Abstract
The Nelson – Siegel – Svensson model is one of the preferred methods by which investors determine the value of bonds in the long run and thus make informed guesses as to the viability of each investment option. It is an accurate method of prediction when an investment portfolio needs to be set up. In this paper, by using the Nelson – Siegel – Svensson process, an attempt will be made to inform investors like to the best option for a fixed income portfolio. The paper would demonstrate how the process is to be used and applied to the data related to treasury bonds and their yield, followed by the estimation of the yield curve which would provide insight into the different scenarios that can manifest over the period of a year.
Introduction
The purpose of this paper is to advise an investorand prepare a report to that end, as to investment possibilities and threats for the US treasury market for a period of one year. The total amount to be invested is $950 million.
The Nelson – Siegel – Svensson model is widely used by central banks and other participants in the investment business as a reliable model for estimating yields of bonds and government investments over a period. It has also found acceptance in the circle of academic studies that have proved that it can be a valuable tool for forecasting the term structure.
Fitting the full treasury yield curve using Nelson – Siegel – Svensson Model
The first step towards completion of this paper is to provide the values of the US Treasury bond yields so that the value of the yield for each term can be estimated.
This is an important part of the process because this estimation would make it possible for an investor or financial advisor to make informed estimates about the probable yield that an investment might generate over a fixed period. Since these investments are of a fixed income nature, they form an important part of every investment portfolio. Yields for every time are not available so when an investment decision has to be made about a bond or treasury bill which does not fall into the specified time category, this process can be of immense help in estimating the yield generated with approximate accuracy.
For the purpose of this paper, the following process has been used to provide the entire treasury yield curve by making use of this process. The values were laid down as per the time distribution specified which was one year, two years, five years, 10 years and 20 years. Next the figures corresponding to these values were calculated for the entire range of time, from 1 year to 30 years. In this paper, the following formula has been used to estimate the values of the yield curve:
(BETA1)+(BETA2*((1-EXP(-A12/LAMBDA1))/(A12/LAMBDA1))) +(BETA3*((((1-EXP(-A12/LAMBDA1))/(A12/LAMBDA1)))-(EXP(-A12/LAMBDA1))))+(B*((((1-EXP(-A12/LAMBDA2))/ (A12/LAMBDA2)) -(EXP(-A12/LAMBDA2))))
Once these values had been calculated for each time of maturity, the differences or errors were estimated. These errors need to be minimized if the yield curve has to be fitted the desired pattern of values.
Next the calibration values were fixed for beta 1, beta 2, beta 3, beta 4, lambda 1 and lambda 2. These values would help in approximating the value of the yield curve which would be fitted as per the Treasury bond yield rates. Once the values are put in place, the calculation is completed and the following yield curve is presented with the values calculated:
Changes to form of the yield curve under the different bond market scenarios
The shape of the yield curve helps in understanding the expectations of the business about interest rates of the bonds and government bills and also as to the extent of economic activity. Precisely, a yield curve is the graphical representation between the yields to maturity of multiple bonds and their corresponding time to maturity. (Wattenberg, M., 1999) Normally the yield curve is positively sloping which is an indication of positive and progressive returns on investments. This happens because, in the long run, the expectations of investors for a higher yield increases and also because the risk associated with long term investments is higher since it is difficult to determine the value of returns after such an extended period.
Treasury bonds are usually used to construct the yield curve because they are considered as the most reliable indicators of other bonds with similar maturity period. There are three major types of yield curves that have been observed with respect to market conditions and the changing situation of the bond market.
Normal Yield Curve: With the curve a higher degree of risk is associated in long term bonds which result in higher yield and progressive returns for investors. The market sentiment is average, and there is an expectation of growth and no number of significant risk. A standard yield curve exhibits an increasing design which means that, on the graph, the curve moves to the right towards higher terms. As the curve moves to the right, it gets flatter that means that the differences between the yields with respect to the unit change in maturity also goes down. In simple terms, this can be understood as the difference between yield of short term bonds such as 1 year and 2 years would be greater as compared to long term bonds. (Wattenberg, M., 1999)
Flat Yield Curve: This curve exhibits a model where the yield for long term bonds and short term bonds are very similar. Since there is not much change in the yield values, the yield curve remains flat or unchanged. With respect to economic conditions, this model is seen when there is much uncertainty in the investment business. The investors are unsure whether the market will go up or will crash and in such a market situation the yields for different bonds tend to converge and give the samereturns. This is only a temporary phase because if this phase prolongs then there would be a high level of instability in the market and people would pull out their investments from long term bonds and invest in short term bonds. The yield curve, when it comes to the flat stage, corrects itself in a short span to time to reflect the way the economy would move. At such times, the general behavior of investors is to buy bonds that offer minimum risk since thereiswould no advantage in taking higher risk bonds for a longer period.
Inverted Yield Curve: This curve exhibits itself in the market situation when the yield of bonds with short term maturity is lower than that of yield of the bond with long term maturity. This is a very rare market situation, and when this pattern is seen in the bond market, it is an indication that interest rates are set to go down. An inverted yield curve is downward sloping curve. Thisyield curve is also an indicator that the economy is either in a time of recovery from depression or economic meltdown or any other form of economic and financial crisis. It seems unlikely that investors would go into buy and purchase bonds or any other form of security which would give lower yield at high risk, which would the case in the present situation being discussed, over a long time. Many investors consider this as a sign that interest would be further reduced and so believe that they should lock their investments in long term bonds to get the maximum benefit possible before rates decline.
There are other types of yield curves as well which are an indicator of the market situation, especially the bond market situation. A steep yield curve is a sign that since the economy is recovering it is set to enter a phase of rapid expansion. This yield curve is seen when there is an increasing gap between the yield of short term bills and long term bills or bonds. A humped yield bond indicates that the yields of medium term bonds are higher than short term or long term bonds.
