In this section, we focus on the results associated with optimal portfolios given the assumed parameterization. Using the method we discussed in Section3:4, , the optimal gross holding of home equity by the home country, is computed to be 20:92. Figure 3:5plots its 5components, as listed and discussed in Section
3:6, and the related net asset allocations in each country.
The left half of the …gure shows the5components of with5bars. From left to right, they are the portfolio diversi…cation term, the term representing hedg- ing of the current net portfolio return, the term representing hedging of future net portfolio returns, the term representing hedging of new-born’s consumption and the term representing hedging of consumption tilting. To represent their signs, negative components are accumulated from the top line (whose height denotes the value of the assets stock in steady state, i.e. z) downwards while positive components are accumulated the other way around. The area of the bars corresponds to their sizes.
For the …rst and longest bar to the left, as explained, because home endow- ment income always moves in the same direction as the home asset return, as a bad hedge against the risk, the home asset will be shorted by home households, i.e. a negative diversi…cation term [1] = 12:58<0.
The second bar represents hedging of the current net portfolio return, [2]. We know that 0 < re1 < re2 from the model dynamics described above, so according to our discussion in Section 3:6, because asset 2’s return increases as endowments increase in either country, but it rises less in response to a home shock than to a foreign shock, there is a smaller increase in interest payments on the net external position at home. The home equity return is therefore posi- tively correlated with the home net portfolio current returns. Home households therefore further short the home asset [2] = 6:21<0.
We also see from last subsection that the sum of all discounted expected future asset returns declines as endowment increases in either country. And it responds to the two shocks in the same way ( sre1 = sre2), which implies that no risk arises associated with future net portfolio returns. The term representing hedging of future net portfolio returns, [3]; and that of consumption tilting,
…fth bars collapse into two lines [3] = [5] = 0.
Lastly, as explained in Section 3:6, the term representing the hedging of new-born’s consumption is always positive. This is veri…ed by our result that
[4] = 1:87>0(the fourth bar in the …gure).
Let us compare the sizes of these components. Because self-hedging is linked to the risk associated with total GDP which is the most important source of risk, the diversi…cation term is the largest component. Under global imbalances, the hedging of the current net portfolio return is linked to the risk associated with the income di¤erence betweenGN P and GDP, which should be secondary comparing to totalGDP, the hedging is thus less substantial. However, with the very large external net position here, the hedging of the net portfolio return is still considerable. Lastly, as an adjustment whose emergence is due to a small growth rate of population, the term representing the hedging of new-born’s consumption is small.
Now let us turn to the pattern of net portfolio allocations associated with the level of . The right half of …gure shows this in more detail. There are two wide grey columns representing, from left to right, respectively home and foreign equity supplies. The height of both of these columns is steady state value of asset stocks which are equal to z = 1=(r 1) = 29:41. The values are divided by two solid lines so that there are four cells, i.e. upper left, bottom left, bottom right and upper right anti-clockwise. The starting axes for home and foreign holdings are respectively the bottom and the top lines. So the area of the upper left cell represents the foreign holding of the home asset which equals
1 = 1 = 20:92:(Note that foreign buying is home selling of the home equity).
The home (net) holding of home asset is thus the sum of its endowment and gross external holding, i.e. z + 1 = 8:49, which explains the area of the bottom left
cell. The area of the bottom right cell, i.e. the home holding of the foreign asset, is given by 2 = w 1 = 8:44. Lastly, the area of the upper right cell is the
foreign holding of the foreign asset, z 2 = 20:97.
To compare the allocation to that in a symmetric model, we draw a dashed line in the middle of the two columns. It divides the two columns into four cells of the same area which corresponds to the situation of fully diversi…ed portfolio allocation when the two countries are identical. Inspecting the …gure, we …nd that the current model deviates from the symmetric case (benchmark) in two
ways. First, the steady-state net foreign asset at home is negative. The two solid lines move from the benchmark down to create an area which represents the home country net foreign asset position, i.e. the area above the solid lines but below the dashed line. Second, the net portfolio allocations under global imbalances exhibit asset home bias, i.e. the home holding of the home asset is larger than the home holding of the foreign asset even though the two assets are supplied equally in the world portfolio. The left solid line is higher than the right one. Further experiments show that, as the asymmetry between countries becomes more severe, the two solid lines move downwards (i.e. the global N F A
imbalance is exacerbated) and the gap between the two widens (i.e. asset home bias deepens).