FNCE 3030 Midterm 1
(M1 Short Answer) You learned that the standard deviation of any portfolio, regardless of the number of holdings, can be calculated using matrix math. In your own words, describe the construction of a 3x3 variance-covariance matrix. Also, state how many terms will there be in the equation?
A 3-by-3 matrix will result in nine terms (3 x 3). Each asset in the portfolio is compared to itself and every other asset. The relevant data include the weighting of each asset and the standard deviation of each asset. When you compare asset A to itself, the result is the squared weight of A times the variance of A. When you compare asset A to asset B, the result is the weight of A times the weight of B times the covariance between the two assets. That process is applied to all of the assets, resulting in a variance-covariance matrix. The standard deviation of the 3x3 would be equal to the square root of the product of the nine terms.
(M1 Short Answer) What is the covariance between securities A and B given the following information? Stock A - Expected Return 12.5%, Variance .050176, Standard Deviation 22.4%, Beta 1.25 Stock B - Expected Return 17.10%, Variance .104976, Standard Deviation 32.4%, Beta 1.9 Correlation coefficient between Stocks A and B 0.65
Answer: 0.047174 Refer to the formula sheet The formula for covariance is: COV = correlation coefficient x standard dev x standard deviation. Inputting the data: covariance = 0.65 x .224 x .324 = 0.047174
(M1 Short Answer) Part 1 - What is the beta of Asset T given the following data? - Variance of Asset T = 5.9049% - Standard deviation of market = 18.2000% - Correlation coefficient = .86 Part 2 - Given that the market increases by 20%, then what is the expected price change of Asset T?
Answer: 1.1484 Refer to the formula page when calculating beta. The formula for Beta is: (correlation coefficient x standard deviation of the security) / (standard deviation of the market). The first step is to calculate the standard deviations of the security. Std dev Asset T = .059049^(1/2) = .2430 You are given that the correlation coefficient is .86. Inputting the data and solving you get: (.86 x .2430) / .1820 = .2090/ .1820 = 1.1484 The beta of Asset T is 1.1484 Part 2 - The market has a beta of 1. If the market experiences a 20% price increase, then Asset T (which has a beta of 1.1484) will increase by 1.1484 x 20% = 22.97%.
(M1 Short Answer) An investor places 70% of his wealth in a risky asset with an expected return of 10.2% and a standard deviation of 15.8%. The remainder of his wealth is invested in T-Bills yielding 1.5% with zero risk. His portfolio's expected return and standard deviation are ___ and ____, respectively. (In answering the question show your data inputs and calculate your answer.)
Answer: expected return of 7.59% and a standard deviation of 11.06% The expected return of the 2-asset portfolio is the weighted sum of the expected returns: .7 x 10.2 + .3 x 1.5 = 7.59% Refer to the formula page for standard deviation of a two-asset portfolio = SQRT ((Wa^2 x variance A) + Wb^2 x variance B) + (2 x Wa x Wb x covarianceAB)) The standard deviation of a 2-asset portfolio in which one of the assets is risk-free (i.e., zero standard deviation) is equal to the square root of the product of the squared weight of the risky asset times the variance of the risky asset. That is because the standard deviation of zero for the risk-free asset will cancel out the second and third terms in the formula. .7 squared = .49. The variance of the risky asset is .158 squared = .0250. .49 x .0250 = 0.012232 The square root of 0.12232 = 11.06%
(M1 Short Answer) Part 1 - What is the correlation coefficient between Security A and Security B, given the following information? - Security A - 8.6% expected return, 15.6% standard deviation - Security B - 12.5% expected return, 23.8% standard deviation - Covariance = .028217 Part 2 - Describe what that correlation coefficient means in respect to direction and magnitude of Security A's move compared to Security B.
Part 1 Answer: Covariance is equal to the correlation coefficient times the standard deviation of the first security (index) times the standard deviation of the second security (index). COV = ρ x σA x ρB Rearranging the terms, the correlation coefficient is equal to the covariance divided by the product of the two standard deviations .028217 / (.156 x .238) = .028217 / .037128 = .76 Part 2 Answer: Since the correlation is positive, Security A will move in the same direction as the Security B; however, since the correlation coefficient is .76 the magnitude will be less.
