Research Report with Quantitative Analysis Assignment Sample

Introduction Of : Research Report with Quantitative Analysis

Part 1: Quantitative Analysis of Fixed Income Securities

Current Yield Curve

To determine the value of the fixed-income securities in the portfolio, it require a current US yield curve that depicts the securities' interest rate (Tuckman and Serrat, 2022). In this case, the data was obtained from the United States Department of the Treasury. Linear interpolation was used to estimate some rates that may have been unavailable during data collection. For instance, in the event that a 4-year rate was not available, it would be estimated by taking the mean of 3-year and 5-year rates.

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Valuation and Yields to Maturity

The yield curve can be used to calculate the present values and yields to maturity (YTM) for the 3-year US Treasury Notes and 10-year US Treasury Bonds.

**3Year US Treasury Notes:**

 Coupon rate: 4% semiannual

 Par value: $10,000

 Number of notes: 5

 Semiannual coupon payment: $200

The present value (PV) of the 3year US Treasury Notes is calculated using the formula:

\[ PV = \sum_{t=1}^{6} \frac{C}{(1 + r/2)^t} + \frac{FV}{(1 + r/2)^6} \]

Where:

 \( C \) = Semiannual coupon payment = $200

 \( r \) = Yield to maturity (annual rate) = 2.00%

 \( FV \) = Par value = $10,000

\[ PV = \frac{200}{(1 + 0.01)^1} + \frac{200}{(1 + 0.01)^2} + \cdots + \frac{200 + 10,000}{(1 + 0.01)^6} \]

\[ PV = 200 \left(\frac{1 (1 + 0.01)^{6}}{0.01}\right) + \frac{10,000}{(1 + 0.01)^6} \]

The YTM can be solved using financial calculators or spreadsheet software (Excel).

**10Year US Treasury Bonds:**

 Coupon rate: 10% annual

 Par value: $100,000

 Annual coupon payment: $10,000

The present value (PV) of the 10year US Treasury Bond is calculated using the formula:

\[ PV = \sum_{t=1}^{10} \frac{C}{(1 + r)^t} + \frac{FV}{(1 + r)^{10}} \]

Where:

 \( C \) = Annual coupon payment = $10,000

 \( r \) = Yield to maturity (annual rate) = 2.75%

 \( FV \) = Par value = $100,000

\[ PV = \frac{10,000}{(1 + 0.0275)^1} + \frac{10,000}{(1 + 0.0275)^2} + \cdots + \frac{10,000 + 100,000}{(1 + 0.0275)^{10}} \]

Risk Analysis and Yield Spread

Microsoft Corporate Bonds:

 Coupon rate: 5% per annum

 Par value: $15,000

 Number of bonds: Just Best selling 8

Risks:

• Credit risk: The probability that Microsoft would be unable to meet its loan financial obligations (Bhatore, Mohan and Reddy, 2020).
• Liquidity risk: The bond might not be very marketable, mainly if it cannot be sold at excellent prices.
• Interest rate risk is the variation in the bond’s price with respect to variations in the rate of interest (Kranz, Bennani and Neuenkirch, 2024).

Fannie Mae Mortgage PassThrough Certificates:

Biannual payments according to the table suggested below.

It is assumed that the par value of each certificate is $ 10000.

Risks:

Prepayment risk: The chance of the homeowners prepaying the loans alters the cash flow.

Credit risk: Extra risks are linked to the value of the pooled assets, that is, the credit risks concerning the quality of the underlying mortgages (Naili and Lahrichi, 2020).

Similar to the previous chapter, Microsoft corporate bond yield spread is estimated by subtracting YTM from YTM of similar maturity Treasury bonds. For instance, if the YTM on a 5-year Treasury bond is 2. ranged between 25% and the YTM of the Microsoft bond is 3. 75%, the yield spread is 1 Berkeley, California ≤250 employees: 750/100 × 75% = 281 employees. 50%.

The yield spread for Fannie Mae mortgage passthrough certificates is estimated similarly to calculate its YTM with Treasury securities of similar maturity.

Portfolio Valuation, Return, and Duration

The portfolio consists of:

• Five 3-year US Treasury Notes
• 1-10-year treasury bond
• Eight, five-year Microsoft corporate bonds
• Two 7 investment dollar Fannie Mae mortgage pass-through certificates

Current Value:

The formula shown above determines each security’s present value. Therefore, the total portfolio value is the sum of the present values of all securities included in the portfolio (S, 2022).

Expected Return:

Borrowing from the conceptual framework above, the expected return is obtained by adding the annual coupon payments and dividing the value by the current portfolio value (Kranz, Bennani and Neuenkirch, 2024).

