Bond And Fixed Interest Markets Quiz Exam Quiz 36

The calculation involves understanding the concept of modified duration and its application in estimating the price change of a bond due to a change in yield. Modified duration provides an approximate percentage change in the bond’s price for a 1% change in yield. The formula to estimate the price change is: Price Change ≈ – (Modified Duration) * (Change in Yield) * (Initial Price) In this scenario, the modified duration is given as 7.5, the initial yield is 4.5%, and the yield increases by 35 basis points (0.35%). The initial price is £104.50. Price Change ≈ – (7.5) * (0.0035) * (£104.50) ≈ – £2.74 The new estimated price is the initial price minus the price change: New Price ≈ £104.50 – £2.74 ≈ £101.76 This calculation demonstrates how sensitive a bond’s price is to changes in interest rates, particularly when the bond has a higher modified duration. Modified duration is a crucial tool for bond portfolio managers to assess and manage interest rate risk. For instance, consider a portfolio manager who is expecting interest rates to rise. To protect the portfolio, they might reduce their holdings of bonds with high modified durations and increase their holdings of bonds with low modified durations, or even short sell high duration bonds. This would reduce the portfolio’s overall sensitivity to interest rate changes. The manager could also use derivatives, such as interest rate swaps or bond futures, to hedge against interest rate risk. The choice of hedging strategy depends on the manager’s risk tolerance, investment horizon, and expectations about the shape of the yield curve.

The question assesses the understanding of bond valuation, yield to maturity (YTM), and the impact of coupon rate changes on bond prices. The core concept revolves around how a bond’s price adjusts to reflect prevailing market interest rates. The YTM represents the total return anticipated on a bond if it is held until it matures. It is influenced by the bond’s coupon payments, face value, purchase price, and time to maturity. The calculation involves understanding the inverse relationship between interest rates and bond prices. When market interest rates (and therefore required yields) rise above a bond’s coupon rate, the bond’s price falls below its face value (it trades at a discount) to compensate investors for the lower coupon payments relative to prevailing yields. Conversely, if market interest rates fall below the coupon rate, the bond trades at a premium. To determine the bond’s price after the coupon change, we must first understand the initial YTM calculation. While a precise YTM calculation requires iterative methods or a financial calculator, the question focuses on conceptual understanding rather than exact numerical precision. The key is to recognize that the bond’s price will adjust to reflect the new coupon rate while maintaining the same approximate YTM, given the assumption of constant market conditions. Let’s assume the initial price is close to par for simplicity in understanding the concept. If the coupon decreases, the price must decrease to compensate investors. The new price is calculated using the present value of the future cash flows (coupon payments and face value) discounted at the YTM. The difference between the original coupon and the new coupon impacts the present value of the coupon payments, leading to a lower overall bond price. This price change reflects the need for the bond to offer a competitive return in the market, even with a reduced coupon. The calculation is complex and generally involves financial calculators or software, but understanding the direction and relative magnitude of the change is crucial.

The question assesses the understanding of bond valuation when embedded with an option, specifically a call option. The key is to understand that the price of a callable bond will never exceed the call price because if the bond’s value rises to the call price, the issuer will exercise their right to call the bond back. This caps the upside potential for the investor. The yield to call (YTC) calculation is crucial. First, determine the future value of the bond at the call date, which is the call price of £103. Then, determine the number of coupon payments until the call date (3 years * 2 payments per year = 6 payments). Calculate the present value of the coupon payments and the call price discounted at the YTC. The YTC is the discount rate that equates the present value of the future cash flows (coupon payments and call price) to the current market price of the bond. The approximate YTC can be found using the following formula: \[ YTC = \frac{C + \frac{Call Price – Current Price}{Years to Call}}{ \frac{Call Price + Current Price}{2}} \] Where: C = Annual coupon payment (£5) Call Price = £103 Current Price = £98 Years to Call = 3 \[ YTC = \frac{5 + \frac{103 – 98}{3}}{ \frac{103 + 98}{2}} = \frac{5 + \frac{5}{3}}{\frac{201}{2}} = \frac{5 + 1.67}{100.5} = \frac{6.67}{100.5} = 0.0664 \] YTC = 6.64% The investor should be aware that the bond’s price is capped at the call price. Therefore, even if interest rates fall further, the bond’s price will not increase significantly above £103. This is because the issuer will likely call the bond, limiting the investor’s potential gains. The yield to call provides a more realistic estimate of the return the investor can expect if the bond is called. In this scenario, the investor needs to consider if the 6.64% YTC is attractive enough, given the capped upside potential and the risk of the bond being called early.

The question tests understanding of bond pricing and yield calculations, specifically the impact of changing required yields on bond prices. The key is to calculate the present value of the bond’s future cash flows (coupon payments and face value) at both the initial and the revised required yields. The percentage change in price reflects the bond’s price sensitivity to yield changes, a concept known as duration. Here’s the step-by-step calculation: 1. **Initial Bond Price:** The bond pays a coupon of 6% annually, meaning £60 per year. Since the yield is also 6%, the bond is trading at par, meaning its price is £1000. 2. **Revised Yield:** The yield increases to 7%. We need to calculate the present value of the bond’s cash flows at this new yield. This involves discounting each coupon payment and the face value back to the present. 3. **Present Value Calculation:** The present value of each coupon payment is calculated as \( \frac{Coupon}{(1 + Yield)^t} \), where Coupon is the annual coupon payment, Yield is the required yield, and t is the number of years until the payment. The present value of the face value is \( \frac{Face Value}{(1 + Yield)^n} \), where n is the number of years to maturity. 4. **Summation:** Summing the present values of all coupon payments and the face value gives the bond’s price at the new yield. In this case: Price = \( \sum_{t=1}^{10} \frac{60}{(1.07)^t} + \frac{1000}{(1.07)^{10}} \) Using a financial calculator or spreadsheet, this calculates to approximately £929.49. 5. **Percentage Change:** The percentage change in price is calculated as \( \frac{New Price – Initial Price}{Initial Price} \times 100 \). Percentage Change = \( \frac{929.49 – 1000}{1000} \times 100 = -7.051\% \) Therefore, the bond’s price decreases by approximately 7.051%. The reason for the price decrease is that as the required yield increases, the present value of the bond’s future cash flows decreases. Investors demand a higher return (yield) for holding the bond, and this is reflected in a lower price. This inverse relationship between bond prices and yields is a fundamental concept in fixed-income markets. The magnitude of the price change depends on the bond’s maturity and coupon rate; longer-maturity bonds and lower-coupon bonds are more sensitive to yield changes. The calculation demonstrates the application of present value concepts to bond pricing and highlights the importance of understanding yield changes and their impact on bond values. The example showcases a practical scenario where a portfolio manager needs to assess the impact of changing market conditions on the value of their bond holdings.

