Strategies for modern bond portfolio management

Transcription

1 dr Marcin Halicki 1 Strategies for modern bond portfolio management Introduction These days many investors often prefer investing in bonds (mostly bills), even though the annual rate of return of units of participation are very low, reaching even -41% [4]. It also involves indices. For the introduction, it is worth noting that the WIG (Warsaw Stock Exchange Index - the longest listed on the Polish Stock Exchange [9]) reached its highest historical value of ,51 points on 6 July 2007 [9]. On 6 July 2012, it amounted ,05 points [12], and therefore the fifth period decreased by 40,27%. For that reason, investments in equities are now considered risky and associated with obtaining negative annual rates of return. Therefore, investors from around the world are increasingly guided by their interests towards bonds. As the result, according to the dealers, (...) Polish debt is being bought by foreign investors who are focusing on the safety of financial instruments guaranteeing relatively decent growth [5]." Thus, the global bonds (in this case issued by Poland) are seen as safe investments that offer low risk at "decent" rate of return. In addition, the advantages are: even smaller price fluctuations and less common speculative bubbles. Although the prices of debt securities 2 are also subject to change and may be too high in relation to their actual values defined for example by the expected cash flows and the structure of interest rates, the fluctuations are much lower (expressed as a percentage of the standard deviation of changes in the market price) than it is in case of equity instruments (shares) and derivatives (options, futures). Given the above, it is worth showing modern methods for debt instruments management which, in the author's view, can be used not only by institutional investors, but also the individuals. In addition, you can see that among the growing interest in investing capital bond funds [8], which translates into an increase in demand for debt instruments, as well as to 1 PhD in Economics, Marcin Halicki, University of Rzeszów, Department of Regional Policy and Food Economics 2 The concepts of "bonds" and "debt" will be used to interchange, because the bonds are classified as debt instruments. 1

2 increase their liquidity. This, as you know, makes it easy to buy and sell rate bonds, increasing the comfort of investing. The presented considerations are an introduction to outline the definitions and the essence of analyzed instruments. 1. Definition of bond For a better understanding of the presented topics, you must first define the concept of a financial instrument. According to the International Accounting Standards it is "(...) any contract that gives rise to a financial asset of one entity and a financial liability or equity instrument of another entity [7]." Bonds can be defined as a financial instrument, which is a kind of contractual right to receive cash. And if this law is contractual, in certain circumstances the owner may not get the cash (such a situation is due to the so-called issuer credit risk). In conclusion, the author shares the view [3, p. 1] that "(...) a bond is a debt instrument, the issuer (debtor) agrees with the investor (creditor) to pay the amount borrowed plus interest at a specified time." The introduction and definition give admission to present the debt essence analyzed, and show their greatest advantages and risks. 2. Presentation of the bonds essence In the world of finance, bonds are considered to be securities that provide a steady income to the holder [6, p. 9]. According to the author, it is the most important feature of presented debt financial instruments as, for example, shares are deemed to be securities of variable yield [6, p. 9], and therefore difficult to predict. For this reason alone, they are regarded by investors around the world as risky securities. Bonds are, just like stocks, securities held for trading. They are traded on a variety of financial markets, such as the interbank market as well as the stock exchanges. To sum up, bonds are debt financial instruments whose issuers borrow money from investors. Thus, issuers are borrowers and investors, known also as the bondholders, are lenders. Issuers of course borrow funds for a specified period to finance various projects and 2

3 activities. However, they commit themselves to investors for a specific benefit, which may be either in cash or in kind. In practice, most bonds are characterized by cash benefits. In literature, it is assumed that the most important feature of discussed debt financial instruments is the nature of the issuer [3, p. 3]. Issuers may include: treasury (Treasury issues bonds), municipality or city (municipal bonds) and enterprise (corporate bonds). Other important concepts related to the subject matter described include: par value of bonds - the amount on which the issuer pays interest, and which must be repaid on the maturity date of the bond (i.e., on the redemption date). price of the bond - the price at which the issuer sells bonds to investors. maturity of the bond - this is the date on which the issuer has to pay an amount equal to the nominal value. Maturity date can vary from year to tens of years. However, the period to maturity is the number of years in which the issuer should fulfill all obligations on the bonds. coupon - (also called the coupon rate) is the interest rate that is used to calculate the percentage of the face value that the issuer must pay to investors. Significant is the fact that in the United States and Japan issuers pay a coupon twice a year, and on the European markets - once a year. yield curve - a graphical representation of the relationship between the rate of return achieved on bonds, which are characterized by the same credit quality and the various terms of maturity [3, p. 23]. The author s characterization of all types of yield curve is beyond the scope of this publication, but for its better understanding, a normal yield curve - the most popular in the financial markets, is presented in graphical form in picture no. 1. 3

