Chapter 20, Problem 6PS

a.

Summary Introduction

To compute: The rate of return when the investment amount is completely invested in the stocks by the investor in one year.

Introduction:

Rate of return: When the annual income earned through an investment is expressed as a proportion in the form of percentage of the original investment, it is called as rate of return.

Answer to Problem 6PS

The table comparing the rate of return in percentages at different stock prices at maturity is as follows:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Rate of return in percentages	-20%	0	10%	20%

Explanation of Solution

Stock price S₀=$100

Call option with exercise price X=$100

Call option’s selling price C=$10

Call option’s expiration=1 year

Available amount for investment=$10000

Let us follow the following steps to calculation the rate of return.

Step 1: Calculation of investment amount:

  

So, therefore in each case of price variation at an expiry period of 1 year i.e., at, $80, $100, $110, $120 the investment amount will $10000.

Step 2: Calculation of profit/Loss in different maturity prices

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Profit/ Loss per share when the current price is $100. (Stock price after 1 year − Current price)
Profit/Loss per total shares		0

Step 3: Calculation of rate of return in different prices at maturity

Calculation of rate of return:

  

The same formula is used in calculations shown in the table.

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Rate of return		0
Rate of return in percentages (Rate of return *100)		0

The maximum profit earned is 20 % and maximum loss to be borne is -20% when all of the investment amount is invested in stocks by the investor.

b.

Summary Introduction

To compute: The rate of return when the investment amount is invested in the stock options.

Introduction:

Rate of return: When the annual income earned through an investment is expressed as a proportion in the form of percentage of the original investment, it is called as rate of return.

Answer to Problem 6PS

The table comparing the rate of return in percentages at different stock prices at maturity is as follows:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Rate of return in percentages	-300%	-100%	0	100%

Explanation of Solution

Stock price S₀=$100

Call option with exercise price X=$100

Call option’s selling price C=$10

Call option’s expiration=1 year

Available amount for investment=$10000\

Let us follow the following steps to calculate the rate of return in this alternative.

Step 1: Calculation of investment amount:

  So, therefore in each case of price variation at an expiry period of 1 year i.e., at, $80, $100, $110, $120 the investment amount will $10000.

Step 2: Calculation of profit/loss in different maturity prices

Note1: Calculation of profit/loss for long call= Stock price at maturity − Strike Price- Option premium paid by the investor

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Payoff per share when the strike price is $100. (Payoff=Stock price after 1 year − Strike price)
Option premium per share paid by the investor	10	10	10	10
Profit/Loss per share (Note 1)
Profit/Loss for 10 contracts			0

Calculation of value of total contracts:

  

The same is used in all price variation cases in the above table.

Step 3: Calculation of rate of return:

  

The same formula is used in calculations shown in the table.

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Rate of return			0
Rate of return in percentages (Rate of return *100)			0

In this alternative, a maximum return of 100% and maximum loss to be borne is 300%. The reason is simple. It is a type of insurance contract where investor pays a premium and exercise the option only when required.

c.

Summary Introduction

To compute: The rate of return when $1000 is invested in options and $9000 is invested in money market fund paying 4% annual interest.

Introduction:

Money market fund: There are many types of securities in which the investment can be made. When the investor has the intention of investing in short term debt securities he/she can always opt for the money market fund. The money market fund is supposed to be an open-minded type of mutual fund. These are managed to maintain the net asset value’s stability at the highest point and at the same time pay the sufficient dividend to the investors in the form of dividends.

Answer to Problem 6PS

The combined weighted average rate of return at different stock prices at maturity is as follows:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Weighted average rate of return from options contract	-30	-10	0	10
Weighted average rate of return from money market fund	3.60	3.6	3.6	3.6
Total	-26.40	-6.40	3.60	13.60

Explanation of Solution

Stock price S₀=$100

Call option with exercise price X=$100

Call option’s selling price C=$10

Call option’s expiration=1 year

Available amount for investment=$10000

Let us follow the following steps to calculate the rate of return in this alternative

Step 1: Calculation of investment amount when $1000 is invested in options contract

  The same amount is applicable in all prices at maturity.

Step2: Calculation of Profit/Loss at different prices at maturity:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Payoff per share when the strike price is $100. (Payoff=Stock price after 1 year − Strike price)
Option premium per share paid by the investor	10	10	10	10
Profit/Loss per share (Note 1)
Profit/Loss for 1 contracts			0

Calculation of value of total contracts:

  

The same is used in all price variation cases in the above table.

Step 3: Calculation of rate of return:

  

The same formula is used in calculations shown in the table.

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Rate of return			0
Rate of return (profit/loss amount) in percentages (Rate of return *100)			0

Step 4: Calculation of Weighted average rate of return- Note 2

  

Calculation of weighted average rate of return for option contract:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Weight of option contract investment	0.10	0.10	0.10	0.10
Weighted average rate of return			0

Calculation of Profit/Loss of investment in money market fund at different price at maturity:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Return from money market fund	360	360	360	360
Rate of return	0.04	0.04	0.04	0.04
Rate of return in percentages (Rate of return *100)	4	4	4	4
Weight of option contract investment	0.90	0.90	0.90	0.90
Weighted average rate of return	3.60	3.6	3.6	3.6

Step5: Calculation of combined weighted average rate of return:

Particulars	Amount (in $) when stock price is $80	Amount (in $ ) when stock price is $100	Amount (in $) when stock price is $110	Amount (in $) when stock price is $120
Weighted average rate of return from options contract	-30	-10	0	10
Weighted average rate of return from money market fund	3.60	3.6	3.6	3.6
Total	-26.40	-6.40	3.60	13.60