The question assesses the understanding of bond pricing sensitivity to yield changes, specifically focusing on the impact of coupon rates and yield to maturity (YTM) on price volatility. A bond with a lower coupon rate is more sensitive to yield changes than a bond with a higher coupon rate, given the same maturity. This is because a larger portion of the bond’s value is derived from the discounted value of the principal, which is more sensitive to changes in the discount rate (yield). Similarly, bonds trading at lower YTMs are more sensitive to yield changes than bonds trading at higher YTMs. The price change for each bond can be approximated using duration. Duration measures the percentage change in bond price for a 1% change in yield. Modified duration adjusts duration for the yield level. The bond with the lower coupon rate and lower YTM will exhibit the greatest price change for a given yield increase. Bond A’s modified duration = Macaulay Duration / (1 + YTM) = 7.5 / (1 + 0.04) = 7.21 Bond B’s modified duration = Macaulay Duration / (1 + YTM) = 7.5 / (1 + 0.06) = 7.08 Price change approximation for Bond A = -Modified Duration * Change in YTM = -7.21 * 0.005 = -0.03605, or -3.605% Price change approximation for Bond B = -Modified Duration * Change in YTM = -7.08 * 0.005 = -0.0354, or -3.54% Therefore, Bond A will experience a greater price decrease.

The question revolves around calculating the dirty price of a bond, considering accrued interest. The clean price is given, and we need to calculate the accrued interest and add it to the clean price to arrive at the dirty price. The accrued interest is calculated based on the coupon rate, face value, and the fraction of the coupon period that has elapsed since the last coupon payment. First, calculate the annual coupon payment: Coupon Rate * Face Value = 6% * £1,000 = £60. Next, determine the coupon payment per day: £60 / 365 = £0.16438 (approximately). Then, calculate the accrued interest: £0.16438 * 120 days = £19.7256 (approximately). Finally, calculate the dirty price: Clean Price + Accrued Interest = £980 + £19.7256 = £999.73 (approximately). A crucial aspect is understanding that the accrued interest represents the portion of the next coupon payment that the seller is entitled to since they held the bond for that period. The buyer compensates the seller for this accrued interest, which is why it’s added to the clean price to arrive at the dirty price. This ensures a fair transaction where the seller receives the interest earned during their holding period. This is governed by standard market practices and principles of fairness in bond trading, rather than specific UK laws or regulations. However, transparency in disclosing both clean and dirty prices is often mandated by market conduct rules to prevent misleading investors. The FCA (Financial Conduct Authority) in the UK emphasizes fair and clear pricing to protect investors.

The question assesses the understanding of bond pricing and its sensitivity to yield changes, particularly the concept of duration and convexity. Duration measures the approximate percentage change in a bond’s price for a 1% change in yield. Convexity accounts for the fact that the relationship between bond prices and yields is not linear; duration is a linear approximation of a curved relationship. A higher convexity implies that the bond’s price is less sensitive to yield increases and more sensitive to yield decreases than predicted by duration alone. The modified duration is given as 7.2, which means that for every 1% (or 100 basis points) change in yield, the bond’s price is expected to change by approximately 7.2% in the opposite direction. The convexity is given as 65. First, calculate the price change due to duration: Yield change = 0.75% = 0.0075 Price change due to duration = – (Modified Duration × Yield Change) = – (7.2 × 0.0075) = -0.054 or -5.4% Next, calculate the price change due to convexity: Price change due to convexity = 0.5 × Convexity × (Yield Change)^2 = 0.5 × 65 × (0.0075)^2 = 0.5 × 65 × 0.00005625 = 0.00183 or 0.183% Finally, combine the price changes due to duration and convexity: Total price change = Price change due to duration + Price change due to convexity = -5.4% + 0.183% = -5.217% Therefore, the estimated percentage change in the bond’s price is approximately -5.217%. The question uses modified duration and convexity to estimate the price change of a bond. Modified duration estimates the sensitivity of a bond’s price to changes in interest rates. Convexity measures the curvature of the price-yield relationship, providing a more accurate estimate of price changes, especially for large yield changes. By combining both duration and convexity, we get a more precise estimate of the bond’s price movement.

The question assesses the understanding of how a bond’s price reacts to changes in yield to maturity (YTM) and how duration and convexity modify this relationship. The scenario involves a bond portfolio manager, requiring the candidate to consider both duration (a linear approximation of price change) and convexity (a quadratic adjustment for the curvature of the price-yield relationship) to estimate the new price of the bond. First, calculate the approximate price change due to the yield increase using duration: Price Change (Duration) = -Duration * Change in Yield * Initial Price Price Change (Duration) = -7.5 * 0.005 * 98 = -3.675 Next, calculate the price change due to convexity: Price Change (Convexity) = 0.5 * Convexity * (Change in Yield)^2 * Initial Price Price Change (Convexity) = 0.5 * 80 * (0.005)^2 * 98 = 0.098 Finally, add the two price changes to the initial price to find the estimated new price: Estimated New Price = Initial Price + Price Change (Duration) + Price Change (Convexity) Estimated New Price = 98 – 3.675 + 0.098 = 94.423 The role of duration and convexity can be further explained using an analogy of driving a car around a bend. Duration is like setting your steering wheel angle based on the initial curvature of the bend. It gives a good approximation for small changes in direction (yield changes). However, convexity is like adjusting your steering angle as you progress around the bend because the curvature isn’t constant. It accounts for the fact that the relationship between price and yield isn’t perfectly linear. In bond pricing, convexity becomes increasingly important for larger yield changes or when comparing bonds with different convexity characteristics. A higher convexity means the bond’s price will increase more when yields fall and decrease less when yields rise, compared to a bond with lower convexity. The impact of the FCA (Financial Conduct Authority) regulations on bond trading practices is also relevant. The FCA emphasizes fair pricing and transparency. Therefore, portfolio managers are expected to use sophisticated tools, including duration and convexity measures, to ensure accurate valuation and risk management. Ignoring convexity, especially in volatile markets, could lead to mispricing and potential regulatory scrutiny. The FCA’s focus on investor protection encourages the use of these advanced techniques to mitigate risk and provide fair outcomes for investors.