Impact of Yield Curve Shift

Macaulay Duration:

\[ D = \sum_{t=1}^{T} \left( \frac{t \times PV(CF_t)}{PV} \right) \]

Modified Duration:

\[ D_{mod} = \frac{D}{1 + \frac{YTM}{n}} \]

Where:

- \( t \) = Time period

- \( PV(CF_t) \) = Present value of cash flow at time \( t \)

- \( PV \) = Present value of all cash flows

- \( YTM \) = Yield to Maturity

- \( n \) = Number of compounding periods per year

Assume a 5% parallel upward shift in the yield curve.

Change in Portfolio Value:

\[ \Delta PV \approx -D_{mod} \times \Delta r \times PV \]

Where:

- \( \Delta PV \) = Change in portfolio value

- \( D_{mod} \) = Modified duration of the portfolio

- \( \Delta r \) = Change in interest rate (0.05 or 5%)

- \( PV \) = Current portfolio value

Part 2: Market Efficiency and Role of Manager in Bond Portfolio Management

Yield Curve Forecasting and Active Management

Projection of the yield curve of bonds becomes significant in the dynamic management of bond portfolios (Christensen, Lopez and Mussche, 2021). The yield curve represents the interest rate that investors expect in the future, economic activity, and inflation. This information means that through forecasts made in the portfolio’s duration, convexity and the sector, the portfolio managers can adjust the portfolio to factor in the returns.

There are three primary changes in the yield curve: Parallel shifts, twists, and butterflies, which are other types of dance moves (Davies, 2023). Historical shifts are of two types known as parallel shifts Since they are an upward shift of the entire yield curve by the same margin or a downward shift of the same. It is the most frequent type of change, responsible for most of the return on a Treasury portfolio. Inversions occur when the yield curve steepens or flattens and becomes steeper than before. Management styles that involve the yield curve forecast are the measures such as duration management, curve positioning as well as sector rotations. Duration management focuses on the changes of the portfolio’s interest rate elasticity (Best et al., 2019). Curve positioning is the process of holding more or less of a particular maturity than others, depending on the expected change in yield. Sector rotation provides a way of moving from one sector to another, for instance, from treasuries, corporates or municipals, depending on perceived relative value and trends in yield curves.

Efficiency of Bond Markets

There are always controversies as to how efficient bond markets really are among economists and other financial stakeholders. Efficient Market Hypothesis (EMH) indicates that the market adjusts to information efficiently and thus, it becomes hard for an investor to gain above-average returns on bonds (Kelikumea, Olaniyib and Iyohab, 2020).

There are three forms of market efficiency: these comprising weak form, semi-strong form and strong form. In the weak form, all past information in terms of price and volume is earmarked in the present bond prices. In semi-strong form, information ranging from the balance sheet to any current event that affects a firm is reflected in the bond prices (Kingstone Nyakurukwa and Yudhvir Seetharam, 2023). In the strong form all public as well as private information regarding a company or any other organization is already incorporated in bond rates.

Bond markets are less efficient than equity markets because their trading volume is lower and there is less information available on them, but a skilled portfolio manager can always find some mispriced bonds. Liquidity risk, credit risk, and interest rate risk can be considered active management factors.

Impact of Yield Curve Changes on Treasury Portfolio Returns

By analyzing the return data on a Treasury portfolio, Frank J. Jones (1991) noted that most of the return is explained by parallel movements in the yield curve. Twists and butterfly changes also help in the formation of returns, although not in the same measure as a curve. It is necessary to understand the outcomes of such changes to be able to manage a portfolio successfully.

Parallel shifts enable the portfolio managers to either add to or subtract length, depending on expected changes in interest rates. A longer duration will get a protective downward direction while a shorter duration will be protected by an upward shift. Twists let the managers place the portfolio in between various segments of the yield curve in anticipation of changes in the slope of the curve. For instance, if there is a maturity gradient that is predicted to steepen, then traits of the portfolio can be adjusted to invest in longer points. Butterflies enable managers to control the percentage of portfolios in other maturities as they derive gains from curvature change. For instance, if a positive butterfly is expected, then the portfolio can load up towards intermediate maturities (Constantinides, Czerwonko and Perrakis, 2019).

Role of Portfolio Manager in Active Management

The primary responsibility of a portfolio manager in managing an active bond portfolio lies in the ability to exploit particular market anarchies to the advantage of getting higher returns. Some of the roles include compilation and appraisal, risk management, portfolio construction, and performance monitoring.

