Learning Module 1 - Economics and Investment Markets (EOC)

84 Learning Module 1 Economics and Investment Markets PRACTICE PROBLEMS 1. All else equal, which of the following would most likely explain the fall in price of a particular company’s shares? A. The expected inflation rate falls. B. The company’s future cash flows are expected to increase. C. The yield to maturity on real default-free investments rises. The following information relates to questions 2-8 Julie Carlisle is a financial planner at a large wealth management firm. One of her clients, Esteban Blake, just received a sizable inheritance. He invests a portion of the inheritance in an annuity that will immediately increase his income by a substantial amount. He enlists Carlisle’s help to invest the remaining amount of the inheritance. Blake informs Carlisle that he would like some short-term bonds in his portfolio. Carlisle proposes purchasing a one-year domestic government zero-coupon bond. It has a face value of $100 and is currently priced at $96.37. Carlisle estimates the one-year real risk-free rate at 1.15% and expects inflation over the next year to be 2.25%. In an effort to provide Blake with some exposure to international markets, Carlisle proposes three countries to look for investment opportunities. Selected data on the three countries are presented in Exhibit 1. Exhibit 1: Selected Macroeconomic Data Nominal GDP Growth Inflation Rate Volatility of Real GDP Growth Yield Curve Shape Trailing 12-Month Equity Index P/E Country #1 6.5% 4.0% Low Flat 16.5 Country #2 5.0% 2.5% High Upward slope 17.3 Country #3 3.5% 2.0% Low Flat 18.2 In her analysis, Carlisle observes that the spread between the three-year default-free nominal bond and the default-free real zero-coupon bond in Country #3 is 2.0%. Blake expresses concern that stocks may be currently overvalued in Country 3 given its 20-year historical equity index P/E of 16.0. Carlisle comments, I think the equilibrium P/E in Country #3 has increased because of changes in market conditions. Carlisle predicts that Country #3 will slip into a recession next quarter. She thinks it will be short-lived, lasting only 12 months or so, and considers the impact of such a recession on the performance of the country’s stocks and bonds. Practice Problems 85 Exhibit 2: Three-Year Corporate Bonds from Country #3 Corporate Bond Moody’s Investors Service Rating Spread* Bond A Aaa 1.4% Bond B Baa1 3.2% Bond C B3 5.3% *Spread versus three-year sovereign bond 2. Holding all else constant, the change in Blake’s income will most likely result in: A. an increase in his marginal utility of consumption. B. an increase in his inter-temporal rate of substitution. C. a decrease in his required risk premium for investing in risky assets. 3. The implied premium for inflation uncertainty for the one-year government zero-coupon bond proposed by Carlisle is closest to: A. 0.23%. B. 0.37%. C. 1.10%. 4. Based on the data in Exhibit 1, current real short-term interest rates would most likely be highest in: A. Country #1. B. Country #2. C. Country #3. 5. The recent change in Country #3’s break-even inflation rate suggests that the expected rate of inflation over the next three years is: A. less than 2.0%. B. equal to 2.0%. C. greater than 2.0%. 6. Which of the following changes in market conditions best supports Carlisle’s comment regarding the equilibrium P/E for Country #3? A. An increase in the equity risk premium B. A decrease in uncertainty about future inflation C. A decrease in expectation of future real earnings growth 7. If Carlisle’s prediction about the economy of Country #3 is realized, the yield curve in Country #3 will most likely: A. remain flat. B. become upward sloping. 86 Learning Module 1 Economics and Investment Markets C. become downward sloping. 8. Based on Exhibit 2, if Carlisle’s prediction for Country #3 is realized, then over the next 12 months: A. Bond A would be expected to outperform Bond C. B. Bond B would be expected to outperform Bond A. C. Bond C would be expected to outperform Bond B. 9. The covariance between a risk-averse investor’s inter-temporal rate of substitution and the expected future price of a risky asset is typically: A. negative. B. zero. C. positive. 10. The prices of one-period, real default-free government bonds are likely to be most sensitive to changes in: A. investors’ inflation expectations. B. the expected volatility of economic growth. C. the covariance between investors’ inter-temporal rates of substitution and the expected future prices of the bonds. 11. Default-free real interest rates tend to be relatively high in countries with high expected economic growth because investors: A. increase current borrowing. B. have high inter-temporal rates of substitution. C. have high uncertainty about levels of future consumption. 12. Positive output gaps are usually associated with: A. deflation. B. high unemployment. C. economic growth beyond sustainable capacity. 13. All else equal, an investor expects future inflation to increase, but the uncertainty of future inflation to fall. For such an investor the break-even inflation rate: A. is uncertain. B. is expected to fall. C. is expected to rise. 14. The difference between the yield on a zero-coupon, default-free nominal bond and the yield on a zero-coupon, default-free real bond of the same maturity reflects: A. investors’ expectations about future inflation only. Practice Problems B. a premium for the uncertainty of future inflation only. C. both, investors’ expectations about future inflation and a premium for the uncertainty of future inflation. 15. During a recession, the slope of the yield curve for default-free government bonds is most likely to: A. flatten. B. steepen. C. become inverted. 16. One interpretation of an upward sloping yield curve is that the returns to short-dated bonds are: A. uncorrelated with bad times. B. more positively correlated with bad times than are returns to long-dated bonds. C. more negatively correlated with bad times than are returns to long-dated bonds. 17. An analyst, who measures yield as a combination of interest rates and premiums, observes an upward-sloping, default-free government bond nominal yield curve. Which of the following statements is correct? A. Interest rates must be expected to rise in the future. B. Bond risk premiums must be expected to rise in the future. C. Expectations relating to the future direction of interest rates are indeterminate. 18. A corporate bond has a remaining maturity of 1 year, has a face value of EUR100, and is currently priced at EUR90.90. The real risk-free rate is 3.25%. Inflation is expected to be 2.0% next year, and the premium required by investors for inflation uncertainty is 0.25%. The implied credit risk premium embedded in the bond’s price is best described as: A. equal to (100/90.90) − 1 = 10%. B. 10% reduced by the real risk-free rate and expected inflation. C. 10% reduced by the real risk-free rate, expected inflation, and the premium for inflation uncertainty. 19. A decrease in the prices of AAA-rated corporate bonds during a recession would most likely be the result of: A. expectations of higher inflation. B. increases in credit risk premiums. C. increases in short-term, default-free interest rates. 20. During an economic period when spreads between corporate and government 87 88 Learning Module 1 Economics and Investment Markets bonds are narrowing, and spreads between higher- and lower-rated corporate bond categories are also narrowing, it can be expected that: A. government bonds will outperform corporate bonds. B. lower-rated corporate bonds will outperform higher-rated corporate bonds. C. higher-rated corporate bonds will outperform lower-rated corporate bonds. 21. The sensitivity of a corporate bond’s spread to changes in the business cycle is most likely to be: A. uncorrelated with the level of cyclicality in the company’s business. B. positively correlated with the level of cyclicality in the company’s business. C. negatively correlated with the level of cyclicality of the company’s business. 22. The category of bonds whose spreads can be expected to widen the most during an economic downturn are bonds from the: A. cyclical sector with low credit ratings. B. cyclical sector with high credit ratings. C. non-cyclical sector with low credit ratings. 23. With regard to the credit risk of the sovereign debt issued by country governments, which of the following statements is correct? The credit risk premium on such debt is: A. zero because governments can print money to settle their debt. B. negligibly small because no country has defaulted on sovereign debt. C. a non-zero and positive quantity that varies depending on a country’s creditworthiness. 24. Risk-averse investors demanding a large equity risk premium are most likely expecting their future consumption outcomes and equity returns to be: A. uncorrelated. B. positively correlated. C. negatively correlated. 25. Which of the following financial assets is likely to offer the most effective hedge against bad consumption outcomes? A. Equities. B. Short-dated, default-free government bonds. C. Long-dated, default-free government bonds. 26. When assessing investment opportunities in equities, investors should: A. assign higher equity risk premiums to non-cyclical companies, relative to cyclical companies. Practice Problems B. forecast lower volatility in the growth rate of earnings for cyclical companies, relative to non-cyclical companies. C. forecast higher growth rates in earnings for cyclical companies coming out of a recession, relative to non-cyclical companies. 27. Other things equal, equilibrium price-to-earnings ratios (P/Es) will most likely decrease if: A. real interest rates decrease. B. inflation is expected to increase. C. there is less uncertainty about future inflation. 