Faktor yang memengaruhi convexity

Penilaian dan Analisis Obligasi dengan Python

Joshua Mayhew

Options Trader

Convexity itu menguntungkan

Harga obligasi naik lebih banyak saat yield turun, turun lebih sedikit saat yield naik

Menganalisis convexity

Bandingkan convexity dua obligasi secara langsung
Plot grafik faktor terhadap convexity
Amati langsung kelengkungan hubungan harga/yield

Kupon vs. convexity

Obligasi 10 tahun yield 5%: pertama tanpa kupon, kedua kupon 10%

price_1 = -npf.pv(rate=0.05, nper=10, pmt=0, fv=100)

price_up_1 = -npf.pv(rate=0.06, nper=10, pmt=0, fv=100)

price_down_1 = -npf.pv(rate=0.04, nper=10, pmt=0, fv=100)

convexity_1 = (price_down_1 + price_up_1 - 2 * price_1) / (price_1 * 0.01 ** 2)

price_2 = -npf.pv(rate=0.05, nper=10, pmt=10, fv=100)
price_up_2 = -npf.pv(rate=0.06, nper=10, pmt=10, fv=100)
price_down_2 = -npf.pv(rate=0.04, nper=10, pmt=10, fv=100)
convexity_2 = (price_down_2 + price_up_2 - 2 * price_2) / (price_2 * 0.01 ** 2)

print("Low Coupon Bond Convexity: ", convexity_1)
print("High Coupon Bond Convexity: ", convexity_2)

Low Coupon Bond Convexity:  99.89
High Coupon Bond Convexity:  64.09

Jatuh tempo vs. convexity

bond_yields = np.arange(0, 20, 0.1)
bond = pd.DataFrame(bond_yields, columns=['yield'])

bond['price_10y'] = -npf.pv(rate=bond['yield'] / 100, 
    nper=10, pmt=0, fv=100)
bond['price_30y'] = -npf.pv(rate=bond['yield'] / 100, 
    nper=30, pmt=0, fv=100)

plt.plot(bond['yield'], bond['price_10y'])
plt.plot(bond['yield'], bond['price_30y'])
plt.xlabel('Yield (%)')
plt.ylabel('Harga (USD)')
plt.title('Jatuh Tempo Obligasi vs. Convexity')
plt.legend(["Obligasi 10 Tahun", "Obligasi 30 Tahun"])
plt.show()

Yield vs. convexity

bond_yields = np.arange(0, 20, 0.1)
bond = pd.DataFrame(bond_yields, columns=['bond_yield'])

bond['price'] = -npf.pv(rate=bond['bond_yield'] / 100, 
    nper=10, pmt=5, fv=100)

bond['price_up'] = -npf.pv(rate=bond['bond_yield'] / 100 
    + 0.01, nper=10, pmt=5, fv=100)

bond['price_down'] = -npf.pv(rate=bond['bond_yield'] / 100 
    - 0.01, nper=10, pmt=5, fv=100)

bond['convexity'] = (bond['price_down'] + bond['price_up'] 
- 2 * bond['price']) / (bond['price'] * 0.01 ** 2)

plt.plot(bond['bond_yield'], bond['convexity'])
plt.xlabel('Yield (%)')
plt.ylabel('Convexity (%)')
plt.title("Convexity Obligasi 10T Kupon Tahunan 5%")
plt.show()

Ringkasan

Convexity positif menguntungkan:
- Rugi lebih kecil saat yield naik, untung lebih besar saat yield turun

Convexity meningkat jika obligasi:
- Jatuh tempo lebih lama
- Kupon lebih rendah
- Yield lebih rendah

Ayo berlatih!

Penilaian dan Analisis Obligasi dengan Python