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selected for further analysis. In addition, an attempt will be made to extend the traditional
model from Lund Larsen (2007) with the housing asset, as well as the investor’s mortgage.
Finally, the selected, existing model will be compared to the extended Campbell and Viceira
model, using a selection of fictive investors, to examine if the two models predict the same
allocation between the risky and risk-free asset.
Results and conclusions
All of the three existing models predict similar portfolio weights. Therefore, only Cocco
(2002) will be discussed here. The model is a positive model, meaning that it seeks to explain
actual investor behaviour, rather than predicting the optimal behaviour. According to Cocco,
the model does reasonably well in explaining the life-cycle pattern observed for real investors.
It generates several regressions explaining investor’s stock shares, including explanatory
factors such as income, age, real estate and financial net value. The model predicts that
housing will keep the average investor’s financial capital low early in life, as well as for low
values of financial net value – reducing the stock share for young and poorer investors.
Further, the stock share will increase as the investor ages and/or increases his wealth. Hence,
Cocco solves the three puzzles discussed earlier.
Note that since Cocco is a positive model, the behaviour predicted by the model might not be
what is optimal for the average investor.
The results for the extended model are somewhat different from Cocco’s. Although it solves
all of the three puzzles for a moderate correlation between the labour income and stock
market index, its results are similar to the ones predicted by the traditional model, though
somewhat closer to Cocco, in case of a correlation of zero – the value selected in Cocco
(2002). Also, the extended model predicts a positive connection between the housing asset
and stock share – the opposite of Cocco’s result. This connection depends on the correlation
between the housing asset’s return and the return on the stock market index – a low
correlation leads to a positive connection. Finally, the extended model will predict a negative
connection between the investor’s mortgage value and stock share – despite of the positive
connection predicted by Cocco.
Hence, the extended model partly solves all of the three puzzles in case of a correlation
between work income and stock market index of zero, and fully solves them in case of a
positive, moderate correlation.