steve and Edie's indifference curves might intersect. II) Steve's indifference curves will have flatter slopes than Edie's. III) Steve's indifference curves will have steeper slopes than Edie's. IV) Steve and Edie's indifference curves will not intersect. V) Steve's indifference curves will be downward sloping, and Edie's will be upward sloping. I and V I and III III and IV I and II II and IV
I and III
Which of the following statement(s) is(are) true regarding the variance of a portfolio of two risky securities? I) The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance. II) There is a linear relationship between the securities' coefficient of correlation and the portfolio variance. III) The degree to which the portfolio variance is reduced depends on the degree of correlation between securities. I only II only III only I and II I and III
III only The lower the correlation between the returns of the securities, the more portfolio risk is reduced.
You purchased a share of stock for $120. One year later, you received $1.82 as a dividend and sold the share for $136. What was your holding-period return? 15.67% 22.12% 18.85% 13.24% None of the options are correct.
None of the options are correct ($1.82 + $136 − $120)/$120 = 0.1485, or 14.85%.
Which of the following is not a component of the money market? Repurchase agreements Eurodollars Real estate investment trusts Money market mutual funds Commercial paper
Real estate investment trusts Real estate investment trusts are not short-term investments.
The best measure of a portfolio's risk adjusted performance is the _________. return standard deviation Sharpe measure All of them
Sharpe measure The Sharpe ratio is the only measurement that factors in risk adjusted returns.
Which of the following is true regarding private placements of primary security offerings? Extensive and costly registration statements are required by the SEC. For very large issues, they are better suited than public offerings. They trade in secondary markets. The shares are sold directly to a small group of institutional or wealthy investors. They have greater liquidity than public offerings.
The shares are sold directly to a small group of institutional or wealthy investors. Firms can save on registration costs, but the result is that the securities cannot trade in the secondary markets and therefore are less liquid. Public offerings are better suited for very large issues.
The largest component of the fixed-income market is _______ debt. Treasury asset-backed corporate tax-exempt mortgage-backed
Treasury According to Figure 2.9 Treasury debt is the largest component of the fixed-income market.
The process of marketing a public offering is usually referred to as ____________. Underwriting Investment banking Brokerage Discounting IPO
Underwriting
Which of the following measures of risk best highlights the potential loss from extreme negative returns? Standard deviation Variance Upper partial standard deviation Value at risk (VaR) None of the options are correct.
Value at risk (VaR)
An example of a derivative security is a common share of Microsoft. a call option on Intel stock. a commodity futures contract. a call option on Intel stock and a commodity futures contract. a common share of Microsoft and a call option on Intel stock.
a call option on Intel stock and a commodity futures contract. The values of a call option on Intel stock and a commodity futures contract are derived from that of an underlying asset; the value of a common share of Microsoft is based on the value of the firm only.
An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the capital allocation line must lend some of her money at the risk-free rate. borrow some money at the risk-free rate. invest only in risky securities. borrow some money at the risk-free rate, invest in the optimal risky portfolio, and invest only in risky securities Such a portfolio cannot be formed.
borrow some money at the risk-free rate, invest in the optimal risky portfolio, and invest only in risky securities The only way that an investor can create a portfolio that lies to the right of the capital allocation line is to create a borrowing portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free security, but will hold only risky securities.
A call option allows the buyer to sell the underlying asset at the exercise price on or before the expiration date. buy the underlying asset at the exercise price on or before the expiration date. sell the option in the open market prior to expiration. sell the underlying asset at the exercise price on or before the expiration date and sell the option in the open market prior to expiration. buy the underlying asset at the exercise price on or before the expiration date and sell the option in the open market prior to expiration.
buy the underlying asset at the exercise price on or before the expiration date.
The risk premium for common stocks is negative, as common stocks are risky. cannot be zero, for investors would be unwilling to invest in common stocks and must always be positive, in theory. cannot be zero, for investors would be unwilling to invest in common stocks and is negative, as common stocks are risky. is undefined
cannot be zero, for investors would be unwilling to invest in common stocks and must always be positive, in theory. If the risk premium for common stocks were zero or negative, investors would be unwilling to accept the lower returns for the increased risk.
Financial assets permit all of the following except consumption timing. allocation of risk. separation of ownership and control. elimination of risk.
elimination of risk Financial assets do not allow risk to be eliminated. However, they do permit allocation of risk, consumption timing, and separation of ownership and control.
If a distribution has "fat tails," it exhibits positive skewness. negative skewness. a kurtosis of zero. excess kurtosis. None of the options are correct.
excess kurtosis.
The means by which individuals hold their claims on real assets in a well-developed economy are investment assets. depository assets. derivative assets. financial assets. exchange-driven assets.
financial assets Financial assets allocate the wealth of the economy. Example: it is easier for an individual to own shares of an auto company than to own an auto company directly.
Kurtosis is a measure of how fat the tails of a distribution are. the downside risk of a distribution. the normality of a distribution. the dividend yield of the distribution.
how fat the tails of a distribution are.
Firms raise capital by issuing stock in the secondary market. in the primary market. to unwary investors. only on days when the market is up.
in the primary market Funds from the sale of new issues flow to the issuing corporation, making this a primary market transaction.
