Homework 3

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University of Rhode Island *

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424

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Finance

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Jan 9, 2024

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Homework 3 [Due on Wednesday, November 15, 2023] Chapter 24 11. Answer the below questions. (a) What is meant by systematic risk factors? Answer: Systematic risk factors, also known as market risk or undiversifiable risk, refer to the sources of risk that affect the entire market or a large segment of it. These factors cannot be eliminated through diversification because they are inherent to the overall market conditions. Systematic risk influences the entire economy and is beyond the control of individual investors or companies. Common examples of systematic risk factors include economic recessions, interest rate changes, inflation, political instability, and natural disasters. Investors need to consider and manage systematic risk when making investment decisions, as it has the potential to impact a broad range of assets simultaneously. (b) What is the difference between term structure and non-term structure risk factors? Answer: The term structure of risk factors is related to the maturity or time horizon of financial instruments. In the context of interest rates, it specifically refers to the variation in interest rates across different maturities of fixed-income securities. For instance, the yield curve represents the term structure of interest rates, showing the relationship between interest rates and the time to maturity of debt securities. Changes in the term structure can affect the pricing and performance of fixed-income securities, influencing investment decisions. Factors such as market expectations of future interest rates and economic conditions contribute to fluctuations in the term structure. On the other hand, non- term structure risk factors encompass a broader range of risks that are not directly tied to the maturity of financial instruments. These risks can include but are not limited to, credit risk, liquidity risk, market risk, and operational risk. Unlike term structure risk factors, which are more focused on the time dimension, non-term structure risk factors can impact various aspects of financial markets simultaneously. Credit risk, for example, is associated with the potential of a borrower defaulting on debt obligations, and it affects both short and long-term investments. Market risk, including systematic factors, falls under the category of non-term structure risk as it is not confined to a specific maturity. 17. A portfolio manager owns $5 million par value of bond ABC. The bond is trading at 70 and has a modified duration of 6. The portfolio manager is considering swapping out of bond ABC and into bond XYZ. The price of this bond is 85 and it has a modified duration of 3.5. (a) What is the dollar duration of bond ABC per 100-basis-point change in yield? Answer : Dollar duration of bond ABC = 0.06 * 70= 4.2 Page 1 of 4
(b) What is the dollar duration for the $5 million position of bond ABC? Answer : (70/100)5 million =3.5 million 3.5 million x 0.06= 210,000 (c) How much in market value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC? Answer : 210,000/(3.5/100)=$6,000,000 (d) How much in par value of bond XYZ should be purchased so that the dollar duration of bond XYZ will be approximately the same as that for bond ABC? Answer : 6million /0.85 =7.059 million 26. Suppose that the initial value of an unlevered portfolio of Treasury securities is $200 million and the duration is 7. Suppose further that the manager can borrow $800 million and invest it in the identical Treasury securities so that the levered portfolio has a value of $1 billion. What is the duration of this levered portfolio? Answer: Duration = (7 * $200 million) / $1 billion = 1.4years 27. Suppose a manager wants to borrow $50 million of a Treasury security that it plans to purchase and hold for 20 days. The manager can enter into a reverse repo agreement with a dealer firm that would provide financing at a 4.2% repo rate and a 2% margin requirement. What is the dollar interest cost that the manager will have to pay for the borrowed funds? Answer : 50,000,000 x 0.042 x (20/365)= $ 115,068.49 Chapter 25 6. Why is the tracking error more important than portfolio variance of returns when a portfolio manager’s performance is measured versus a benchmark? Answer : Tracking error takes precedence over portfolio variance when assessing a portfolio manager's performance against a benchmark because it directly measures the deviation of the portfolio's returns from the benchmark. Unlike portfolio variance, tracking error isolates the risk associated with active decisions made by the manager, such as stock selection and asset allocation. Investors are primarily concerned with the manager's ability to outperform the benchmark, and tracking error provides a more targeted assessment of this outperformance or underperformance. It facilitates a clear attribution of performance, helping investors understand the sources of returns and whether they stem from the manager's skill or broader market movements. Additionally, tracking error aligns with investor objectives tied to a specific benchmark, making it a more relevant and communicative metric for Page 2 of 4