28. Which of the following statements relating to commercial real estate is correct? A. Rental income from commercial real estate is generally unstable across business cycles. B. Commercial real estate investments generally offer a good hedge against bad consumption outcomes. C. The key difference in the discount rates applied to the cash flows of equity investments and commercial real estate investments relates to liquidity. 89 90 Learning Module 1 Economics and Investment Markets SOLUTIONS 1. C is correct. According to the fundamental pricing equation, the market value of an asset is affected by economic factors that influence the asset’s expected future cash flows, default-free interest rates, expected inflation rates, or the asset’s risk premium. From Equation 1, expected cash flows are in the numerator, while expected inflation and the real risk-free rate are in the denominator. Consequently, a rise in the real risk-free rate (the yield to maturity on a default-free instrument) will lead to a fall in the price of a risky asset, such as stock, by increasing the rate at which its cash flows are discounted. 2. C is correct. The additional annuity payment substantially increases Blake’s income and wealth, which decreases his marginal utility of consumption. As a result, the average loss of marginal utility from any risk taking decreases as his wealth increases. Thus, he requires a lower risk premium and is willing to buy more risky assets. 3. B is correct. The pricing equation for a default-free nominal coupon-paying bond is N C ​F​i ​ t+s ​​Pt​i​ = ​∑ _______________ ​   s ​. s=1(​1 + ​lt,s ​ ​+ ​θt,s ​ ​+ ​π​t,s​)​ ​ For a one-year bond, the pricing formula reduces to C ​Ft+1 ​ ​ ​​Pt​​ = ________________ ​   1 ​. ​(​1 + ​lt,1 ​ ​+ ​θt,1 ​ ​+ ​π​t,1​)​ ​ Thus, the implied premium for inflation uncertainty for the one-year government zero-coupon bond is calculated as ​ ​P​​ ​− ​(​ ​1 + ​lt,1 ​ ​+ ​θt,1 ​ ​) πt,1 = _ C ​Ft+1 ​ ​ 100 t ( ) = ​_ 96.37 ​− ​​ ​1 + 0.0115 + 0.0225​ = 1.0377 − 1.0340 = 0.0037, or 0.37%. 4. B is correct. Real short-term interest rates are positively related to both real GDP growth and the volatility of real GDP growth. Country 1 and Country 2 have the highest real GDP growth, as estimated by the difference between nominal GDP growth and average inflation (6.5% − 4.0% = 2.5% and 5.0% − 2.5% = 2.5%, respectively), while Country 3 has the lowest real GDP growth (3.5% − 2.0% = 1.5%). Looking at the volatility of real GDP growth, Country 2 has high real GDP growth volatility, whereas Country 1 and Country 3 have low real GDP growth volatility. Therefore, Country 2 would most likely have the highest real short-term interest rates. 5. A is correct. The difference, or spread, between the yields on the country’s three-year default-free nominal bond and on the default-free real zero-coupon bond is 2.0%. This spread is known as the break-even rate of inflation (BEI), which is composed of the expected rate of inflation plus a risk premium for the uncertainty of future inflation. Because this risk premium component is most likely positive, because investors are unlikely to be very confident in their ability to predict inflation accurately, the expected rate of inflation component would be less than 2.0%. Solutions 6. B is correct. Stock prices are a function of expected cash flows discounted by inflation expectations, the uncertainty of future inflation, and the equity risk premium, among other factors. Holding all else equal, a decline in the uncertainty of future inflation would result in lower discount rates and higher valuations. This result would support a higher equilibrium P/E, thus justifying Country 3’s current trailing P/E being higher than its historical average. 7. B is correct. The yield curve in Country 3 is currently flat (Exhibit 1), and Carlisle predicts a recession. During a recession, short-term rates tend to be lower because central banks tend to lower their policy rate in these times. However, the impact of monetary policy on longer-term rates will not be as strong because the central bank will usually be expected to bring short-term rates back to normal as the recession recedes. Thus, the slope of the yield curve will likely become upward sloping during the recession. 8. A is correct. If Country 3 experiences a recession over the next 12 months, the credit spreads for corporate bonds would be expected to widen as investors sell the low-quality debt of issuers with high default risk and trade up to the higher-quality debt of issuers with low default risk. The issuers with a good credit rating (such as Aaa rated Bond A) tend to outperform those with lower ratings (such as B3 rated Bond C) as the spread between low- and higher-quality issuers widens. As a result, Bond A would be expected to outperform Bond C over the next 12 months. 9. A is correct. For risk-averse investors, when the expected future price of the investment is high (low), the marginal utility of future consumption relative to that of current consumption is low (high). Hence, the covariance of the inter-temporal rate of substitution with asset price is expected to be negative for risk-averse investors. 10. B is correct. Only changes in default-free real interest rates will affect the price of real, default-free bonds. The average level of default-free real interest rates is positively related to the volatility of economic growth in the economy; thus, changes in the expected volatility of economic growth would likely lead to changes in default-free real interest rates, which in turn would affect the prices of real, default-free government bonds. 11. A is correct. The average level of default-free real interest rates is positively related to the expected rate of growth of the underlying economy and also to the volatility of economic growth in the economy. During periods of high expected economic growth, investors are less worried about the future and their consumption abilities in the future; that is, their inter-temporal rate of substitution is low, so they borrow more today and save less. Other things being equal, this means that the average level of default-free real interest rates (the reciprocal of the rate of substitution, see Equation 4) should be higher in an economy with high growth and lower in an economy with lower, more stable growth. 12. C is correct. An economy operating with a positive output gap—that is, where the level of actual GDP exceeds potential GDP—is producing beyond its sustainable capacity. Positive output gaps are usually associated with high and/or rising inflation, while high levels of unemployment usually accompany negative output gaps. 13. A is correct. The break-even inflation rate is the difference between the yield on a zero-coupon, default-free nominal bond and on a zero-coupon, default-free real bond of the same maturity. The rate incorporates changing expectations about inflation and changing perceptions about the uncertainty of the future inflation 91 92 Learning Module 1 Economics and Investment Markets environment. Consequently, if inflation is expected to rise while the uncertainty about future inflation falls (in Equation 10, θt,s rises but πt,s falls), it is unclear in which direction break-even inflation rates will move. 14. C is correct. The difference between the yield on a zero-coupon, default-free nominal bond and the yield on a zero-coupon, default-free real bond of the same maturity is known as the break-even inflation rate. This break-even inflation rate will incorporate the inflation expectations of investors over the investment horizon of the two bonds, plus a risk premium to compensate investors for uncertainty about future inflation. Break-even inflation rates are not simply the market’s best estimate of future inflation over the relevant investment horizon, because break-even inflation rates also include a risk premium to compensate investors for their uncertainty about future inflation. 15. B is correct. During a recession, short rates are often lower because central banks tend to lower their policy rate in these times because the output gap is likely to be negative. However, the impact of such monetary policy on longer-term rates will not be as strong, so long rates may not fall by as much as short rates. The central bank will usually be expected to bring short-term rates back to normal as the recession recedes, and the risk-free rates will increase as economic growth recovers. Thus, the slope of the yield curve will typically steepen during a recession. 16. C is correct. One interpretation of an upward-sloping yield curve is that returns to short-dated bonds are more negatively correlated with bad times than are returns to long-dated bonds. This interpretation is based on the notion that investors are willing to pay a premium and accept a lower return for short-dated bonds if they believe that long-dated bonds are not a good hedge against economic “bad times.” 17. C is correct. An upward-sloping yield curve may be caused by a combination of expected rate increases and positive bond risk premiums. It may also be a combination of expectations that interest rates will be unchanged in the future coupled with positive bond risk premiums. Lastly, an upward-sloping yield curve may actually be a reflection of expected rate cuts that are more than offset by the existence of positive bond risk premiums. So, expectations relating to the future direction of interest rates are indeterminate. 