Analysis of the bond’s investment characteristics under the different scenarios
There are three possible scenarios, as were discussed in the previous section, which can impact the bond market in the short term and the long term. The investment characteristic would depend on the same. The first scenario would be a high risk driven business environment. In such a case, the yield for the long term bonds would be increased, and the same design would follow for the short term bonds, but the increase would be to a smaller scale as compared to long term bonds. In such cases, the features of the 1 year bond would be to exhibit an increase in its yield.
Bond yield is closely tied with the fed funds because since they are long term in nature this gives them more potential for an increase in their yield over the time. In general, longer the maturity of a security, more will be the result that it registers of changes in the business. This potential for significant changes in the price makes investors willing to accept lower yield rates on bonds and go in for long term securities.
Scenario 1: 40% chance of increase in Federal Funds by 1.5%
In the case the Federal Funds increase by 1.5%, of which there is a minority probability of 40%, the yield of the long term bond securities would also increase which would mean that the yield on the 20 year and 30 year bonds would decrease as a consequence. The maximum result will most likely be seen, however, on the intermediate treasuries like three years, five years, seven years and ten year yields. This would be a good time to invest in these securities since the return would be higher even in the one year period for which the bonds would be held. So if these situation manifests then it would be in the benefit of the investor to invest in either short term bonds or intermediate bonds since they would be able to provide a positive return inone year period as compared to the long term bonds.
Scenario 2: 60% chance that Federal Funds rate would remain constant
In case the rate of interest on the federal funds remains constant, then the market situation would remain unchanged and so the yield on the bonds and the bond market would also remain unchanged. Bonds and interest rate share an inverse relationship, so in this case the yield on the long term bond would not change and thus it would be a good option to consider investing in the long term bonds. (Plaisant, C., Chintalapani, G., Lukehart, C., Schiro, D. and Ryan, J., 2003)
Impact of market scenarios on recommendation for the choice of bonds for the portfolio
In the current situation, it would be my recommendation to invest in the 20 year treasury bond since, in the long run, it would provide a positive and increased yield or return on the investment. If, however, the business situation changes and the federal funds rate increases, then the recommendation would also change. In that case, my recommendation would have to be to invest in the ten year treasury bond since the intermediate bonds would provide the highest return on investments in the event the bond market rates decrease. The short term bonds would decline in value by a large margin because they would not be able to meet the required yield requirements. The long-term bonds would become less attractive as investment options because the yield on them would also diminish in value. In such a situation, the intermediate bonds would provide the best return especially if the investment has to be made for only a year. So my recommendation would be to go in for the intermediate bonds in this event.
However, considering the possibility of this event occurring is also important. The probability of this event occurring is 40% while that of the federal funds rates remaining the same is 60%. Since there is very less margin for decision making in this situation, it would be appropriate to consider an investment plan which would provide assured positive returns in the both the cases. So keeping this in mind, my original recommendation of investing in the 10 year treasury bonds stand, which would include a margin of risk associated with changes in the business situation.
Potential risk management strategies
One of the main jobs of portfolio managers is to assess risks and take appropriate actions to mitigate that risk to keep the investment safe and assure positive returns to the investor. In this case, the following risk management strategies can be adopted to ensure that changes in the business situation do not reduce the value of the investment portfolio of the customer.
Immunization: This strategy ensures that a change in market rates of interest will not affect the overall value of the portfolio. This can be applied to pension funds as well and other categories of investment funds. This can be achieved by cash flow matching, duration matching as well as volatility and convexity matching. Trading it in bond forwards, the futures market or commodity options. In this case, when the portfolio needs to be kept protected from risks of changes in the interest rates of federal funds, in which case cash flow matching would be an appropriate immunization strategy. Under this, the company or investor can buy and hold bonds and coupons for different periods to supplement for the changes in the cash flow. It can be an expensive practice, but it has proved effective for firms that have a large number of fund, as in this case, the value of the fund is $ 950 million. Immunization strategy would have the benefit of matching expected withdrawals from the fund and supplementing the same with the cash flow generated from the new investments. In this manner, it would keep the original fund supplied with the necessary inflow of cash to supplement for any changes in the fixed income due to change in interest rates. Since in this case, the client seeks a fixed income portfolio this would be an appropriate risk mitigating strategy.
Passive bond strategy: The objective of this investment is to maximize income for the client from one year duration time. In such a case, the passive bond approach would also be very effective since the premise of this approach is that bonds are considered to be safe investments. Buy and hold involve buying bonds and holding them to maturity. As the cash flow immunization strategy, this process can also be used to protect the investment fund against loss or reduction in income due to changes in interest risks.
Index Bond strategy: This strategy is similar to the passive bond approach but has more options for flexibility that makes it possible for an investor to make changes as per the market scenarios and conditions. This approach is considered quasi – passive by design and it provides risk and return characteristic closely tied to an index that is targeted by the portfolio or the investor.
Active Bond strategy: The goal of this strategy is to maximize returns that again would be an appropriate strategy to be used in this case. A part of this method is interest rate anticipation, timing, valuation and spread exploitation and multiple interest rate scenarios. This approach is based on the risk taking ability of the investor and the returns are higher in comparison to the passive bond business method.
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Tools to Gain Insight Into Your Data, Proc. of Society of Petroleum Engineering Annual
Technical Conference, Denver, CO (2003)
Wattenberg, M., Visualizing the Stock Market. In Proceedings of Extended Abstracts of
Human Factors in Computing Systems (CHI 99) ACM Press, New York, (1999) 188-189.
