| Abstract | Odabrana tema doktorskog rada pripada području investicijske analize koja je usmjerena na upravljanje vrijednošću putem upravljanja portfeljem investicija te se zasniva na modernoj teoriji portfelja koja započinje s Markowitzevom analizom portfelja (1952). Nakon Markowitzeve analize portfelja razvijeni su brojni jednoindeksni i višeindeksni modeli koji uključuju faktore sistematskog rizika. Inicijalno su provedena brojna teorijska i empirijska istraživanja o faktorima sistematskog rizika na tržištu dionica te su trenutno aktualna na tržištu obveznica. Za tržišta obveznica uglavnom su testirani tradicionalni faktori sistematskog rizika vezani uz razinu, nagib i zakrivljenost krivulje prinosa. Navedeni faktori sistematskog rizika predstavljaju parametre krivulje prinosa putem kojih je moguće opisati kretanje krivulje prinosa. Zbog posebne važnosti koju ima krivulja prinosa u sklopu provođenja istraživanja u ovom radu za potrebe modeliranje krivulje prinosa odabran je Nelson-Siegelov model čiji parametri pružaju mogućnost ekonomske interpretacije. Budući da na hrvatskom financijskom tržištu postoji ograničeni broj opažanja o državnim obveznicama procjena krivulje prinosa Nelson-Siegelovim modelom temeljena je na cijenama obveznica.
Nelson-Siegelov model opisuje krivulju prinosa pomoću parametara razine, nagiba i zakrivljenosti te pomoću vremenske komponente lambda. Temeljem procijenjenih parametara ispitana je mogućnost njihovog prognoziranja, čime je ispitana mogućnost prognoziranja tradicionalnih faktora sistematskog rizika ulaganja u obveznice. Provedena istraživanja na temu prognoze parametara krivulje prinosa najčešće su koristila modele slučajnog hoda (RW), autoregresije (AR) te vektorske autoregresije (VAR) zbog čega su navedene metode upotrijebljene i u ovom istraživanju. Dodatno, uz standardno korištene metode primijenjen je i model promjene režima, koji predstavlja sofisticiraniju metodu s ciljem ispitivanja detekcije režima u analiziranim podacima kako bi se ispitao doprinos prognozi krivulje prinosa. Dodatno, u radu su uspoređeni procijenjeni nul-kupon prinosi dobiveni putem prognoziranih parametra Nelson-Siegelovim modelom s nul-kupon prinosima dobivenim izravnom prognozom temeljem njihovih povijesnih vrijednosti. Prethodna istraživanja na razvijenim tržištima pokazala su da se navedeni parametri (razina, nagib i zakrivljenost) mogu promatrati kao faktori koji objašnjavaju veliki dio promjene kretanja krivulje prinosa. S tim u vezi, metodom glavnih komponenti ispitan je broj tradicionalnih faktora koji utječu na varijabilnost krivulje prinosa na hrvatskom financijskom tržištu. Budući da su za razvijena financijska tržišta istraživanja pokazala postojanje dodatnih faktora sistematskog rizika za obveznice, u radu je ispitano postojanje takvog faktora za slabije razvijeno i slabije likvidno hrvatsko tržište. S obzirom da je faktor momentum najčešće testiran na tržištu obveznica ovo istraživanje ispitalo je postojanje tog faktora. Zaključci doktorskog rada mogu se sažeti na sljedeći način: (1) moguće je procijeniti krivulju prinosa Nelson-Siegelovim modelom polazeći od cijena državnih vrijednosnih papira na hrvatskom financijskom tržištu, (2) na hrvatskom financijskom tržištu moguće je dobiti konzistentne procjene parametara Nelson-Siegelovim modelom za uzorke obveznica bez i s valutnom klauzulom te za dva dodatna uzorak koji uz obveznice uključuju trezorske zapise, (3) uklapanje opažanja procijenjenim parametrima krivulje prinosa za američki puni uzorak te američke krnje uzorke nastale temeljem uzorka hrvatskih obveznica sa i bez valutne klauzule, rezultira usporedivom kvalitetom oslanjajući se na relativne mjere odstupanja, (4) upotreba modela promjene režima pomaže kod prognoze parametara Nelson-Sigelovog modela, (5) prognoza nul-kupon prinosa temeljem njihovih povijesnih vrijednosti rezultira preciznijim procjenama kamatnih stopa u odnosu na prognoze dobivene modelom, (6) dovoljna su dva faktora za objašnjenje kretanja krivulje prinosa na hrvatskom financijskom tržištu, (7) dodatan faktor sistematskog rizika momentum pokazao se statističkim značajnim te se temeljem njega na hrvatskom tržištu obveznica mogu formirati ekonomski isplative strategije. |
| Abstract (english) | The research area of the doctoral thesis belongs to the field of investment analysis, which is focused on the value management through investment portfolio management. This research field is contemporary investment analysis, which is based on the modern portfolio theory and begins with Markowitz's portfolio analysis (1952). Markowitz's portfolio selection (1952) was characterized through return and risk as two main variables with the goal of evaluating a portfolio that optimizes the relationship between expected return and risk, measured by variance. Portfolio optimization evaluates an efficient portfolio that, with a given risk rate, provides the highest return, which means that it achieves the maximum return at the lowest risk. Although before Markowitz's (1952) diversification was known as an investment strategy, he was the first to prove this claim with a mathematical model. At the time, the modern portfolio theory was challenging to implement . In order to simplify the theory, single-factor and multi-factor models were developed that define the interdependence of risk and investment rewards through linear relationships. Fama and French (1993) were among the first to analyze bond systematic risk factors and develop a multi-factor model in which they defined stock and bond factors of systematic risk, showing that selected systematic risk factors explain the movement of returns on stocks and bonds.
