Pembahasan Ujian PAI: F10 – No. 18 – Mei 2026

$$\omega_{1} = \frac{\sigma_{2}^{2} – \sigma_{1,2}}{\sigma_{1}^{2} + \sigma_{2}^{2} – 2\sigma_{1,2}}$$

Kovarians antara 2 aset:

$$\sigma_{1,2} = \sigma_{1}\,\sigma_{2}\,\rho_{1,2}$$

$$\omega_{1} = \frac{\sigma_{2}^{2} – \sigma_{1,2}}{\sigma_{1}^{2} + \sigma_{2}^{2} – 2\sigma_{1,2}}$$
$$\omega_{1} = \frac{(0{,}3)^{2} – (-0{,}012)}{(0{,}2)^{2} + (0{,}3)^{2} – 2(-0{,}012)}$$
$$\omega_{1} = \frac{0{,}09 + 0{,}012}{0{,}04 + 0{,}09 + 0{,}024}$$
$$\omega_{1} = \frac{0{,}102}{0{,}154}$$
$$\omega_{1} = 0{,}662338 \approx 66{,}2\%$$

Jadi, bobot aset pertama dalam minimum variance portfolio adalah sebesar 66,2%.