The capital allocation line can be described as the investment opportunity set formed with a risky asset and a risk-free asset. investment opportunity set formed with two risky assets. line on which lie all portfolios that offer the same utility to a particular investor. line on which lie all portfolios with the same expected rate of return and different standard deviations.
investment opportunity set formed with a risky asset and a risk-free asset. The CAL has an intercept equal to the risk-free rate. It is a straight line through the point representing the risk-free asset and the risky portfolio, in expected-return/standard deviation space.
The variance of a portfolio of risky securities is a weighted sum of the securities' variances. is the sum of the securities' variances. is the weighted sum of the securities' variances and covariances. is the sum of the securities' covariances. None of the options are correct.
is the weighted sum of the securities' variances and covariances. The variance of a portfolio of risky securities is a weighted sum taking into account both the variance of the individual securities and the covariances between securities.
New issues of securities are sold in the ________ market(s). primary secondary over-the-counter primary and secondary
primary New issues of securities are sold in the primary market.
Which combination of returns and standard deviation provides the highest Sharpe ratio? Assume a 3% risk-free rate. return = 12%, standard deviation = 20% return = 15%, standard deviation = 22% return = 21%, standard deviation = 25% return = 25%, standard deviation = 35%
return = 21%, standard deviation = 25% Sharpe ratio = (0.21 − 0.03 ) / 0.25 = 0.72
Investors trade previously issued securities in the ________ market(s). primary secondary primary and secondary derivatives
secondary Investors trade previously issued securities in the secondary market.
A put option allows the holder to buy the underlying asset at the strike price on or before the expiration date. sell the underlying asset at the strike price on or before the expiration date. sell the option in the open market prior to expiration. sell the underlying asset at the strike price on or before the expiration date and sell the option in the open market prior to expiration. buy the underlying asset at the strike price on or before the expiration date and sell the option in the open market prior to expiration.
sell the underlying asset at the strike price on or before the expiration date.
When a distribution is negatively skewed, standard deviation overestimates risk. standard deviation correctly estimates risk. standard deviation underestimates risk. the tails are fatter than in a normal distribution
standard deviation underestimates risk.
Historical records regarding return on stocks, Treasury bonds, and Treasury bills between 1926 and 2018 show that stocks offered investors greater rates of return than bonds and bills. stock returns were less volatile than those of bonds and bills. bonds offered investors greater rates of return than stocks and bills. bills outperformed stocks and bonds. Treasury bills always offered a rate of return greater than inflation.
stocks offered investors greater rates of return than bonds and bills. The historical data show that, as expected, stocks offer a greater return and greater volatility than the other investment alternatives. Inflation sometimes exceeded the T-bill return.
T-bills are financial instruments initially sold by ________ to raise funds. commercial banks the U.S. government state and local governments agencies of the federal government the U.S. government and agencies of the federal government
the U.S. government Only the U.S. government sells T-bills in the primary market.
The holding-period return (HPR) on a share of stock is equal to the capital gain yield during the period plus the inflation rate. the capital gain yield during the period plus the dividend yield. the current yield plus the dividend yield. the dividend yield plus the risk premium. the change in stock price.
the capital gain yield during the period plus the dividend yield.
The capital allocation line provided by a risk-free security and N risky securities is the line that connects the risk-free rate and the global minimum-variance portfolio of the risky securities. the line that connects the risk-free rate and the portfolio of the risky securities that has the highest expected return on the efficient frontier. the line tangent to the efficient frontier of risky securities drawn from the risk-free rate. the horizontal line drawn from the risk-free rate.
the line tangent to the efficient frontier of risky securities drawn from the risk-free rate. The capital allocation line represents the most efficient combinations of the risk-free asset and risky securities.
In the event of the firm's bankruptcy, the most shareholders can lose is their original investment in the firm's stock. common shareholders are the first in line to receive their claims on the firm's assets. bondholders have claim to what is left from the liquidation of the firm's assets after paying the shareholders. the claims of preferred shareholders are honored before those of the common shareholders. the most shareholders can lose is their original investment in the firm's stock and the claims of preferred shareholders are honored before those of the common shareholders.
the most shareholders can lose is their original investment in the firm's stock and the claims of preferred shareholders are honored before those of the common shareholders. Shareholders have limited liability and have residual claims on assets. Bondholders have a priority claim on assets, and preferred shareholders have priority over common shareholders.
The bid price of a T-bill in the secondary market is the price at which the dealer in T-bills is willing to sell the bill. the price at which the dealer in T-bills is willing to buy the bill. greater than the asked price of the T-bill. the price at which the investor can buy the T-bill. never quoted in the financial press.
the price at which the dealer in T-bills is willing to buy the bill. T-bills are sold in the secondary market via dealers; the bid price quoted in the financial press is the price at which the dealer is willing to buy the bill.
Skewness is a measure of how fat the tails of a distribution are. the downside risk of a distribution. the symmetry of a distribution. the dividend yield of the distribution. None of the options are correct.
the symmetry of a distribution. Skewness is a measure of the normality of a distribution