Tutorial 1 Finance PDF

**Tutorial 1** **Question 1** An analyst gathers the following information: Security **Standard Deviation (%)** **Beta** ------------ ---------------------------- ---------- Security 1 25 1.50 Security 2 15 1.40 Security 3...

**Tutorial 1** **Question 1** An analyst gathers the following information: Security **Standard Deviation (%)** **Beta** ------------ ---------------------------- ---------- Security 1 25 1.50 Security 2 15 1.40 Security 3 20 1.60 1. With respect to the capital asset pricing model, if the expected market risk premium is 6% and the risk-free rate is 3%, the expected return for Security 1 is *closest* to...? 2. With respect to the capital asset pricing model, if expected return for Security 2 is equal to 11.4% and the risk-free rate is 3%, the expected return for the market is *closest* to...? 3. With respect to the capital asset pricing model, if the expected market risk premium is 6% the security with the *highest* expected return is...? 4. With respect to the capital asset pricing model, a decline in the expected market return will have the *greatest* impact on the expected return of...? 5. If the correlation between the security 3 and the market is 0.7, what is the standard deviation of the market return? A British pension fund has employed three investment managers, each of whom is responsible for investing in one-third of all asset classes so that the pension fund has a well-diversified portfolio. Information about the managers is given below. Manager Return σ β --------------------- -------- ----- ----- X 10% 20% 1.1 Y 11% 10% 0.7 Z 12% 25% 0.6 Market (M) 9% 19% ? Risk-free rate (Rf) 3% ? ? 1. Calculate the expected return, Sharpe ratio, Treynor ratio, M2, and Jensen's alpha. Analyze your results and plot the returns and betas of these portfolios. **\ ** **Tutorial 3** **The following information relates to Questions 1--5** Ed Smith is a new trainee in the foreign exchange (FX) services department of a major global bank. Smith's focus is to assist senior FX trader, Feliz Mehmet, CFA. Mehmet mentions that an Indian corporate client exporting to the United Kingdom wants to estimate the potential hedging cost for a sale closing in one year. Smith is to determine the premium/discount for an annual (360 day) forward contract using the exchange rate data presented in Exhibit 1. Exhibit 1. Select Currency Data for GBP and INR Spot (INR/GBP) 79.5093 ------------------------------ --------- Annual (360-day) Libor (GBP) 5.43% Annual (360-day) Libor (INR) 7.52% Mehmet is also looking at two possible trades to determine their profit potential. The first trade involves a possible triangular arbitrage trade using the Swiss, US and Brazilian currencies, to be executed based on a dealer's bid/offer rate quote of 0.5161/0.5163 in CHF/BRL and the interbank spot rate quotes presented in Exhibit 2. Exhibit 2. Interbank Market Quotes **Currency Pair** **Bid/Offer** ------------------- --------------- CHF/USD 0.9099/0.9101 BRL/USD 1.7790/1.7792 Mehmet is also considering a carry trade involving the USD and the Euro. He anticipates it will generate a higher return than buying a one-year domestic note at the current market quote due to low US interest rates and his predictions of exchange rates in one year. To help Mehmet assess the carry trade, Smith provides Mehmet with selected current market data and his one-year forecasts in Exhibit 3. Exhibit 3. Spot Rates and Interest Rates for Proposed Carry Trade -------------------------------------------------------------------------------------------------------------------- **Today's one-year Libor** **Currency pair\ **Spot rate today** **Projected spot rate in one year** (Price/Base)** ---------------------------- ------------------ --------------------- ------------------------------------- -------- USD 0.80% CAD/USD 1.0055 1.0006 CAD 1.71% EUR/CAD 0.7218 0.7279 EUR 2.20% -------------------------------------------------------------------------------------------------------------------- Finally, Mehmet asks Smith to assist with a trade involving a US multinational customer operating in Europe and Japan. The customer is a very cost-conscious industrial company with a AA credit rating and strives to execute its currency trades at the most