To determine the change in the price of Bond Alpha, we need to calculate the approximate price change using the bond’s modified duration and the change in yield. The formula for approximate price change is: Approximate Price Change (%) = – (Modified Duration) * (Change in Yield) First, we need to calculate the modified duration. Modified duration is calculated as Macaulay Duration / (1 + Yield to Maturity). Given: Macaulay Duration = 7.5 years Yield to Maturity (YTM) = 6% or 0.06 Modified Duration = 7.5 / (1 + 0.06) = 7.5 / 1.06 ≈ 7.075 years Next, we need to calculate the change in yield. The yield increased from 6% to 6.3%. Change in Yield = 6.3% – 6% = 0.3% or 0.003 Now, we can calculate the approximate price change: Approximate Price Change (%) = – (7.075) * (0.003) ≈ -0.021225 or -2.1225% This means the bond price decreased by approximately 2.1225%. Now we calculate the change in price in monetary terms. Initial Price = £104 Price Change = -2.1225% of £104 = -0.021225 * 104 ≈ -£2.2074 Therefore, the new approximate price is £104 – £2.2074 ≈ £101.7926 However, this is just an approximation. The actual price change might differ due to convexity effects, which are not accounted for in the duration calculation. Convexity becomes more significant when yield changes are larger. A bond with positive convexity will experience a price increase that is larger than predicted by duration when yields fall, and a price decrease that is smaller than predicted by duration when yields rise. In the context of UK bond markets and regulations, it’s crucial to understand that the Financial Conduct Authority (FCA) requires firms to provide clients with clear and accurate information about the risks associated with fixed income investments. This includes explaining the impact of interest rate changes on bond prices and the limitations of using duration as a sole measure of interest rate sensitivity. Furthermore, UK regulations emphasize the importance of considering both duration and convexity when assessing the potential price volatility of bonds, especially in portfolios with long-dated bonds or significant exposures to interest rate risk. The CISI syllabus stresses the importance of understanding these concepts for advising clients appropriately and managing fixed income portfolios effectively.

The question assesses understanding of yield curve shapes and their implications for investment strategies, particularly in the context of bond maturities and reinvestment risk. The key concept is that a steepening yield curve suggests that longer-term bonds offer higher yields compared to shorter-term bonds. The investor must consider the trade-off between locking in higher yields now versus the potential to reinvest at even higher rates in the future if the yield curve continues to steepen. A barbell strategy involves holding bonds at the short and long ends of the maturity spectrum. In a steepening yield curve environment, the investor benefits from the higher yields on the long-term bonds and the flexibility to reinvest the proceeds from the maturing short-term bonds at potentially higher rates. The calculation involves comparing the potential return from holding the 10-year bond versus reinvesting in a 1-year bond and then a 9-year bond. First, calculate the total return from the 10-year bond: 10-year bond return = 6.0% per year for 10 years. Next, calculate the return from the 1-year bond and subsequent 9-year bond: 1-year bond return = 4.0% After 1 year, the investor reinvests in a 9-year bond. If the yield curve steepens by 50 basis points (0.5%), the new 9-year bond yield will be 5.5% (5.0% + 0.5%). Total return from reinvestment = 4.0% for 1 year + 5.5% for 9 years. To compare these two strategies effectively, we must calculate the average annual return of each strategy. For the 10-year bond, the average annual return is simply 6.0%. For the reinvestment strategy, we calculate a weighted average: Average annual return of reinvestment = \(\frac{(4.0\% \times 1) + (5.5\% \times 9)}{10}\) = \(\frac{4.0 + 49.5}{10}\) = \(\frac{53.5}{10}\) = 5.35% The difference between the 10-year bond return and the reinvestment strategy return is: 6.0% – 5.35% = 0.65% Therefore, the investor would have been 0.65% better off per year by holding the 10-year bond to maturity, given the yield curve steepening scenario.

The question explores the impact of a change in the yield curve shape on a bond portfolio’s duration and market value. It combines understanding of duration, yield curve dynamics, and portfolio management. First, we calculate the initial modified duration of the portfolio. The modified duration is calculated as: Modified Duration = \(\frac{Duration}{1 + (Yield/Number of Periods per Year)}\) For a bond portfolio, the overall duration is the weighted average of the durations of the individual bonds. Given the portfolio is equally weighted, the modified duration is: Modified Duration = \(\frac{7 + 4}{2} = 5.5\) We assume annual compounding, so the modified duration is simply 5.5 years. Next, we determine the yield change. The yield curve flattens, meaning short-term yields rise and long-term yields fall. The spread between the 1-year and 10-year yields decreases from 3% (6% – 3%) to 1% (5.5% – 4.5%). This means short-term yields increased by 0.5% (from 3% to 3.5% for the 1-year) and long-term yields decreased by 0.5% (from 6% to 5.5% for the 10-year). The portfolio’s initial yield is the average of the 1-year and 10-year yields, which is 4.5%. Now, we calculate the estimated percentage change in the portfolio’s market value using the duration approximation: Percentage Change ≈ – Modified Duration * Change in Yield Percentage Change ≈ -5.5 * (0.055 – 0.045) = -5.5 * 0.01 = -0.055 or -5.5% However, the question introduces convexity. Convexity measures the curvature of the price-yield relationship. A positive convexity means that as yields fall, the price increase is greater than predicted by duration alone, and as yields rise, the price decrease is smaller than predicted by duration alone. The convexity effect can be approximated as: Convexity Effect ≈ 0.5 * Convexity * (Change in Yield)^2 Convexity Effect ≈ 0.5 * 2.5 * (0.01)^2 = 0.5 * 2.5 * 0.0001 = 0.000125 or 0.0125% Therefore, the total estimated percentage change in the portfolio’s market value is the sum of the duration effect and the convexity effect: Total Percentage Change ≈ -5.5% + 0.0125% = -5.4875% Rounding to two decimal places, the estimated percentage change is -5.49%. This calculation combines several concepts: modified duration, yield curve shifts, and convexity. It tests the candidate’s ability to apply these concepts in a practical scenario and understand their combined impact on a bond portfolio’s value. The scenario is unique because it combines a yield curve flattening with specific bond durations and portfolio weights, requiring the candidate to synthesize multiple pieces of information.