Research and analysis consist of carrying out investigations of macroeconomic indicators and estimating the trends in interest rates and the quality of the issuers (S, 2022). Managing risks involves various risks, such as interest rate risk, credit risk, and liquidity risk. Portfolio construction, therefore, entails assembling a portfolio that contains various securities that have an acceptable risk/return ratio, given the manager’s assessment and outlook of the market. Performance monitoring cannot be done without constantly evaluating the portfolio and going to the market to ensure that the objective of the portfolio is met.(Kelikumea, Olaniyib and Iyohab, 2020)

Finally, mathematical models on fixed-income securities, the efficiency of the market, and active management are crucial when dealing with bond portfolios. References to yield curve forecasting are an important component of active management due to its capability to provide portfolio managers with additional information for the decisions on change in portfolios. It is imperative to understand that bond markets are mostly efficient. Yet, the efficacy of managers’ efforts depends on their ability to identify the inefficiencies, collect sufficient information, and apply systematic risk management and turnover across the portfolio. Thus, the findings of this research reveal that quantitative and qualitative factors should be considered to achieve a successful management of bond portfolios.

References

• Best, M.C., Cloyne, J.S., Ilzetzki, E. and Kleven, H.J. (2019). Estimating the Elasticity of Intertemporal Substitution Using Mortgage Notches. The Review of Economic Studies, 5(4). doi:https://doi.org/10.1093/restud/rdz025.
• Bhatore, S., Mohan, L. and Reddy, Y.R. (2020). Machine Learning Techniques for Credit Risk evaluation: a Systematic Literature Review. Journal of Banking and Financial Technology, [online] 4(1), pp.111–138. doi:https://doi.org/10.1007/s42786-020-00020-3.
• Christensen, J.H.E., Lopez, J.A. and Mussche, P.L. (2021). Extrapolating Long-Maturity Bond Yields for Financial Risk Measurement. Management Science, 5(4). doi:https://doi.org/10.1287/mnsc.2021.4215.
• Constantinides, G.M., Czerwonko, M. and Perrakis, S. (2019). Mispriced index option portfolios. Financial Management, 49(2), pp.297–330. doi:https://doi.org/10.1111/fima.12288.
• Davies, J. (2023). The Art of Dance Composition: Writing the Body. [online] Google Books. Taylor & Francis. Available at: https://books.google.com/books?hl=en&lr=&id=xKPREAAAQBAJ&oi=fnd&pg=PT6&dq=There+are+three+primary+changes+in+the+yield+curve:+Parallel+shifts [Accessed 27 Jul. 2024].
• Fabozzi, F.J. and Fabozzi, F.A. (2021). Bond Markets, Analysis, and Strategies, tenth edition. [online] Google Books. MIT Press. Available at: https://books.google.com/books?hl=en&lr=&id=b-QhEAAAQBAJ&oi=fnd&pg=PR9&dq=Borrowing+from+the+conceptual+framework+above [Accessed 27 Jul. 2024].
• Kelikumea, I., Olaniyib, E. and Iyohab, F.A. (2020). Efficient Market Hypothesis in the Presence of Market Imperfections: Evidence from Selected Stock Markets in Africa. International Journal of Management, Economics and Social Sciences, 9(1). doi:https://doi.org/10.32327/ijmess/9.1.2020.3.
• Kingstone Nyakurukwa and Yudhvir Seetharam (2023). Alternatives to the efficient market hypothesis: an overview. Journal of capital markets studies, 7(2), pp.111–124. doi:https://doi.org/10.1108/jcms-04-2023-0014.
• Kranz, T., Bennani, H. and Neuenkirch, M. (2024). Monetary policy and climate change: Challenges and the role of major central banks. [online] www.econstor.eu. Available at: https://www.econstor.eu/handle/10419/283499 [Accessed 27 Jul. 2024].
• Naili, M. and Lahrichi, Y. (2020). The determinants of banks’ credit risk: Review of the literature and future research agenda. International Journal of Finance & Economics, 27(1). doi:https://doi.org/10.1002/ijfe.2156.
• S, K. (2022). SECURITY ANALYSIS AND PORTFOLIO MANAGEMENT, THIRD EDITION. [online] Google Books. PHI Learning Pvt. Ltd. Available at: https://books.google.com/books?hl=en&lr=&id=BtyLEAAAQBAJ&oi=fnd&pg=PP1&dq=+the+total+portfolio+value+is+the+sum+of+the+present+values+of+all+securities+included+in+the+portfolio.&ots=cvbD0ISvgA&sig=RIPzXQyEoJPJY7N8wFljO-lbn4Y [Accessed 27 Jul. 2024].
• Tuckman, B. and Serrat, A. (2022). Fixed Income Securities: Tools for Today’s Markets. [online] Google Books. John Wiley & Sons. Available at: https://books.google.com/books?hl=en&lr=&id=2oKFEAAAQBAJ&oi=fnd&pg=PR9&dq=To+determine+the+value+of+the+fixed-income+securities+in+the+portfolio [Accessed 27 Jul. 2024].

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