evaluating a portfolio manager's success in meeting performance expectations. (a) Compute the tracking error from the following information: Month 2001 Portfolio A’s Return (%) Lehman Aggregate Bond Index Return (%) January 2.15 1.65 February 0.89 –0.10 March 1.15 0.52 April –0.47 –0.60 May 1.71 0.65 June 0.10 0.33 July 1.04 2.31 August 2.70 1.10 September 0.66 1.23 October 2.15 2.02 November –1.38 –0.61 December –0.59 –1.20 Answer : Month Portfolio return benchmark return Portfolio return- benchmark return Jan 2.15 1.65 0.5 Feb 0.89 -0.1 0.99 Mar 1.15 0.52 0.63 Apr -0.47 -0.6 0.13 May 1.71 0.65 1.06 Jun 0.1 0.33 -0.23 Jul 1.04 2.31 -1.27 Aug 2.7 1.1 1.6 Sep 0.66 1.23 -0.57 Oct 2.15 2.02 0.13 Nov -1.38 -0.61 -0.77 Dec -0.59 -1.2 0.61 Sum 0.0281 mean 0.0023 standard deviation = 0.83% tracking error in basis point 83bps b. Is the tracking error computed in part (a) a backward-looking or forward-looking tracking error? Answer : a backward looking tracking error . 14. You are reviewing a report by a portfolio manager that indicates that a fund’s predicted Page 3 of 4
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(forward-looking) tracking error is 94.87 basis points. Furthermore, it is reported that the predicted tracking error due to systematic risk is 90 basis points and the predicted tracking error due to non-systematic risk is 30 basis points. Why doesn’t the sum of these two tracking error components total up to 94.87 basis points? Answer : The reported tracking error due to systematic risk and non-systematic risk in the fund are distinct components that represent different sources of risk. The predicted tracking error due to systematic risk reflects the fund's exposure to overall market conditions or a specific benchmark, while the non- systematic risk component captures the risk specific to the fund's individual holdings. These components are not simply additive because they measure different aspects of the fund's risk profile. The sum of the two components does not equal the overall predicted tracking error, as they provide unique insights into the various factors contributing to the fund's deviation from its benchmark. In essence, the reported values underscore that the overall predicted tracking error is a composite of these distinct and non- additive sources of risk within the fund's portfolio. Chapter 26 4. What is meant by contribution to spread duration? Answer: Contribution to spread duration refers to the impact a particular security or asset has on the overall spread duration of a portfolio. Spread duration measures the sensitivity of a bond or portfolio to changes in credit spreads. When analyzing the contribution to spread duration, investors assess how individual securities influence the overall spread risk of the portfolio. It helps in understanding the potential impact of changes in credit spreads on the portfolio's value and risk exposure 17. How does a yield-spread pickup trade differ from a credit-upside trade? Answer: A yield-spread pickup trade involves investing in securities with higher yield spreads over benchmark rates, aiming to capture additional yield. This strategy is based on the expectation that the yield spread will narrow over time, resulting in capital gains. On the other hand, a credit-upside trade focuses on securities with potential credit improvement. Investors in this trade anticipate that the credit quality of the securities will improve, leading to an increase in their market value. While both strategies involve credit considerations, a yield-spread pickup trade primarily seeks higher yield, while a credit-upside trade looks for potential credit rating upgrades 18. What is the motivation for a new-issue swap trade? Answer: The motivation for a new-issue swap trade lies in optimizing a portfolio's risk and return profile. In a new-issue swap trade, an investor may exchange or swap newly issued securities for existing positions, aiming to enhance the overall portfolio characteristics. Motivations could include improving yield, adjusting the portfolio's duration, or managing sector exposures. By participating in a new-issue swap, investors seek to capitalize on the unique attributes of recently issued securities, taking advantage of market conditions and evolving investment objectives. Page 4 of 4