The calculation of the bond’s approximate yield to maturity (YTM) involves several steps. First, determine the annual coupon payment. This is calculated by multiplying the coupon rate by the face value of the bond: \(0.065 \times £1000 = £65\). Next, determine the capital gain or loss, which is the difference between the face value and the purchase price: \(£1000 – £960 = £40\). Then, annualize this gain or loss by dividing it by the years to maturity: \(£40 / 8 = £5\). Add the annual coupon payment to the annualized gain or loss: \(£65 + £5 = £70\). Finally, divide this sum by the average of the bond’s purchase price and face value: \( (£960 + £1000) / 2 = £980\). The approximate YTM is then \(£70 / £980 \approx 0.0714\), or 7.14%. The yield to maturity (YTM) is a crucial metric for bond investors, representing the total return anticipated on a bond if it’s held until it matures. It’s more comprehensive than the coupon rate because it factors in the bond’s current market price. When a bond is trading at a discount (below its face value), as in this scenario, the YTM will be higher than the coupon rate. This is because the investor not only receives the coupon payments but also realizes a capital gain when the bond matures and is redeemed at face value. Conversely, if a bond trades at a premium, the YTM will be lower than the coupon rate. Understanding YTM is essential for comparing different bonds, especially those with varying coupon rates and maturities. Investors use YTM to assess the relative attractiveness of different investment opportunities and to make informed decisions about their bond portfolios. In the UK market, the YTM calculation and bond trading practices are subject to regulations by the Financial Conduct Authority (FCA), ensuring transparency and fair trading practices. For instance, the FCA mandates that bond prices and yields are quoted accurately and that investors are provided with clear information about the risks associated with bond investments.

Imagine a bond as a stream of future cash flows. These cash flows consist of periodic coupon payments and the return of the principal (face value) at maturity. The price of the bond represents the present value of all these future cash flows, discounted at a rate that reflects the investor’s required rate of return (yield to maturity). In this scenario, we have a bond that pays coupons semi-annually. This means we need to adjust our calculations to reflect the shorter compounding period. Instead of using the annual coupon rate and yield to maturity directly, we divide them by two to get the semi-annual rates. The present value of the coupon payments is calculated using the present value of an annuity formula. This formula essentially sums up the present value of each individual coupon payment. It takes into account the time value of money, meaning that money received today is worth more than money received in the future. The present value of the face value is calculated by discounting the face value back to the present using the semi-annual yield to maturity. This reflects the fact that the investor will not receive the face value until the bond matures. Finally, the bond price is simply the sum of the present value of the coupon payments and the present value of the face value. This represents the total amount that an investor would be willing to pay for the bond, given their required rate of return. The example illustrates how bond pricing works in practice, taking into account the time value of money and the specific characteristics of the bond, such as the coupon rate, yield to maturity, and time to maturity. Understanding these concepts is crucial for investors who want to make informed decisions about buying and selling bonds.

The question assesses understanding of bond pricing, yield to maturity (YTM), current yield, and the impact of coupon rate and market interest rates on bond valuation. It specifically tests the ability to apply these concepts in a scenario involving a bond with a call provision. The calculation involves understanding the relationship between YTM, current yield, and coupon rate, and how a call provision can affect the realized yield. First, calculate the bond’s current yield: Current Yield = (Annual Coupon Payment / Current Market Price) * 100 = (£60 / £950) * 100 = 6.32%. Next, we need to understand the relationship between coupon rate, current yield, and YTM. Since the bond is trading at a discount (£950, below its par value of £1000), the YTM must be higher than the current yield, and the current yield must be higher than the coupon rate. This is because the investor not only receives the coupon payments but also realizes a capital gain when the bond matures or is called at par. The bond being callable at £1020 in three years introduces complexity. If market interest rates decline significantly, the issuer might call the bond. This limits the investor’s potential upside. The investor’s realized yield will be somewhere between the YTM and the yield-to-call (YTC). Since we don’t have enough information to calculate the exact YTM or YTC, we must rely on the relationships between coupon rate, current yield, and YTM, along with the call provision’s impact. Given the discount and the call feature, the most likely scenario is that the realized yield will be *higher* than the current yield but *lower* than the full YTM would have been without the call provision, as the potential capital appreciation is capped by the call price. Therefore, the most plausible answer is a yield higher than 6.32% but lower than what a standard YTM calculation (without considering the call) would suggest. Option a) is the only option that fits this description.

The question assesses the understanding of bond pricing sensitivity to yield changes, specifically focusing on the impact of coupon rates and maturity on price volatility. To answer this, we need to understand duration and convexity. Duration measures the approximate percentage change in a bond’s price for a 1% change in yield. Convexity measures the curvature of the price-yield relationship, providing a more accurate estimate of price changes, especially for large yield movements. In this scenario, we are comparing two bonds with different coupon rates and maturities. A lower coupon bond is more sensitive to interest rate changes because a larger portion of its return comes from the face value received at maturity, which is discounted at the prevailing yield. A longer maturity bond is also more sensitive to interest rate changes because the present value of its future cash flows is affected more by changes in the discount rate (yield). Bond A: 3% coupon, 10-year maturity. Bond B: 7% coupon, 5-year maturity. We can intuitively understand this through an analogy. Imagine two streams of income: one stream (Bond A) that pays very little regularly but gives you a large lump sum after 10 years, and another stream (Bond B) that pays a substantial amount regularly and a smaller lump sum after 5 years. If the interest rate (discount rate) changes, the present value of the large lump sum in Bond A is affected more than the smaller lump sum in Bond B because it is further into the future. Similarly, the higher regular payments of Bond B cushion it against interest rate changes. The question asks which bond will experience a greater percentage price change for a given yield change. Since Bond A has a lower coupon and a longer maturity, it will be more sensitive to interest rate changes. Therefore, Bond A will experience a greater percentage price change.

The question assesses understanding of yield curve impact on bond portfolio strategy, considering duration, convexity, and investor risk appetite. A steepening yield curve means longer-term rates are rising faster than short-term rates. * **Duration Impact:** A portfolio with longer duration is more sensitive to interest rate changes. If a yield curve steepens, longer-term bond prices will fall more than shorter-term bond prices, leading to losses for portfolios with longer durations. * **Convexity Impact:** Convexity measures the curvature of the price-yield relationship. Higher convexity provides greater price appreciation when yields fall and smaller price depreciation when yields rise. A portfolio with higher convexity will benefit slightly from a steepening yield curve, as the gains from shorter-term bonds will slightly offset the losses from longer-term bonds. * **Risk Appetite Impact:** Risk-averse investors typically prefer shorter-duration bonds to minimize interest rate risk. In a steepening yield curve environment, they would be less inclined to hold longer-duration bonds. The optimal strategy depends on the investor’s risk tolerance and the magnitude of the expected yield curve shift. A risk-averse investor would likely reduce duration, even at the cost of some potential yield. A more aggressive investor might maintain or even increase duration if they believe the steepening is temporary and will reverse. However, given the increased losses in a steepening environment, it is generally prudent to reduce duration to some extent. Calculation is not directly required, but understanding the interplay of duration, convexity, and risk appetite is crucial to determine the optimal portfolio adjustment. A steepening yield curve generally favors a shorter duration portfolio, especially for risk-averse investors. The losses from longer-dated bonds outweigh the gains from convexity, and reducing duration mitigates the overall negative impact.

