# **Figure AII.2. Constrained debt portfolio strategy.**

# **a.  Efficient Frontier. Cost and Risk (% of GDP).**

<!-- Start of picture text -->
1.40%<br>1.20%<br>1.00%<br>0.80%<br>0.60%<br>0.40%<br>0.20%<br>0.00%<br>Risk<br>Cost<br>0.10% 0.10% 0.10% 0.11% 0.11% 0.11% 0.12% 0.13% 0.13% 0.14% 0.15%<br><!-- End of picture text -->

Source: World Bank calculations

# **b.  Efficient Portfolios. Cost and Risk (% of GDP) and Composition (% share of instruments).**

|**Risk**|**Cost**|**I1**|**I2**|**I3**|**I4**|**I5**|**I6**|**I7**|**I8**|**I9**|**I10**|
|---|---|---|---|---|---|---|---|---|---|---|---|
|0.10%|1.26%|---|---|---|---|87.96%|0.00%|0.04%|3.36%|0.04%|3.36%|
|0.10%|1.25%|---|---|---|---|89.0%|0.0%|0.0%|3.3%|0.0%|3.3%|
|0.10%|1.24%|---|---|---|---|87.4%|2.4%|0.0%|3.2%|0.0%|3.2%|
|0.10%|1.22%|---|---|---|---|81.3%|8.9%|0.0%|3.1%|0.0%|3.1%|
|0.10%|1.21%|---|---|---|---|75.2%|15.5%|0.0%|2.9%|0.0%|2.9%|
|0.10%|1.20%|---|---|---|---|69.1%|22.0%|0.0%|2.8%|0.0%|2.8%|
|0.11%|1.19%|---|---|---|---|62.9%|28.5%|0.0%|2.6%|0.0%|2.6%|
|0.11%|1.18%|---|---|---|---|56.8%|35.1%|0.0%|2.5%|0.0%|2.5%|
|0.11%|1.17%|---|---|---|---|50.7%|41.6%|0.0%|2.3%|0.0%|2.3%|
|0.11%|1.16%|---|---|---|---|44.6%|48.1%|0.0%|2.2%|0.0%|2.2%|
|0.11%|1.15%|---|---|---|---|38.5%|54.7%|0.0%|2.0%|0.0%|2.0%|
|0.12%|1.14%|---|---|---|---|15.7%|77.1%|0.5%|1.9%|0.5%|1.9%|
|0.12%|1.13%|---|---|---|---|0.0%|92.7%|0.8%|1.7%|0.8%|1.7%|
|0.12%|1.12%|---|---|---|---|0.0%|93.5%|0.6%|1.6%|0.6%|1.6%|
|0.13%|1.11%|---|---|---|---|0.0%|94.3%|0.5%|1.5%|0.5%|1.5%|
|0.13%|1.10%|---|---|---|---|0.0%|95.1%|0.4%|1.3%|0.4%|1.3%|
|0.13%|1.09%|---|---|---|---|0.0%|95.8%|0.2%|1.2%|0.2%|1.2%|
|0.14%|1.08%|---|---|---|---|0.0%|96.6%|0.1%|1.0%|0.1%|1.0%|
|0.14%|1.06%|---|---|---|---|0.0%|97.5%|0.0%|1.0%|0.0%|1.0%|
|0.14%|1.05%|---|---|---|---|0.0%|98.6%|0.0%|1.1%|0.0%|1.1%|
|0.15%|1.04%|---|---|---|---|0.0%|100.0%|0.0%|0.0%|0.0%|0.0%|

Source: World Bank calculations

**c.  Optimal Portfolios for Different Levels of Risk Tolerance λ. Composition (% share of instruments).**

# **d.  Optimal Portfolios for Different Levels of Risk Tolerance λ. Composition (% share of instruments) and Certainty Equivalent CE (% of GDP).**

<!-- Start of picture text --> λ CE Risk Cost I1 I2 I3 I4 I5 I6 I7 I8 I9 I10<br>100% 5.00% 1.22% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>10.00% 1.13% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>90% 15.00% 1.10% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>20.00% 1.09% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>80% 25.00% 1.08% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>30.00% 1.07% 0.10% 1.25% --- --- --- --- 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%<br>70% 40.00%35.00% 1.07%1.07% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>60% I10 50.00%45.00% 1.06%1.06% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>50% I9 60.00%55.00% 1.06%1.06% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>40% I8 70.00%65.00% 1.06%1.06% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>30% I7 80.00%75.00% 1.05%1.05% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>20% I6 90.00%85.00% 1.05%1.05% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>10% I5 100.00%95.00% 1.05%1.05% 0.10%0.10% 1.25%1.25% ------ ------ ------ ------ 0.0%0.0% 100.0%100.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%<br>0%<br>Risk Tolerance (λ)<br>Share in optimal portfolio<br>5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100%<br><!-- End of picture text --> Source: World Bank calculations Source: World Bank calculations 37