18. C is correct. The implied credit risk premium embedded in the bond’s price is the yield (10%) less the default-risk-free nominal interest rate, which includes a premium for inflation uncertainty. See Example 15. The credit risk premium can be calculated as 4.51% in this case: 100 i ​ = ​_​− ​(​ ​1 + 0.0325 + 0.02 + 0.0025​)​​. ​γ​t,s 90.90 ​      i ​γ​t,s​ = 4.51 % . 19. B is correct. During recessions, the risk premium that investors demand on financial assets, particularly those that are not default-free, such as corporate bonds, may rise because investors in general may be less willing and able to take on heightened default risk during such periods. Specifically, the credit risk premium demanded by investors tends to rise in times of economic weakness, when the probability of a corporate default and bankruptcy is highest. 20. B is correct. When spreads are narrowing, investors seem to be less discerning between issues with weak versus strong credit, and the rate of improvement will tend to be greater for those bonds issued by entities with a relatively weaker ability to pay. Thus, during times when corporate bond spreads are narrowing relative to government bonds and the spreads between higher- and lower-rated Solutions bond categories are also narrowing, corporate bonds will generally outperform government bonds and lower-rated corporate bonds will tend to outperform higher-rated corporate bonds. 21. B is correct. The sensitivity of a corporate bond’s spread to changes in the business cycle and the level of cyclicality tend to be positively correlated. The greater the level of cyclicality, the greater the sensitivity of the bond’s spread to changes in the business cycle. 22. A is correct. During an economic downturn, the spreads of corporate bonds can be expected to widen, because the risk premium that investors demand on risky financial assets will increase. When spreads widen, the spreads on bonds issued by corporations with a low credit rating and that are part of the cyclical sector will tend to widen the most. 23. C is correct. Credit premiums have been an important component of the expected return on bonds issued by countries (sovereign debt). The credit premium varies from country to country depending on how creditworthy investors consider it to be. The fact that countries have both printed money to pay back debt and defaulted on it gives rise to a non-zero credit risk premium. 24. B is correct. If investors demand high equity risk premiums, they are likely expecting their future consumption and equity returns to be positively correlated. The positive correlation indicates that equities will exhibit poor hedging properties, because equity returns will be high (i.e., pay off ) during “good times” and will be low (i.e., not pay off ) during “bad times.” In other words, the covariance between risk-averse investors’ inter-temporal rates of substitution and the expected future prices of equities is highly negative, resulting in a positive and large equity risk premium. This is the case because in good times, when equity returns are high, the marginal value of consumption is low. Similarly, in bad times, when equity returns are low, the marginal value of consumption is high. Holding all else constant, the larger the magnitude of the negative covariance term, the larger the risk premium. 25. B is correct. The relative certainty about the real payoff from short-dated, default-free government bonds and, therefore, the relative certainty about the amount of consumption that the investor will be able to undertake with the payoff indicate that an investment in such bonds would be a good hedge against bad consumption outcomes. 26. C is correct. During recessions, cyclical companies are likely to experience sharp declines in earnings, more so than non-cyclical companies. In contrast, while coming out of a recession, cyclical companies are likely to generate higher earnings growth relative to non-cyclical companies. 27. B is correct. Other things being equal, an increase in inflation expectations would result in lower equity prices relative to current earnings. This would result in lower equilibrium P/Es. 28. C is correct. To arrive at an appropriate discount rate to be used to discount the cash flows from a commercial real estate investment, a liquidity premium is added to the discount rate applicable to equity investments. The added liquidity premium provides additional compensation for the risk that the real estate investment may be very illiquid in bad economic times. 93 142 Learning Module 2 Analysis of Active Portfolio Management PRACTICE PROBLEMS 1. Wei Liu makes two statements about active portfolio management: Statement 1 The “active return” of an actively managed portfolio is the difference between the portfolio’s return and the return on the benchmark portfolio, and it is equal to the managed portfolio’s alpha. Statement 2 The active weights are the differences in the managed portfolio’s weights and the benchmark’s weights. Are Liu’s statements correct? A. Only Statement 1 is correct. B. Only Statement 2 is correct. C. Both statements are correct. 2. The benchmark weights and returns for each of the five stocks in the Capitol Index are given in the following table. The Tukol Fund uses the Capitol Index as its benchmark, and the fund’s portfolio weights are also shown in the table. Portfolio Weight (%) Benchmark Weight (%) 20X2 Return (%) 1 30 24 14 2 30 20 15 3 20 20 12 4 10 18 8 5 10 18 10 Stock What is the value added (active return) for the Tukol Fund? A. 0.00% B. 0.90% C. 1.92% 3. Consider the following asset class returns for calendar year 20X2: Asset Class Domestic equities Portfolio Weight (%) Benchmark Weight (%) Portfolio Return (%) Benchmark Return (%) 55 40 10 8 International equities 20 30 10 9 Bonds 25 30 5 6 What is the value added (or active return) for the managed portfolio? A. 0.25% B. 0.35% C. 1.05% Practice Problems 143 The following information relates to questions 4-10 James Frazee is chief investment officer at H&F Capital Investors. Frazee hires a third-party adviser to develop a custom benchmark for three actively managed balanced funds he oversees: Fund X, Fund Y, and Fund Z. (Balanced funds are funds invested in equities and bonds.) The benchmark needs to be composed of 60% global equities and 40% global bonds. The third-party adviser submits the proposed benchmark to Frazee, who rejects the benchmark based on the following concerns: Concern 1: Many securities he wants to purchase are not included in the benchmark portfolio. Concern 2: One position in the benchmark portfolio will be somewhat costly to replicate. Concern 3: The benchmark portfolio is a float-adjusted, capitalization-weighted portfolio. After the third-party adviser makes adjustments to the benchmark to alleviate Frazee’s concerns, Frazee accepts the benchmark portfolio. He then asks his research staff to develop risk and expected return forecasts for Funds X, Y, and Z as well as for the benchmark. The forecasts are presented in Exhibit 1. Exhibit 1: Forecasted Portfolio Statistics for Funds X, Y, and Z and the Benchmark Fund X Fund Y Fund Z Benchmark Global equities (%) 60.0 65.0 68.0 60.0 Global bonds (%) 40.0 35.0 32.0 40.0 Expected return (%) 10.0 11.6 13.2 9.4 Expected volatility (%) 17.1 18.7 22.2 16.3 Active risk (%) 5.2 9.2 15.1 N/A Sharpe ratio (SR) 0.45 0.50 0.49 0.44 Portfolio weights: Note: Data are based on a risk-free rate of 2.3%. Frazee decides to add a fourth offering to his group of funds, Fund W, which will use the same benchmark as in Exhibit 1. Frazee estimates Fund W’s information ratio to be 0.35. He is considering adding the following constraint to his portfolio construction model: Fund W would now have maximum over- and underweight constraints of 7% on single-country positions. Frazee conducts a search to hire a manager for the global equity portion of Fund W and identifies three candidates. He asks the candidates to prepare risk and return forecasts relative to Fund W’s benchmark based on their investment strategy, with the only constraint being no short selling. Each candidate develops independent annual forecasts with active return projections that are uncorrelated and constructs a portfolio made up of stocks that are diverse both geographically and across economic sectors. Selected data for the three candidates’ portfolios are presented in Exhibit 2. 144 Learning Module 2 Analysis of Active Portfolio Management Exhibit 2: Forecasted Portfolio Data for Equity Portion of Fund W Rebalancing Candidate A Candidate B Candidate C Annually Annually Annually Number of securities 100 64 36 Information ratio (IR) 0.582 0.746 0.723 Transfer coefficient (TC) 0.832 0.777 0.548 Information coefficient* 0.07 0.12 0.22 * Information coefficient based on previously managed funds. Frazee asks Candidate C to re-evaluate portfolio data given the following changes: Change 1: Fix the number of securities to 50. Change 2: Rebalance on a semi-annual basis. Change 3: Add maximum over- or underweight constraints on sector weightings. 4. Which of Frazee’s concerns best justifies his decision to reject the proposed benchmark? A. Concern 1 B. Concern 2 C. Concern 3 5. Based on Exhibit 1, the expected active return from asset allocation for Fund X is: A. negative. B. zero. C. positive. 6. Based on Exhibit 1, which fund is expected to produce the greatest consistency of active return? A. Fund X B. Fund Y C. Fund Z 7. Based on Exhibit 1, combining Fund W with a fund that replicates the benchmark would produce a Sharpe ratio closest to: A. 0.44. B. 0.56. C. 0.89. 8. If Frazee added the assumption he is considering in Fund W’s portfolio construc- Practice Problems 145 tion, it would most likely result in: A. a decrease in the optimal aggressiveness of the active strategy. B. the information ratio becoming invariant to the level of active risk. C. an increase in the transfer of active return forecasts into active weights. 