Financial Markets and Institutions
Financial Markets and Institutions
6th Edition
ISBN: 9780077641825
Author: SAUNDERS
Publisher: Mcgraw-Hill Course Content Delivery
Question
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Chapter 23, Problem 15P

a)

Summary Introduction

To compute: The number of put option bonds are required to hedge portfolio of bond.

a)

Expert Solution
Check Mark

Explanation of Solution

The computation of number of put option bond is as follows:

Number of put option bond(Np)=D×P|δ|×D×B=× $100,000,0000.625 × 10.1 ×$96,157=823.74824 Contracts

b)

Summary Introduction

To compute: The anticipated gain or loss in the hedge on the put option.

b)

Expert Solution
Check Mark

Explanation of Solution

The computation of gain or loss is as follows:

A $100,000 20year, 8% bond vending at $96,157 indicates 8.4% yield.

Put option hedge(ΔP)=NP×ΔP=824×(0.625)×(10.1)×10.1×$96,157×0.011.084=$4,614,028 Gain.

Hence, the gain from the put option hedge is $4,614,028.

c)

Summary Introduction

To discuss: The anticipated change in the market value of portfolio of bond.

c)

Expert Solution
Check Mark

Explanation of Solution

The computation of change in market value of portfolio of bond is as follows:

Change in bond (ΔB)=D×1Million×0.01(1+Cupon rate)=5×$100,000,000×0.011.08=$4,629,630

Hence, the change in bond is $4,629,630.

d)

Summary Introduction

To discuss: Whether the payoff of hedge set off cost of placing the hedge.

d)

Expert Solution
Check Mark

Explanation of Solution

The computation of payoff of hedge is as follows:

Pay off of hedge(ΔP)=(Number of contracts ×Premium=Number of contracts ×Delta×Duration×Market value×Δ1.084)=(824 × 3,250=824 × (0.625) × (10.1) × $96,157 ×Δ1.084)For solving Δ=(Premium×1.084)(Delta×Duration×Market value)=($3,250 × 1.084)(0.625 × 10.1 × $96,157)=0.005804 or 0.58%.

Hence the payoff of hedge is 0.58%.

e)

Summary Introduction

To discuss: Whether the gain on the portfolio bonds set off cost of placing the hedge.

e)

Expert Solution
Check Mark

Explanation of Solution

The computation of gain from the bond portfolio is as follows:

Gain from the bond(ΔB) =(Premium ×Number of contracts=Bond duration× Δ1.084)=(3,250 × 824 = 5 × $100,000,000 ×Δ1.084 )For solving Δ=(Premium ×Number of contracts×1.08Bond duration×1Million)=0.0057845 Or0.58%

Hence the gain from bond is -0.58%.

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