in the government portfolio (they returns covary positively), their optimal shares decrease.
The long position in foreign assets also decrease as Selic and price indexed bonds are hedged
by dollar denominated bonds.
The risk minimizing debt structure calls for issuing large amounts of indexed instruments
to fund unlimited holdings of foreign assets. Since taking such position is clearly unfeasible,
in Column 3 we restrict the shares of dollar denominated debt and fixed rate debt to be
non-negative. In this case, risk minimization clearly favors price indexation over Selic rate
indexation.
The optimal debt composition does not change when cost minimization is considered
along with risk insurance. Column 4 shows that both Selic rate and price indexed bonds
should be issued if large holdings of foreign assets were feasible. However, when the debt
shares are constrained to be non-negative price indexation clearly emerges as the optimal
choice: Column 5 shows that all the debt should be indexed to the price level.
5.2.2 Supply shocks
Table 7 shows the optimal debt composition that stabilizes the debt ratio against supply
shocks, i.e. against shocks to the inflation equation. Column 1 shows that fixed-rate bonds,
Selic rate and price indexed bonds, all provide insurance against variations in the primary
surplus and in the debt ratio due to lower than expected inflation and output growth. In
particular, more than one third of the debt should be at fixed rate while the other two
thirds should be indexed to the Selic rate and the price level. Although, Selic-rate and
price indexed bonds are good hedges against lower than expected inflation, they provide
limited insurance against budget risk, since their returns are now negatively correlated with
output (see Table 6). Since supply shocks lead to a negative covariance of output with both
inflation and the Selic rate, fixed-rate debt helps to stabilize the debt ratio.
Column 2 shows that, when we consider the risk of variations in debt returns along with
budget risk and debt-ratio uncertainty, a role emerges for dollar denominated bonds. The
optimal composition for risk minimization comprises a small share of dollar denominated
bonds and a negative share of Selic indexed bonds. The reason is that, even if dollar de-
nominated bonds are poor hedges against variations in the primary surplus, they help to
stabilize the interest payments on price indexed bonds. This is because, the exchange rate
covaries negatively with inflation; it appreciates when the Selic rate is raised to counter neg-
ative supply shocks. Since Selic indexed bonds are close substitutes for price indexed bonds
but offer a limited insurance against inflation uncertainty, their share becomes negative. By
contrast, fixed-rate bonds still appear to play an important role in risk minimization; about
one fourth of the debt should be at fixed rate.
Although fixed-rate debt helps to stabilize the debt ratio by insulating the budget from
supply shocks, its higher expected cost has a negative impact on the probability of stabiliza-
tion. Columns 3 shows the debt composition that maximizes the probability of stabilizing
the debt ratio when cost considerations are taken into account. Since variable-rate bonds
have lower expected returns than fixed-rate bonds, their shares increase substantially leav-
ing no role for fixed-rate bonds; it would even be optimal to hold fixed-rate assets and fund
this position with the other instruments. Finally, Column 4 shows that, when the opti-
mal shares are constrained to be non-negative, there is a strong case for price-indexation;
more than 80% of the debt should be indexed to the price level with the remaining part
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