Hitung ukuran convexity

Ingat kembali dari Bab Tiga bahwa durasi tidak cukup menyesuaikan sifat cembung (convex) dari hubungan antara harga dan imbal hasil. Untuk meningkatkan estimasi harga obligasi berbasis durasi, kita dapat menambahkan suku berdasarkan ukuran convexity.

Pada Bab Tiga, Anda mempelajari bahwa rumus pendekatan untuk convexity adalah:

$$(P(up) + P(down) - 2 * P) / (P * \Delta y^2)$$

Dengan \(P\) adalah harga obligasi, \(P(up)\) adalah harga obligasi saat imbal hasil naik, \(P(down)\) adalah harga obligasi saat imbal hasil turun, dan \(\Delta y\) adalah perubahan imbal hasil yang diharapkan.

Anda telah menghitung objek px, px_up, dan px_down sebelumnya dan ketiganya tersedia di ruang kerja Anda. Untuk latihan ini, anggap perubahan imbal hasil yang diharapkan adalah 1%. Hitung ukuran convexity, perkiraan persen perubahan harga akibat convexity, dan perkiraan dampak dolar pada harga akibat convexity.

Latihan ini adalah bagian dari kursus

Penilaian dan Analisis Obligasi di R

Petunjuk latihan

Gunakan rumus di atas dengan px, px_up, dan px_down untuk menghitung convexity. Simpan sebagai convexity.
Gunakan convexity dan pengetahuan Anda tentang perubahan imbal hasil untuk menghitung dan melihat efek persentase convexity pada harga (convexity_pct_change).
Gunakan convexity untuk menghitung dan melihat efek dolar convexity pada harga (convexity_dollar_change).

Latihan interaktif praktis

Cobalah latihan ini dengan menyelesaikan kode contoh berikut.

# Calculate convexity measure
convexity <-

# Calculate percentage effect of convexity on price
convexity_pct_change <-
convexity_pct_change

# Calculate dollar effect of convexity on price
convexity_dollar_change <-
convexity_dollar_change

Edit dan Jalankan Kode

Latihan ini adalah bagian dari kursus

Penilaian dan Analisis Obligasi di R

SkillTag.level.intermediateSkillTag.label

4.9+

Mulai Kursus Gratis

The fixed income market is large and filled with complex instruments. In this course, we focus on plain vanilla bonds to build solid fundamentals you will need to tackle more complex fixed income instruments. In this chapter, we demonstrate the mechanics of valuing bonds by focusing on an annual coupon, fixed rate, fixed maturity, and option-free bond.

Exercise 1: Introduction Exercise 2: Price vs. value Exercise 3: Time value of money Exercise 4: Computing a bond's future value Exercise 5: Computing a bond's present value Exercise 6: Bond valuation Exercise 7: Laying out the bond's cash flows Exercise 8: Discounting bond cash flows with a known yield Exercise 9: Convert your code into a function Exercise 10: Convert your code into a bond valuation function

Estimating Yield To Maturity - The YTM measures the expected return to bond investors if they hold the bond until maturity. This number summarizes the compensation investors demand for the risk they are bearing by investing in a particular bond. We will discuss how one can estimate YTM of a bond.

Exercise 1: Price-yield relationship Exercise 2: Credit ratings Exercise 3: The yield on the Moody's Baa index Exercise 4: Value the 5% bond using the Baa yield you found Exercise 5: Plotting the price/yield relationship Exercise 6: Components of yield Exercise 7: Risk-free yield Exercise 8: Plotting US Treasury yields Exercise 9: Plotting the investment grade spread Exercise 10: Estimating the yield of a bond Exercise 11: Finding a bond's yield Exercise 12: Use uniroot function to find YTM

Interest rate risk is the biggest risk that bond investors face. When interest rates rise, bond prices fall. Because of this, much attention is paid to how sensitive a particular bond's price is to changes in interest rates. In this chapter, we start the discussion with a simple measure of bond price volatility - the Price Value of a Basis Point. Then, we discuss duration and convexity, which are two common measures that are used to manage interest rate risk.

Exercise 1: Bond price volatility and the price value of a basis point Exercise 2: Price value of a basis point Exercise 3: Calculate PV01 of a 10% bond Exercise 4: Duration Exercise 5: Duration of a zero-coupon bond Exercise 6: Calculate approximate duration for a bond Exercise 7: Estimating effect on bond price using duration Exercise 8: Convexity Exercise 9: Calculate approximate convexity for a bond Exercise 10: Estimating effect of convexity on bond price Exercise 11: Estimating the bond price using duration and convexity

We will put all of the techniques that the student has learned from Chapters One through Three into one comprehensive example. The student will be asked to value a bond by using the yield on a comparable bond and estimate the bond's duration and convexity.

Exercise 1: Merangkum pelajaran utama Exercise 2: Cari imbal hasil obligasi AAA per 30 September 2016 Exercise 3: Valuasi obligasi Exercise 4: Kode vektor arus kas alternatif Exercise 5: Durasi dan konveksitas Exercise 6: Arah perubahan harga Exercise 7: Hitung durasi Exercise 8: Hitung ukuran convexity

Latihan Saat Ini

Exercise 9: Estimasi perubahan harga menggunakan durasi dan konveksitas Exercise 10: Selamat!