Derivatives and Portfolio Management

This assignment delves into the world of derivatives, specifically focusing on options and their application in portfolio management. It explores concepts like put-call parity and delta hedging, demonstrating how investors can use options to mitigate risk and potentially enhance returns. The assignment includes three tables analyzing different scenarios where a portfolio is hedged using options strategies. Each table provides insights into the changing value of the portfolio, the impact of volatility, and adjustments made to the hedge position based on market conditions.

Running head: FUTURE OPTIONS AND OTHER DERIVATES
Future options and other derivates
Name of the Student:
Name of the University:
Author’s Note:
Course ID:

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FUTURE OPTIONS AND OTHER DERIVATES
Table of Contents
Question 1:.................................................................................................................................2
Question 2:.................................................................................................................................3
Reference:..................................................................................................................................6

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FUTURE OPTIONS AND OTHER DERIVATES
Question 1:
Constructing the synthetic treasury bill position Value
Stay long with the stock 61
Keep the put long 0.08
Keep the call short -2
Synthetic 59.08
exercise price 60
The difference in value of exercise price and risk free rate is 6.23%
T-bill 61,000.00
interest rate 1.13%
position of the T-bill 60,321.38
Position of the synthetic bill Value
Long stock 61,000.00
Long put 80.00
Short call (2,000.00)
Total value 59,080.00
Net cash flow from operations 1,241.38
The overall table mainly uses put call parity, which directly help in identifying the
arbitrage opportunity. This put call parity mainly includes being long on stock, long on put
and short of call, which directly helps in gathering relevant value of the portfolio. Moreover,
the arbitrage opportunity has mainly allowed the investors to gain a net cash flow from

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FUTURE OPTIONS AND OTHER DERIVATES
operations of 1,241.38 by selling 1000 shares of the company. Cerreia-Vioglio, Maccheroni
and Marinacci (2015) stated that put call parity mainly allows the investors to adequately take
advantage of the arbitrage opportunity portrayed in the stock.
Question 2:
Particulars Value
Portfolio worth 150,000,000
Put option worth 145,000,000
Volatility 15%
Risk free rate 4%
Term 0.46
Dividend yield 3%
D1 0.43
D2 0.33
Call 10,482,628.83
Put 2,830,264.45
Delta 0.67
Shorting 99,901,488.09
Percentage of short 33.40%
The above table mainly depicts that overall 33.40% of the portfolio value i been sold
for attaining adequate hedge.
Particulars Value
Portfolio worth 145,000,000

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FUTURE OPTIONS AND OTHER DERIVATES
Put option worth 145,000,000
Volatility 15%
Risk free rate 4%
Term 0.44
Dividend yield 3%
D1 0.09
D2 (0.01)
Call 7,028,476.44
Put 4,485,652.36
Delta 0.54
Shorting 77,942,091.51
Percentage of short 46.25%
Shorting more shares 12.85%
The above table mainly states that value of the portfolio has declined, which directly
resulted in additional shares being sold for adequately hedging the portfolio.
Particulars Value
Portfolio worth 148,000,000
Put option worth 145,000,000
volatility 15%
Risk free rate 4%
Term 0.42
Dividend yield 3%
D1 0.30

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FUTURE OPTIONS AND OTHER DERIVATES
D2 0.20
Call 8,733,518.31
Put 3,300,318.84
Delta 0.62
Shorting 91,565,955.57
Percentage of short 38.13%
Buying shares -8.12%
The above table mainly states relevant increment in portfolio, which resulted in
buying back the shares for achieving adequate hedged portfolio. This could eventually allow
the investors to adjust its position according to the delta of the stock. Imai and Arai (2015)
mentioned that with the help of delta hedging organisation are mainly able to reduce the risk
of their portfolio and adequately hedge their exposure in the volatile capital and currency
market.