Portfolio Management: Options Strategies, Premium & Value Analysis

This assignment delves into the intricacies of options trading, contrasting bullish and bearish strategies and examining the components of option premiums. It clarifies the differences between buying a call and writing a put, analyzing the advantages and disadvantages of each approach when one is bullish on a stock. The assignment further dissects option premiums into intrinsic and time value, explaining how these values are determined and their implications for in-the-money and out-of-the-money options. It also presents a comprehensive analysis of options as bets on stock price direction and explores the impact of interest rate changes on option premiums, using the Black-Scholes model for option pricing. Practical problems are solved to illustrate the concepts of time value, intrinsic value, and profit/loss calculations, providing a thorough understanding of options trading dynamics. Desklib offers a variety of resources, including past papers and solved assignments, to aid students in mastering these concepts.

Answer to Question 7
Bullish vs Bearish:
Bullish ("Bullish | Definition Of Bullish In English By Oxford Dictionaries") in context
of stock market means characterized by rising share prices and in context of the
behavior of investor means – inclined to buy because of an anticipated rise in
prices.
It refers to being optimistic about the prospects of the asset under consideration. If
you say that you are bullish in respect to an asset, it means that you are
anticipating that the price of the asset will rise.
Bearish ("Bearish | Definition Of Bearish In English By Oxford Dictionaries") in the
context of stock market means characterized by or associated with falling share
prices.
It is being pessimistic about the prospects of the asset under consideration and
implies that you are anticipating a decline in the market price of the asset.
Buying a Call vs writing a Put:
Buying a call refers to buying a right (without any obligation attached) to acquire
the underlying asset at a predetermined price (called Strike Price) on a
predetermined date. The holder of the call (buyer) exercises his right to buy only
when the price on the date of exercise is more than the strike price.
Writing a put refers to selling a right (without any obligation attached) to sell the
underlying asset at a predetermined strike price on or before a predetermined date.
The buyer of put option exercises his right to sell only when the price on the date of
exercise is less than the strike price.
Advantage or disadvantage of
Buying a call when you are bullish on a stock:
If the prediction goes right, the price of the stock increases above the strike price
and the holder (buyer) of the call exercise his right to buy and gets a profit of
(Market price on the date of exercise – Strike Price) – Premium paid for buying the
call.
Writing a put when bullish on a stock:
If the prediction goes right, the price of the stock increases above the strike price
and the holder (buyer) of the call will not exercise his right and the writer of the
option will get a profit to the extent of premium received for selling the put

Answer to Question 12
The Option Premium:
Option Premium is the amount paid by the buyer of the option to the seller of the
option at the beginning of the contract.
Components of Option Premium:
The option premium consists of an intrinsic value and time value. Where,
• Intrinsic value = Stock Price – Strike Price and
• Time Value = Premium – Stock Price.
The statement is correct. As per the definition, only in-the-money options will have
intrinsic value and since out-of-money options cannot have any intrinsic value, the
entire premium consists of time value alone. Therefore it can be said that the option
which is out-of-the-money must have time value
Answer to Question 13
In-the-money Option:
The Option is said to be in-the-money if:
• Strike Price is less than Underlying Price in case of a Call Option, and
• Underlying Price is less than Strike Price in case of Put Option
Intrinsic Value:
The intrinsic value of an option is computed as follows:
• Intrinsic Value = Underlying Asset Price – Strike Price (in case of Call)
• Intrinsic Value = Strike Price – Underlying Asset Price (in case of Put)
By comparing the description about both ‘in-the-money’ option and ‘intrinsic value’
it can be understood that only ‘in-the-money’ options can have intrinsic value and
hence it can be said that the option which is in-the-money must have intrinsic value.
Answer to Question 14:
The statement is squarely correct.
A typical transaction of an option contract involves two persons. A buyer of option
and a seller (or) writer of the option. Let us consider an example of a call option.
While the buyer is optimistic that the price of the stock will incline, the writer of the

option expects the price of the stock to decline. The buyer, with his confidence,
pays a premium with an anticipation that he will get more profit than the amount of
premium paid. Indirectly we can say that the buyer is betting his stake (premium)
on an anticipated increase of stock. Conversely, the seller with an anticipation of
the decline in price is getting premium and is acquiring an obligation to sell the
stock in potentially unfavorable conditions. This can be seen as seller betting on the
decline of the price of the stock. Usually, the bet has the following characteristics.
1. The persons involving in betting should have something to gain or lose. In
case of the option, the writer may either gain premium or lose the capital
appreciation of underlying. On the other hand, the buyer may either gain the
benefits of capital appreciation of the underlying or lose the premium paid.
2. The outcome of the bet should be contingent upon future uncertain events
not in the control of parties to the bet. In the case of options, the outcome of
the transaction is dependent upon the increase or decrease of the price of
the underlying which is not under the control of the parties to the transaction.
Therefore it can be said that options are nothing more than side bet on the direction
stock prices are going to take.
Answer to Question 24:
A rise in the interest rate of the economy as a whole and its impact on
option premium:
The Call Premium rises with a given rise in risk-free interest rate (other factors
remaining constant) since the call premium is directly related to the interest rate
prevalent in the economy.
The relevance of Interest rates in Option Pricing:

To understand the relevance of interest rates in option pricing, let us consider an
example of a call option. If the call option ends in-the-money, the holder will
exercise the call option. This will require the holder to pay for the value of the
underlying asset on the date of exercise. Since the exercise is going to happen in a
future date, if we consider the time value of money, the present value of exercise
price that is expected to be paid in future is lesser in real terms. Such a difference
between the actual outflow of cash towards exercise price and the present value
will be higher for higher interest rates. In other words, the higher the interest rate,
the lower the present value of strike price will be and the higher and as a result the
higher the value of the call option
Answer to Problem 1:
a. The Time value in Smith Electronics (SELE) FEB 60 Call option is $1.87 (Refer
Table 1.1)
b. The Intrinsic Value of a SELE JAN 65 Call is $1.38 (Refer Table 1.1)
c. The Intrinsic Value of SELE APR 75 Put is $8.62 (Refer Table 1.1)
d. The maximum profit an investor can obtain by writing a Western Oil (WO) FEB
65 Call is $8.38 (since the maximum amount that any writer of call can get is
restricted to the premium he receives while the loss he can get is unlimited)
e. The profit obtained from purchase of NILE.Com FEB 115 PUT option if the
underlying price on date of expiry of option is $85.38 is $21.62.
Computation: Purchase of Put Option gives the buyer a right to sell the stock
at the time of expiry of option. The buyer will exercise the option to sell if the
underlying price as on the date of exercise is less than the strike price. In the

given situation, the strike price is $115 and the price as on date of expiry of
option is $85.38. The buyer will get a gain of $29.62. However, the buyer of
option paid a premium of $8.00 to acquire the option. Hence the net gain
would be $29.62 - $8.00 = $21.62
f. Maximum profit that can be obtained if a WO FEB 70 Call (rather any call
option) is bought is unlimited
Computation of Intrinsic Value and Time Value:
Table 1.1
Nature of option Strike
Price
Underlying
Value
Premiu
m
Intrinsic
Value
Time
Value
(a) (b) (c ) (d) = (a) -
(b) / (b) - (a)
(e) = (c ) -
(d)
SELE 60 Call Option 60 66.38 8.25 6.38 1.87
SELE JAN 65 CALL 65 66.38 2.5 1.38 1.12
SELE APR 75 PUT 75 66.38 9.75 8.62 1.13
Note:
 In case of Call Option, Intrinsic Value = Underlying Asset Price – Strike Price
 In case of Put Option, Intrinsic Value = Strike Price – Underlying Asset Price
Answer to Problem 2:
The Investor will end up getting a loss of $3,590
Computation:
Table 2.1
Particulars Computation / Reason Amount
Purchase Price => Current Price * 400 shares $ (26,552)
Less: Price on expiry
of option
=> Price at expiration * 400 shares $ 22,952
Loss on purchase of
shares
$ (3,600)
Profit on writing a
put
Since the underlying value at expiry is more
than the strike price, the holder will not
exercise the price and profit for writer is the
amount of premium received = $5 * 2 Puts
$ 10

Total Gain / (loss) $ (3,590)
Answer to Problem 6:
The Call Premium C is determined under Black-Scholes Option Pricing Model using the following
formula: (Strong 477)

Given Parameters:
 Current Selling Price of the Stock (S)= $43.50
 Strike Price (K) = $45.00
 Time till expiry (t) = 67 days => 67 / 365 =0.1836
 Risk-free rate of return = 5.3% (or) 0.053
 Volatility of stock = 44% (or) 0.44
Let us first compute d1 and d2
d1 = (ln (S/K) + [R + (σ2 / 2) t]) / σ √t
 d1 = {ln (43.50 / 45.00) + [5.3% + (0.442 / 2) 0.1836]} / (0.44 √0.1836)
 d1 = {ln (0.97) + [5.3% + (0.442 / 2) * 0.1836]} / (0.44 * 0.4285)
 d1 = {-0.033899 + [0.053 + (0.1936 / 2) * 0.1836]} / (0.44 * 0.4285)
 d1 = -0.0340
d2 = d1 - σ √t
 d2 = -0.0340 – 0.44 * √0.1836
 d2 = -0.2225
By substituting all the values in the equation, we get:
C = $43.50 * N(-0.0340) - $45.00 * e0.053 * 0.1836 * N(-0.2225)
Let us find the values of N(d1) and N(d2) from normal distribution table
N(-0.0340) => 0.4880
N(-0.2225) => 0.4129
By substituting the values, we get:
C = $43.50 * 0.4880 - $45.00 * e0.053 * 0.1836 * 0.4129

 C = $2.8095 (approx.)
Bibliography:
Strong, Robert A. Portfolio Construction, Management And Protection. 5th ed. Canada: South-Western
Cengage Learning, 2009. Print.
"Bullish | Definition Of Bullish In English By Oxford Dictionaries." Oxford Dictionaries | English. N.p.,
2018. Web. 7 Dec. 2018.
"Bearish | Definition Of Bearish In English By Oxford Dictionaries." Oxford Dictionaries | English. N.p.,
2018. Web. 7 Dec. 2018.