9. Based on the data presented in Exhibit 2, the candidate with the greatest skill at achieving active returns appears to be: A. Candidate A. B. Candidate B. C. Candidate C. 10. Which proposed change to Fund W would most likely decrease Candidate C’s information ratio? A. Change 1 B. Change 2 C. Change 3 The following information relates to questions 11-14 John Martinez is assessing the performance of the actively managed diversified asset portfolio. The diversified asset portfolio is invested in equities, bonds, and real estate, and allocations to these asset classes and to the holdings within them are unconstrained. Selected return and financial data for the portfolio for 2019 are presented in Exhibit 1. Exhibit 1: Diversified Asset Portfolio 2019 Portfolio Performance Sub-Portfolio Return (%) Benchmark Return (%) Portfolio Allocation (%) Strategic Asset Allocation (%) Equities sub-portfolio 36.9 31.6 63 60 Bond sub-portfolio −2.4 −2.6 28 35 Real estate sub-portfolio 33.4 28.3 9 5 Martinez uses several risk-adjusted return metrics to assess the performance of the diversified asset portfolio, including the information ratio and the Sharpe ratio. Selected risk, return, and statistical data for the portfolio are presented in Exhibit 2. 146 Learning Module 2 Analysis of Active Portfolio Management Exhibit 2: Diversified Asset Portfolio Data, 2000-2019 Transfer Coefficient (TC) Information Coefficient (IC) Breadth (BR) Equities sub-portfolio 0.90 0.091 21 Bond sub-portfolio 0.79 0.087 23 Real estate sub-portfolio 0.86 0.093 19 Martinez has recently hired Kenneth Singh to help him evaluate portfolios. Martinez asks Singh about the possible effects on the portfolio’s information ratio if cash were added to the diversified asset portfolio or if the aggressiveness of the portfolio’s active weights were increased. Singh responds with two statements: Statement 1 Adding cash to the portfolio would change the portfolio’s information ratio. Statement 2 Increasing the aggressiveness of active weights would not change the portfolio’s information ratio. 11. Based on Exhibit 1, the value added to the diversified asset portfolio attributable to the security selection decision in 2019 was closest to: A. 2.3%. B. 3.9%. C. 6.1%. 12. Based on Exhibit 1, the value added of the diversified asset portfolio attributable to the asset allocation decision in 2019 was closest to: A. 2.3%. B. 3.9%. C. 6.1%. 13. Based on data in Exhibit 2 and using the information ratio as the criterion for evaluating performance, which sub-portfolio had the best performance in the period 2000–2019? A. The bond sub-portfolio. B. The equities sub-portfolio. C. The real estate sub-portfolio. 14. Which of Singh’s statements regarding the information ratio is correct? A. Only Statement 1 B. Only Statement 2 C. Both Statement 1 and Statement 2 Practice Problems 147 15. Gertrude Fischer mentions two properties of the Sharpe ratio and the information ratio that she says are very useful. Property 1 The Sharpe ratio is unaffected by the addition of cash or leverage in a portfolio. Property 2 The information ratio for an unconstrained portfolio is unaffected by the aggressiveness of the active weights. Are Fischer’s two properties correct? A. Yes. B. No. Only Property 1 is correct. C. No. Only Property 2 is correct. 16. An analyst is given the following information about a portfolio and its benchmark. In particular, the analyst is concerned that the portfolio is a closet index fund. The T-bill return chosen to represent the risk-free rate is 0.50%. Benchmark Portfolio Return 8.75% 8.90% Risk 17.50% 17.60% Active return 0.00% 0.15% Active risk 0.00% 0.79% Sharpe ratio 0.4714 0.4773 N/A 0.1896 Information ratio Which of the following three statements does not justify your belief that the portfolio is a closet index? i. The Sharpe ratio of the portfolio is close to the Sharpe ratio of the benchmark. ii. The information ratio of the portfolio is relatively small. iii. The active risk of the portfolio is very low. A. Statement I B. Statement II C. Statement III 17. You have a portfolio 100% allocated to a manager with an ex post, active risk at 8.0%. You choose to allocate a 75% position to the active manager and 25% to the benchmark to bring the portfolio back to your target active risk of 6.0%. If the manager’s information ratio is 0.50, what happens to the information ratio of the portfolio after the reallocation? A. The information ratio increases because the lower active risk reduces the denominator of the ratio. B. The information ratio remains unchanged because allocations between the active portfolio and the benchmark don’t affect the information ratio. 148 Learning Module 2 Analysis of Active Portfolio Management C. The information ratio decreases because allocating some of the portfolio to the benchmark means that the external manager generates less active return. The following information relates to questions 18-19 S&P 500 Indigo Fund Expected annual return 9.0% 10.5% Return standard deviation 18.0% 25.0% Sharpe ratio 0.333 0.30 Active return 1.2% Active risk 8.0% Information ratio 0.15 Note: Data are based on a risk-free rate of 2.3%. 18. What is the maximum Sharpe ratio that a manager can achieve by combining the S&P 500 benchmark portfolio and the Indigo Fund? A. 0.333 B. 0.365 C. 0.448 19. Which of the following pairs of weights would be used to achieve the highest Sharpe ratio and optimal amount of active risk through combining the Indigo Fund and benchmark portfolio, respectively? A. 1.014 on Indigo and −0.014 on the benchmark B. 1.450 on Indigo and −0.450 on the benchmark C. 1.500 on Indigo and −0.500 on the benchmark 20. The benchmark portfolio is the S&P 500. Which of the following three portfolios can be combined with the benchmark portfolio to produce the highest combined Sharpe ratio? S&P 500 Portfolio A Portfolio B Portfolio C Expected annual return 9.0% 10.0% 9.5% 9.0% Return standard deviation 18.0% 20.0% 20.0% 18.0% Sharpe ratio 0.333 0.350 0.325 0.333 Active return 0 1.0% 0.5% 0 Active risk 0 10.0% 3.0% 2.0% Note: Data are based on a risk-free rate of 2.3%. A. Portfolio A B. Portfolio B Practice Problems 149 C. Portfolio C 21. You are considering three managers for a small-cap growth mandate. After careful analysis, you produce the following forward-looking expectations about the managers’ active risk and active return: Manager A Manager B Manager C Active return 0.7% 0.6% 1.2% Active risk 3.2% 3.1% 6.3% If you intend to rely on the information ratio to make your decision, which manager should you choose? A. Manager A B. Manager B C. Manager C 22. Based on the fundamental law of active management, if a portfolio manager has an information ratio of 0.75, an information coefficient of 0.1819, and a transfer coefficient of 1.0, how many securities are in the portfolio manager’s fund, making the assumption that the active returns are uncorrelated. A. About 2 B. About 4 C. About 17 23. Two analysts make the following statements about the transfer coefficient in the expanded fundamental law of active management: Analyst One says, “The transfer coefficient measures how well the realized returns correlate with the anticipated returns, adjusted for risk.” Analyst Two says, “The transfer coefficient measures how well the realized returns correlate with the active weights, adjusted for risk.” Which, if either, analyst is correct? A. Only Analyst One is correct. B. Only Analyst Two is correct. C. Neither analyst is correct. 24. The expanded fundamental law of active management is stated as follows: _ ​E​(​ ​RA​ ​)​​ = ​(​ ​TC​)​​(​ ​IC​)​​√ BR ​σ​ ​A​​. Which component on the righthand side represents the extent to which the portfolio manager’s expectations are realized? The A. transfer coefficient, TC. B. information coefficient, IC. C. breadth, BR. 150 Learning Module 2 Analysis of Active Portfolio Management The following information relates to questions 25-26 You are analyzing three investment managers for a new mandate. The following table provides the managers’ ex-ante active return expectations and portfolio weights. The last two columns include the risk and the ex post, realized active returns for the four stocks. Use the following data for the following two questions: Manager 1 Manager 2 Manager 3 Δw E(RA) Δw E(RA) Δw E(RA) Risk Realized RA Security 1 −0.125 0.03 0.2 0.04 −0.05 0.025 0.17 0.06 Security 2 0.025 0.04 0 0.01 0.05 0.015 0.10 0.07 Security 3 0.075 0.05 −0.1 0 0.05 0.005 0.12 0.04 Security 4 0.025 0.06 −0.1 0.02 −0.05 0.015 0.25 0.02 25. Suppose all three managers claim to be good at forecasting returns. According to the expanded fundamental law of active management, which manager is the best at efficiently building portfolios by anticipating future returns? A. Manager 1 B. Manager 2 C. Manager 3 26. Suppose all three managers claim to be efficient in portfolio construction. According to the expanded fundamental law of active management, which manager is the best at building portfolios to make full use of their ability to correctly anticipate returns? A. Manager 1 B. Manager 2 C. Manager 3 27. Manager 1 has an information coefficient of 0.15, a transfer coefficient of 1.0, and invests in 50 securities. Manager 2 has a different strategy, investing in more securities; however, he is subject to investment constraints that reduce his transfer coefficient. Manager 2 has an information coefficient of 0.10, a transfer coefficient of 0.8, and invests in 100 securities. The investment selections of each manager are independent decisions. If both managers target an active risk of 5.0%, which manager will have the greater expected active return? A. Manager 1 B. Manager 2 C. Both managers will have the same active return. 