*Appendix A.3. Theoretical Framework for Policy Recommendation*

Policy implications for this research are based on a theoretical framework, detailed below. Since Asian bonds are characterized by higher relative risks and returns, we derive the optimal portfolio of a theoretical investor, who can choose to assign a weight *α* on green bonds not issued in Asia and a weight (1 − *α*) on Asian bonds.

The rate of return and associated variance of this portfolio is given by Equations (A.1) and (C.2), respectively:

$$r = ar\_{NA} + (1 - a)r\_A \tag{A1}$$

$$
\sigma^2 = a^2 \sigma\_{NA}^2 + (1 - a)^2 \sigma\_A^2 + 2a(1 - a)\sigma\_{NA/A} \tag{A2}
$$

where *r*, *rNA*, and *rA* denote the rate of return of portfolio, non-Asian bonds, and Asian bonds respectively, and *σ*2, *σ*<sup>2</sup> *NA*, *<sup>σ</sup>*<sup>2</sup> *<sup>A</sup>*, and *σNA*/*<sup>A</sup>* denote the variance of portfolio, non-Asian bonds, Asian bonds, and covariance between Asian and non-Asian bonds.

Then, the theoretical investor aims at maximizing the utility derived from their portfolio. This study assumes that their utility function is given by:

$$
\mathcal{U}(r, \sigma) = r - \beta \sigma \tag{A3}
$$

Substituting (A1) and (A2) into (A3), we obtain:

$$\mathcal{U}(r,\sigma) = ar\_{NA} + (1-a)r\_A - \beta \left\{ a^2 \sigma\_{NA}^2 + (1-a)^2 \sigma\_A^2 + 2a(1-a)\sigma\_{NA/A} \right\} \tag{A4}$$

Thus,

The investor's utility maximization problem is given by Equation (A5):

$$\max\_{\boldsymbol{\alpha}} \mathbb{L}I(\boldsymbol{r}, \boldsymbol{\sigma}) \tag{A5}$$

The first-order condition, with respect to *α*, is:

$$\frac{\partial \mathcal{U}}{\partial \mathfrak{a}} = (r\_{NA} - r\_A) - \beta \left\{ 2a^\* \sigma\_{NA}^2 - 2(1 - a^\*) \sigma\_A^2 + (2 - 4a^\*) \sigma\_{NA/A} \right\} = 0 \tag{A6}$$

Solving this equation for *α*∗, we obtain the optimal weight the investor can put on non-Asian bonds:

$$\alpha^\* = \frac{\frac{1}{\mathcal{B}}(r\_{NA} - r\_A) - \left(2\sigma\_{NA/A} - 2\sigma\_A^2\right)}{2\sigma\_{NA}^2 + 2\sigma\_A^2 - 4\sigma\_{NA/A}}\tag{A7}$$

To change this optimal weight, policymakers in Asia and the Pacific can act on parameters of this utility maximization problem, namely on *rA* and *σ*<sup>2</sup> *A*.

For instance, one can increase the weight put on Asian bonds by increasing the rate of return, *rA*, by subsidising bonds through tax spillover, denoted by *θtax*. The new rate of return of this subsidised portfolio, denoted by *rspillover*, is given by Equation (A8):

$$r\_{spilllower} = ar\_{NA} + (1 - a)(r\_A + \theta\_{tax}), \text{ where } \theta\_{tax} \ge 0 \tag{A8}$$

Then, the investor's utility becomes:

$$\mathcal{U}(r,\sigma)\_{spillovr} = ar\_{NA} + (1-a)(r\_A + \theta\_{lux}) - \beta \left\{ a^2 \sigma\_{NA}^2 + (1-a)^2 \sigma\_A^2 + 2a(1-a)\sigma\_{NA/A} \right\} \tag{A9}$$

Solving the utility maximization problem, we obtain the new optimal weight for this investor:

$$\alpha\_{spilllower}^\* = \frac{\frac{1}{\mathcal{F}}(r\_{NA} - (r\_A + \theta\_{\rm{lax}})) - \left(2\sigma\_{NA/A} - 2\sigma\_A^2\right)}{2\sigma\_{NA}^2 + 2\sigma\_A^2 - 4\sigma\_{NA/A}}\tag{A10}$$

Note that

$$
\alpha^\*\_{tax} \le \alpha^\* \tag{A11}
$$

where the equality holds if and only if *θtax* = 0.

Since *α*∗ denotes the optimal portfolio weight attributed to bonds not issued in Asia and the Pacific, policymakers can make green bonds more attractive for investors by using spillover from tax returns.