(M1) Your friend seeks a combination of low volatility and an inflation hedge. Which of the following would be the best recommendation? a. Purchase a U.S. Treasury Note and a TIPS b. Purchase a GIC and ADR c. Purchase a municipal bond and high-yield corporate bond d. Purchase an emerging markets bond fund and a callable bond
a. Purchase a U.S. Treasury Note and a TIPS *Purchase a U.S. Treasury Note and a TIPS The U.S. Treasury Note (1-10 years in duration) is a very high-quality security. The Treasury Inflation-adjusted Security provides adjustment to face value based on inflation. The adjustment protects purchasing power. The ADR represents ownership in a foreign stock, while the emerging markets bond fund is subject to market volatility.
(M1) An investor puts in the following order, "Sell 300 shares ABC at market." At what price would the trade occur, given the following Level 2 price quotes? Table: Bid Size Ask Size 52.45 1000 52.48 500 52.43 500 52.50 5000 52.41 600 52.52 6000 52.38 3600 53.00 10000 52.35 300 53.04 3000 a.$52.45 b. $52.465 c. $52.48 d. $52.41 e. $52.52
a.$52.45 *$52.45 An "at market" order would fill at the highest available ask price, which is $52.45
(M1) Which of the following statements regarding open-end mutual funds and ETFs is correct? a. Open-end mutual funds and ETFs always trade at their net asset value b. ETFs can be bought and sold intraday, while a purchases or sales of open-end mutual funds clear at the end of the day. c. ETFs often have higher expenses and loads, as compared to comparable mutual funds d. Mutual funds are very liquid while ETFs are not.
b. ETFs can be bought and sold intraday, while a purchases or sales of open-end mutual funds clear at the end of the day. *ETFs can be bought and sold intraday, while a purchases or sales of open-end mutual funds clear at the end of the day. Open-end mutual funds are sold at NAV; however, ETFs reflect market pricing (supply and demand), which means they are often bought or sold at or above NAV.ETFs typically have lower advisory fees than mutual funds, and they never have a sales load. Both mutual funds and ETFs are liquid.
(M1) Each of the following statements regarding modern portfolio theory is correct, except for one. Which statement is INCORRECT? a. The capital allocation line describes the relationship between the portfolio's expected return and total risk. b. The capital market line describes the relationship between the portfolio's expected return and systematic risk. c. The security market line provides the expected return of a portfolio as a function of beta, rather than total risk. d. The investor's optimal portfolio is represented by the point of tangency between the asset allocation line (i.e., risk-free and risky asset) and indifference curve.
b. The capital market line describes the relationship between the portfolio's expected return and systematic risk. *The capital market line describes the relationship between the portfolio's expected return and systematic risk. The capital market line is a straight line between the risk-free rate and the point of intersection on the efficient frontier; the slope of the line is defined as the market return premium divided by the standard deviation of the market (i.e., Sharpe Ratio), not beta. Each of the other statements is correct.
(M1) Which of the following statements is true given that the correlation coefficient between Security K and the S&P500 is .65? a. 65% of the price volatility of Security K is explained by the S&P500 index. b. approximately 42% of the price volatility of Security K is explained by the S&P500 index. c. approximately 58% of the priced volatility of Security K is explained by the S&P500 index. d. 35% of the priced volatility of Security K is explained by the S&P500 index.
b. approximately 42% of the price volatility of Security K is explained by the S&P500 index. *approximately 42% of the price volatility of Security K is explained by the S&P500 index. Given that the correlation coefficient between Security A and the S&P500 is .65 we know that 42% of the price volatility of Security A is explained by the index (.65 ^2 = .4225%). If 42% is explained by the index, then 58% is explained by other factors.
(M1) What measure of statistical distribution would capture the historical tendency for stock market returns to either be concentrated around the mean (peaked) or distributed into the tails (flatness of distribution) is _____. a. normal distribution b. kurtosis c. skewness d. variance
b. kurtosis *kurtosis Kurtosis describes the "flatness" of a distribution (outliers in the tail) or the tendency of distribution to be clustered around the mean ("peakedness"). Skewness describes the normality of the distribution (i.e., asymmetric deviation from the shape of the normal distribution), either distortion to the left or right. A normal distribution describes a symmetrical distribution around the mean. The width of that distribution is described by standard deviation.
