Investments, 11th Edition (exclude Access Card)
Investments, 11th Edition (exclude Access Card)
11th Edition
ISBN: 9781260201543
Author: Zvi Bodie Professor; Alex Kane; Alan J. Marcus Professor
Publisher: McGraw-Hill Education
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Chapter 21, Problem 44PS
Summary Introduction

(A)

To Compute:

If the desired put option were traded. How much would it cost to purchase?

Introduction:

The value of put option is calculated using the formula given below.

Expert Solution
Check Mark

Explanation of Solution

a) Computation of value of put:

Here, the investor would hold a put position. The current price is $100. This price could either

increase or decrease by 10%

  Exercise price of put option (X) $100Time to expiration (T)1 yearDividend =0Stock price(S0) $100Probability of stock price increasing to $110 (P1) 0.5Probability of stock price decreasing to $90(P2) 0.5

Factor by which stock increases is u

Factor by which stock decreases is d

Tbills rate (r)5%

Calculation of option value

The two possible stock prices are

S1=$110 and S2=$90

since, the exercise price is $100, and the corresponding two possible put values are

Pd$0 (outofthemoney) and Pu=10 (inthemoney).

Calculation of the hedge ratio (H)

The hedge ratio can be calculated by using the following formula:

H=(PdPu)uS0dS0

Here,

The value of the call option in case of in-the-money scenario is Pu

The value of the call option in case of out-of-the-money scenario is Pd

Factor by which stock increases u.

Factor by which stock decreases is d.

Stock price in case stock price increases is uS0

Stock price in case stock price decreases is dS0

Substitute:

  Pu=$10,Pd=$0,uS0=$110,dS0=$90,u=1.1,andd=.9:H=(PdPu)uS0dS0=(010)(11090)=1020=0.5

Hence, the hedge ratio is -.5

The portfolio combining of two puts and one share brings an assured payoff $ 110 making it a riskless portfolio.

Calculation of the present value of certain stock price of $110 with a one-year interest rate of 5%:

  Presentvalueofstockprice=S1( 1+r)1Substitute:S1=$110andr=5%

  Presentvalueofstockprice=S1( 1+r)1=$1101+.05=$1101.05=$104.76

Hence, the present value of certain stock price of $110 with a one-year interest rate of 5% $104.76

Comparing the protective put strategy and present value of stock we get,

One stock and two put options

  So +2P =$104.76

Solve for the value of put (P):

  So +2P =$104.76Substitute:S0=$100(current price)S0+2P=$104.76P=$104.76$1002=$4.762= $2.38

Hence, the value of put option is $2.38.

Conclusion

Hence, the value of put option is $2.38.

Summary Introduction

(B)

To Compute:

What would have been the cost of the protective put portfolio? Introduction: The cost of protective put portfolio that comes out is calculated based on the given formula below.

Expert Solution
Check Mark

Explanation of Solution

(b) Computation of cost of protective put portfolio:

The cost of the protective put portfolio is the cost of one share plus the cost of one put. It

can be calculated by using the following formula:

  Cost of protective put =S0+PSubstitute:S0$100 and P=$2.38Cost of protective put=S0+P=$100+S2.38=$102.38

Hence, the cost of protective put portfolio comes out to be $102.38.

Conclusion

Hence, the cost of protective put portfolio comes out to be $102.38.

Summary Introduction

(C)

To Compute:

What portfolio position in stock and T-bills ill ensure you a payoff equal to the payoff that would be provided by a protective put with X-$100? Show that the payoff to this portfolio and

the cost of establishing the portfolio match those of the desired protective put.

Introduction:

The strategy is calculated in the table to determine the pay-off using the below calculation.

Expert Solution
Check Mark

Explanation of Solution

To ensure equal pay-off in stock and T-bills and protective put is as follows

The hedge ratio is 0.50. The investor will invest 0.50 in stocks which costs $50 and

remaining in T-bills to earn 5% interest.

Investments, 11th Edition (exclude Access Card), Chapter 21, Problem 44PS

The above strategy will give same pay-off as the protective put option.

Conclusion

The above strategy will give same pay-off as the protective put option.

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