Midterm review questions with answers

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Apr 3, 2024

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Professor Adams FRE 6123 Midterm Review Questions with Answers IRR YTM PV In order to obtain full credit on midterm exam questions, please show your work for calculations and answer any written responses thoroughly in complete sentences: 1.) An investor buys a stock for $50.00 and sells it in two years for $60.00. She receives a $5.00 dividend at the end of each year and can reinvest cash flows at 2%. What is her annualized return after two years? Answer: The investor pays $50.00 at time zero and receives $70.10 in two years’ time which includes the future value of the first year’s dividend ($5.00 × 1.02 = $5.10), the second dividend of $5.00 paid at the end of year two and the sale price of $60.00. The annualized return may be calculated as follows: $50 = $70.10 / (1+r) 2 , where r equals the annualized return. Solve for r to get 18.4%. 2.) You are asked to choose between two $1 million investment projects which pay no coupons or dividends and are expected to generate the following returns each year based upon the following schedule: Year / Investment Sunshine LLC Spark LLC Year 1 15% 7% Year 2 -3% 8% Year 3 -5% 7% Year 4 25% 7% a.) Calculate and show which investment generates the highest annualized return. Answer: The correct answer is based upon the geometric mean (not the arithmetic mean!). The geometric mean return is T √ ∏ t = 1 T ( 1 + R it ) - 1 Sunshine LLC: 7.28% = {[(1.15) × (0.97) × (0.95) × (1.25)] 1/4 – 1} Spark LLC: 7.25% = {[(1.07)× (1.08)× (1.07) × (1.07)] 1/4 – 1} Sunshine generates an average 7.28% per year versus Spark’s annualized return of 7.25%. b.) Explain which other important statistic(s) you might consider when deciding whether to invest in Sunshine LLC or Spark LLC. Answer: In order to compare these investments, it is important to consider both risk as well as expected return. Variance measures the dispersion of returns, the square root of which is the standard deviation. The Sharpe ratio is a relative return versus risk measure equal to the

ratio of expected return over standard deviation. We should calculate the Sharpe ratios of both and choose the one with the highest Sharpe ratio reflecting the best return for a given risk level. 3.) An investor is considering an equally weighted portfolio between the S&P 500 and the MSCI Europe Stock Index. She expects the S&P to return 8% with standard deviation of 15%, while the MSCI ESI is expected to return 7% with a 12% standard deviation. Expected covariance between the two indexes is 0.25% or 0.0025 (units are expressed as % 2 ). Calculate the expected portfolio return and standard deviation. Answer: Expected portfolio return is equal to: R P = w 1 R 1 + ( 1 − w 1 ) R 2 = ( 0.5 ∗ 0.08 ) + ( 0.5 ∗ 0.07 ) = 7.5% . Expected portfolio risk (standard deviation) is the square root of: w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2 w 1 w 2 cov 12 σ P 2 = ¿ (0.5 2 * 0.15 2 ) + (0.5 2 * 0.12 2 ) + (2 * 0.5 * 0.5 * 0.0025) = 0.010475; σ P = √ 0.010475 = 10.234 % 4.) Abbott Laboratories (ABT) is a dividend paying stock with a spot price of $100 per share and a continuously compounded dividend yield of 1%. An investment manager seeks to benefit from a rise in ABT’s share price over the next six months and contracts with a bank for a six-month forward purchase of 1,000 shares. Assume a risk-free rate of 1% and a flat yield curve. a.) What is the ABT six-month forward price? Answer : We calculate the forward price for a dividend paying stock as follows: F 0 ( T ) = S 0 e ( r − q ) ( T − t ) F = $100 = $100e (.01-.01)(0.5) as S = $100, r = 0.01, q = 0.01 and (T-t) = 0.5. b.) How would the six-month ABT forward price change if the dividend yield rises to 2%? Answer : The increase in dividend yield decreases the forward price, as the holder of the shares benefits from the dividend over the forward period. F 0 ( T ) = S 0 e ( r − q ) ( T − t ) F = $99.50 = $100e (.01-.02)(0.5) as S = $100, r = 0.01, q = 0.02 and (T-t) = 0.5. 5.) A European investor purchases a $50 million five-year CDS contract at a 400 bp spread for a U.S. high yield issuer with EffSpreadDur CDS of 4.8. a.) What is the upfront fee if the current USD/EUR spot exchange rate is currently 1.20 and who pays whom?

Answer: The high-yield CDS contract has a fixed coupon of 5%, and the price is approximated as follows: CDS Price ≈ Notional × ((Fixed Coupon – CDS Spread) ⨯ EffSpreadDur CDS ) Seller pays buyer EUR 2,000,000 = $2,400,000 (= 50,000,000 × (5.00% – 4.00%) × 4.8) as the buyer will pay an “ above-market” coupon for CDS protection on the issuer. b.) What is the European protection buyer’s return in EUR if the high-yield issuer’s CDS spread immediately widens to 475 bps and the spot USD/EUR exchange rate rises to 1.25? Calculate the return and interpret the results. Answer: Contract value to the protection buyer has appreciated due to the widening in credit spreads. Contract MTM equals EUR 480,000 = $600,000 (= 50,000,000 × (5.00% – 4.75%) × 4.8) which the protection buyer owes to the seller. Since the investor (contract buyer) received EUR 2,000,000 on day one and now owes EUR 480,000, she has earned a return of EUR 1,520,000 (2,000,000-480,000) . The protection buyer’s return in USD terms of $1,800,000 is attributable to a 75 bp widening of credit spreads, while the depreciation in the U.S. dollar slightly reduced the investor’s EUR functional currency earnings. 6.) An investor has the choice between two investments with anticipated annual cash flows as in the below table (negative numbers are outflows). Which project should she choose? Year / Investment Elgin LLC Erie LLC Year 1 -500 -500 Year 2 +100 0 Year 3 +425 +525 Answer: Calculate annual IRR for each investment using the formula: ∑ t = 0 T CF t ( 1 + IRR ) t = 0 This is best done using a financial calculator (either the IRR or CFLO function), as doing so by hand involves iteration through trial and error. Set up the problem as follows: Elgin: − 500 ( 1 + IRR ) 0 + 100 ( 1 + IRR ) 1 + 425 ( 1 + IRR ) 2 = 2.74% Erie: − 500 ( 1 + IRR ) 0 + 0 ( 1 + IRR ) 1 + 525 ( 1 + IRR ) 2 = 2.47% She should therefore choose Elgin. 7.) You are borrowing funds to finance a project and have the choice between paying 0.4% interest monthly or 1% interest quarterly. Which should you choose to minimize cost?