28. Nick Young is concerned that Goudon Partners, one of his money managers, overestimates its expected active return because Goudon overstates its strategy Practice Problems 151 breadth. Young makes two notes about his concern: Note 1 Although Goudon claims that the number of independent asset decisions is high because it uses 200 stocks, many of these stocks cluster in industries where the same general analysis applies to several stocks. Note 2 Goudon claims that each stock is independent and evaluated each month, or 12 times per year. These analyses are not independent because some of their strategies, such as favoring a particular industry or favoring value stocks, persist beyond one month. For example, a strategy of favoring low-P/E stocks will persist for several months and the investment decisions are not independent. If his judgments are correct, are Young’s notes about the overstatement of breadth correct? A. Only Note 1 is correct. B. Only Note 2 is correct. C. Both Notes 1 and 2 are correct. 29. Caramel Associates uses the fundamental law to estimate its expected active returns. Two things have changed. First, Caramel will lower its estimate of the information coefficient because they felt their prior estimates reflected overconfidence. Second, their major clients have relaxed several constraints on their portfolios—including social screens, prohibitions on short selling, and constraints on turnover. Which of these changes will increase the expected active return? A. Only the lower information coefficient. B. Only the relaxation of several portfolio constraints. C. Both the lower information coefficient and the relaxation of portfolio constraints. 152 Learning Module 2 Analysis of Active Portfolio Management SOLUTIONS 1. B is correct. Although the first part of Statement 1 is correct (active return, or value added, equals the difference between the managed portfolio return and the benchmark return), active return is not the same as alpha. In other words, R A = RP − RB, while αP = RP − βP × RB. Statement 2 correctly defines active weights. 2. B is correct. The portfolio active return is equal to the portfolio return minus the benchmark return: RA = RP − RB. n ​ i​​​; The portfolio return is ​RP​ ​ = ​∑ ​w​P,i​R i=1 RP = 0.30(14%) + 0.30(15%) + 0.20(12%) + 0.10(8%) + 0.10(10%) = 12.9%. n The benchmark return is ​RB​ ​ = ​∑ ​w​B,i​​Ri​​​; i=1 RB = 0.24(14%) + 0.20(15%) + 0.20(12%) + 0.18(8%) + 0.18(10%) = 12.0%. Thus, the active return is RA = RP − RB = 12.9% − 12.0% = 0.9%. Note that this same correct answer can be obtained in two other equivalent ways. The active weights are the differences between the portfolio and benchmark weights, or Δwi = wP,i − wB,i. Computing the active weights from the table provided, the active return is N RA = ​∑ ​Δ ​w​i​​Ri​​ i=1 = 0.06(14%) + 0.10(15%) + 0(12%) − 0.08(8%) − 0.08(10%) = 0.9%. Finally, we could express the active security returns as their differences from the benchmark return, or R Ai = Ri − RB. Computing the active security returns from the table provided, the portfolio active return is the sum product of the active weights and the active security returns: N RA = ​∑ ​Δ ​w​i​​RAi ​ ​ i=1 = 0.06(2%) + 0.10(3%) + 0(0%) − 0.08(−4%) − 0.08(−2%) = 0.9%. 3. C is correct. The active return is equal to the portfolio return minus the benchmark return: M M ​​RA​ ​ = ​RP​ ​− R ​ B​ ​ = ​∑ ​w​P,j​​RP,j ​ ​− ​∑ ​w​B,j​​RB,j ​ ​​. j=1 j=1 n The portfolio return is RP = ​∑ ​w​P,i​​Ri​​= 0.55(10%) + 0.20(10%) + 0.25(5%) = 8.75%. i=1 n The benchmark return is RB = ​∑ ​w​B,i​​Ri​​= 0.40(8%) + 0.30(9%) + 0.30(6%) = i=1 7.70%. Thus, RA = RP − RB = 8.75% − 7.70% = 1.05%. 4. A is correct. Because the benchmark does not contain many assets that Frazee wants to invest in, the benchmark may not be representative of his investment approach. Concern 2, as stated, is less important because it does not imply that Solutions 153 the cost of replicating the benchmark is a serious concern. Finally, Concern 3 actually states a generally positive feature of the benchmark. 5. B is correct. Active return from asset allocation is derived from differences between the benchmark weight and the portfolio weight across asset classes. For Fund X, the expected active return from asset allocation is calculated as M ​​∑ ​Δ ​w​j​​RB,j ​ ​+ ​(​ ​40 − 40​)​​RB,b ​ ​ = 0​, ​ ​ = ​(​ ​60 − 60​)​​RB,e j=1 where Δwj is the difference in the active portfolio and the benchmark asset weights, RB,e is the benchmark’s return from global equities, and RB,b is the benchmark’s return from global bonds. Because Fund X has the same asset weights as the benchmark across the two asset classes (60% global equities, 40% global bonds), the expected active return from asset allocation is zero. 6. C is correct. The IR measures the consistency of active return. The IR is calculated for the three funds as follows: ​R​ ​− ​R​ ​ ​R​ ​ ​IR = _ ​ P B ​= _ ​​σ​AA​​​. σ​​(​PP​ ​− ​RB​ ​)​​ IR for Fund X = (10.0 − 9.4)/5.2 = 0.6/5.2 = 0.12. IR for Fund Y = (11.6 − 9.4)/9.2 = 2.2/9.2 = 0.24. IR for Fund Z = (13.2 − 9.4)/15.1 = 3.8/15.1 = 0.25. Fund Z has the largest IR and thus is expected to produce the greatest consistency of active return. 7. B is correct. Given the IR for Fund W of 0.35 and the benchmark’s SR of 0.44, the combination of the benchmark portfolio and Fund W would produce an SR of 0.56, calculated as follows: ​​SR​2P​ = ​SR​2B​+ ​IR​​2​​; SRP = (0.442 + 0.352)0.5 = 0.56. 8. A is correct. The new assumption adds constraints to Fund W. The IR for a constrained portfolio generally decreases with the aggressiveness of the strategy because portfolio constraints reduce the transfer of active return forecasts into active weights. Furthermore, the optimal active risk is given by the following formula: IR ​​σ​A​ = TC​_ ​SR​B​​​σ​B​​. The addition of portfolio constraints reduces the TC, thus also reducing the optimal active risk. So, having maximum over- and underweight constraints on single-country positions decreases the optimal aggressiveness of the active management strategy. 9. B is correct. The IR measures the consistency of active return generation. A higher ratio generally indicates better managerial skill at achieving active returns on a risk-adjusted basis. The IR for Candidate B (0.746) is higher than the IR for Candidate A (0.582) and Candidate C (0.723). Thus, Candidate B appears to have the greatest skill, as indicated by the highest IR of 0.746. 154 Learning Module 2 Analysis of Active Portfolio Management _ 10. C is correct. The IR is calculated as ​IR = ​(​ ​TC​)​​​(​IC​)​​√BR ​, where BR is breadth. Change 3, establishing new constraints of caps on the over- and underweight of sectors, reduces the correlation of optimal active weights with the actual active weights, which results in a decreased TC and thus a decrease in the IR. Change 1 (increasing portfolio size from 36 to 50) and Change 2 (increasing the frequency of rebalancing from annually to semi-annually) would both likely have the effect of increasing the BR of the portfolio, which would increase the IR. 11. B is correct. Based on the differences in returns for the portfolio and benchmark in Exhibit 1, the value added by each asset class within the portfolio is shown in the following table: Sub-Portfolio Return (%) Benchmark Return (%) Value Added (%) Portfolio Allocation (%) Equities sub-portfolio 36.9 31.6 5.3 63 Bond sub-portfolio −2.4 −2.6 0.2 28 Real estate sub-portfolio 33.4 28.3 5.1 9 The value added from security selection is calculated as the sum of the actual portfolio weights multiplied by each sub-portfolio’s value added measure. Thus, the value added from security selection is calculated as: Value added from security selection = 0.63(5.3%) + 0.28(0.2%) + 0.09(5.1%) = 3.9%. A is incorrect. It represents the value added from asset allocation (2.3%). C is incorrect. It represents the total value added (2.3% + 3.9% = 6.1%, with rounding). 12. A is correct. The value added from asset allocation is calculated as the sum of the differences in the weights between the strategic (benchmark) allocation and the actual sub-portfolio allocation multiplied by each sub-portfolio’s benchmark return. Benchmark Return (%) Actual Asset Allocation (%) Strategic Asset Allocation (%) Actual − Strategic Asset Allocation (%) Equities sub-portfolio 31.6 63 60 +3 Bond sub-portfolio −2.6 28 35 −7 Real estate sub-portfolio 28.3 9 5 +4 Thus, the value added by the active asset allocation decision is calculated as Value added from asset allocation decision = 0.03(31.6%) − 0.07(−2.6%) + 0.04(28.3%) = 2.3%. B is incorrect. It is the value added from security selection. C is incorrect. It is the total value added. 13. B is correct. The information ratio for a portfolio can be expressed as follows: Solutions 155 _ ​IR = ​(​ ​TC​)​​(​ ​IC​)​​√ BR .​​ The information ratios for the three sub-portfolios are calculated as follows: Information Ratio Equities sub-portfolio Bond sub-portfolio Real estate sub-portfolio 0.90 × 0.091 × (21)0.5 = 0.38 0.79 × 0.087 × (23)0.5 = 0.33 0.86 × 0.093 × (19)0.5 = 0.35 Based on the information ratio, the equities sub-portfolio outperformed the real estate sub-portfolio. The information ratio for the equities sub-portfolio of 0.38 was higher than the information ratio for the real estate sub-portfolio of 0.35 and the bond sub-portfolio of 0.33. 14. C is correct. The information ratio for a portfolio of risky assets will generally shrink if cash is added to the portfolio. Because the diversified asset portfolio is an unconstrained portfolio, its information ratio would be unaffected by an increase in the aggressiveness of active weights. 