The question assesses understanding of bond pricing, yield to maturity (YTM), current yield, and the impact of coupon rate relative to YTM on bond price behavior. It specifically tests the ability to decompose the total return on a bond into its current yield and capital gain/loss components. The calculation involves first determining the annual coupon payment. The current yield is then calculated by dividing the annual coupon payment by the current market price. Finally, the capital gain or loss is calculated as the difference between the redemption value and the current market price. In this scenario, the bond has a redemption value of £105, a coupon rate of 6%, and is trading at £98. Annual coupon payment = Coupon rate * Redemption value = 0.06 * £105 = £6.30 Current yield = Annual coupon payment / Current market price = £6.30 / £98 = 0.0642857 or 6.43% (rounded to two decimal places) Capital gain = Redemption value – Current market price = £105 – £98 = £7 The total return is the sum of the current yield and the capital gain. Total return = Current yield + Capital gain = 6.43% + (£7/£98) = 6.43% + 7.14% = 13.57% The unique aspect is the non-standard redemption value, which is not par value. This forces students to calculate the coupon payment based on the redemption value, not the market price. The question also requires students to understand that a bond trading below its redemption value will generate a capital gain if held to maturity, and to correctly calculate and incorporate this gain into the total return. This tests a deeper understanding of bond pricing dynamics than simply calculating YTM. The scenario requires a multi-step calculation and understanding of the relationship between coupon rate, current yield, capital gain, and total return, making it a challenging application of bond market fundamentals.

The question assesses the understanding of bond pricing sensitivity to yield changes, specifically focusing on how duration and convexity affect price fluctuations. The scenario involves a portfolio manager making investment decisions based on predicted yield movements and requires calculating the expected price change using duration and convexity adjustments. The formula for approximating the percentage price change of a bond is: \[ \text{Percentage Price Change} \approx (-\text{Modified Duration} \times \Delta \text{Yield}) + (\frac{1}{2} \times \text{Convexity} \times (\Delta \text{Yield})^2) \] In this scenario: Modified Duration = 7.2 Convexity = 65 Yield Change (\(\Delta \text{Yield}\)) = -0.75% = -0.0075 First, calculate the duration effect: \[ -\text{Modified Duration} \times \Delta \text{Yield} = -7.2 \times (-0.0075) = 0.054 \] This represents a 5.4% increase in price due to the yield decrease, based on duration alone. Next, calculate the convexity effect: \[ \frac{1}{2} \times \text{Convexity} \times (\Delta \text{Yield})^2 = \frac{1}{2} \times 65 \times (-0.0075)^2 = \frac{1}{2} \times 65 \times 0.00005625 = 0.001828125 \] This represents a 0.1828125% increase in price due to convexity. Finally, combine the duration and convexity effects to estimate the total percentage price change: \[ \text{Total Percentage Price Change} = 0.054 + 0.001828125 = 0.055828125 \] This equates to approximately 5.58%. The inclusion of convexity refines the price change estimate, particularly when yield changes are substantial. Without convexity, the price change would be underestimated. Convexity is more important for larger yield changes and for bonds with higher convexity values. The negative yield change (yield decrease) results in a positive price change, consistent with the inverse relationship between bond yields and prices. The example highlights the importance of considering both duration and convexity when managing bond portfolios, especially in anticipation of significant yield movements. A portfolio manager using only duration would have an incomplete picture of the potential price impact.

The question assesses the understanding of bond pricing and the impact of various yield measures, specifically yield to worst (YTW), on investment decisions. YTW is the lowest potential yield an investor can receive on a callable bond, assuming the issuer exercises its call options in the most disadvantageous way for the investor. It’s crucial for risk management, especially when dealing with callable bonds. The scenario involves a complex bond structure with multiple call dates and prices, requiring the calculation of yield to call (YTC) for each call date and comparing them with the yield to maturity (YTM) to determine the YTW. The calculation steps are as follows: 1. **Calculate Yield to Maturity (YTM):** This requires an iterative process or a financial calculator. Given the current price (105), face value (100), coupon rate (6%), and maturity (5 years), the YTM is approximately 4.84%. 2. **Calculate Yield to Call (YTC) for each call date:** * **Year 2, Call Price 103:** We need to find the yield that equates the present value of the coupon payments until year 2 and the call price of 103 to the current price of 105. This involves solving for \(r\) in the following equation: \[105 = \frac{6}{(1+r)} + \frac{103+6}{(1+r)^2}\] Solving this yields an approximate YTC of 1.95%. * **Year 4, Call Price 101:** Similarly, we calculate the yield that equates the present value of the coupon payments until year 4 and the call price of 101 to the current price of 105: \[105 = \frac{6}{(1+r)} + \frac{6}{(1+r)^2} + \frac{6}{(1+r)^3} + \frac{101+6}{(1+r)^4}\] Solving this yields an approximate YTC of 4.02%. 3. **Determine Yield to Worst (YTW):** The YTW is the minimum of YTM and all YTCs. In this case, it is the lowest of 4.84%, 1.95%, and 4.02%, which is 1.95%. Therefore, the Yield to Worst is approximately 1.95%. This represents the most conservative estimate of the bond’s potential return, considering the possibility of the issuer calling the bond at the most disadvantageous time for the investor. Understanding YTW is crucial for investors to accurately assess the risk associated with callable bonds and make informed investment decisions.

