Pembahasan Ujian PAI: F10 – No. 14 – November 2025

• \(E\left(r_{A}\right) = 12\%\) ; \(E\left(r_{B}\right) = 9\%\)
• \(\beta_{A} = 1{,}2\) ; \(\beta_{B} = 0{,}8\)
• Perekonomian memiliki 1 faktor

• Persamaan awal CAPM:
  $$\begin{aligned}
  E\left(r_{A}\right) &= r_{f} + \beta_{A}\left(E\left(r_{M}\right) – r_{f}\right) \\
  E\left(r_{B}\right) &= r_{f} + \beta_{B}\left(E\left(r_{M}\right) – r_{f}\right)
  \end{aligned}$$
• Eliminasi \(r_{f}\):
  Kurangkan persamaan untuk aset A dengan aset B:
  $$\begin{aligned}
  E\left(r_{A}\right) – E\left(r_{B}\right) &= \left[r_{f} + \beta_{A}\left(E\left(r_{M}\right) – r_{f}\right)\right] – \left[r_{f} + \beta_{B}\left(E\left(r_{M}\right) – r_{f}\right)\right] \\
  &= \beta_{A}\left(E\left(r_{M}\right) – r_{f}\right) – \beta_{B}\left(E\left(r_{M}\right) – r_{f}\right) \\
  &= \left(\beta_{A} – \beta_{B}\right)\left(E\left(r_{M}\right) – r_{f}\right)
  \end{aligned}$$
• Substitusikan nilai yang diketahui:
  $$\begin{aligned}
  12\% – 9\% &= (1{,}2 – 0{,}8)\left(E\left(r_{M}\right) – r_{f}\right) \\
  3\% &= 0{,}4\left(E\left(r_{M}\right) – r_{f}\right) \\
  E\left(r_{M}\right) – r_{f} &= \frac{3\%}{0{,}4} = 7{,}5\%
  \end{aligned}$$
• Hitung \(r_{f}\):
  $$\begin{aligned}
  E\left(r_{A}\right) &= r_{f} + \beta_{A}\left(E\left(r_{M}\right) – r_{f}\right) \\
  12\% &= r_{f} + 1{,}2\,(7{,}5\%) \\
  12\% &= r_{f} + 9\% \\
  r_{f} &= 12\% – 9\% = 3\%
  \end{aligned}$$

Jadi, tingkat suku bunga bebas risiko yakni sebesar 3%.