This thesis focuses on the modeling of the yield curve and the importance of model selection and its interpretation in the economic context. The Nelson-Siegel model was selected to analyze the yield curve on the Croatian financial market as one of the multi-factor models. There are several studies that deal with the modeling of the yield curve in Croatian market, but those studies have modelled the yield curve using the yields of government bonds, which is problematic due to the lack of available data. To address that, the estimation of the yield curve using the Nelson-Siegel model was based on bond prices. Additionally, the sensitivity of the Nelson-Siegel model was analyzed using the prices of government securities with different maturities. Also, an artificially missing data set was generated for US market to test the efficiency of term structure estimation with Nelson-Siegel model. Croatia and the US sample are compered for each observed month and bonds of comparable maturity in the US sample are retained so that the US sample closely resembles to the Croatian one.
In the Nelson-Siegel model, β1 represents the long-term component of the yield curve, β2 represents the short-term component, while the coefficient β3 represents the medium-term component. Parameters mentioned above can be interpreted as systematic risk factors, that is as level, slope and curvature of the yield curve. The thesis examines the possibility of forecasting parameters of the yield curve using the random walk, autoregression and vector autoregression models, thereby examining the possibility of forecasting the traditional factors of systematic risk (time-series risk factors) of investing in bonds. In addition to the standard methods, the regime switching model was also applied, which represents a more sophisticated forecasting method. Using forecasted parameters, zero-coupon yields were estimated and compared with market zero-coupon yields on treasury bills.
Previous research on developed markets has shown that the mentioned parameters (level, slope and curvature) can be seen as factors that explain a large part of the change in the movement of the yield curve. In this regard, the number of factors influencing the variability of the yield curve on the Croatian financial market was examined using the principal components analysis. Additional systematic risk factors (cross-sectional risk factors) were primarily tested on the stock market and proved to be significant in explaining stock returns. Since the cross-sectional factors of systematic risk proved to be significant in the stock market, they were also tested in the bond market. In this regard, there are currently a number of theoretical and empirical studies that test the factors of systematic risk in the developed bond market, while there is a research gap in less developed markets. Since systematic factor momentum as one of the cross-sectional systematic risk factors is mostly tested on bond market, factor momentum was selected for testing on the Croatian financial market, which represents a less developed market.
The conclusions can be summarized as follows:
(1) it is possible to estimate the yield curve with the Nelson-Siegel model using the government securities on the Croatian financial market,
(2) on the Croatian financial market it is possible to obtain consistent parameter estimates with the Nelson-Siegel model for bond samples without and with a currency clause and for two additional samples that include treasury bills in addition to bonds,
(3) fitting the data with the estimated parameters of the yield curve for the US full sample and the US missing data set samples based on the sample of Croatian bonds with and without a currency clause, results in comparable quality relying on relative deviation measures,
(4) the use of the regime switching model helps in forecasting the parameters of the Nelson-Sigel model,
(5) the forecast of zero-coupon yields based on their historical values results in more accurate estimates of interest rates compared to the forecasts obtained by the model,
(6) two factors are sufficient to explain the movement of the yield curve on the Croatian financial market,
(7) the additional factor of systematic risk, momentum, proved to be statistically significant, so economically profitable strategies can be formed on the Croatian bond market. |