4 Picture 1. Normal shape of the yield curve Yield Maturity Source: own study based on: F. J. Fabozzi, Fixed Income Analysis Second Edition, CFA Institute Investment Series, John Wiley&Sons Inc., 2007, p. 186 For a better understanding of further consideration, it is better to present basic types of debt instruments, which include bonds: zero-coupon bonds- that means not paying interest on the nominal value. These bonds are usually sold at a discount, which is below the nominal value. However, their redemption is by the nominal value. coupon bonds - they require the issuer to pay a periodic coupon (which, as mentioned, is the percentage of the nominal value). Coupon payment dates are determined by bonds (payment can be made for example at the end of each half-year or year). fixed rate bonds- the interest rate in this case is determined by the time of sale and is valid until the day of redemption. floating rate bonds - interest on such bonds is usually based on the so-called base rate plus a margin. The base rate may be, for example, the rate of inflation or interest rates determined by the interbank markets. convertible bonds- give the investor the right to convert the bonds into shares of the issuer of the bonds. exchangeable bonds- give the investor the right to convert the bonds into shares of another entity than the issuer of the bonds. 4

5 with embedded options: o call (callable bonds): give the issuer the right to prepay all or part of the debt o put ( puttable bonds): give the investor the right to sell the bond to an issuer at a specified price at predetermined dates. Given the above, it is easy to conclude that issuers may choose, depending on their needs and demand prevailing in the capital markets, the right type of debt instrument that best meets their needs, at least in terms of cost of capital. However, bonds, being less risky than stocks instruments, but still characterized by risk, are yet tempted to present this subject by the author. 3. A short presentation of the risks of bonds In this publication, the bonds were indicated as risky instruments. It must first be noted that the literature is distinguished by the 11. risks to which investors are exposed [1, p ]. These include: interest rate risk - occurs when the change in interest rates is required by the market. The increase is accompanied by decline in bond prices and falling-rising prices. According to the author it is the basic nature of the risk, which is born by the investors. The relationship between the price of a normal rate of return on bonds without additional options, is presented in picture 2. 5

6 Picture 2. Price/Discount rate relationship curve for an option-free bond Price Discount rate Source: own study based on: F. J. Fabozzi, Fixed Income Analysis Second Edition, CFA Institute Investment Series, John Wiley&Sons Inc., 2007, p. 100 early repurchase risk refers to bonds with additional options. It follows therefore that in the case of debt instruments cannot predict the cash flows generated by them, and thus the rate of return achieved from such instruments can be much lower than those achieved with coupon bonds. yield curve risk is due to the shape of the curve and shifts in interest rates that affect the price and reinvestment of coupon payments. This means that the change in shape of this curve and the shift may change the value of the portfolio consisting of bonds. reinvestment risk - relates to changes in interest rates, which are used for reinvestment of bond coupon payments. So, if interest rates fall, the amount received from investment interest on the bonds are reduced. Conversely, the amount increases. credit risk - is the risk that the issuer will not stick to deadlines while paying coupon payments and par value. liquidity risk - defines the efficiency within which debt instruments can be sold, with a minimum loss of value in relation to the market price. According to recent empirical studies it was found [10, p. 2110] that there is an effective way to reduce the liquidity risk of bonds issued by the companies. Well, global bonds, and therefore issued on many foreign markets are much more liquid than domestic securities issued by the same company. An increase in liquidity is reflected in higher market valuations. This in turn affects the growth rates of return earned by investors who buy them. Therefore, 6