favorable bid/offer spread. Because its Japanese subsidiary is about to close on a major European acquisition in three business days, the client wants to lock in a trade involving the Japanese yen and the Euro as early as possible the next morning, preferably by 8:05 AM New York time. At lunch, Smith and other FX trainees discuss how best to analyze currency market volatility from ongoing financial crises. The group agrees that a theoretical explanation of exchange rate movements, such as the framework of the international parity conditions, should be applicable across all trading environments. They note such analysis should enable traders to anticipate future spot exchange rates. But they disagree on which parity condition best predicts exchange rates, voicing several different assessments. Smith concludes the discussion on parity conditions by stating to the trainees: "I believe that in the current environment both covered and uncovered interest rate parity conditions are in effect." 1. Based upon Exhibit 1, what is the forward premium (discount) for a 360-day INR/GBP forward contract is? 2. Based on Exhibit 2, what is the *most* appropriate recommendation regarding the triangular arbitrage trade? 3. Based on Exhibit 3, compute the potential all-in USD return on the carry trade. 4. Which factor is *least likely* to lead to a narrow bid/offer spread for the industrial company's needed currency trade? 5. If Smith's statement on parity conditions is correct, how future spot exchange rates are *most likely* to be forecast? **Tutorial 4** 5. An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information: **ETF** **Time Since Inception** **Return Since Inception (%)** --------- -------------------------- -------------------------------- 1 146 days 4.61 2 5 weeks 1.10 3 15 months 14.35 The ETF with the highest annualized rate of return is...? 6. With respect to capital market theory, which of the following asset characteristics is *least likely* to impact the variance of an investor's equally weighted portfolio? A. Return on the asset. B. Standard deviation of the asset. C. Covariances of the asset with the other assets in the portfolio. 7. A portfolio manager creates the following portfolio: **Security** **Security Weight (%)** **Expected Standard Deviation (%)** -------------- ------------------------- ------------------------------------- 1 30 20 2 70 12 If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is *closest* to...? 8. A portfolio manager creates the following portfolio: **Security** **Security Weight (%)** **Expected Standard Deviation (%)** -------------- ------------------------- ------------------------------------- 1 30 20 2 70 12 If the covariance of returns between the two securities is −0.0240, the expected standard deviation of the portfolio is *closest* to...? **Tutorial 5** **Question 1** 1. Compare the assumptions of the arbitrage pricing theory (APT) with those of the capital asset pricing model (CAPM). 2. Last year the return on Harry Company stock was 5 percent. The portion of the return on the stock not explained by a two-factor macroeconomic factor model was 3 percent. Using the data given below, calculate Harry Company stock's expected return. **Variable** **Actual Value (%)** **Expected Value (%)** **Stock's Factor Sensitivity** ------------------------- ---------------------- ------------------------ -------------------------------- Change in interest rate 2.0 0.0 --1.5 Growth in GDP 1.0 4.0 2.0 3. Assume that the following one-factor model describes the expected return for portfolios: **Portfolio** **Expected Return** **Factor Sensitivity** --------------- --------------------- ------------------------ A 0.20 0.80 B 0.15 1.00 C 0.24 1.20 4. Which type of factor model is most directly applicable to an analysis of the style orientation (for example, growth vs. value) of an active equity investment manager? Justify your answer. 5. Suppose an active equity manager has earned an active return of 110 basis points, of which 80 basis points is the result of security selection ability. Explain the likely source of the remaining 30 basis points of active return. 