Question

How to accurately estimate the price change of non-option bond under the situation of market interest rate change? Please give a practical example and perform calculation verification

Answer 1

Bond prices change inversely with the interest rates and hence thre is interest rate riskk. One method of measuring interest rate risk due to change in market interest rate is by the full vauation approach, which simply calculates whatbond price will be if the interest rate changed by specific amount.

Bond Value = Present Value of Coupon Payments + Present Value of Par Value.

And Duration Approximation Formula

Duration	=	P- – P+2 × P0(Δy)
P0 = Bond price. P- = Bond price when interest rate is incremented. P+ = Bond price when interest rate is decremented. Δy = change in interest rate in decimal form.

Modified Duration FormulaModified Duration=DMac1 + y/k

• DMac = Macaulay Duration
• dP/P = small change in bond price
• dy = small change in yield
• y = yield to maturity
• k = number of payments per year

Illustration:

Given:

• Modified Duration = 7.45% = 7.45/100 = .0745

Case #1:

• Market Price of Bond = $1,000
• BPV = .0745 × .01 × 1,000 = 0.75
• So if the yield fell by 1 basis point, the bond price would rise to $1000 + 0.75 = $1000.75

Case #2:

• Market Price = $900
• BPV = 0.0745 × .01 × 900 = 0.67
• So if the yield rose by 1 basis point, the bond price would decline to $900 – 0.67 = $899.33