1. **Initial Assessment:** The bond is trading at a premium, meaning its price is above par. This occurs because the coupon rate (6%) is higher than the yield to maturity (5%). Investors are willing to pay more for this bond because it provides a higher stream of income (coupon payments) than what they could obtain from newly issued bonds with a 5% yield. 2. **Impact of Market Interest Rate Increase:** If market interest rates rise to 7%, newly issued bonds will offer a higher return than the existing bond. This makes the existing bond less attractive. As a result, its price must fall to compensate for the lower yield relative to the market. The bond will now trade at a discount (below par). 3. **Impact of Time to Maturity:** A bond with a longer time to maturity is more sensitive to interest rate changes than a bond with a shorter time to maturity. This is because the investor is locked into the lower coupon payments for a longer period, making the bond’s value more susceptible to erosion when interest rates rise. Conversely, a bond with a shorter time to maturity will have a smaller price change because the investor will receive par value sooner, allowing them to reinvest at the higher market rates. 4. **Scenario Application:** Given the initial premium and the subsequent rise in market interest rates, the bond will transition from trading at a premium to trading at a discount. The longer the remaining time to maturity, the greater the price decline. The question asks for the scenario where the price decrease is most pronounced. This will occur when the market interest rates rise significantly, and the bond has a long remaining time to maturity. 5. **Conceptual Analogy:** Imagine two identical rental properties. One has a lease locked in at a high rental rate for 20 years. The other has a lease locked in at the same high rate, but only for 2 years. If market rental rates suddenly drop, the property with the 20-year lease will suffer a much larger decrease in value. This is because the owner is stuck receiving below-market rent for a much longer period. Similarly, a bond with a longer maturity is more sensitive to interest rate changes. 6. **Regulations:** All bond trading in the UK is subject to regulations aimed at ensuring fair and transparent markets, including rules about market abuse and insider dealing as set out in the Financial Services and Markets Act 2000.

The question assesses understanding of bond pricing, yield to maturity (YTM), and the impact of changing interest rates. The scenario involves a complex bond with semi-annual coupons and a specific redemption value. To solve this, we need to calculate the present value of all future cash flows (coupon payments and redemption value) discounted at the yield to maturity rate. First, determine the semi-annual coupon payment: \(5.5\% \text{ of } £100 = £5.5 \text{ per year} \), so \( £5.5 / 2 = £2.75 \) semi-annually. Next, calculate the number of semi-annual periods: \( 7 \text{ years } \times 2 = 14 \text{ periods} \). The semi-annual yield to maturity is \( 6.2\% / 2 = 3.1\% \). The bond price is the present value of the coupon payments plus the present value of the redemption value. The present value of the coupon payments is calculated using the present value of an annuity formula: \[ PV_{\text{coupons}} = C \times \frac{1 – (1 + r)^{-n}}{r} \] Where: \( C = £2.75 \) (semi-annual coupon payment) \( r = 0.031 \) (semi-annual YTM) \( n = 14 \) (number of semi-annual periods) \[ PV_{\text{coupons}} = 2.75 \times \frac{1 – (1 + 0.031)^{-14}}{0.031} \] \[ PV_{\text{coupons}} = 2.75 \times \frac{1 – (1.031)^{-14}}{0.031} \] \[ PV_{\text{coupons}} = 2.75 \times \frac{1 – 0.6528}{0.031} \] \[ PV_{\text{coupons}} = 2.75 \times \frac{0.3472}{0.031} \] \[ PV_{\text{coupons}} = 2.75 \times 11.20 \] \[ PV_{\text{coupons}} = £30.80 \] The present value of the redemption value is: \[ PV_{\text{redemption}} = \frac{FV}{(1 + r)^n} \] Where: \( FV = £103 \) (redemption value) \( r = 0.031 \) (semi-annual YTM) \( n = 14 \) (number of semi-annual periods) \[ PV_{\text{redemption}} = \frac{103}{(1.031)^{14}} \] \[ PV_{\text{redemption}} = \frac{103}{1.531} \] \[ PV_{\text{redemption}} = £67.27 \] The bond price is the sum of the present values: \[ \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{redemption}} \] \[ \text{Bond Price} = £30.80 + £67.27 \] \[ \text{Bond Price} = £98.07 \] Therefore, the closest answer is £98.07. This question is designed to be difficult by requiring multiple steps and calculations. It also tests the understanding of how bond prices are affected by interest rates and redemption values. It’s not simply memorizing a formula but applying it in a nuanced situation.

The question explores the impact of embedded options, specifically a call provision, on a bond’s price sensitivity to interest rate changes. A callable bond gives the issuer the right to redeem the bond before its maturity date, typically when interest rates fall. This call feature caps the bond’s upside potential because if interest rates decline significantly, the issuer is likely to call the bond, preventing the bondholder from fully benefiting from further price appreciation. The concept of effective duration is used to measure the bond’s price sensitivity to interest rate changes, considering the impact of embedded options. Effective duration is calculated as: Effective Duration = \[\frac{P_{-} – P_{+}}{2 \times P_{0} \times \Delta y}\] Where: \(P_{-}\) = Price if yield decreases \(P_{+}\) = Price if yield increases \(P_{0}\) = Initial Price \(\Delta y\) = Change in yield (in decimal form) In this scenario, the callable bond’s price behavior differs from a similar non-callable bond due to the call option. When interest rates fall, the callable bond’s price appreciation is limited by the call option, meaning \(P_{-}\) will be smaller than it would be for a non-callable bond. When interest rates rise, the callable bond behaves more like a non-callable bond, as the call option becomes less relevant. Given the provided prices, we can calculate the effective duration: Effective Duration = \[\frac{99.50 – 96.50}{2 \times 98 \times 0.01}\] = \[\frac{3}{1.96}\] ≈ 1.53 Therefore, the effective duration of the callable bond is approximately 1.53. This value reflects the reduced price sensitivity of the callable bond due to the call option, which limits its upside potential when interest rates fall. The lower effective duration, compared to a similar non-callable bond, signifies that the callable bond’s price is less sensitive to interest rate fluctuations, particularly decreases. The callable feature acts as a dampener on price appreciation, making the bond behave differently from a straight bond.

The question assesses understanding of bond pricing, yield to maturity (YTM), and the impact of changing interest rates. The scenario involves a bond with a specific coupon rate, face value, and time to maturity, purchased at a premium. Calculating the approximate YTM requires considering the annual coupon payments, the difference between the purchase price and face value (amortization of the premium), and the time remaining until maturity. The formula for approximate YTM is: \[YTM \approx \frac{Annual \ Coupon \ Payment + \frac{Face \ Value – Purchase \ Price}{Years \ to \ Maturity}}{\frac{Face \ Value + Purchase \ Price}{2}}\]. In this case, the annual coupon payment is 6% of £1000, which is £60. The difference between the face value and purchase price is £1000 – £1080 = -£80 (a premium). The time to maturity is 5 years. Therefore, the approximate YTM is: \[YTM \approx \frac{60 + \frac{-80}{5}}{\frac{1000 + 1080}{2}} = \frac{60 – 16}{1040} = \frac{44}{1040} \approx 0.0423\] or 4.23%. Understanding the impact of an immediate increase in interest rates by 50 basis points (0.5%) requires recognizing the inverse relationship between bond prices and interest rates. If interest rates rise, the value of existing bonds with lower coupon rates decreases. This is because investors can now purchase newly issued bonds with higher yields, making the older, lower-yielding bonds less attractive. The immediate impact would be a decrease in the bond’s market value to reflect the new prevailing interest rate environment. The approximate YTM calculation is used to estimate the bond’s return if held to maturity, considering both coupon payments and the amortization of the premium. This concept is vital for fixed-income investors in the UK, who must constantly assess and manage interest rate risk within their portfolios. This question tests the candidate’s ability to apply these principles in a practical scenario, going beyond rote memorization of formulas.

