You are a corporate treasurer who will purchase $1 million of bonds for the sinking fund in 3 months. You believe rates will soon fall, and you would like to repurchase the company’s sinking fund bonds (which currently are selling below par) in advance of requirements. Unfortunately, you must obtain approval from the board of directors for such a purchase, and this can take up to 2 months. What action can you take in the futures market to hedge any adverse movements in bond yields and prices until you can actually buy the bonds? Will you be long or short? Why? A qualitative answer is fine.
> In Figure 25.2, we provide stock market returns in both local and dollar-denominated terms. Which of these is more relevant? What does this have to do with whether the foreign exchange risk of an investment has been hedged?
> The Generic Genetic (GG) Corporation pays no cash dividends currently and is not expected to for the next four years. Its latest EPS was $5, all of which was reinvested in the company. The firm’s expected ROE for the next four years is 20% per year, duri
> Do you agree with the following claim? “U.S. companies with global operations can give you international diversification.” Think about both business risk and foreign exchange risk.
> Consider the two (excess return) index-model regression results for stocks A and B. The risk-free rate over the period was 6%, and the market’s average return was 14%. Performance is measured using an index model regression on excess re
> Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 12% and 16%, respectively. The beta of A is .7, while that of B is 1.4. The T-bill rate is currently 5%, whereas the expected rate of retu
> A manager buys three shares of stock today and then sells one of those shares each year for the next three years. His actions and the price history of the stock are summarized below. The stock pays no dividends. a. Calculate the time-weighted geometric a
> XYZ’s stock price and dividend history are as follows: An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaini
> Consider the rate of return of stocks ABC and XYZ. a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? c. Calculate the geometric average returns of each stock.
> We have seen that market timing has tremendous potential value. Would it therefore be wise to shift resources to timing at the expense of security selection?
> We know that the geometric average (time-weighted return) on a risky investment is always lower than the corresponding arithmetic average. Can the IRR (the dollar-weighted return) similarly be ranked relative to these other two averages?
> Kelli Blakely is a portfolio manager for the Miranda Fund, a core large-cap equity fund. The market proxy and benchmark for performance measurement purposes is the S&P 500. Although the Miranda portfolio generally mirrors the asset class and sector w
> Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been hearing more and more about benchmark portfolios and is interested in trying this approach. As such, the company hired Sally Jones, CFA, as a consulta
> Recalculate the intrinsic value of Rio Tinto shares using the free cash flow model of Spreadsheet 18.2 (available in Connect; link to Chapter 18 material) under each of the following assumptions. Treat each scenario independently. a. Rio Tinto’s P/E rati
> Is it possible for a positive alpha to be associated with inferior performance? Explain.
> Primo Management Co. is looking at how best to evaluate the performance of its managers. Primo has been hearing more and more about benchmark portfolios and is interested in trying this approach. As such, the company hired Sally Jones, CFA, as a consulta
> Bill Smith is evaluating the performance of four large-cap equity portfolios: Funds A, B, C, and D. As part of his analysis, Smith computed the Sharpe ratio and the Treynor measure for all four funds. Based on his finding, the ranks assigned to the four
> During a particular year, the T-bill rate was 6%, the market return was 14%, and a portfolio manager with beta of .5 realized a return of 10%. a. Evaluate the manager based on the portfolio alpha. b. Reconsider your answer to part (a) in view of the empi
> Conventional wisdom says that one should measure a manager’s investment performance over an entire market cycle. What arguments support this convention? What arguments contradict it?
> A global equity manager is assigned to select stocks from a universe of large stocks throughout the world. The manager will be evaluated by comparing her returns to the return on the MSCI World Market Portfolio, but she is free to hold stocks from variou
> Evaluate the market timing and security selection abilities of four managers whose performances are plotted in the accompanying diagrams.
> A household savings-account spreadsheet shows the following entries: Use the Excel function XIRR to calculate the dollar-weighted average return between the first and final dates.