7 according to the author, they should choose the bonds of these entities, which are listed on various bond markets. exchange-rate risk applies to exchange rate at which cash flows are exchanged in foreign currencies of bonds owned. volatility risk - is the risk that changes in interest rates required by the market will adversely affect the bond they hold. inflation risk - results from a situation where inflation contributes to a reduction in the real value of cash flows generated by the bond. event risk - is the result of adverse events affecting the issuer, which does not affect, for example, natural disaster, or change in the law. It causes the uncertainty in the coupon payments and the par value. sovereign risk - is the risk that the issuer does not want to pay the cash payments to the holders of debt from abroad. According to the author, risks presented above should be analyzed by any investor who wants to buy bonds. In addition to obtaining high rates of return, the forecast of interest rates required by the market is also important, as well as the shape and shift of the yield curve. Continuation of the foregoing is a brief presentation of the methods of valuation of bonds, which are needed to understand how to manage a portfolio composed of them. 4. A brief presentation of the methods of valuation of bonds In this part of the study, the general principles of valuation of debt instruments will be explained. Valuation of bonds, according to the author, should be understood as the process of determining the fair value of financial assets that bring a set income in the future. According to Fabozzi, it consists of three steps [1, p. 97]: estimation of expected and future cash flows generated by the bond, estimation of the interest rate or the interest rates that will be used to discount future cash flows, calculation of the present value of expected cash flows generated by the bond, which corresponds to its fair value. 7

8 Steps presented above are very general, but it is also worth noting that they are universal. They show that the essence of the bonds is expected cash flow that can be obtained during its ownership. To understand the stages presented, it is worth measuring a sample coupon bond discount using the simplest method. Assuming that the analysis will be subject to a three-year bond with a par value of 100 PLN, and coupon payments equal 6 PLN, paid at the end of each year, the value estimated using a rate, equals to 4,5% is 104,12 PLN. This value was calculated using the discount method as follows: 6 Present value of cash flow= 1 (1 4,5%) (1 4,5%) (1 4,5%) and therefore: Present value of cash flows=value of bond=5,74+5,49+92,89=104,12 It is also worth noting that if the rating of investment grade debt instrument is reduced because the issuer is increasingly unlikely to be able to pay in terms of the assumed par value of coupons, then to estimate the expected cash flows, one should use interest rates higher than normal, taking into account risk premium. In short, the essence of the bonds are cash flows and the risk that has been presented in the earlier part of the publication. Regardless of the method of discounting, the valuation principles are similar. In addition to the valuation methods presented earlier in the literature, another one, that takes into account the volatility of interest rates, can be found. It uses a binomial interest rate tree [3, p ], which graphically presents the one-period forward rates. This method entails, as mentioned, the structure of the tree, based on: curve of rates of return for the issuer, previously assumed process of generating interest rates, previously assumed interest rates volatility. An in-depth presentation of the model based on the binomial interest rate tree, according to the author, goes beyond the scope of this publication. But for investors, important information 8

9 is that such a model exists and can be used in practice to estimate the fair value of the bonds. However, they should take into account the risk of exposure to the model [3, p. 407], under the assumptions that may result as a consequence of erroneous results. The considerations were presented to show the essence of bonds and their key features and risks. This approach will allow a better understanding of the characteristics of modern methods dedicated to management. 5. Characteristics of modern bond portfolio management strategies As previously mentioned, the bonds are increasingly acquired investment assets, because it is easier to calculate the cash flow generated by them, than it is in the case of shares. Investors appreciate the analyzed instruments issued by the Treasury, as they are considered to be very safe. The previous sections presented the key features of bonds, and all the risks that are associated with these instruments. This structure of the publication will allow for in-depth understanding of the methods of debt portfolio management. Most of these methods have been developed in such a way to make the best use of the advantages of the bond. The literature emphasizes that all investment firms divide the portfolio management into the following steps: [3, p. 466]: defining the investment objectives, defining the investment policy, selection of management strategy, selection of investment assets, measurement and evaluation of investment performance of selected strategies. With respect to the bond portfolio management, the process is the same. However, due to the nature of the publication, only the selection of management strategy will be presented, although other steps are also cognitively interesting and can be a contribution to the specific publication. Generally speaking, bond portfolio management strategies can be divided into [3, p. 468]: active strategies, passive strategies, structured portfolio strategies, 9

