Description
1. A 5-year bond with face value $1,000 (paid at maturity) and coupon rate 5%
(coupon paid in arrears annually) has yield-to-maturity 4.5%. What is the
convexity of the bond?
2. Assume that stock returns follow a 2-factor structure. The risk-free return is
3%. Portfolio A has average return 8% and factor-betas 0.7 and 0.9 (for
factor 1 and 2, respectively). Portfolio B has average return 10% and factor betas 1.2 and 1.1 (for factor 1 and 2, respectively). What is the average
return for portfolio C that has factor-betas 1 and 1 (for factor 1 and 2,
respectively)?
Explanation & Answer
please review and let me know if you have any questions
1. A 5-year bond with face value $1,000 (paid at maturity) and coupon rate 5% (Coupon
paid in arrears annually) has yield-to-maturity 4.5%. What is the Convexity of the bond?
The bond convexity formula is a function of yield-to-maturity, coupon rate, bond price, Cash
flow and maturity time in years given as
𝑇
1
𝐶𝐹𝑡
) ∗ ∑ [(
) ∗ (𝑡 2 + 𝑡)]
𝐵𝑜𝑛𝑑 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 = (
2
(1 + 𝑦)𝑡
𝑃 ∗ (1 + 𝑦)
𝑡=1
Where t is time, P= bond price, CF= cash flow, r= coupon rate, and y= yield to maturity
Given are:
Time to maturity (T) = 5 years, Bond Face Value (CF)= $1000, Coupon rate (r) =5%
(annually), Yie...
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