# Fixed Interest Securities & Related Derivatives Essay

Fixed Interest Securities & Related Derivativesa) Maturity refers to the maturity date that is mentioned on the bond. It is the date when the issuer pays back the face value of the bond to the buyer.

On the other hand duration refers to the life of a fixed-income bond that is expected when factoring in its call features, maturity, interest payments and coupon yield.[1] The duration is subject to change, with changes in market interest rates. With an increase in the market interest rate the duration is expected to decrease and conversely with a decrease in the market interest rate the duration will increase.With the passage of time there is a reduction in maturity, however, with the passage of time there are changes in market interest rates and so there are changes in duration. This necessitates a restructuring of the portfolio. In case interest rates are expected to increase, the optimal investment strategy is to reduce the duration of the fixed-income securities purchased so that adverse movements in the market value of the portfolio is minimized. Usually the strategies adopted include shortening of maturities, adjusting the credit quality of the instruments or using a barbell strategy.

From the standpoint of investors who face longer investment periods, the investors tend to go in for investments with longer maturities.[2] They undertake the risk of missing out on opportunities to reinvest. However, from the perspective of optimal investment strategy, the duration of the fixed-income securities purchased when there are expectations of increasing interest rates should be of short maturities.[3] This will allow the investor to take advantage of reinvesting at more attractive interest rates and prevent the value of his portfolio from declining.The trade off is very clear, when the interest rates are expected to rise, the investor has the option of choosing between investing in short-term, fixed-income securities that bring a return of a lower interest rate but allows the investor to restructure his portfolio at higher interest rates when the interest rates go up, and investing in long-term, fixed-income securities that bring a return of a higher interest rate ( in accordance to the current interest rate) but does not allow the investor to restructure his portfolio at higher interest rates when the interest rates go up. Let us consider an example, the current interest rate for five years fixed interest securities is 7% and the current interest rate for one year fixed interest securities is 5%. The interest rates are expected to increase during the current year.

If the investor has an investment horizon of five years and he invests in fixed income securities at the rate of 7% then his income over the five-year period will be at the rate of 7%. On the other hand an investor using an optimal investment strategy and wanting to immunize himself from missing out on investment opportunities invests for one year at 5%. After the passage of one year the rate on fixed securities for one year is 8% and the rate on fixed securities for four years is 9%. In addition, there is further expectation of interest rate increase. Again the investor using an optimal investment strategy and concerned with immunizing himself from missing out on investment opportunities invests for one year at 8%.After the passage of the second year the investor with the optimal investment strategy finds that the rate on securities for one year is 9% and the rate on fixed securities for three years is 10%. However, now there is an expectation that the interest rate is likely to fall.

When interest rates are expected to fall the advice to investors is to go in for long-term investment to protect their portfolios from falling in value. At this time the optimal investment strategy is to go in for long term investment and so the investor purchases fixed securities for three years at the rate of 10%. It can be seen that the investment strategy of the second investor will not only get him a higher income on his investment but also provide immunization from loss of opportunities to invest. It was crucial for the investor to restructure the portfolio annually.The question mentions the reduction in maturity and duration with the passage of time. Duration is essentially a measure of price sensitivity to changes in interest rate and other variables. One commonly used measure of price sensitivity to yield changes is called Macaulay’s duration, this measures the percentage change in the bond’s price with a 1% alteration in its yield.[4] Then there is a ‘duration to worst’ that measures the percentage change in the bond’s price with a 1% alteration in its yield-to-call or yield-to-maturity, whichever is lower.

That is why the term ‘to worst’ Finally, there is duration that is based on the average percentage change n the bond’s price based on the changes or movement of interest rates. Usually, the treasury rates are taken into account.Every investor has an income objective over the length of his planning period.

The duration of an income stream, for example a bond, measures how long, the investor has to wait before receiving a payment.To sum, with the passage of time there is a reduction in maturity as well as a reduction in duration. However, since the reduction in duration is affected by the changes in interest rates, the investor needs to restructure his portfolio at least every year so that the duration remains equal to the remaining length of his planning period. Otherwise there is a risk that the duration may become longer than the planning period and on the expiry of the planning period the payment may not be available to the investor.b)In case of a zero coupon bond there is no interest that is paid to the investor but the bond is sold at deep discount, the full return on investment is realized when the bond is paid back at its full face value.

[5] So, in the case described to us the zero coupon bond will be sold to the investor at a deep discount such that after eight years when the bond is redeemed, the yield of 10% per annum is realized. There are also some other bonds from which coupons are removed by financial institutions and are resold as zero coupon bonds at deep discounts.[6] These zero coupon bonds also perform in the manner described above.On the other hand coupon-paying bond yielding 10% per annum and having duration equal to the investor’s investment horizon of eight years will pay interest rate printed on the bond when it is issued.

The reason this fixed interest payment is called a coupon is because in the past some bonds actually had coupons fixed on them. On due dates the holders of the bonds detached the coupons and received the interest.[7] Currently most of the operations are done electronically but the rate is referred to as the coupon rate or coupon percent rate.From the point of view of the investor both these options are feasible and will guarantee the investor a 10% yield. However, there are differences. If he goes in for zero-coupon bonds yielding 10% then he will not be getting coupon payments or semi-annual interest payments that most coupon bonds offer.