10 mixed strategies. The first of these is the active strategy. It is based on the fact that the investor has the maximum rate of return on the portfolio consisting of bonds at a given level of risk. This means that the objective is to maximize the rate of return on invested capital in bonds, at a certain risk that the investor is able to bear. The first type of active strategies is the " interest rate expectations strategy" [2, p. 112]. As previously mentioned, the value (and thus also the price) of bonds depends greatly on the level of interest rates. Thus, if an investor is able to accurately predict the level of interest rates, it can quickly respond by changing the sensitivity of the portfolio to changes in these rates. This means that he must know the level of sensitivity of the portfolio (and bonds) to changes in interest rates. This sensitivity is expressed by so-called "duration 3 ". An investor using this strategy should reduce the duration of the portfolio, if it is certain that interest rates will rise in the near future. If he expects decline in interest, he must extend the duration. According to the author, structure of the strategy appears to be effective in theory, but in practice it is extremely difficult due to the prediction. The second type of active strategies is the "yield curve strategy 4 " [3, p. 473]. Investor who employs it, builds a portfolio of bonds in such a way as to obtain the maximum rate of return in the case provided for changes in the yield curve slope or offset. You will notice that the yield curve strategy requires accurate forecasts. If the estimates prove incorrect, then the investor may incur losses. In addition, in literature 3. types of yield curve strategy are distinguished [1, p. 509]. They include: bullet strategy - which involves the construction in such a way that the term to maturity of the bond in the portfolio is highly concentrated on one point of the yield curve. barbell strategy - in which the bond portfolio must be such that their terms to maturity focus on two extreme maturities. 3 Duration, as mentioned, is a measure of the sensitivity of bond prices (portfolio consisting of bonds) to changes in interest rates. This means that if the duration of the bond (or portfolio) is 3, then when interest rates change by 1% (increase or decrease), the price of bonds (the portfolio) changes by 3% (decrease or increase). 4 As it is known, the concept of the yield curve has been previously explained. 10

11 ladder strategy by which the bonds in the portfolio should be leveraged during certain periods and equal values. It is assumed that the investor will receive equal (or almost equal) payments in established periods. As you can see, the strategy of the yield curve is not complicated, and therefore there is no need, according to the author, for further clarification. However, it requires that investors accurately predicted the shape of the yield curve and change. The third kind of active strategies is " inter- and intra-sector allocation strategy" [1, p. 510]. It is the most demanding of active strategies in terms of the required quantity of time that must be paid by the investor. This results primarily from the fact that in this case manager should build a portfolio of bonds belonging to different sectors of the market in order to achieve a high rate of return on the portfolio, which will result in the expected changes of spread of rates of return on bonds, which are appropriately selected. It is assumed that the spread increases in times of economic downturn, as investors demand higher risk premium on debt instruments of the issuer. However, the spread decreases in times of economic growth. According to the author, this strategy is also risky because the bonds selected for reasons beyond, may be in the possession of the portfolio of a high rate of return, which will not be reduced, which will result in a low return on capital by the investor. Furthermore, the high rate of return may result in the issuer's financial problems, but it will still be a temptation for investors who may want to replace the bonds with a low rate of return, but without the credit and liquidity risk, to the bonds with a high rate of return, but with a high credit risk and low liquidity. Last active strategy, which has been called " individual security selection strategy" [1, p. 513], relies on the fact that the portfolio manager selects undervalued bonds, and thus having an attractive rate of return, but who have a low credit risk, which will cause that its market value will increase. In addition, an investor who uses the strategy described, may acquire debt instruments with a high yield and high credit risk which will be the risk as expected decreases. As can be seen, the last active strategy is presented in theoretical terms, so understood, it does not require further description. Although it is also characterized by risk choosing the right debt instrument, seems to be best suited for investors who are profoundly analyzing the bond of their interest, and who have in-depth information about the issuer. Of all active strategies presented, the author would recommend for potential investors just the last one. Passive strategies, however, are quite different from active ones described previously. It has its justification in the fact that they require far fewer investors forecast data, which 11