6. Address the following questions about the information ratio. A. What is the information ratio of an index fund that effectively meets its investment objective? A. What are the two types of risk an active investment manager can assume in seeking to increase his information ratio? 7. A wealthy investor has no other source of income beyond her investments and that income is expected to reliably meet all her needs. Her investment advisor recommends that she tilt her portfolio to cyclical stocks and high-yield bonds. Explain the advisor's advice in terms of comparative advantage in bearing risk. **Question 2** Carlos Altuve is a manager-of-managers at an investment company that uses quantitative models extensively. Altuve seeks to construct a multi-manager portfolio using some of the funds managed by portfolio managers within the firm. Maya Zapata is assisting him. Altuve uses arbitrage pricing theory (APT) as a basis for evaluating strategies and managing risks. From his earlier analysis, Zapata knows that Funds A and B in Exhibit 1 are well diversified. He has not previously worked with Fund C and is puzzled by the data because it is inconsistent with APT. He asks Zapata gather additional information on Fund C's holdings and to determine if an arbitrage opportunity exists among these three investment alternatives. Her analysis, using the data in Exhibit 1, confirms that an arbitrage opportunity does exist. Exhibit 1. Expected Returns and Factor Sensitivities (One-Factor Model) **Fund** **Expected Return** **Factor Sensitivity** ---------- --------------------- ------------------------ A 0.02 0.5 B 0.04 1.5 C 0.03 0.9 The manager of Fund C makes some modifications to his portfolio and eliminates the arbitrage opportunity. Using a two-factor model, Zapata now estimates the three funds' sensitivity to inflation and GDP growth. That information is presented in Exhibit 2. Zapata assumes a zero value for the error terms when working with the selected two-factor model. Exhibit 2. Expected Returns and Factor Sensitivities (Two-Factor Model) **Fund** **Expected Return** **Factor Sensitivity** ---------- --------------------- ------------------------ ---------------- **Inflation** **GDP Growth** A 0.02 0.5 1.0 B 0.04 1.6 0.0 C 0.03 1.0 1.1 Altuve asks Zapata to calculate the return for Portfolio AC, composed of a 60% allocation to Fund A and 40% allocation to Fund C, using the surprises in inflation and GDP growth in Exhibit 3. Exhibit 3. Selected Data on Factors **Factor** **Research Staff Forecast** **Actual Value** ------------ ----------------------------- ------------------ Inflation 2.0% 2.2% GDP Growth 1.5% 1.0% Finally, Altuve asks Zapata about the return sensitivities of Portfolios A, B, and C given the information provided in Exhibit 3. 1. Which of the following is *not *a key assumption of APT, which is used by Altuve to evaluate strategies and manage risks? A. A factor model describes asset returns. A. Asset-specific risk can be eliminated through diversification. A. Arbitrage opportunities exist among well-diversified portfolios. 1. The arbitrage opportunity identified by Zapata can be exploited with: A. Strategy 1: Buy \$50,000 Fund A and \$50,000 Fund B; sell short \$100,000 Fund C. A. Strategy 2: Buy \$60,000 Fund A and \$40,000 Fund B; sell short \$100,000 Fund C. A. Strategy 3: Sell short \$60,000 of Fund A and \$40,000 of Fund B; buy \$100,000 Fund 1. The two-factor model Zapata uses is a: A. statistical factor model. A. fundamental factor model. A. macroeconomic factor model. 1. Based on Exhibit 2, what is the *most likely* benefit of taking a short position in Fund B relative to an equally sized long position in Fund C? A. Lower inflation risk A. Higher expected return A. Lower GDP growth risk 1. Based on the data in Exhibits 2 and 3, the return for Portfolio AC, given the surprises in inflation and GDP growth, is *closest* to: A. 2.02%. A. 2.40%. A. 4.98%. 