> You manage a $23 million portfolio, currently all invested in equities, and believe that the market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction co
> Suppose that the value of the S&P 500 stock index is 2,000. a. If each E-mini futures contract (with a contract multiplier of $50) costs $25 to trade with a discount broker, how much is the transaction cost per dollar of stock controlled by the futures c
> The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyrong Corporation has a beta coefficient of 1.2. Xyrong pays out 40% of its earnings in dividends, and the latest earnings announced were $1
> Consider the futures contract written on the S&P 500 index and maturing in one year. The interest rate is 3%, and the future value of dividends expected to be paid over the next year is $35. The current index level is 2,000. Assume that you can short sel
> You believe that the spread between municipal bond yields and U.S. Treasury bond yields is going to narrow in the coming month. How can you profit from such a change using the municipal bond and T-bond futures contracts?
> Both gold-mining firms and oil-producing firms might choose to use futures to hedge uncertainty in future revenues due to price fluctuations. But trading activity sharply tails off for maturities beyond one year. Suppose a firm wishes to use available (s
> Consider these futures market data for the June delivery S&P 500 contract, exactly one year from today. The S&P 500 index is at 2,145, and the June maturity contract is at F0 = 2,146. a. If the current interest rate is 2.5%, and the average dividend rate
> Suppose the 1-year futures price on a stock-index portfolio is 1,914, the stock index currently is 1,900, the 1-year risk-free interest rate is 3%, and the year-end dividend that will be paid on a $1,900 investment in the market index portfolio is $40. a
> Suppose that at the present time, one can enter 5-year swaps that exchange LIBOR for 5%. An off-market swap would then be defined as a swap of LIBOR for a fixed rate other than 5%. For example, a firm with 7% coupon debt outstanding might like to convert
> Firm ABC enters a 5-year swap with firm XYZ to pay LIBOR in return for a fixed 6% rate on notional principal of $10 million. Two years from now, the market rate on 3-year swaps is LIBOR for 5%; at this time, firm XYZ goes bankrupt and defaults on its swa
> Suppose the U.S. yield curve is flat at 4% and the euro yield curve is flat at 3%. The current exchange rate is $1.20 per euro. What will be the swap rate on an agreement to exchange currency over a 3-year period? The swap calls for the exchange of 1 mil
> Suppose that the price of corn is risky, with a beta of .5. The monthly storage cost is $.03 per bushel, and the current spot price is $5.50, with an expected spot price in three months of $5.88. If the expected rate of return on the market is 0.9% per m
> A U.S. exporting firm may use foreign exchange futures to hedge its exposure to exchange rate risk. Its position in futures will depend in part on anticipated payments from its customers denominated in foreign currency. a. In general, however, should its
> FinCorp’s free cash flow to the firm is reported as $205 million. The firm’s interest expense is $22 million. Assume the corporate tax rate is 21% and the net debt of the firm increases by $3 million. What is the market value of equity if the FCFE is pro
> If the corn harvest today is poor, would you expect this fact to have any effect on today’s futures prices for corn to be delivered (post-harvest) two years from today? Under what circumstances will there be no effect?
> a. If the spot price of gold is $1,500 per troy ounce, the risk-free interest rate is 2%, and storage and insurance costs are zero, what should be the forward price of gold for delivery in one year? Use an arbitrage argument to prove your answer. b. Show
> A corporation plans to issue $10 million of 10-year bonds in three months. At current yields the bonds would have modified duration of 8 years. The T-note futures contract is selling at F0 = 100 and has modified duration of 6 years. How can the firm use
> Yields on short-term bonds tend to be more volatile than yields on long-term bonds. Suppose that you have estimated that the yield on 20-year bonds changes by 10 basis points for every 15-basis-point move in the yield on 5-year bonds. You hold a $1 milli
> Return to Figure 23.7. Suppose the LIBOR rate when the first listed Eurodollar contract matures in January is 3.0%. What will be the profit or loss to each side of the Eurodollar contract?