15. A is correct. Both properties are correct. For Property 1, if wP is the weight of an actively managed portfolio and (1 − wP) is the weight on risk-free cash, changing wP does not change the Sharpe ratio, as can be seen in this equation: ​RC ​ ​− ​RF​ ​ ​w​ ​(​ ​R​ ​− ​R​ ​)​​ ​ ​σ​C​ ​ = ___________ ​ P ​w​PP​​σ​P​ F ​ = ​SR​P​​. ​​SR​C​ = _ For Property 2, the information ratio of an unconstrained portfolio is unaffected by multiplying the active security weights, ∆wi, by a constant. 16. B is correct. A closet index will have a very low active risk and will also have a Sharpe ratio very close to the benchmark. Therefore, Statements I and III are consistent with a closet index portfolio. A closet index’s information ratio can be indeterminate (because the active risk is so low) and is often negative due to management fees. 17. B is correct. The information ratio is unaffected by rebalancing the active portfolio and the benchmark portfolio. In this case, the active return and active risk are both reduced by 25% and the information ratio will be unchanged. 18. B is correct. The highest squared Sharpe ratio of an actively managed portfolio is ​​SR​2P​ = ​SR​2B​+ ​IR​​2​ = ​0.333​​2​+ 0​ .15​​2​ = 0.1334​. _ The highest Sharpe ratio is SRP = √ ​ 0.1334 ​= 0.365. 19. A is correct. The optimal amount of active risk is 0.15 ​​SIR ​ ​B​ = _ ​0.333 ​18.0 %   = 8.11%​. ​​σ​A​ = _ R​ ​​σ B The weight on the active portfolio (Indigo) would be 8.11%/8.0% = 1.014, and the weight on the benchmark portfolio would be 1 − 1.014 = −0.014. We can demonstrate that these weights achieve the maximum Sharpe ratio (of 0.365). Note that 8.11% is the optimal level of active risk and that Indigo has an expected active return of 1.014(1.2%) = 1.217% over the benchmark and a total excess return of 6.0% + 1.217% = 7.217%. The portfolio total risk is σP2 = σB2 + σA2 = 18.02 + 8.1112 = 389.788. Taking the square root, σP = 19.743, and the optimal Sharpe ratio is indeed 7.217/19.743 = 0.365. 156 Learning Module 2 Analysis of Active Portfolio Management 20. B is correct. The optimal active portfolio is the portfolio with the highest information ratio, the ratio of active return to active risk. The IRs for the three active portfolios are as follows: IRA = 1.0/10.0 = 0.10 IRB = 0. 5/3.0 = 0.167 IRC = 0/2.0 = 0.00 Portfolio B has the highest IR and is the best active portfolio; it is therefore the best portfolio to combine with the benchmark. 21. A is correct. Manager A has the highest information ratio. The information ratio active return ​. The managers in this example have the following is defined as IR = ​_ active risk information ratios: Information ratio Manager A Manager B Manager C 0.7/3.2 = 0.219 0.6/3.1 = 0.194 1.2/6.3 = 0.190 _ 22. C is correct. Using the equation IR* = IC × √ ​ BR ​and assuming that breadth can be interpreted as number of securities in the portfolio, solving for breadth in the 0.75 ​ ​2​= 17.000. equation yields ​(_ ​0.1819 ) 23. C is correct. The transfer coefficient measures how well the anticipated (ex ante), risk-adjusted returns correlate with the risk-adjusted active weights. This is also expressed in the equation for the transfer coefficient: TC = ρ(μi/σi,Δwiσi). 24. B is correct. The IC measures an investment manager’s ability to forecast returns. 25. C is correct. The proper statistic to calculate is the information coefficient, and it is defined as follows: ​​σ​i​ ​, _ ​​σ​i​) ​ ​​​. ​IC = ρ​( ​_ ​RAi ​ ​ ​μ​i​ A manager is a good forecaster if his or her ex ante, active return expectations (forecasts) are highly correlated with the realized active returns. The information coefficient requires that these forecasts and realized returns be risk-weighted. When this is done for the three managers, the risk-weighted forecasts and realized returns are: Risk-Weighted Forecasts, μi/σi Manager 1 Manager 2 RAi/σi Manager 3 Realized Security 1 0.176 0.235 0.147 0.353 Security 2 0.400 0.100 0.150 0.700 Security 3 0.417 0.000 0.042 0.333 Security 4 0.240 0.080 0.060 0.080 The ICs are found by calculating the correlations between each manager’s forecasts and the realized risk-weighted returns. The three managers have the following ICs: Solutions 157 Manager 1 Manager 2 Manager 3 0.5335 0.0966 0.6769 Information coefficient Manager 3 has the highest IC. 26. B is correct. The proper statistic to calculate is the transfer coefficient, and it is defined as follows: TC = ρ(μi/σi,Δwiσi) The TC is the cross-sectional correlation between the forecasted active security returns and the actual active weights, adjusted for risk. Risk-Weighted Forecasts, μi/σi Risk-Adjusted Weights, Δwiσi Manager 1 Manager 2 Manager 3 Manager 1 Manager 2 Manager 3 Security 1 0.1765 0.2353 0.1471 −0.0213 0.0340 −0.0085 Security 2 0.4000 0.1000 0.1500 0.0025 0.0000 0.0050 Security 3 0.4167 0.0000 0.0417 0.0090 −0.0120 0.0060 Security 4 0.2400 0.0800 0.0600 0.0063 −0.0250 −0.0125 The three managers have the following TCs: Manager 1 Manager 2 Manager 3 0.7267 0.8504 −0.0020 Transfer coefficient Manager 2 has the highest TC. _ _ 27. A is correct. Manager_ 1’s IR = TC × IC × √ ​ BR ​= 1.0 × 0.15 × √ ​ 50 ​= 1.06. Manager 2’s IR = 0.8 × 0.10 × √ ​ 100 ​= 0.80. Manager 1’s active return is 1.06(5.0) = 5.3%, and Manager 2’s expected active return is 0.80(5.0) = 4.0%. Manager 1 has the greater expected active return. 28. C is correct. If the decisions about each of the 200 stocks are not independent, and if the decisions about a stock from one month to the next are not independent, then Goudon Partners is overstating its estimates of its breadth and its expected active returns. 29. B is correct. Although the relaxation of portfolio constraints will increase the transfer coefficient (and expected active returns), the lower information coefficient reduces the information ratio and the expected active return. © CFA Institute. For candidate use only. Not for distribution. Practice Problems PRACTICE PROBLEMS The following information relates to questions 1-10 Brian Johnson is a senior manager at Star Asset Management (SAMN), a large asset management firm in the United States. Tim Martin has just earned his advanced degree in statistics and was hired to support the trading team at SAMN. Martin meets with Johnson to undergo a training relating to SAMN’s trading activities. Johnson begins the training with a review of the limit order book for Light Systems, Inc., which is presented in Exhibit 1. Three dealers make market for the shares of Light Systems. Based on these prices, SAMN’s trading desk executes a market sell order for 1,100 shares of Light Systems. Exhibit 1: Limit Order Book for Light Systems, Inc. Bid Dealer Time Entered Ask Price Size Dealer Time Entered Price Size B 10.10 a.m. $17.15 900 C 10.11 a.m. $17.19 1,200 C 10.11 a.m. $17.14 1,500 B 10.10 a.m. $17.20 800 A 10.11 a.m. $17.12 1,100 A 10.12 a.m. $17.22 1,100 Johnson then discusses a market buy order for 5,000 shares of an illiquid stock. The order was filled in three trades, and details about the three trades are presented in Exhibit 2. Exhibit 2: Buy Trade Order Details Trade # Time Trade Price Trade Size Bid Price Ask Price 9.45 a.m. $25.20 1,200 $25.17 $25.20 2 9.55 a.m. $25.22 1,300 $25.19 $25.22 3 11.30 a.m. $25.27 2,500 $25.22 $25.26 1 Johnson explains to Martin that the number of venues trading the same instruments has proliferated in recent years, and trading in any given instrument has now been distributed across these multiple venues. As a result, the available liquidity on any one of those exchanges represents just a small portion of the aggregate liquidity for that security. As a result, SAMN has had to adapt its trading strategies, particularly for large trades. Johnson asks Martin about his views on how the introduction of electronic trading might have impacted SAMN. Martin tells Johnson: 193 194 Learning Module 3 Trading Costs and Electronic Markets Statement 1 Once built, electronic trading systems are more efficient and cheaper to operate than floor-based trading systems. Statement 2 Electronic trading systems have attracted a lot of new buy-side traders, and the increased competition has resulted in narrower bid–ask spreads. Statement 3 The introduction of electronic markets has had a much greater impact on the trading of corporate and municipal bonds than on the trading of equities. Johnson tells Martin that communication speed is SAMN’s current highest priority. All of SAMN’s competitors have increased their communication speeds in recent months, and Johnson says management wants SAMN to be faster than its competitors. SAMN’s trading desk is located in a residential area far from downtown where the exchanges it works with are located. SAMN’s trading team is relatively large with experienced investment professionals, and the firm recently invested in fast computers with the latest algorithms. At the end of the training, Johnson gives Martin his first assignment. The assignment is for Martin to use the vast amount of data that SAMN has collected to design a machine learning (ML) model using advanced statistical methods to characterize data structures and relations. Then he has to build a trading algorithm based on the same model. Since electronic trading has added systemic risk to the market, Johnson asks Martin to suggest ways to minimize the systemic risk introduced by his algorithm. Martin offers two suggestions: Suggestion 1 Perform extensive testing of the algorithm before its launch. Suggestion 2 Impose mandatory trading halts if prices change outside a threshold range. A month into the job, Johnson sends Martin to an investment conference focused on abusive trading practices. Based on what he learned at the conference, Martin recommends to Johnson that SAMN incorporate a new rule that news be validated before a trade triggered by news is executed. 