1. The surprise in which of the following had the greatest effect on fund returns? A. Inflation on Fund B A. GDP growth on Fund A A. GDP growth on Fund C 1. Based on the data in Exhibit 2, which fund is most sensitive to the combined surprises in inflation and GDP growth in Exhibit 3? A. Fund A A. Fund B A. Fund C **Tutorial 6** 1. The benchmark weights and returns for each of the five stocks in the Capitol index are given below. The Tukol Fund uses the Capitol Index as its benchmark, and the fund's portfolio weights are also shown in the table. Stock Portfolio Weight (%) Benchmark Weight (%) 2016 Return (%) ------- ---------------------- ---------------------- ----------------- 1 30 24 14 2 30 20 15 3 20 20 12 4 10 18 8 5 10 18 10 A. 0.00% B. 0.90% C. 1.92% 1. Consider the following asset class returns for calendar year 2016: ---------------------------------------------------------------------------- Asset class Portfolio\ Benchmark\ Portfolio\ Benchmark\ Weight (%) Weight (%) Return (%) Return (%) ------------------------ ------------ ------------ ------------ ------------ Domestic equities 55 40 10 8 International equities 20 30 10 9 Bonds 25 30 5 6 ---------------------------------------------------------------------------- A. 0.25% B. 0.35% C. 1.05% And 7. 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% A. Portfolio A A. Portfolio B A. Portfolio C 7. 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 A. About 4 A. About 17 7. Two analysts make the following statements about the transfer coefficient in the full fundamental law of active management: A. Only Analyst One is correct. A. Only Analyst Two is correct A. Neither analyst is correct. 7. The full fundamental law of active management is stated as follows: A. transfer coefficient, TC. A. information coefficient, IC. A. breadth, BR. **Tutorial 7** **Question 1.** A hypothetical portfolio B has an annual 1% VaR of \$45,000. Which of the following statements is *most likely* true about the portfolio? a. The expected minimum loss over one year, 1% of the time, is \$45,000. b. There is a 99% probability that the expected loss over the next year is more than \$45,000. c. The likelihood of losing \$45,000 over the next year is 1%. **Question. 2** The standard deviation of the daily returns of asset A is given as 0.0231, and its mean as 0.0012. Estimate the 5% annual VaR for asset A, given that there are 250 trading days in a year, and the value of A is \$200,000. **Question. 3** You are provided the following information about two assets, Security A and Security B: +--------+--------+--------+--------+--------+--------+--------+--------+ | Securi | Standa | deviat | of | daily | Mean | Covari | daily | | ty | rd | ion | | | daily | ance | | | | | | | | | of | | +========+========+========+========+========+========+========+========+ | Securi | 0.0158 | 0.0004 | **0.00 | | | | | | ty | | | 0106** | | | | | | A | **0.01 | **0.00 | | | | | | | | 12** | 03** | | | | | | | Securi | | | | | | | | | ty | | | | | | | | | B | | | | | | | | +--------+--------+--------+--------+--------+--------+--------+--------+ Use the given information to estimate the 5% VaR for a Portfolio of 10 million that is 60% invested in security A and remaining in security B. **Tutorial 10** **The following information relates to questions 0-9** Aline Nuñes is a junior analyst in the derivatives research division of an international securities firm. Nuñes's supervisor, Cátia Pereira, asks her to conduct an analysis of various options trading strategies relating to shares of three companies: IZD, QWY, and XDF. On 1 February, Nuñes gathers selected option premium data on the companies, which is presented in Exhibit 1. Exhibit 1. Share Price and Options Premiums as of 1 February (share prices and option premiums are in euros) **Share Price** **Call Premium** **Option Date/Strike** **Put Premium** ----- ----------------- ------------------ ------------------------ ----------------- 9.45 April/87.50 1.67 IZD 93.93 2.67 April/95.00 4.49 1.68 April/97.50 5.78 4.77 April/24.00 0.35 QWY 28.49 3.96 April/25.00 0.50 0.32 April/31.00 3.00 0.23 February/80.00 5.52 XDF 74.98 2.54 April/75.00 3.22 2.47 December/80.00 9.73 Nuñes considers the following option strategies relating to IZD. **Strategy 1** Constructing a synthetic long put position in IZD ---------------- ---------------------------------------------------------------------------------- **Strategy 2** Buying 100 shares of IZD and writing the April €95.00 strike call option on IZD **Strategy 3** Implementing a covered call position in IZD using the April €97.50 strike option Nuñes next reviews the following option strategies relating to QWY. **Strategy 4** Implementing a protective put position in QWY using the April €25.00 strike option ---------------- ---------------------------------------------------------------------------------------------------------------------- **Strategy 5** Buying 100 shares of QWY, buying the April €24.00 strike put option, and writing the April €31.00 strike call option **Strategy 6** Implementing a bear spread in QWY using the April €25.00 and April €31.00 strike options Finally, Nuñes considers two option strategies relating to XDF. **Strategy 7** Writing both the April €75.00 strike call option and the April €75.00 strike put option on XDF ---------------- --------------------------------------------------------------------------------------------------------- **Strategy 8** Writing the February €80.00 strike call option and buying the December €80.00 strike call option on XDF Over the past few months, Nuñes and Pereira have followed news reports on a proposed merger between XDF and one of its competitors. A government antitrust committee is currently reviewing the potential merger. Pereira expects the share price to move sharply up or down depending on whether the committee decides to approve or reject the merger next week. Pereira asks Nuñes to recommend an option trade that might allow the firm to benefit from a significant move in the XDF share price regardless of the direction of the move. 1. Strategy 1 would require Nuñes to buy: A. shares of IZD. A. a put option on IZD. A. a call option on IZD. 1. Based on Exhibit 1, Nuñes should expect Strategy 2 to be *least* profitable if the share price of IZD at option expiration is: A. less than €91.26. A. between €91.26 and €95.00. A. more than €95.00. 2. Based on Exhibit 1, the breakeven share price of Strategy 3 is *closest* to: A. €92.25. A. €95.61. A. €95.82. 3. Based on Exhibit 1, the maximum loss per share that would be incurred if Strategy 4 was implemented is: A. €2.99. A. €3.99. A. unlimited. 4. Strategy 5 is *best* described as a: A. collar. A. straddle. A. bear spread. 5. Based on Exhibit 1, Strategy 5 offers: A. unlimited upside. A. a maximum profit of €2.48 per share. A. protection against losses if QWY's share price falls below €28.14. 6. Based on Exhibit 1, the breakeven share price for Strategy 6 is *closest* to: A. €22.50. A. €28.50. A. €33.50. 7. Based on Exhibit 1, the maximum gain per share that could be earned if Strategy 7 is implemented is: A. €5.74. A. €5.76. A. unlimited. 8. Based on Exhibit 1, the *best* explanation for Nuñes to implement Strategy 8 would be that, between the February and December expiration dates, she expects the share price of XDF to: A. decrease. A. remain unchanged. A. increase. 9. The option trade that Nuñes should recommend relating to the government committee's decision is a: A. collar. A. bull spread. A. long straddle. **Tutorial 11** **Question 5** A firm's assets are currently valued at \$700 million, its current liabilities are \$120 million, and long-term liabilities are \$300. The standard deviation of expected asset value is \$76 million. Assume the firm has no other debt and that the ratio of long term liabilities to short term liabilities is less than 1.5. What will be the appropriate distance to default measure when utilizing Moody's KMV Credit Monitor Model? a. 9.21 standard deviation b. 5.66 standard deviation c. 3.68 standard deviation d. 1.87 standard deviation **Question 6** **Calculate the price of call and put options on a stock that does not pay any dividend using the following information:** **Maturity 1year\ Exercise price \$88\ Current price \$83.96\ Expected return volatility 10%\ Risk-free rate of return 6%** **Question 7** Using the Merton model, **calculate** the value of the firm's equity at *t* given that the current value of the firm is \$60 million, the principal amount due in 3 years on the zero-coupon bond is \$50 million, the annual interest rate, *r,* is 5%, and the volatility on the firm, *sigma*, is 10%. **Question 8** Suppose a firm with a value of \$60 million has a bond outstanding with a face value of \$50 million that matures in three years. The current interest rate is 6% and the volatility of the firm is 25%. What is the probability that the firm will default on its debt if the expected return on the firm, XX, is 15%? What is the expected loss given default?