(M1) The efficient frontier of risky assets consists of portfolios that a. offer the highest level of standard deviation for a given level of risk b. offer the highest level of return for a given level of risk c. have zero standard deviations d. have the lowest standard deviations
b. offer the highest level of return for a given level of risk *offer the highest level of return for a given level of risk The efficient frontier represents the minimum-variance frontier. It depicts those portfolios with the lowest possible variance for a given level of return. Modern portfolio theory suggests that given the expected returns, standard deviation and correlations for "N" assets, minimization techniques can be applied to identify those portfolios with the minimum variance at each level of expected return.
(M1) Based on the capital asset pricing model, what is the required return of an individual stock given the following information? - US T-Bill = 2.1% - Long-term corporate bond = 6.2% - Market premium = 8.6% - Beta = 1.3 - Standard deviation = 24.6% a. 8.45% b. 10.55% c. 13.28% d. 13.91%
c. 13.28% *13.28% The capital asset pricing model states that the required rate of return is equal to the risk-free rate plus additional return to compensate for holding higher levels of risk. The formula is: K = Rf + B (Rm - Rf), where, K (or R on the formula sheet) is the required rate of return, Rf is the risk-free rate (US T-Bill), B is beta of the individual security and Rm is the expected return of the market. (The market premium is the return of the market minus the risk-free rate (Rm-Rf).) In this problem you are given Rf = 2.1%, Beta = 1.3, and the market premium 8.6%. Inputting the data: K = 2.1% + (1.3 * 8.6%) = 13.28%
(M1) You learned that the market price of a security is based on risk and return. Which of the following statements is NOT consistent with the risk-return concept? a. U.S. Treasury Bills will have lower market yields than a corporate BBB-rated bond. b. A money market mutual fund will have a lower market yield than an investment grade corporate bond fund. c. A common stock will have a lower expected total return than a preferred stock. d. A cash equivalent asset will have a lower expected annual return compared to a capital asset.
c. A common stock will have a lower expected total return than a preferred stock. *A common stock will have a lower expected total return than a preferred stock. Each of the other alternatives is consistent with the concept that risky securities must compensate investors more in order to compensate risk-averse investors. Remember that money market securities have maturities of one year or less. Capital market securities have maturities greater than one year.
(M1) Which of the following statements INCORRECTLY describes an indifference curve? a. The lower an investors risk aversion, then the flatter the indifference curve. b. The higher an investor's risk aversion, then the steeper the indifference curve c. Each point along an indifference curve has a different risk-return (utility) profile d. An investor would be "indifferent" to any combination of allocation, as described by the particular curve
c. Each point along an indifference curve has a different risk-return (utility) profile *Each point along an indifference curve has a different risk-return (utility) profile That is the incorrect response because each investor's indifference curve depicts all combinations offering the same utility according to expected returns and standard deviations. The more risk averse an investor, the steeper the curve. That's because the investor would require greater increases in return for a corresponding increase in risk than for the risk-loving or risk-neutral investor. The less risk averse, the flatter the curve. Indifference curves represent the trade-off between two variables. In portfolio building, the choice is between risk and return. The investor is indifferent between all possible portfolios lying on one indifference curve. However, indifference curves are contour maps, with all curves parallel to each other. The curve plotting in the most northwest position is the curve offering the greatest utility to the investor. However, this most desirable curve may not be attainable in the market. The point of tangency between an indifference curve (representing what is desirable) and the capital allocation line (representing what is possible) is the optimum portfolio for that investor.
(M1) An investor received a cash windfall of $400,000. Her current $600,000 portfolio is currently yielding an average annual return of 7.6%. Given that her financial need is 8.4% annual return, then which of the following investments would be most appropriate for the $400,000 windfall? a. Investment A with an expected return of 8.4% b. Investment B with an expected return of 8.8% c. Investment C with an expected return of 9.6% d. Investment D with an expected return of 10.2%
c. Investment C with an expected return of 9.6% *Investment C with an expected return of 9.6% The expected return of a portfolio is equal to the weighted sum. The current portfolio represents 60% of the combined sum. (60% x 7.6) + (40% x ___ ) = 8.4% (40% x ___) = 8.4 - 4.56 = 3.84 ___ = (3.84 / .4) = 9.6% Checking calculations: (60% x 7.6%) + (40% x 9.6) = 4.56 + 3.84 = 8.4%
(M1) Which of the following statements is true regarding private and public security offerings? a. SEC registration is required for both private and public security offerings b. A retail investor with annual income of $100,000 is eligible to participate in private security offerings c. Private security offerings offer the benefits of lower transaction costs and quicker time to market as compared to a comparable public security offering. d. Private security offerings have greater liquidity as compared to public offerings.