1. Based on Exhibit 1, the inside bid–ask spread for the limit order book for Light Systems is closest to: A. $0.04. B. $0.07. C. $0.10. 2. Based on Exhibit 1, the total amount that SAMN will receive, on a per share basis, for executing the market sell order is closest to: A. $17.14. B. $17.15. C. $17.22. 3. Based on Exhibit 2, the market impact relating to Trade 2, on a per share basis, is closest to: A. $0.02. B. $0.03. Practice Problems C. $0.07. 4. Based on Exhibit 2, the average effective spread of the three trades is closest to: A. $0.0333. B. $0.0367. C. $0.0400. 5. The reason for SAMN having to adapt its trading strategies is a result of: A. latency. B. market fragmentation. C. high frequency trading. 6. Which of Martin’s statements relating to the introduction of electronic markets is correct? A. Statement 1 B. Statement 2 C. Statement 3 7. Which of the following changes should SAMN make to address its key priority? A. Hire more investment professionals B. Upgrade to more complex operating systems C. Move the trading desk physically closer to the exchanges it works with 8. The model that Martin is tasked with designing will likely be most effective: A. for testing new markets. B. in a well-understood market environment. C. during periods of higher than normal market volatility. 9. Which of Martin’s suggestions will most likely be effective in limiting the systemic risk introduced by his algorithm? A. Only Suggestion 1 B. Only Suggestion 2 C. Both Suggestion 1 and Suggestion 2 10. Which market manipulation strategy is most likely the target of the new rule suggested by Martin? A. Rumormongering B. Gunning the market C. Trading for market impact 195 196 Learning Module 3 Trading Costs and Electronic Markets The following information relates to questions 11-16 Michael Bloomfield is a trader at 2Fast Trading, a proprietary trading company that uses machine learning and algorithms to execute trades. He works with Amy Riley, a junior trader at the company. Bloomfield and Riley meet to review the company’s trading systems and several trades in Bloomfield’s trading account. They discuss the increasing impact of market fragmentation on available liquidity for the company’s trading strategies. Riley makes the following comments regarding market fragmentation: Comment 1 Liquidity aggregation and smart order routing help traders manage the challenges and opportunities presented by fragmentation. Comment 2 With increasing market fragmentation, traders who fill large orders now search for liquidity across multiple venues and across time to control market impact. Bloomfield tells Riley that he noticed trades of 500 shares of BYYP stock were executed every 20 minutes for an hour. Bloomfield saw the same pattern of trading in the stock during the previous trading day. He instructs Riley to submit an order to purchase BYYP shares on the assumption that a trader seeks liquidity and is executing a large buy order by breaking it into pieces. The prices of these trades and the best bids and offers in the market when the BYYP trades occurred are presented in Exhibit 1. Exhibit 1: BYYP Trade Details Trade Trade Price Prevailing Bid Prevailing Offer 1 41.50 41.45 41.50 2 41.75 41.73 41.75 Bloomfield shifts the conversation to AXZ Corp. Bloomfield notes that AXZ’s bid–ask spread is narrow, even though AXZ’s share price has been experiencing a period of high volatility. After extensive research, Bloomfield will purchase AXZ shares using a trading strategy that does not include standing orders. Bloomfield then assesses the risks that 2Fast’s electronic trading strategies introduce into the market. He is concerned that these risks may bring on more regulation. Bloomfield claims that the risks can be reduced by changing the structure of the market, and those structural changes can maintain 2Fast’s primary competitive advantage, which is trading faster than competitors. Bloomfield mentions that a regulatory body is investigating a competitor’s trading practices. The investigation involves a tip that the competitor is manipulating markets by submitting orders and arranging trades to influence other traders’ perceptions of value. Specifically, regulators were informed that the competitor has been buying stock to raise its price, thereby encouraging momentum traders to buy, and then selling the stock to them at higher prices. The regulator confirmed that the competitor did not use standing limit orders or commonly controlled accounts for the trades under investigation. 11. Which of Riley’s comments related to market fragmentation is accurate? A. Only Comment 1 Practice Problems B. Only Comment 2 C. Both Comment 1 and Comment 2 12. Bloomfield’s strategy to purchase BYYP shares is best classified as electronic: A. arbitrage. B. front running. C. quote matching. 13. Based on Exhibit 1, the average effective spread of the BYYP trades is closest to: A. $0.018. B. $0.035. C. $0.070. 14. Bloomfield’s trading strategy for the purchase of AXZ shares most likely includes the use of: A. flickering quotes. B. machine learning. C. leapfrogging quotes. 15. Which structural change for the market associated with electronic trading systems is most consistent with Bloomfield’s claim? A. Delaying order processing by random intervals B. Exchanges using trade halts when prices move too quickly C. Slowing markets by running call markets once a second or more often instead of trading continuously 16. The competitor company’s trading is best described as: A. bluffing. B. spoofing. C. wash trading. 197 198 Learning Module 3 Trading Costs and Electronic Markets SOLUTIONS 1. A is correct. The inside bid–ask spread, or market bid–ask spread, is the difference between the highest bid price and the lowest ask price. The highest bid price for Light Systems is $17.15, and the lowest ask price is $17.19. Therefore, the inside bid–ask spread = $17.19 − $17.15 = $0.04. 2. B is correct. SAMN’s trading desk executes a market sell order for 1,100 shares. Based on the limit order book, the trader would first sell 900 shares at $17.15 (highest bid, Dealer B) and then sell the remaining 200 shares at $17.14 (second highest bid, Dealer C). Therefore, the approximate price per share received by SAMN for selling the 1,100 shares is equal to [(900 × $17.15) + (200 × $17.14)] / 1,100 = $17.1482 per share ($17.15 rounded). 3. A is correct. Market impact, or price impact, is the effect of a trade on transaction prices. After the first trade (Trade 1) was executed at $25.20, Trade 2 was executed at $25.22, which is $0.02 per share higher than the trade price of Trade 1. So, the execution of Trade 1 led to a price impact of $0.02 per share on Trade 2. 4. C is correct. The effective bid–ask spread for buy orders is calculated as: Effective bid–ask spread (buy order) = 2 × {Trade price − [(Ask price + Bid price) / 2)]} or = 2 × (Trade price − Midpoint of the market at the time an order is entered). So, the effective bid–ask spreads for the three buy trades are calculated as: Effective spread of Trade 1 = 2 × {$25.20 − [($25.20 + $25.17)/2]} = $0.0300. Effective spread of Trade 2 = 2 × {$25.22 − [($25.22 + 25.19)/2]} = $0.0300. Effective spread of Trade 3 = 2 × {$25.27 − [($25.26 + $25.22)/2]} = $0.0600. The resulting average effective spread is then calculated as: Average effective spread = (Effective spread of Trade 1 + Effective spread of Trade 2 + Effective spread of Trade 3)/3. Average effective spread = ($0.0300 + $0.0300 + $0.0600)/3 = $0.0400. 5. B is correct. According to Johnson, markets have become increasingly fragmented as the number of venues trading the same instruments has proliferated and trading in any given instrument has been split (or fragmented) across these multiple venues. As a result, the available liquidity on any one exchange represents just a small portion of the aggregate liquidity for that instrument. This phenomenon is known as market fragmentation and creates the potential for price and liquidity disparities across venues. As a result, SAMN has had to adapt its trading strategies to this fragmented liquidity to avoid intensifying the market impact of a large trade. 6. A is correct. Once built, electronic systems are indeed cheaper to operate than floor-based trading systems. They require less physical space than do trading floors, and in contrast to floor-based trading systems, they do not require exchange officials to record and report prices. Furthermore, the widespread use of electronic trading systems significantly decreased trading costs for buy-side Solutions traders. Costs fell as exchanges obtained greater cost efficiencies from using electronic matching systems instead of floor-based manual trading systems. These technologies also decreased costs and increased efficiencies for the dealers and arbitrageurs who provide much of the liquidity offered at exchanges. Competition forced them to pass along much of the benefits of their new technologies to buy-side traders in the form of narrower spreads quoted for larger sizes. New electronic buy-side order management systems also decreased buy-side trading costs by allowing a smaller number of buy-side traders to process more orders and to process them more efficiently than manual traders. While electronic trading has had a significant effect on equity markets, it has not had as much of an effect on the markets for corporate and municipal bonds. The market structures of corporate and municipal bond markets have hardly changed since the late 19th century. Despite the efforts of many creative developers of electronic bond trading systems, most public investors in these markets still trade largely over the counter with dealers. 