> Consider the following information: rUS = 4%; rUK = 7% E0 = 2.00 dollars per pound F0 = 1.98 (1-year delivery) where the interest rates are annual yields on U.S. or U.K. bills. Given this information: a. Where would you lend? b. Where would you borrow? c
> A stock’s beta is a key input to hedging in the equity market. A bond’s duration is key in fixed income hedging. How are they used similarly? Are there any differences in the calculations necessary to formulate a hedge position in each market?
> Determine how a portfolio manager might use financial futures to hedge risk in each of the following circumstances: a. You own a large position in a relatively illiquid bond that you want to sell. b. You have a large gain on one of your Treasuries and wa
> a. Turn to the Mini-S&P 500 contract in Figure 22.1. If the margin requirement is 10% of the futures price times the contract multiplier of $50, how much must you deposit with your broker to trade the June maturity contract? b. If the June futures price
> Evaluate the criticism that futures markets siphon off capital from more productive uses.
> Atech has fixed costs of $7 million and profits of $4 million. Its competitor, ZTech, is roughly the same size and this year earned the same profits, $4 million. However, ZTech operates with fixed costs of only $5 million but higher variable costs. a. Wh
> What is the difference between the futures price and the value of the futures contract?
> Are the following statements true or false? Why? a. All else equal, the futures price on a stock index with a high dividend yield should be higher than the futures price on an index with a low dividend yield. b. All else equal, the futures price on a hig
> a. How should the parity condition (Equation 22.2) for stocks be modified for futures contracts on Treasury bonds? What should play the role of the dividend yield in that equation? b. In an environment with an upward-sloping yield curve, should T-bond fu
> The multiplier for a futures contract on a stock market index is $50. The maturity of the contract is 1 year, the current level of the index is 2,250, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Sup
> It is now January. The current interest rate is 2%. The June futures price for gold is $1,500, whereas the December futures price is $1,510. Is there an arbitrage opportunity here? If so, how would you exploit it?
> Suppose the value of the S&P 500 stock index is currently 2,000. a. If the 1-year T-bill rate is 3% and the expected dividend yield on the S&P 500 is 2%, what should the 1-year maturity futures price be? b. What if the T-bill rate is less than the divide
> We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80. a. Show that the range of S is 50, whereas that of P is 30 across the two states. What is the hedge ratio of
> In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be 4%. Assume the stocks on which these options are written pay no dividends. Which put opti
> Return to Problem 38. a. What will be the payoff to the put, Pu, if the stock goes up? b. What will be the payoff, Pd, if the stock price falls? c. Value the put option using the risk-neutral shortcut described in the box in Section 21.3. d. Confirm that
> Eagle Products’ EBIT is $300, its tax rate is 21%, depreciation is $20, capital expenditures are $60, and the planned increase in net working capital is $30. What is the free cash flow to the firm?
> Return to Problem 36. Value the call option using the risk-neutral shortcut described in the box in Section 21.3. Confirm that your answer matches the value you get using the two-state approach. Problem 36: You are attempting to value a call option with
> Suppose that JPMorgan Chase sells call options on $1.25 million worth of a stock portfolio with beta = 1.5. The option delta is .8. It wishes to hedge its resultant exposure to a market advance by buying a market-index portfolio. a. How many dollars’ wor
> Using the data in Problem 46, suppose that 3-month put options with a strike price of $90 are selling at an implied volatility of 34%. Construct a delta-neutral portfolio comprising positions in calls and puts that will profit when the option prices come
> Suppose that call options on ExxonMobil stock with time to expiration 3 months and strike price $90 are selling at an implied volatility of 30%. ExxonMobil stock price is $90 per share, and the risk-free rate is 4%. a. If you believe the true volatility
> You are a provider of portfolio insurance and are establishing a 4-year program. The portfolio you manage is worth $100 million, and you hope to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pa
> You are holding call options on a stock. The stock’s beta is .75, and you are concerned that the stock market is about to fall. The stock is currently selling for $5 and you hold 1 million options (i.e., you hold 10,000 contracts for 100 shares each). Th
> Goldman Sachs believes that market volatility will be 20% annually for the next three years. Three-year at-the-money call and put options on the market index sell at an implied volatility of 22%. What options portfolio can Goldman establish to speculate
> “The beta of a call option on the S&P 500 index with an exercise price of 2,430 is greater than the beta of a call on the index with an exercise price of 2,440.” True or false?
