Table 6: Summary statistics for holding period return of the portfolio.

Summary statistics for the holding period return of an equally weighted bond portfolio, individual returns, and portfolios are shown in Table 6. For the individual bonds, the mean holding period return was 1.32%. Its standard deviation of 0.05% was remarkably low (indicating minimal variability in returns across the different bonds during this time). Over the period, it was a 5.27% total return. Although having equally weighted portions of 25% for each bond, the mean return of the portfolio is much lower at 0.33%, accompanied by an even more minor standard deviation (at a measurable range) of only 0.01%, which showed that it was very

stable, however, within a subdued performance. This spread highlights the diversification effect, which reduces costs at the expense of (potentially) more individual bond returns. These short-term results over an annual period represent only a conservative, stable investment approach with minimal risk, thus putting the portfolio on an annualized 2.65% return.

Part 2:

A.   Use all available Government bond data to construct and present a yield, spot, and forward curve on 31st January 2024 and 31st July 2024. Estimate the spot curve and forward curve for 5 years. Present and discuss the findings.

Figure 2: YTM, Spot rate, and Forward rate curves on 31st Jan 2024

As of 31st January 2024, government bond yields show the Yield-to-Maturity (YTM), spot rate, and forward rate curves, all derived from the same data to illustrate the expected interest rate regime for the next five years. These three curves move together, indicating a consistent investor expectation regarding future interest rates. Initially, the levels are low for short maturities, suggesting that short-term interest rates are also low. The curves gradually rise across different maturities, peaking around the 5-year mark, indicating that investors expect higher long-term rates. This pattern typically reflects normal market conditions, where longer-maturity securities have higher yields than shorter-maturity securities, indicating increased risk and an expected rise in inflation. The close alignment of the YTM, spot, and forward rate curves suggests a consistent market view on future rates. Additionally, slightly higher short-term forward rates indicate expectations of either rising rates or increased risk in the coming period, which is compensated with a premium.

Figure 3: YTM, Spot rate, and Forward rate curves on 31st July 2024

The graph in Figure 3 displays the yield to maturity (YTM), spot rate, and forward rate curves for government bonds as of July 31, 2024, using a five-year forecast horizon. At this point, the curves indicate a slight decrease in the short term, followed by an increase as the maturity period lengthens. This gives the curves a hump-shaped appearance, particularly in the forward rate curve. This suggests that short-term interest rates are likely to be lower soon than the market’s current price for the medium term. Price movements are influenced by anticipated economic changes, such as policy adjustments or inflationary expectations, making the short to medium end of the yield curve more reactive than immediate or longer-term rates. Beyond the second year, the forward rates appear higher than the spot and YTM long-term rates, potentially indicating that investors expect higher future interest rates, possibly in anticipation of economic growth or inflation that could lead to tighter monetary policy in the coming years. A curve like this could indicate evolving market sentiments and financial forecasts, adjusting for recent economic news or policy announcements from January through July 2024.

Yield to maturity (YTM) curve

The yield-to-maturity (YTM) curve represents the average annual return an investor expects from buying a bond and holding it until maturity, assuming all payments are made on time. In a standard yield curve, such as in January and July 2024, the YTM curves typically rise from left to right on the graph, indicating that bonds with longer maturities have higher coupon rates and, thus, higher yields. This suggests that longer-term bonds need to offer higher returns to compensate for their increased risks, whether due to potential inflation or speculative interest rate changes. Changes in the yield curve may indicate shifts in prevailing market interest rates or investor expectations about future economic conditions.

Spot rate curve

Spot rate curve- Theoretical yield of a zero-coupon bond (a bond that pays no interest but is issued at a discount) for different maturities. As such, it is equivalent to the rate of return on a government bond with no interim cash flows. January and July 2024 share the same pattern (in a more stylized form). I agree to argue that this should be taken to show continuity in the market's view of their pure interest rate over periods. However, in the case of later maturities where surprises are expected and realized with a more significant standard deviation, the curves closely approximate the YTM, which may be due to either stable expectations for future interest rates during this time or that within six months longer longer-duration bondholders do not anticipate any dramatic change in market-wide interests.

Forward rate curve

Derived from spot rates, forward rates are estimates based on the future interest rate between periods. These signify where the whole market sees short-term interest rates heading at various points in the future and are quite sensitive to market volatility and expectations regarding economic conditions. The July forward rate curve is much higher in the longer-term segments than in January. The upward movement could indicate that expectations about future interests have increased and may be driven by expected economic growth, potential inflation, or moves in how monetary policy is set. The prominent hump seen in July indicated that specific rate changes are expected to take place on their respective future dates, and those may be reacting to anticipated central bank moves or alterations in fiscal policy that the market believes will be channelled into the economy at those times.