12 according to the author increases their usefulness. You cannot clearly state that they are characterized, in the case of the acquisition of Polish bonds, a higher rate of return, compared to active strategies. You can, however, say that they are less risky. It is worth noting that that proposition should be verified on the basis of relevant quantitative research conducted by using a representative sample of the research. So it seems that such studies may be interesting contribution to the scientific research work. Generally speaking, passive management strategy for debt instruments is in line with the expectations and limitations of the selected portfolio construction bonds, and then hold up to the end of their investment. The most common type of passive strategy is "indexing strategy" [3, p. 468]. Its purpose is the so-called replication designated bond market index. In this case, the decision to choose a bond market index, which will be replicated, comes from the preferences of the investor. The huge advantage of this strategy compared to the active strategies are: lower management costs and higher rates of return, but it was noted mainly for bonds purchased in the United States [3, p. 500]. It is possible that the portfolio manager in Poland using indexing strategies achieve higher returns than using active strategies. For the reason that the author is an advocate of the policy, it has been shown by a theoretical example illustrating the construction of the bond portfolio, which replicates an exemplary index. The table below shows the composition of the sample index, designed by the author, to which 7. types of coupon bonds belong. Market value of bonds included in its composition, is PLN. Table 1: The bonds included in the exemplary index Nr ,00 0, ,00 0, ,00 0, ,00 0, ,00 0, ,00 0, ,00 0,150 Source: personally prepared. It should be clear that the 1. column of the table is the number of bonds forming part of the issue, in the 2. column are presented in PLN market prices for each of the listed bonds, in the 12

13 3. is shown the par value (for simplicity it was assumed that it amounts 100 PLN for each instrument). Column no. 4. presents value of the coupon to be paid once a year, the 5. column shows the value of each bond issue, and in the 6. is counted the share of the particular bond issue in the value of all issues of the index. To simplify the example, a specific indicator index was not elaborated, but it was assumed that its value would change as much as the market value of bonds included in its composition. The best way to structure the portfolio replicating the index, is, according to the author, the acquisition of securities in proportion to the weight of the securities in the index. For logical reasons, this method will allow to avoid tracking errors. An example of a portfolio constructed by the author, on which construction was allocated PLN, is presented in table 2. Tabela 2: Bonds included in the example portfolio replicating the index Nr , , ,00 2 0, , ,00 3 0, , ,00 4 0, , ,00 5 0, , ,00 6 0, , ,00 7 0, , ,00 Source: personally prepared. Table 2. shows how the portfolio replicating index should be constructed. Thus, on its structure assigned PLN, and the 1. column shows how much of this amount is to be spent on the acquisition of a particular bond issue. In column 2. it is counted, without rounding, what amount should be specifically spent, and in the 3. is shown that the exact number of debt instruments can be purchased, but it was assumed that it is possible to purchase only an integer part of the total number of bonds. Therefore, in column 4. are presented exact amounts to be spend to buy bonds in the composition replicating the index, but not the fraction of these bonds. Well, for this purpose should be allocated PLN. This means that a given amount is lower than the assumed PLN. 13

14 To show the effectiveness of the described strategy, it was assumed that one year after the construction of the portfolio, the market prices of bonds included in the index are changed. They are presented in table 3. Table 3: New market prices of bonds included in the example index Nr , , , , , , ,00 Source: personally prepared. In the table 3 key information is on the 2. and 5. columns. Now, in the 2. are shown the new prices of each bond, and in the 5. prices plus coupon payments that were paid during the year. In summary, the issue of the value of all 7. securities belonging to the index amounted to PLN. This means that it increased compared to the previous year by 6.63%. At this point, it is worth checking that the return obtained from the portfolio replicating the index, one year after it was built. The parameters are shown in table 4. Table 4: New market value of the bonds included in the sample portfolio Nr The number of bonds The value of bonds , , , , , , ,00 Source: personally prepared. In table 4. It is shown the exact number and value of all bonds that were used to build a portfolio that reflects the index. After one year, the sample value of the portfolio was PLN, with the base year was PLN. Thus, the annual rate of return reached 6.64%, which was higher than the rate of return of the index by 0.01%. Of course, this difference is 14

