Optimalt portef ljevalg i en model med intern habit nyttefunktion og stokastiske investeringsmuligheder

Thomas Hemming Larsen

Student thesis: Master thesis


In this thesis we investigate the problem of optimal asset allocation given di erent assumptions on the investor's utility function and the market he can trade in. We start out with the simple CRRA utility function with constant investment opportunities and then move on to the more complex case with an internal habit utility function and stochastic investment opportunities. In total we derive nine models and show numerical results for all of them. The models are solved using the relatively new Martingale method that utilizes a probabilistic approach instead of the usual dynamic programming via the HJB equation. Not surprisingly, the optimal bond portfolio in the case of stochastic interest rates consists of three elements: the rst is a speculative part that tries to take advantage of risk premia; the second is a hedge part that is used to o set changes in the investment oppportunities; the third part is used to ensure that enough wealth is invested in the relevant zero coupon bond so that the habit level consumption is always attainable. The expression for the optimal allocation to the stock is adjusted and compared to the case of constant investment opportunities to take into account the correlation between the interest rate and the stock. With a stochastic Sharpe ratio, the allocation into the stock is reduced by the amount that is required to nance the habit level and a term to hedge changes in the Sharpe ratio. Since the interest rate is constant it is not possible to speculate in the bond market. Our numerical results show that with habit formation in preferences and stochastic investment opportunities investors will have a smaller allocation to the stock. This is not consistent with popular investment advice, which says that the allocation to stocks should increase with the investment horizon. In addition, we compare the numerical results across all models and show that di erent assumptions regarding both utility functions and investment opportunities does in fact yield very di erent optimal portfolios.

EducationsMSc in Business Administration and Management Science, (Graduate Programme) Final Thesis
Publication date2011
Number of pages111