The question assesses understanding of bond pricing sensitivity to yield changes, specifically using duration and convexity. Duration estimates the percentage price change for a 1% change in yield. Convexity refines this estimate, especially for larger yield changes, by accounting for the curvature in the bond price-yield relationship. The formula to approximate the percentage price change is: Percentage Price Change ≈ – (Duration × Change in Yield) + (0.5 × Convexity × (Change in Yield)^2) In this scenario, the bond has a duration of 7.5 and convexity of 60. The yield increases by 150 basis points (1.5%). 1. **Duration Effect:** – (7.5 × 0.015) = -0.1125 or -11.25% 2. **Convexity Effect:** 0.5 × 60 × (0.015)^2 = 0.5 × 60 × 0.000225 = 0.00675 or 0.675% 3. **Combined Effect:** -11.25% + 0.675% = -10.575% Therefore, the estimated percentage price change is approximately -10.575%. The analogy to understand convexity is imagining driving a car. Duration is like steering straight based on the current speed; it assumes a linear relationship. However, the road curves (like the bond price-yield curve). Convexity is like adjusting your steering to account for the curvature of the road, preventing you from drifting off course, especially at higher speeds (larger yield changes). Without considering convexity, the price decline would be overestimated. The application of this concept is critical in portfolio management. Consider a portfolio manager who is immunizing a bond portfolio against interest rate risk. They use duration to match the portfolio’s duration to the investment horizon. However, for large anticipated interest rate movements, relying solely on duration can lead to significant errors. Incorporating convexity provides a more accurate assessment of the portfolio’s risk exposure, enabling the manager to make better-informed decisions about hedging strategies and asset allocation. For instance, if the manager expects significant interest rate volatility, they might prefer bonds with higher convexity, as they will outperform bonds with lower convexity in such scenarios.

The question requires calculating the percentage change in the price of a bond given changes in its yield to maturity (YTM) and modified duration. The bond’s modified duration represents the approximate percentage change in the bond’s price for a 1% change in yield. Since the yield change is given in basis points (bps), we need to convert it to a percentage. 1 basis point is 0.01%, so a 25 bps increase is 0.25%. The formula to calculate the approximate percentage price change is: Percentage Price Change ≈ – (Modified Duration × Change in Yield in Percentage) In this case, the modified duration is 7.5, and the yield increases by 0.25%. Therefore, the percentage price change is: Percentage Price Change ≈ – (7.5 × 0.25%) = -1.875% The bond’s price will decrease by approximately 1.875%. The negative sign indicates an inverse relationship between yield and price; as yield increases, the price decreases. The scenario involves a hypothetical bond issued by a UK-based energy company regulated under UK financial laws, adding a layer of realism and relevance to the CISI Bond & Fixed Interest Markets context. Understanding modified duration is crucial for fixed-income portfolio management and risk assessment, particularly when evaluating the impact of interest rate movements on bond values. The calculation provides a practical application of bond pricing principles, essential for professionals in the fixed-income markets.

The question assesses the understanding of bond pricing and yield calculations, specifically focusing on the impact of changing yield curves and the application of duration to estimate price changes. The scenario involves a complex situation with a bond held by a UK-based investment firm, requiring the candidate to apply their knowledge of UK regulations and market practices. The calculation involves several steps: 1. **Calculate the Modified Duration:** Modified duration is calculated using the formula: Modified Duration = Macaulay Duration / (1 + Yield to Maturity). In this case, Modified Duration = 7.5 / (1 + 0.04) = 7.21 years. 2. **Calculate the Change in Yield:** The yield curve shifts downwards by 35 basis points, which is 0.35%. 3. **Estimate the Percentage Price Change:** The percentage price change is estimated using the formula: Percentage Price Change ≈ – Modified Duration \* Change in Yield. Therefore, Percentage Price Change ≈ -7.21 \* (-0.0035) = 0.025235 or 2.5235%. 4. **Calculate the Estimated New Price:** The initial price is £98.50. The estimated price change is 2.5235% of £98.50, which is £2.4857. The new estimated price is £98.50 + £2.4857 = £100.9857. This calculation demonstrates how changes in the yield curve affect bond prices and how duration can be used to estimate these changes. The negative sign in the formula indicates an inverse relationship between yield changes and bond prices. A decrease in yield leads to an increase in bond price, and vice versa. The question also touches upon the regulatory aspect, specifically the FCA’s (Financial Conduct Authority) role in overseeing firms conducting investment business in the UK. This is crucial as firms must ensure that their valuation models and risk management practices comply with regulatory standards to protect investors and maintain market integrity. The scenario requires the candidate to understand not only the mechanics of bond pricing but also the broader context of regulatory compliance.