15 due only to rounding bonds made during the selection of the portfolio. At the same time on the basis of calculations it can be concluded that the theory of indexing strategy allows a very accurate replication of index and get the same rate of return of the portfolio as the index. It should be added that, in practice, to obtain the same rate of return may not be as easy as building a portfolio as investor must take into account transaction costs and the method of calculating the index value, which has been omitted in this publication. The author has also meant that the investor can make a mistake resulting from reinvestment of coupon payments that the index structure may be different than those recognized in the calculation of the rate of return portfolio. In addition, it is worth noting that the index may consist of a large number of bonds, which would force the investor to acquire a large number of debt instruments of different issues, which would require large amounts of cash to invest. Therefore, in the area of securities management strategies an investor can choose a different strategy, which allows for earlier assumed rate of return on the bonds portfolio, regardless of the change in value of the index, in which are debt instruments held. Classic immunization strategy, described above, is a typical structured portfolio strategy. It was first presented in 1952 by F.M. Redington [11, p ]. It involves the construction of the portfolio consisting of debt instruments that provide income determined in a timely manner, regardless of the volatility of interest rates. Interest received during the holding of such instruments can be reinvested in various ways, but in theory, the rates are used to calculate the value of the bonds. The investor may also use the funds from coupon payments to spend on current consumption, which is the wrong approach, according to the author. In the world of investors, it is assumed that the immunization strategy is used in order to: lower prices of financial instruments caused by an increase in interest rates was fully compensated by the increase in income resulting from the reinvestment of previous income from the portfolio; decrease reinvested the proceeds of revenue caused by the earlier decline in interest rates was fully compensated by the increase in prices of debt instruments. For the presentation of the use of this strategy, the author has prepared an exemplary portfolio of structures allowing the immunization and consisting of the 2. bonds. For the purposes of this example, let s assume that the investment horizon is 2. years and the investor wishes to receive PLN exactly after 2. years to settle the liability in that amount. Furthermore, the investor assumes annual rate of return, valid for 2 years at 10%, and this rate is also used to calculate the prices of bonds. This also means that the investor wishes to 15

16 establish an annual profit of 10%. As you can see, this example is to show that the immunization strategy allows to obtain previously assumed rates of return, regardless of the level of interest rates, which affect the valuation of bonds. Characteristic of the bonds used for the above example is in table 5. Table 5: Data of the bonds used in the bond portfolio immunization strategy Data Bond No. 1 Bond No. 2 Time to maturity 1 year 4 years Par value 100 PLN 100 PLN Duration 1 3,49 Coupon payment zero-coupon bond 10 PLN Price of bonds at the time of purchase (when interest rates are 10% per annum) 90,91 PLN 100 PLN Source: personally prepared. Using immunization strategy one should take into account the fact that the duration of the constructed portfolio must be equal to the duration of the investment horizon. Therefore, it is necessary to construct the following system of equations (of course, it is assumed that the short sale is permitted 5 ): where: w 1+ w 2 =1 w1 1+ w 2 3,49=2 w 1 i w2 are shares of bonds no. 1 and no. 2 in the portfolio of the investor. After the calculations, searches shares accepted values presented below: w 1=0,5984 w 2 =0, Short sale means selling assets without ownership. 16

17 Knowing these values, calculate the amount you need to spend to buy bonds. It looks as follows: (1 10%) CF 0 = 2 CF 0 =82 644,63 PLN The calculations have shown that it is necessary to spend ,63 PLN for the purchase of 2. selected bonds, while knowing their market price (value), you also need to calculate the number of purchased securities. LO 1= w CF 1 0 =544 90,91 LO = w CF 2 0 = where: LO 1 i LO2 are the number of bonds no. 1 and no. 2, which are expected to be purchased by an investor using the immunization strategy (it should be noted that the author applied the rounding in the calculations). Knowing the number of bonds purchased, the initial value of the portfolio should be calculated, as the applicable rounding may differ from the amount allocated for the purchase of bonds. V 0 = LO1 90,91+ LO2 100 V 0 =82 655,04 PLN where: V 0 means the initial value of the portfolio consisting of selected bonds. 17

18 Knowing the above values, you can check the effectiveness of the described strategy. So let's assume that after the purchase of bonds, interest rates will be reduced by 3%, and thus amounts to 7%. Under this assumption, the value of four-year bonds after two years is 105,42 PLN (after two years, or at the end of the investment period this bond becomes a two-year bond). Given the above, the cash flows generated by the portfolio presented, look as follows: t 0 : CF 0 = ,04 PLN t 1 : CF 1 =(544* *10)*1,07=61 760,40 PLN t 2 : CF 2 =332*(105,42+10)=38 319,44 PLN CF 1 + CF 2 = ,84 PLN For these calculations, it is evident that despite the decrease in interest rates that influence the valuation of bonds and reinvestment of coupons, a theoretical portfolio allowed to receive more than the required amount of PLN. Based on calculations made, you can check the resulting annual rate of return on investment. R annual , *100% 82655,04 R annual=10,04% Performed calculations show that immunization strategy allows you to obtain the required rates of return, regardless of the level of interest rates. The condition is, of course, assumptions about portfolio duration, which value must correspond to the duration of the investment horizon. Of course described calculations are purely theoretical, also was rounding, because the rate of return portfolio of sample slightly exceeded the required 10%. However, on the basis of calculations it can be concluded that the portfolio immunization is theoretically efficient and reduces the risk of the investor. The author is an advocate of this strategy, as well as indexing strategy. In practice, however, interest rates can have non-parallel shift and yield curve may not be flat. In addition, the financial markets are transaction costs. Taking into account the above factors, it is easy to conclude that, in practice, to obtain the required rates of return may not be possible, or achieved rate of return will be high, but not as much as required. However, the theoretical 18