Answer: Using r annual =( 1 + r ¿¿ period ) c − 1 ¿ , we can compare cost based upon annualized figures. The monthly cost of 0.4% is 4.91% on an annualized basis (4.91% = (1 + 0.004) 12 – 1), while the quarterly cost is 4.06% (4.06% = (1 + 0.01) 4 – 1). Our borrower should therefore choose the quarterly option to minimize cost. 8.) Define and describe the nature of operational risk among financial firms. Answer: Operational risk in banks or financial institutions results from banks and other financial institutions putting their strategies into practice by employing professionals, developing and defining best practices and establishing infrastructure to achieve strategic objectives. This risk specifically addresses the potential loss from inadequate or failure of people, processes and systems or external events which compromise a financial firm’s operations. 9.) A buy-and-hold investor purchases a fixed-rate coupon bond at a discount and holds the security until it matures. Explain how the investor will calculate his total return over the investment horizon assuming all payments are made as scheduled. Answer: There is no capital g ain (or loss) because the bond is held to maturity. The investor has purchased the security at a discount and receives the principal payment at maturity. This principal payment is a source of return for the investor. The fixed-rate bond pays periodic coupon payments, and the reinvestment of these coupon payments is a source of return for the investor. The investor’s total return is the redemption of principal at maturity and the sum of the reinvested coupons. For example, for a three-year annual coupon bond, this may be represented as follows: FV = C × (1 + r 1 ) 2 + C × (1+r 2 ) + (100 + C); PV = FV / (1+r) 3 where r 1 and r 2 are the respective coupon reinvestment rates. 10.) The Kellogg Company issues a new five-year, 4% annual coupon bond at a spread to the current U.S. Treasury of 75 basis points. If this bond is trading at 104.25 after exactly one year, what is the yield to maturity of the Kellogg bond? Answer: Given the price of the four-year, 4% SA coupon bond, we should set up the problem as: ∑ t = 1 4 4 ( 1 + r ) t + 100 ( 1 + r ) 4 = 104.25 , solvefor r use a financial calculator to solve for a 2.86% yield by entering a 4-year maturity, annual coupon of 4% and price of 104.25. 11.) Daimler AG issued a new ten-year EUR bond with a 5.25% annual coupon which is trading at a yield of 4.78% two years after the issuance date. Calculate the price you would you expect to pay for this bond and whether it is trading at a premium or discount. Answer: Given the 4.78% yield of the eight-year, 5.25% annual coupon bond, solve for:

∑ t = 0 8 5.25 ( 1 + 0.0478 ) t + 100 ( 1 + 0.0478 ) 8 = PV ,solvefor PV Use a financial calculator to solve for a price of 103.06 by entering an 8-year maturity, annual coupon of 5.25% and a yield to maturity of 4.78%. 12.) As a fixed-income manager, you are tasked with analyzing a portfolio consisting of the following three annual coupon fixed-income bonds: Bond Bond Price Coupon Rate Maturity A 100 7% 10 years B 100 7% 5 years C 100 9% 5 years a.) Relative to Bond C, describe whether Bond B will exhibit an equal, greater or smaller percentage price change given a 200 basis point (2%) decrease in the required rate of return and why? Lower coupon ->experience a greater percentage price change Lower coupon -> higher duration longer-term bond has a greater percentage price change than a shorter-term Answer: Bond B will likely exhibit a greater percentage price change than Bond C for a 2% decline in yields. In general, for two bonds with the same time-to-maturity, a lower coupon bond will experience a greater percentage price change than a higher coupon bond when their market discount rates change by the same amount. Bond B and Bond C have the same time-to-maturity (5 years); however, Bond B offers a l ower coupon rate (and therefore a higher duration). Therefore, Bond B will likely experience a greater percentage change in price in comparison to Bond C. b.) Explain which bond in the portfolio will most likely demonstrate the greatest percentage change in price if the market discount rates for all three bonds increase by 100 basis points. Answer: Bond A will likely experience the greatest percentage change in price due to the coupon effect and the maturity effect. For two bonds with the same time-to-maturity, a lower coupon bond has a greater percentage price change than a higher coupon bond when their market discount rates change by the same amount. Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount. Relative to Bond C, Bond A and Bond B both offer the same lower coupon rate of 7%; however, Bond A has a longer time-to-maturity than Bond B. Therefore, Bond A will likely experience the greater percentage change in price if the market discount rates for all three bonds increase by 100 basis points. 13.) Consider the following annual coupon fixed-income securities:

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