Derivatives: Questions and Case Studies

This document contains questions and case studies related to derivatives, including futures contracts, forward contracts, hedging, and the Libor scandal. It also includes a case study on the failure of Long-Term Capital Management (LTCM).

DERIVATIVES 1
Derivatives
Student’s Name
University Affiliation
Date

DERIVATIVES 2
Question 1
Number of contracts is 10
Initial futures price of $276.50 per oz.
Size of one future contract is 100 oz
Initial margin per contract: $1500
Maintenance margin per contract: $1100
a) Initial size of margin account =Initial margin per contract *number of contracts. Thus
1500 x10=15,000
b) Given that the settlement price is $278 per oz, Then the short position has effectively lost
$1.50 for every oz. This is equivalent to the loss of 1.50x100=150 per contract. Because
the position has a total of ten contracts, the overall loss is 150x10=1500.As a result of this
the new balance in the margin account is 15000-1500=13500.A margin call will not occur
because the new balance is greater than the maintenance of $1100.
c) Moving the settlement price to $281 per oz, the short position successfully losses another
$3 for every oz. The loss per every contract will be 3x100=300.The overall loss will be
300x10=3000.Therefore, the balance in the margin account will reduced to 13500-
3000=10500.As a result of this being less than the maintenance margin, margin call will
occur. Assume the account is topped back to $15000.
d) Closing the position out at $276 per oz, the short position will make a gain of 281-276=5
per oz. This is equivalent to a gain of 500 per contract and thus to an overall gain of
5000.Therefore, the closing balance in the margin account will be 15000+5000=20000.

DERIVATIVES 3
e) The said investor began with a margin account of $15000 and made a deposit of another
$4500 to meet the margin call, for a total of $19500.Since the margin account balance at
the time of close out of $ 20000, investor overall gain (costs interest ignored) is $500.
(Thomsett, 2018)
Question 2
It is a three-month forward contract between NZD and USD
Spot exchange rate is 1.60NZD/1USD
The three-month interest rate on the USD is 2% p.a and on NZD is 1.75% p.a
Forward price of USD is 1.61NZD/1USD.
We are given the information that S =1.60 and r =0.02 and d =0. 0175.From these
data, we have the following; F =e(r-d)T S =e(0.02-0.0175)(1/4) (1.60) =1.6010
Thus, at the given forward price of 1.61NZD/1USD, the forward contract is
overvalued relative to spot. To take advantage of the opportunity, forward should be
sold, spot should be bought and borrow to finance the sport purchase. Precisely:
 To deliver New Zealand Dollar in three months at 1.61NZD/1USD, enter into a short
forward contract.
 Buy e-dT =0.9956 New Zealand Dollar spot at price of 1.60NZD/1USD
Cost (1.60) (0.9956) =$1.5930
 Invest the $0.9956 for three months at 1.75%
Amount received after 3 months is $1
 Make a borrowing of 1.5930 at the rate of 2%

DERIVATIVES 4
Amount due after 3 months is $(e(0.02)(1/4) (1.5930) =$1.6010
Cash flows can be summarized as below:
Cash flows in USD Cash flow in NZD
At inception +0.9956 (from purchase). -1.5930(to purchase $)
-0.9956(investment). +1.5930(borrowing)
Net:0 Net:0
At T +1.00 (from investment). -1.6010 (repay borrowing)
-1.00(deliver to forward). +1.61(receive from forward)
Net:0 Net: +0.0090
Because all the cash flows are zero or positive, we have the required arbitrage.
Question 3
a) The futures position is long. The investor commits to buy 1 unit of asset. When an
investor has long positions, it simply means that he/she has bought those shares and owns
them. An investor has much hopes that will benefit from an upward price in future after
time That is reason as to why the investor has call for the option to buy asset that is
underlying at a given price. (Thomsett, 2018)
b) Establishing a forward contract at date T =0 and forward price, F, so that the original
value of the forward contract, fo satisfies the equation fo =0. At any given maturity date,
the contract value is given by fT = (ST-F). Since F=FO and by recalling by construction that
fo=0, then we have ft =(Ft -FO) d(t,T).Given size as h,the net amount paid by the investor
will be given by ST-(FT-F0)h.This is equivalent to ST-h(FT-F0) hence proved.