c. Private security offerings offer the benefits of lower transaction costs and quicker time to market as compared to a comparable public security offering. *Private security offerings offer the benefits of lower transaction costs and quicker time to market as compared to a comparable public security offering. Private security offerings are targeted to a small group of accredited investors. Because they are exempt from registration, time to market is quicker and transactions costs (e.g., underwriting with a public offer) are lower. The SEC protects the public by making firms register securities they seek to offer to the general public (retail investors). SEC registration is required for public security offerings but not for public offerings Retail investors are not eligible to participate in private security offerings. Eligible parties include accredited investors ($200,000 single, $300,000 married, or greater than $1M of assets exclusive of primary residence), registered investment advisors, broker-dealer firm buying for own portfolio, advisor with $100M or more of assets under management. Public offerings are liquid, since they can be sold to other retail investors in the secondary market. Private offerings can only be sold to other qualified institutional buyers.
(M1) An inexperienced investor holds all of his investments in cash equivalent assets and bond mutual funds. Which of the following recommendations would be most appropriate, given that there is a need to both add growth but moderate overall volatility? a. Sell a corporate bond fund and purchase a U.S. Treasury money market portfolio b. Sell an intermediate bond fund and purchase a long-term bond fund c. Sell a long-term bond fund and purchase a large-cap equity fund d. Sell a money market fund and purchase a small-cap equity fund
c. Sell a long-term bond fund and purchase a large-cap equity fund *Sell a long-term bond fund and purchase a large-cap equity fund The large-cap equity fund provides growth, and the expected volatility is significantly less than the small-cap equity fund
(M1) Bonds are debt securities that are issued with maturities over a year in duration. Each of the following statements regarding these fixed income securities is correct, except for one. Which statement is INCORRECT? a. US Treasury notes have durations up to 10 years, while Treasury bonds have durations exceeding 10 years. b. The interest on a municipal bond is tax-exempt at the Federal level. c. TIPS distribute interest and adjustments to principal (linked to inflation) to investors on a semi-annual basis. d. When a coupon bond is sold in the secondary market between interest payments, then buyer pays the seller an amount equal to the market price of the bond plus accrued interest.
c. TIPS distribute interest and adjustments to principal (linked to inflation) to investors on a semi-annual basis. *TIPS distribute interest and adjustments to principal (linked to inflation) to investors on a semi-annual basis. Treasury inflation-protected securities pay interest on a semi-annual basis; however, principal adjustments are not paid out. Rather, the adjustment is not paid until maturity, although the TIPS interest rate applies to the adjusted principal amount. US Treasury notes are issued in durations from 1-10 years, while Treasury bonds are issued with durations of over 10 years. Interest on zero coupon bonds accrues on a semi-annual basis and is taxable, even though the income is not received until the bond matures. Interest on a municipal bond is tax-exempt at the Federal level. When the taxpayer is a resident of the state in which the bond is issued, then the interest will also be tax-exempt at the state level. When a coupon bond is sold in the secondary market, then buyer is required to pay the seller an amount equal to the market price of the bond plus accrued interest.
(M1) The market participant who is responsible for holding and safeguarding investor assets is the ____. a. transfer agent b. clearinghouse c. custodian d. underwriter
c. custodian *Custodian are organizations that are permitted to hold investor assets and responsible for safeguarding the assets. In some cases, the custodian may be the broker-dealer firm. The clearinghouse is an intermediary between the buyers and sellers. Their responsibility includes settling trading accounts, collecting and delivering securities and reporting trading data. The transfer agent is an entity responsible for maintaining ownership records and issuer records and issuing and cancelling certificates of ownership. An underwriter is an entity that builds a book of investors who will purchase shares in the public offering. The underwriter might also be providing investment banking dues, which include evaluating the issuer and recommending pricing, which will create demand for the security.