The question assesses the understanding of bond pricing and yield calculations in a scenario involving a callable bond. The key is to determine the yield to worst (YTW), which is the lower of the yield to call (YTC) and the yield to maturity (YTM). First, we need to calculate the YTM. This requires an iterative process or the use of a financial calculator. Given the price of 97.50, a coupon rate of 6% paid semi-annually, and a maturity of 8 years, we can approximate the YTM. The semi-annual coupon payment is \( \frac{6\%}{2} \times 100 = 3 \). Using an approximation formula, we have: \[ YTM \approx \frac{C + \frac{FV – PV}{n}}{\frac{FV + PV}{2}} \] Where C is the annual coupon payment, FV is the face value, PV is the present value (price), and n is the number of years to maturity. \[ YTM \approx \frac{6 + \frac{100 – 97.50}{8}}{\frac{100 + 97.50}{2}} = \frac{6 + 0.3125}{98.75} = \frac{6.3125}{98.75} \approx 0.0639 \] So, the YTM is approximately 6.39%. Next, we calculate the YTC. The bond is callable in 3 years at 102. The semi-annual coupon payment remains 3. The number of periods is 3 years * 2 = 6. Using a similar approximation formula: \[ YTC \approx \frac{C + \frac{CallPrice – PV}{n}}{\frac{CallPrice + PV}{2}} \] Where CallPrice is the call price, PV is the present value (price), and n is the number of years to call. \[ YTC \approx \frac{6 + \frac{102 – 97.50}{3}}{\frac{102 + 97.50}{2}} = \frac{6 + 1.5}{99.75} = \frac{7.5}{99.75} \approx 0.0752 \] So, the YTC is approximately 7.52%. Since the bond is callable, the investor will receive the lower of YTM and YTC, which in this case is the YTM of 6.39%. However, given the choices, the closest is 6.35%. This question tests not just the ability to calculate YTM and YTC but also the understanding of which yield is relevant for a callable bond, emphasizing a practical application of bond valuation. The distractor options are designed to mislead those who only calculate one yield or misunderstand the concept of yield to worst. The scenario is unique because it combines the complexities of callable bonds with realistic market prices and call provisions.

The current yield is calculated by dividing the annual coupon payment by the current market price of the bond. The annual coupon payment is the coupon rate multiplied by the face value of the bond. In this case, the coupon rate is 4.5% and the face value is £1,000, so the annual coupon payment is \(0.045 \times £1,000 = £45\). The dirty price of the bond includes accrued interest. Accrued interest is calculated as (coupon rate / number of coupon payments per year) * (number of days since last coupon payment / number of days in coupon period). Since the bond pays semi-annual coupons, there are 2 coupon payments per year. The coupon period is 182.5 days (365/2). The bond was purchased 75 days after the last coupon payment. Therefore, the accrued interest is \((0.045 / 2) \times (75 / 182.5) \times £1,000 = £9.25\). The clean price is the dirty price minus accrued interest. So, the clean price is \(£985 – £9.25 = £975.75\). The current yield is then calculated as annual coupon payment divided by the clean price, which is \(£45 / £975.75 = 0.0461\), or 4.61%. Now, let’s consider a scenario where the bond is trading at a premium due to falling interest rates. The clean price could be significantly higher than the face value, say £1,100, while the coupon rate remains at 4.5%. In this case, the current yield would be \(£45 / £1,100 = 0.0409\), or 4.09%. This illustrates how the current yield reflects the current return based on the bond’s market price, rather than the yield to maturity, which considers the total return if the bond is held until maturity, including any capital gain or loss. Another scenario involves a zero-coupon bond, which does not pay any periodic interest. The current yield for a zero-coupon bond is always 0%, as there are no coupon payments. The return comes solely from the difference between the purchase price and the face value at maturity.

The question assesses the understanding of bond pricing and yield calculations, specifically focusing on the impact of coupon rates, yield to maturity (YTM), and accrued interest on the clean and dirty prices of bonds. The scenario presents a situation involving a bond issued by a UK-based corporation, subject to UK tax regulations, requiring the candidate to calculate the clean price given the dirty price, accrued interest, coupon rate, and days since the last coupon payment. The dirty price is the price the buyer pays, which includes the accrued interest. The clean price is the price of the bond without the accrued interest. The accrued interest is calculated based on the coupon rate, the face value of the bond, and the fraction of the coupon period that has passed since the last coupon payment. Accrued Interest Calculation: The formula for accrued interest is: \[ \text{Accrued Interest} = \frac{\text{Coupon Rate} \times \text{Face Value} \times \text{Days Since Last Coupon}}{\text{Days in Coupon Period}} \] In this case: Coupon Rate = 6% or 0.06 Face Value = £100 Days Since Last Coupon = 73 Days in Coupon Period = 182.5 (since coupons are paid semi-annually, 365/2 = 182.5) \[ \text{Accrued Interest} = \frac{0.06 \times 100 \times 73}{182.5} = \frac{438}{182.5} \approx 2.40 \] Clean Price Calculation: The clean price is calculated by subtracting the accrued interest from the dirty price: \[ \text{Clean Price} = \text{Dirty Price} – \text{Accrued Interest} \] Dirty Price = £104.50 Accrued Interest = £2.40 \[ \text{Clean Price} = 104.50 – 2.40 = 102.10 \] Therefore, the clean price of the bond is £102.10. This calculation is essential for understanding the true market value of the bond, excluding the portion of the price that represents accrued interest owed to the seller.

The question requires understanding the impact of a change in the yield curve’s slope on a bond portfolio’s duration and market value, considering the investor’s hedging strategy using bond futures. We need to analyze how the steepening yield curve affects different maturities and how the futures hedge performs under these conditions. The initial portfolio duration is 7 years, meaning the portfolio’s value is expected to change by approximately 7% for every 1% change in yield. The investor is hedging using bond futures with a conversion factor of 0.9, which means the futures contract is less sensitive to yield changes than the underlying bond. A steepening yield curve means longer-term yields increase more than shorter-term yields. This will negatively impact the longer-dated bonds in the portfolio more significantly than the shorter-dated ones. Since the portfolio has a duration of 7 years, the price decline will be substantial. The futures hedge is designed to offset some of this loss. The number of futures contracts required for the hedge is calculated as: Number of contracts = (Portfolio Value * Portfolio Duration) / (Futures Price * Futures Duration * Conversion Factor) Given a portfolio value of £50 million, portfolio duration of 7 years, futures price of £100,000, futures duration of 8 years, and conversion factor of 0.9, the number of contracts is: Number of contracts = (50,000,000 * 7) / (100,000 * 8 * 0.9) = 43750000 / 720000 = 60.76, rounded to 61 contracts. The yield curve steepens, with 2-year yields increasing by 0.10% and 10-year yields increasing by 0.30%. The portfolio duration of 7 years is closer to the 10-year end, so we approximate the portfolio yield change as closer to 0.30%. The portfolio value decreases by approximately 7 * 0.30% = 2.1%. Thus, the portfolio loss is 0.021 * £50,000,000 = £1,050,000. The futures contract duration is 8 years. The futures price is expected to decline as yields increase. We approximate the yield change affecting the futures contract as the 10-year yield change (0.30%). The futures price change is approximately 8 * 0.30% = 2.4%. Thus, the futures price decreases by 0.024 * £100,000 = £2,400 per contract. Since the investor is short 61 contracts, the gain from the futures hedge is 61 * £2,400 = £146,400. The net loss is the portfolio loss minus the futures gain: £1,050,000 – £146,400 = £903,600.