> “The beta of a call option on FedEx is greater than the beta of a share of FedEx.” True or false?
> XYZ Corp. will pay a $2 per share dividend in two months. Its stock price currently is $60 per share. A European call option on XYZ has an exercise price of $55 and 3-month time to expiration. The risk-free interest rate is .5% per month, and the stock’s
> Mary Smith, a CFA candidate, was recently hired for an analyst position at a large bank in London. Her first assignment is to examine the competitive strategies employed by various French wineries. Smith’s report identifies four winerie
> Calculate the value of a put option with exercise price $100 using the data in Problem 36. Show that put-call parity is satisfied by your solution. Problem 36: You are attempting to value a call option with an exercise price of $100 and one year to expi
> A newly issued bond paying a semiannual coupon has the following characteristics: a. Calculate modified duration using the information above. b. Explain why modified duration is a better measure than maturity when calculating the bond’s
> Louise and Christopher Maclin (see Problem 8) have purchased their house and made the donation to the local charity. Now that an investment policy statement has been prepared for the Maclins, Grant Webb recommends that they consider the strategic asset a
> Christopher Maclin, aged 40, is a supervisor at Barnett Co. and earns an annual salary of £80,000 before taxes. Louise Maclin, aged 38, stays home to care for their newborn twins. She recently inherited £900,000 (after wealth-tr
> John Franklin is a recent widower with some experience in investing for his own account. Following his wife’s recent death and settlement of the estate, Mr. Franklin owns a controlling interest in a successful privately held manufacturing company in whic
> Susan Fairfax is president of Reston Industries, a U.S.-based company whose sales are entirely domestic and whose shares are listed on the New York Stock Exchange. The following are additional facts concerning her current situation: ∙ F
> Jarvis University (JU) is a private, multiprogram U.S. university with a $2 billion endowment fund as of fiscal year-end May 31, 2025. With little government support, JU is heavily dependent on its endowment fund to support ongoing expenditures, especial
> Sam Short, CFA, has recently joined the investment management firm of Green, Spence, and Smith (GSS). For several years, GSS has worked for a broad array of clients, including employee benefit plans, wealthy individuals, and charitable organizations. Als
> Angus Walker, CFA, is reviewing the defined benefit pension plan of Acme Industries. Based in London, Acme has operations in North America, Japan, and several European countries. Next month, the retirement age for full benefits under the plan will be low
> After much research on the developing economy and capital markets of the country of Otunia, your firm, GAC, has decided to include an investment in the Otunia stock market in its Emerging Markets Commingled Fund. However, GAC has not yet decided whether
> Sisters Corp. expects to earn $6 per share next year. The firm’s ROE is 15% and its plowback ratio is 60%. If the firm’s market capitalization rate is 10%, what is the present value of its growth opportunities?