DERIVATIVES 5
c) Assuming that the cash flow is given by y=STW= +(FT -F0). letting σ 2 S = Var (ST), σ 2
F = Var (FT) and σST = Cov (ST, FT ). σy = W σS × B.
σ 2 y = W2σ 2 S + W2S2o / F 2 0* σ 2 F − 2 W2S0/ F0 *σS, F
d) YT = ZT + h (FT − F0). Main objective here is to minimize Var (YT) =
Var (ZT) + h2Var (FT) + 2 hCov (ZT, FT).h=-cov (Zr, Fr)/Var (Fr).
Var (YT)=Var (ZT)-Cov (Zr, Fr)2 /Var (Fr). (Boyle, 2019)
Question 4
Number of produces per year is 10000
20% for making gold jewelry to be sold is equivalent to 20/100*10000=2000 ounces of gold per
year
The rest to be sold in the market is equivalent to 80% which is equivalent to
80/100*10000=8000.I would recommend hedging because there can be increase in the expected
future price by x and remove the associated exchange risk.
Question 5
Company A want to invest in New Zealand
Company B want to invest Australia
Two-year swap on a principal of NZD 105 million which is equivalent to 100million AUD
Spot exchange rate is 1.05usd per AUD
For company A we have;104/100*100 million AUD=104 million AUD
For company B we have;105/100*105 million NZD=110.25 million NZD
Assuming that both companies make payments after every six months then
For company A
After 0.5 years;100(1.75/1.50) =116.6667 million AUD
After one year;116.67(1.90/1.75) =126.6667MILLION AUD
After 1.5 year;126.6667(2.20/2) =139.3334 million AUD
After two years 139.3334(2.50/2.25) =154.8149 million AUD
For company B
After 0.5 105(1.50/1.75) =90.0000 NZD million
After 1 year 90(1.75/1.90) =82.8947 NZD million
After 1.5 years 82.8947(2/2.20) =75.3588 NZD million
After two years 75.3588(2.25/2.50) =67.8229 NZD million (Boyle, 2019)
2 Case study

DERIVATIVES 6
a) Libor simply stands for London Interbank Offered Rate. It simply means the average rate
of interest calculated through submissions of rates of interest by super and major banks
across all over the world.
b) Libor scandal was all about sequences of actions which were fraudulent and connected to
the libor which simply stands for London Interbank Offered Rate as well as the
investigation resulting from the reaction. Libor scandal after it was discovered that the
banks were falsely deflating or inflating their rates in order to profit from trades as well
as to give impression that were very creditworthy compared to what they were.
c) According to British Bankers` Association dated 25 September 2012, it promised to
transfer oversight of Libor to UK regulators just in line with what was predicted by bank
analysts and it was proposed by Financial Services Authority managing director by the
name Martin Wheatley. According to wheatley, s recommends that banks submitting
rates to Libor must bas them on actual inter-bank deposit market transactions and make
records of every transactions stating each banks’ Libor submissions be at interval of three
months and criminal sanctions be recommended specifically for benchmarking of
manipulation of interest rates. AS a result of this, customers of financial institutions may
be influenced by more and higher volatile hedging and borrowing costs. Wheatley
reforms came into effect in the year 2013 and later in 2014 new administration took over.
3 Case study
a) It used absolute-return trading and high financial leverage. The absolute
return is a measure of either gain or loss on a portfolio investment expressed
as a percentage of capital invested. Leverage is a technique involving the use
borrowed funds than using fresh equity in the purchase of an asset expecting
that after taxation, profit to equity holders from any transaction will surpass
cost of borrowing. The main trading strategies include the following:
 Fixed Income Arbitrage
 Leverage and Portfolio Composition
 Secret and opaque operations
 UBS Investment
b) LCTM failed to raise more money by their own. As a result of this it was
very clear that it was running of options. They rejected to out the fund’s
partners and operate under their names. After remaining with no option, the
Federal Reserve Bank of New York had to organize bailout of $3.65billion
by creditors who were major to avoid more collapse in the financial markets.
The money received by the banks were completely consumed by the existing
depts. The chain reaction brings closure as the securities of the company
were liquidated to cover depts. Swaps, volatility, emerging trends, developed
countries, Dual-listed company, yield curve arbitrage S&P 500 stocks and
junk bond arbitrage were the major losses incurred which eventually brings
the company down.

DERIVATIVES 7
Works Cited

DERIVATIVES 8
Boyle, P. &. (2019). Trading and pricing financial derivatives : a guide to futures, options, and
swaps. Boston Berlin: De|G Pres.
Thomsett, M. (2018). Options : the Essential Guide for Getting Started in Derivatives Trading,
Tenth Edition. Boston: DEG Press.