(M1) What is the portfolio's beta given the following data? - Security 1 - portfolio value $750,000 beta 1.2 - Security 2 - portfolio value $250,000, beta 0.6 - Security 3 - portfolio value $800,000, beta 1.8 - Security 4 - portfolio value $200,000, beta 2.0 a. portfolio beta of 1.28 b. portfolio beta of 1.40 c. portfolio beta of 1.45 d. portfolio beta of 1.47
c. portfolio beta of 1.45 *Answer: beta of 1.45 The beta of a portfolio is equal to the weighted beta of the individual securities. Step 1 - determine the weights Step 2 - calculated the sum of the weighted betas (37.5% x 1.2) + (12.5% x 0.60) + (40% x 1.8) + (10% x 2.0) = 1.45
(M1) Common shares represent ownership in a company. Each of the following statements is correct, except for one. Which statement is INCORRECT? a. The common shareholders of large-cap companies should expect annual dividends, while owners of small-cap companies should not. b. If a shareholder sells their position after six months, then any gain will be taxed at short-term capital gain rates. c. The shares of large-cap companies with high daily trade volume will typically trade at a narrower bid-ask spread (e.g., $10.45 x $10.48) as compared to small-cap companies with lower daily trade volume. d. Based on long-term statistical data, small-cap stocks offer the investor a lower level of price volatility as compared with large-cap stocks
d. Based on long-term statistical data, small-cap stocks offer the investor a lower level of price volatility as compared with large-cap stocks *Based on long-term statistical data, small-cap stocks offer the investor a lower level of price volatility as compared with large-cap stocks The long-term historical record confirms that small-cap stocks have a higher-level of expected return, as compared to large-cap securities. Large-cap companies will typically have mature cash flows. Since their growth prospects are less than emerging small-cap companies, the company leadership is obligated to return a percentage of net earnings to shareholders in the form of dividends. Holders of small-cap companies expect company leadership to reinvest free cash flow since they have higher growth opportunities. Large-cap companies typically have higher liquidity than small issues. That liquidity translates into narrower bid-ask trading spreads. The sale of a capital asset after a holding period of 365 days or less is taxed as a short-term capital gain. The sale of a capital asset after 365 days (i.e., 366 days or longer) is taxed as a long-term capital gain.
(M1) Based on long-term historical records regarding return and risk for stocks, bonds, and U.S. Treasury instruments, which of the following asset classes would you expect to exhibit the lowest level of price volatility over an extended holding period? a. Equity REITs b. Domestic large-cap stocks c. Long-term corporate bonds d. Intermediate-term U.S. government bonds e. Domestic small-cap stocks
d. Intermediate-term U.S. government bonds *Intermediate-term U.S. government bonds The historical data show that, as expected, stocks offer a greater return and greater volatility than the other investment alternatives while bonds offer lower returns with lower levels of price volatility. Refer to slide 23, handout 3.1 Investment Risks, which depicts annual returns and standard deviation over the 1972-2019 time period (Morningstar data).
(M1) Each of the following statements regarding the capital allocation line is correct, except for one. Which statement is INCORRECT? a. The slope of the capital allocation line is referred to as the Sharpe Ratio b. Any point on the capital allocation line will have the same reward to variability ratio. c. The capital allocation line connects the risk-free rate and the point of tangency on the risky portfolio's efficient frontier d. There is one capital allocation line for all investors, and the only choice is how much to invest in the risk-free asset and how much to invest in the risky portfolio
d. There is one capital allocation line for all investors, and the only choice is how much to invest in the risk-free asset and how much to invest in the risky portfolio *There is one capital allocation line for all investors, and the only choice is how much to invest in the risk-free asset and how much to invest in the risky portfolio The CAL connects the risk-free rate and the point of tangency with the risky portfolio's efficient frontier. Since the risky portfolio can be different for everyone, there can be unlimited capital allocation line. The capital market line (CML) makes the assumption that all investors hold the market portfolio (e.g., S&P500). Given this assumption, there would only be one market line for everyone.
(M1) Which of the following statements regarding security risk is incorrect? a. standard deviation is an appropriate measure of risk for an individual security b. beta is an appropriate measure of risk for a portfolio c. unsystematic risk can be diversified away d. systematic risk is eliminated when on the efficient frontier
d. systematic risk is eliminated when on the efficient frontier *systematic risk is eliminated when on the efficient frontier A well-diversified portfolio "diversifies away" company or unsystematic risk; however, market or systematic risk cannot be eliminated. The efficient frontier represents the highest level of expected return for a given level of expected risk.