> a. Pamela Itsuji, a currency trader for a Japanese bank, is evaluating the price of a 6-month Japanese yen/U.S. dollar currency futures contract. She gathers the following currency and interest rate data: Japanese yen/U.S. dollar spot currency exchange r
> The Windsor Foundation, a U.S.-based, not-for-profit charitable organization, has a diversified investment portfolio of $100 million. Windsor’s board of directors is considering an initial investment in emerging market equities. Robert Houston, treasurer
> A global manager plans to invest $1 million in U.S. government cash equivalents for the next 90 days. However, she is also authorized to use non–U.S. government cash equivalents, as long as the currency risk is hedged to U.S. dollars us
> You are a U.S. investor considering purchase of one of the following securities. Assume that the currency risk of the Canadian government bond will be hedged, and the 6-month discount on Canadian dollar forward contracts is −.75% versus
> John Irish, CFA, is an independent investment adviser who is assisting Alfred Darwin, the head of the Investment Committee of General Technology Corporation, to establish a new pension fund. Darwin asks Irish about international equities and whether the
> An analyst wants to evaluate portfolio X, consisting entirely of U.S. common stocks, using both the Treynor and Sharpe measures of portfolio performance. The following table provides the average annual rate of return for portfolio X, the market portfolio
> The Retired Fund is an open-ended mutual fund composed of $500 million in U.S. bonds and U.S. Treasury bills. This fund has had a portfolio duration (including T-bills) of between 3 and 9 years. Retired has shown first-quartile performance over the past
> Carl Karl, a portfolio manager for the Alpine Trust Company, has been responsible since 2023 for the City of Alpine’s Employee Retirement Plan, a municipal pension fund. Alpine is a growing community, and city services and employee payr
> James Chan is reviewing the performance of the global equity managers of the Jarvis University endowment fund. Williamson Capital is currently the endowment fund’s only large-capitalization global equity manager. Performance data for Wi
> Trustees of the Pallor Corp. pension plan ask consultant Donald Millip to comment on the following statements. What should his response be? a. Median manager benchmarks are statistically unbiased measures of performance over long periods of time. b. Medi
> During the annual review of Acme’s pension plan, several trustees questioned their investment consultant about various aspects of performance measurement and risk assessment. a. Comment on the appropriateness of using each of the following benchmarks for
> a. Footnote 7 presents the formula for the convexity of a bond. Build a spreadsheet to calculate the convexity of a 5-year, 8% coupon bond making annual payments at the initial yield to maturity of 10%. b. What is the convexity of a 5-year zero-coupon bo
> You and a prospective client are considering the measurement of investment performance, particularly with respect to international portfolios for the past five years. The data you discussed are presented in the following table: a. Assume that the data fo
> You ran a regression of the yield of KC Company’s 10-year bond on the 10-year U.S. Treasury benchmark’s yield using month-end data for the past year. You found the following result: YieldKC = 0.54 + 1.22 YieldTreasury where YieldKC is the yield on the K
> You are provided the information outlined as follows to be used in solving this problem. Situation A A fixed-income manager holding a $20 million market value position of U.S. Treasury 11¾% bonds maturing November 15, 2035, expects the econ
> Janice Delsing, a U.S.-based portfolio manager, manages an $800 million portfolio ($600 million in stocks and $200 million in bonds). In reaction to anticipated short-term market events, Delsing wishes to adjust the allocation to 50% stock and 50% bonds
> After studying Iris Hamson’s credit analysis, George Davies is considering whether he can increase the holding-period return on Yucatan Resort’s excess cash holdings (which are held in pesos) by investing those cash ho
> René Michaels, CFA, plans to invest $1 million in U.S. government cash equivalents for the next 90 days. Michaels’s client has authorized her to use non–U.S. government cash equivalents, but only if the cu
> Suppose your client says, “I am invested in Japanese stocks but want to eliminate my exposure to this market for a period of time. Can I accomplish this without the cost and inconvenience of selling out and buying back in again if my expectations change?
> Donna Doni, CFA, wants to explore potential inefficiencies in the futures market. The TOBEC stock index has a spot value of 185. TOBEC futures contracts are settled in cash and underlying contract values are determined by multiplying $100 times the index
> Ken Webster manages a $400 million equity portfolio benchmarked to the S&P 500 index. Webster believes the market is overvalued when measured by several traditional fundamental/ economic indicators. He is concerned about potential losses but recogniz
> A stock index is currently trading at 50. Paul Tripp, CFA, wants to value 2-year index options using the binomial model. The stock will either increase in value by 20% or fall in value by 20%. The annual risk-free interest rate is 6%. No dividends are pa