He will be getting his payment at the end of eight years and that will be the full face value of the bonds. As he has purchased the bonds at a deep discount such that he realizes the yield of 10% per annum at the end of the eight years, he realizes his interest payment at the end of the eight years. On the other hand if he goes in for coupon bond yielding 10% per annum and having duration equal to eight years, the investor will receive semi-annual interest payments every year. Currently, most of the bonds do not have physical coupons that need to be redeemed but the records are electronically maintained and semi-annual interest payments will be received. As both these investments are feasible, it is the investor that has to decide if he wants semi-annual payments or if he wants to go in for one time payment at the end of eight years. Even in case of coupon bonds the face value will be realized only at the end of the eight years and not earlier. Even though the gain of the investor having a horizon of eight years is same the source of gain is different. In case of zero coupon bond yielding 10% per annum, the gain is made when the face value of the zero coupon bond is realized.

On the other hand in case of a coupon bond yielding 10% per annum the source of gain is the coupon payments made over the period of eight years. Both these methods guarantee that the investor will get the yield of 10%.There are some other issues that are pertinent to zero coupon bonds and coupon bonds that our investor should keep in mind. For instance, the coupon paying bond has the tendency to trade around the price of its face value, on the other hand a zero coupon bond tends to fluctuate more than coupon bonds as the entire payment is made at maturity.[8] If the investor has exigencies and decides to sell off his bonds on the market, he is less likely to make losses on the coupon paying bonds; its trading price tends to hover around its face value. On the other hand the zero-coupon bonds may lead to greater losses if the price of the bonds is unfavorable. From this point of view investing in zero coupon bonds with 10% yields is more risk prone. The zero-coupon bond does guarantee the yield of 10% per annum if the bond is held to maturity.

However, since these bonds may be highly volatile there may be substantial losses if these bonds need to be sold early. That is before the expiry date.The choice of zero coupon bonds or coupon paying bonds depends on the purpose for which the investor wants to use these bonds.

If the investor has got a specific objective at the end of the planning horizon of eight years, then he should go in for the zero coupon bonds. For example, if the investor is a corporation and at the end of the eight-year period it needs funds to purchase machinery that will become obsolete then zero coupon bonds are suitable for him. This is because the investor will get his principal plus the accumulated interest earned at the end of the eight-year period. The interest is compounded annually so the investor does not lose out on interest. If the investor is an individual and at the end of the eight year period he expects himself to retire and he needs a lump sum payment to purchase a house.

The zero coupon bond is suitable for him.The main difficulty with zero-coupon bonds is that even though the investor does not receive interest half-yearly as in case of coupon bonds, the investor is required to pay tax every year. In case the investor with the eight-year horizon is an individual investor then he can purchase the zero-coupon bonds in a tax deferred retirement account. There are other situations in which the investor can avoid immediate tax payment.[9] For example, if the investor purchases zero-coupon bonds for his child’s education and opens a custodial account for the child where the child pays little or no tax.To sum, even though the zero coupon bonds or a coupon paying bonds are feasible and guarantee the yield to the investor, it is the specific purpose of the investor that will determine the final decision.Bilbliography:Cusatis, P.

& Thomas, M, Hedging Instruments and Risk Management, McGraw Hill, 2005.DFA Australia Limited, Fixed Interest, 2005, Retrieved October 29, 2006 <http://www.dimensional.com.au/strategies/fixed/>Fabozzi, F & Fabozzi, D, The Handbook of Fixed Income Securities, 5th edition, Irwin, 1997.Financial Pipeline Inc.

, “Valuing Zero Coupon Bonds”, 2006, Retrieved October 29, 2006 <http://www.finpipe.com/zerovalu.htm>Investopedia.com, Advanced Bond Concepts: Duration, 2000, Retrieved October 29, 2006 <http://www.investopedia.com/university/advancedbond/advancedbond5.

asp>Krefetz, G., The Basics of Bonds, Dearborn Financial Publication, 1992.Little, K. “Understanding Zero Coupon Bonds”, 2006, Retrieved October 29, 2006<http://stocks.about.com/od/bonds/a/Zeroone012505.htm>Stallman, C, Zero-coupon Bonds, Financial Content, 1999, Retrieved October 29, 2006<http://www.teenanalyst.

com/bonds/zerocoupon.html>The Bond Market Association, “Putting Compound Interest to Work”, 2005, Retrieved October 29, 2006<http://www.investinginbonds.com/learnmore.

asp?catid=6&id=46>Wilson, R & Fabozzi, F, Corporate Bonds: Structure and Analysis, John Wiley and Sons, 1996, 339.[1] Investopedia.com, Advanced Bond Concepts: Duration, 2000, Retrieved October 29, 2006 <http://www.investopedia.

com/university/advancedbond/advancedbond5.asp>[2] DFA Australia Limited, Fixed Interest, 2005, Retrieved October 29, 2006 <http://www.dimensional.com.

au/strategies/fixed/>[3] Fabozzi, F & Fabozzi, D, The Handbook of Fixed Income Securities, 5th edition, Irwin, 1997.[4] Wilson, R & Fabozzi, F, Corporate Bonds: Structure and Analysis, John Wiley and Sons, 1996, 339.[5] Stallman, C, Zero-coupon Bonds, Financial Content, 1999, Retrieved October 29, 2006<http://www.teenanalyst.com/bonds/zerocoupon.

html>[6] The Bond Market Association, “Putting Compound Interest to Work”, 2005, Retrieved October 29, 2006<http://www.investinginbonds.com/learnmore.asp?catid=6&id=46>[7] Financial Pipeline Inc., “Valuing Zero Coupon Bonds”, 2006, Retrieved October 29, 2006 <http://www.finpipe.com/zerovalu.htm>[8] Little, K.

“Understanding Zero Coupon Bonds”, 2006, Retrieved October 29, 2006<http://stocks.about.com/od/bonds/a/Zeroone012505.htm>[9] Cusatis, P. & Thomas, M, Hedging Instruments and Risk Management, McGraw Hill, 2005.

64Krefetz, G., The Basics of Bonds, Dearborn Financial Publication, 1992. 25