Danish mortgage bond portfolio: Using the Mean-Variance Approach

Rita Ambrozaite & Lena Søndergaard

Student thesis: Master thesis


In the wake of the recent demise of the US housing mortgage market, with a stream of subprime defaults, the Danish model of financing private housing has attracted great interest from around the world, driven by the fact that there has not been a single case of default of the bond instruments used to finance Danish private housing, in their 250 year history (Association of Danish Mortgage Banks, 2009). From a pure risk perspective, it would therefore seem highly attractive to invest in Danish mortgage bonds. An important question, though, is what bond or bonds to invest in at any given time, in order to optimize return on investment. As first shown by Markowitz in 1952, diversified portfolios result in the best return while mitigating the level of risk, both in the case of stocks and when combining stocks and bonds (Markowitz, 1952). However, there has been a paucity of research into whether the same applies for pure bond portfolios. This may, at least in part, have been driven by a common misperception of bonds being “simple” assets with predictable cash flows. Bonds have therefore mainly been used to mitigate risk in portfolios of other securities, e.g. creating derivative instruments with the bond ensuring a return of a certain amount and the other security creating a larger upside potential. There are indications, however, that diversification benefits also exist in the case of pure bond portfolios (Korn & Koziol, 2006, Roll, 1971, Yawitz et. al., 1976). The aim of this thesis was to determine how to create the highest possible return on investment in Danish mortgage bonds, for the unit of risk taken; in other words, maximizing the Sharp ratio (Sharpe, 1964) of the bond investment. A mean-variance model according to Markowitz (Markowitz, 1959) was applied to available data from the Danish mortgage bond market. Sharp ratios of individual bonds were compared to those of portfolios of various types of bonds, including non-callable, callable and floating rate bonds. In addition, the effect of allowing short selling of bonds within the portfolios was assessed. Lastly, the sensitivity of the value of the optimal portfolio to market interest rate fluctuations was compared to the sensitivity of suboptimal portfolios. In conclusion, the Sharp ratio of a hypothetical investment in Danish mortgage bonds was optimized by creating a portfolio of multiple bonds, rather than investing in individual bonds. The diversification benefits were even more pronounced when short selling of bonds was allowed in the portfolios. Furthermore, combining all three types of bonds – non-callable, callable and floating rate bonds – in a portfolio, yielded higher Sharp ratios than portfolios consisting of only one or two distinctly different types of bonds. Finally, the sensitivity of the value of the optimal portfolio to market interest rate fluctuations was not markedly different c.f. the sensitivity of suboptimal portfolios to market interest rate fluctuations.

EducationsMSc in Applied Economics and Finance, (Graduate Programme) Final Thesis
Publication date2010
Number of pages147