19 structure of the portfolio shows that the strategy is effective, and therefore it can be used in practice, while applying it, investors should bear in mind keeping track of the value of the bonds and the yield curve, at any time to respond, making reconstruction of the portfolio. According to the author, this approach will increase the practical effectiveness of immunization strategy. In addition to the previously presented, there are, in practice, mixed strategies of portfolio management. Mixed strategies involve the simultaneous use of elements of active and passive strategies. This allows the selection of assets, for example, using the passive strategy, but the reconstruction of the portfolio using the active strategy. Analyzing the issue purely in theory, it can also be inferred that the portfolio within the mixed strategies can be built to meet the principles of immunization, but in the case of the non-parallel shifts of the yield curve stayed rebuilt using the active strategy. This would achieve high rates of return and risk reduction. The author thinks that this argument seems to be interesting, but to justify it, empirical quantitative study based on a representative sample of the research is required. In summary, this section describes the various strategies for managing a bonds portfolio, and the author showed the practical application of indexing and immunization strategies, which are considered to be the most effective in terms of risk reduction. However, demonstrated effectiveness of the theoretical, based on a model approach, does not include transaction costs or non-parallel shift of the yield curve. Evidence of this can be achieved in practice, a low rate of return. Despite this, the author recommends strategies presented to investors, who, in times of low value stock indices, want to invest their cash in safe assets. Conclusions This publication describes modern methods of debt portfolio management. At the same time mathematically proven effectiveness of indexing strategies and immunization, which according to the author should be applied in practice, with the rate of return generated by these strategies in practice may differ from the rates obtained in the theoretical models. Despite this, the author has made their recommendations. In addition, the bonds are shown as being financial instruments, including the definition, which allows us to understand their construction. Additionally, the risks, which may accompany investors who want to purchase these instruments, were characterized. However, according to the author, they are safer than stocks, so should be the subject of in-depth analysis and investment recommendations. 19

20 Abstract Strategies for modern bond portfolio management This publication presents the most important features of bonds and definitions. In addition, there were enumerated all risks which investors who want to acquire debt instruments face. However, the main aim of the publication was to present modern methods for managing a bonds portfolio, together with mathematical calculations, showing the theoretical performance of index- and immunization strategies which, according to the author, are worth recommending to investors seeking methods for risk mitigation of the managed debt instruments. References 1. Fabozzi F.J, Fixed Income Analysis Second Edition, CFA Institute Investment Series, John Wiley&Sons Inc., Fabozzi F.J., Fong, Zarządzanie portfelem inwestycji finansowych przynoszących stały dochód, Wyd. PWN, Warszawa Fabozzi F.J., Rynki Obligacji, Analiza i Strategie, Wyd. WIG-Press, Warszawa Fundi.pl, ( 5. Gazeta Giełdy Parkiet, ( bezpieczna-przystania-.html) 6. Haugen R.A., Teoria nowoczesnego inwestowania, Wyd. WIG-Press, Warszawa Międzynarodowy Standard Rachunkowości 32 - Instrumenty finansowe: prezentacja 8. Moja Przyszła Emerytura, ( 9. Money Makers, ( 10. Petrasek L., Multimarket trading and corporate bond liquidity, Journal of Banking & Finance 36 (2012) 11. Redington F.M., Review of the Principles of Life Office Valuations, Journal of the Institute of Actuaries, 1952, vol Stooq, ( Słowa kluczowe: obligacje, strategie zarządzania portfelem, ryzyko, krzywa dochodowości Keywords: bonds, portfolio management strategies, risk, yield curve 20