7. C is correct. The speed required by electronic traders is affected by fast communication and fast computations. The shorter the distance between the trader and the exchange, the faster the communication. Many exchanges allow electronic traders to place their servers in the rooms where the exchange servers operate, a practice called collocation. 8. B is correct. Many trading problems are ideally suited for machine learning analyses because the problems repeat regularly and often. For such problems, machine-based learning systems can be extraordinarily powerful. However, these systems are often useless—or worse—when trading becomes extraordinary, as when volatilities shoot up. Machine learning systems frequently do not produce useful information during volatility episodes because they have few precedents from which the machines can learn. Thus, traders often instruct their electronic trading systems to stop trading—and sometimes to close out their positions— whenever they recognize that they are entering uncharted territory. Many traders shut down when volatility spikes—both because high-volatility episodes are uncommon and thus not well understood and because even if such episodes were well understood, they represent periods of exceptionally high risk. 9. C is correct. Both suggestions will likely be effective in minimizing the systemic risk introduced by electronic trading. First, exhaustive testing of the algorithm prior to its launch can minimize risk relating to programming errors, which could result in an extreme market reaction that could trigger an even more extreme market reaction. Second, imposing mandatory trade halts in case of large price changes (outside a given threshold) would limit potential undesired results and help minimize systemic risk. 10. A is correct. Rumormongering is the dissemination of false information about fundamental values or about other traders’ trading intentions in an attempt to alter investors’ value assessments. Martin’s suggested news validation rule would reduce the likelihood that SAMN would be adversely affected by this market manipulation strategy. 11. C is correct. Both of Riley’s comments are correct. Electronic algorithmic trading techniques, such as liquidity aggregation and smart order routing, help traders manage the challenges and opportunities presented by fragmentation. Liquidity aggregators create “super books” that present liquidity across markets for a given instrument. These tools offer global views of market depth (available liquidity) for each instrument regardless of the trading venue that offers the liquidity. Smart order-routing algorithms send orders to the markets that display the best quoted prices and sizes. Additionally, with increasing market fragmentation, traders 199 200 Learning Module 3 Trading Costs and Electronic Markets filling large orders adapt their trading strategies to search for liquidity across multiple venues and across time to control the market impacts of their trades. 12. B is correct. Bloomfield noticed a pattern of trading in BYYP and decided to front run shares on the assumption that a trader is in the market filling a large buy order by breaking it into pieces. Electronic front runners trade in front of traders who demand liquidity. They identify when large traders or many small traders are trying to fill orders on the same side of the market. The order anticipation strategies of electronic front runners try to identify predictable patterns in order submission. They may search for patterns in order submissions, trades, or the relations between trades and other events. A is incorrect because electronic arbitrageurs look across markets for arbitrage opportunities in which they can buy an undervalued instrument and sell a similar overvalued one. His decision to purchase BYYP shares is based on the pattern of trading that Bloomfield observed. C is incorrect because quote matchers trade in front of traders who supply (not demand) liquidity. Bloomfield decides to purchase BYYP shares on the assumption that a trader is in the market seeking (not supplying) liquidity, which is consistent with front running (not quote matching). Quote matchers trade in front of traders who supply liquidity and try to exploit the option values of standing orders. Quote matchers buy when they believe they can rely on standing buy orders to get out of their positions, and they sell when they can do the same with standing sell orders. 13. B is correct. The effective spread is calculated as follows: ​Effective spread = 2 × ​(​ ​Trade price − Midpoint of market at time of order entry​) ​Effective spread of Trade 1 = 2 × ​(​ ​$41.50 − $41.475​)​​ = $0.05 ​Effective spread of Trade 2 = 2 × ​​(​$41.75 − $41.74​)​​ = $0.02 ​Average Effective Spread = ​(​ ​$0.05 + $0.02​)​​/ 2 = $0.035 14. A is correct. Flickering quotes are exposed limit orders that electronic traders submit and then cancel shortly thereafter, often within a second. Electronic dealers and algorithmic buy-side traders submit and repeatedly cancel and resubmit their orders when they do not want their orders to stand in the market; rather, they want other traders to see that they are willing to trade at the displayed price. Bloomfield does not want his orders to stand in the market; using flickering quotes to purchase AXZ shares would satisfy that objective. B is incorrect because AXZ shares are currently in a period of high volatility, so Bloomfield would not likely use machine learning to execute his trades. Machine-learning systems frequently do not produce useful information during volatility episodes because these episodes have few precedents from which the machines can learn. Machine-learning methods produce models based on observed empirical regularities rather than on theoretical principles identified by analysts. Many traders shut down when volatility spikes, both because high-volatility episodes are uncommon and thus not well understood and because even if such episodes were well understood, they represent periods of exceptionally high risk. C is incorrect because market participants use leapfrogging quotes when spreads are wide (not narrow), and Bloomfield noted that the bid–ask spread for AXZ shares is narrow. When bid–ask spreads are wide, dealers often are willing to trade at better prices than they quote. They quote wide spreads because they hope to trade at more favorable prices. When another trader quotes a better Solutions price, dealers often immediately quote an even better price. If the spread is sufficiently wide, a game of leapfrog may ensue as the dealer jumps ahead again. 15. B is correct. To reduce the systemic risks associated with fast trading, some exchanges have adopted trade halts when prices move too quickly. These rules stop trading when excess demand for liquidity occurs. They also prevent the extreme price changes that can occur in electronic markets when market orders arrive and no liquidity is present. 2Fast Trading’s competitive advantage will be maintained despite exchange trading halts because the company will be free to trade faster than its competitors once trading resumes. Therefore, exchanges using trade halts to stop trading is the risk reduction strategy that most likely maintains 2Fast Trading’s competitive advantage and is consistent with Bloomfield’s claim that risks can be reduced by changing the structure of the market. A is incorrect because delaying order processing by random intervals reduces the benefits of high-frequency traders being faster than their competitors and investing in speed. Therefore, delaying order processing by random order intervals does not maintain 2Fast Trading’s primary competitive advantage, which is trading faster than competitors, because that advantage will be reduced. C is incorrect because slowing markets by running call markets once a second or more often instead of trading continuously diminishes the benefits of high-frequency traders being faster than their competitors and investing with speed. Therefore, slowing markets once a second or more often instead of trading continuously does not maintain 2Fast Trading’s primary competitive advantage, which is trading faster than competitors, because that advantage will be reduced. 16. A is correct. Bluffing involves submitting orders and arranging trades to influence other traders’ perceptions of value. Bluffers often prey on momentum traders, who buy when prices are rising and sell when prices are falling. Similarly, Bloomfield mentioned that regulators were informed that 2Fast’s competitor has been submitting orders and arranging trades to influence other traders’ perceptions of value; regulators were informed the competitor has been buying stock to raise its price, thereby encouraging momentum traders to buy, and then selling the stock to them at higher prices. B is incorrect because the competitor did not use standing limit orders—those orders that are used in a spoofing strategy—for the trades the regulator is investigating. Spoofing is a trading practice in which traders place exposed standing limit orders to convey an impression to other traders that the market is more liquid than it is or to suggest to other traders that the security is under- or overvalued. C is incorrect because the competitor did not use commonly controlled accounts—those accounts that are used in a wash trading strategy—for the trades that regulators are investigating. Wash trading consists of trades arranged among commonly controlled accounts to create the impression of market activity at a particular price. The purpose of wash trading is to fool investors into believing that a market is more liquid than it truly is and to thereby increase investors’ confidence both in their ability to exit positions without substantial cost and in their assessments of security values. 201