Public Debt Management in Brazil

where TPt is the term premium on fixed-rate bonds and where Etit+1 is the expected average
Selic rate between time t and t +1.

Equation (9) shows that the expected cost of funding with Selic-indexed bonds is lower
than fixed-rate bonds because of the term premium but, ex-post, the cost may be greater
if the Selic rate turns out to be higher than expected. It is also worth noting that equa-
tion (9) implicitly assumes that investors expectations coincides with the expectations of
the government. If this were not the case, the expected cost differential relevant for the
government, TPt, would include an informational spread:

TPt=TPt^I+(Et^Iit+1 -Etit+1)                         (10)

where E_t^I denotes investors’ expectations and TP_t^I is the true term premium.

The difference between the cost of funding with dollar denominated bonds and fixed-rate
bonds depends on the realization of the exchange rate. Between time t and t + 1 the return
on dollar denominated bonds (evaluated in domestic currency) differs from the return on
fixed-rate bonds as follows

R_t^US + RPt + et+1 - et - Rt = et+1 - Etet+1 - FPt               (11)

where FP_t is the 1-year exchange-rate risk premium which is relevant for the government.
Although the true exchange-rate risk premium is likely to be small, dollar denominated
bonds may enjoy a liquidity premium due to the greater liquidity and efficiency of inter-
national bond markets. FPt may also reflect the different views of the investors and the
government regarding the exchange rate. If we consider this “credibility spread”, FP_t, is
equal to

FPt=FPt^I+Et^Iet+1-Etet+1                        (12)

where E_t^I denotes investors’ expectations and FP_t^I is the true foreign exchange risk pre-
mium.

Finally, the difference between the interest payments on price-indexed bonds and fixed-
rate bonds is equal to

R_t^I + π_t+1 - R_t = π_t+1 - E_tπ_t+1 - IP_t                     (13)

where IP_t is the inflation risk premium which is relevant to the government and may include,
in addition to the true premium, a spread reflecting the lack of credibility of the announced
inflation target:

IPt = IPt^I + Et^Iπt+1 - Etπt+1                         (14)

The return differentials (9)-(11)-(13) allow us to write the first order conditions (6)-(8)
as follows

E_tφ(A_t+1 - ∆B_t^T₊₁)(i_t+1 - E_ti_t+1)=TP_tE_tφ(A_t+1 - ∆B_t^T₊₁)        (15)

E_tφ(A_t+1 - ∆B_t^T₊₁)(e_t+1 - E_te_t+1) = FP_tE_tφ(A_t+1 - ∆B_t^T₊₁)        (16)

E_tφ(A_t+1 - ∆B_t^T₊₁)(π_t+1 - E_tπ_t+1) = IP_tE_tφ(A_t+1 - ∆B_t^T₊₁)        (17)

Equations (15)-(17) show the trade off between the risk and expected cost of debt service
that characterizes the choice of debt instruments.

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