Financial Modelling 2557A/B Lecture Notes - Lecture 3: Arbitrage, Risk Management

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sapphiretortoise72

17 Apr 2017

School

Western University

Department

Financial Modelling

Course

Financial Modelling 2557A/B

Professor

Xiaoming Liu

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Document Summary

Forward contract: an agreement/obligation to buy/sell an underlying asset in the future, at a pre- determined price. Party who agrees to buy is in long position; party who agrees to sell is in short position. The law of one price: if the payoffs of two different assets are same, their prices must be the same as well. If asset has higher payoff than another asset in all situations, then it must also require higher price to possess. Arbitrage involves simultaneous buying and selling an asset. In economics and finance, arbitrage is the practice of taking advantage of a price different between 2 or more markets o. Free-lunch opportunity: paying 0 for an investment and receiving a positive gain at time t. No-arbitrage condition: f=s0(1+i), where s0=spot price, and i=current interest rate. Hedging: taking an offsetting position in a derivative in order to balance any gains and losses to the underlying asset.

Related Questions

A call option gives the holder (Points : 4) the obligation to buy something the right to sell something the right to buy something the obligation to sell something none of the above Question 2. 2. A call option priced at $2 with a stock price of $30 and an exercise price of $35 allows the holder to buy the stock at (Points : 4) $2 $32 $33 $45 $35 Question 3. 3. A put option in which the stock price is $60 and the exercise price is $65 is said to be (Points : 4) in-the-money out-of-the-money at-the-money exercisable none of the above Question 4. 4. Organized options markets are different from over-the-counter options markets for all of the following reasons except (Points : 4) exercise terms physical trading floor regulation standardized contracts credit risk Question 5. 5. The advantages of the over-the-counter options market include all of the following except (Points : 4) customized contracts privately executed freedom from government regulation lower prices none of the above Question 6. 6. The option price is also referred to as the (Points : 4) strike spread premium fee none of the above Question 7. 7. An investor who exercises a call option on an index must (Points : 4) accept the cash difference between the index and the exercise price purchase all of the stocks in the index in their appropriate proportions from the writer immediately buy a put option to offset the call option immediately write another call option to offset none of the above Question 8. 8. What amount must a call writer pay if a cash-settled index call is exercised? (Points : 4) difference between the index level and the exercise price exercise price difference between the exercise price and the index level index level none of the above Question 9. 9. You are the purchaser of a call option with $5 premium and $145 exercise price. You bought this option when the stock price was $120. If the stock price now is $155, what is the net cash flow to you if you exercise? (Points : 4) $10 $5 $30 $35 Question 10. 10. You are the purchaser of a put option where the premium is $4 and exercise price is $52. You bought this option when the stock price was $52. If the stock price is $42 right now, what is your net cash flow? (Points : 4) negative $14 negative $6 $6 $4 Question 11. 11. You wrote a call option with premium of $5 and exercise price of $55. You sold this when the stock price was $45. If the stock price now is $65, what is your net cash flow? (Points : 4) negative $5 $25 $20 $5 negative $10 Question 12. 12. You wrote a put option with a premium of $3 and exercise price of $22. You sold this option when the stock price was $25. If the stock price is $22 now, what is your net cash flow? (Points : 4) $6 $3 negative $3 $0 negative $6 Question 13. 13. The maximum gain of the writer of a put option with a premium of $3 and an exercise price of $120 is: (Points : 4) $120 $117 $3 $123 unlimited Question 14. 14. The maximum gain of the purchaser of a put option with a premium of $3 and exercise price of $120 would be: (Points : 4) unlimited $120 $117 $3 $123 Question 15. 15. The maximum gain of the writer of a call option with a premium of $3 and an exercise price of $120 would be (Points : 4) unlimited $3 $117 $120 $123 Question 16. 16. The maximum gain of the purchaser of a call option with a premium of $3 and an exercise price of $120 would be (Points : 4) unlimited $120 $117 $123 $3 Question 17. 17. You have the following information: Put: X=$40, Premium=$4 Call: X=$50, Premium=$6 You bought the stock at $45 Scenarios: S=20, S=45, S=90 Given above information, please calculate the net payouts for a protective put strategy for each different scenario. (Points : 4) -$9, -$4, $41 $25, $0, $0 -$5, $-9, $0 $16, -$4, $45 Question 18. 18. You have the following information: Put: X=$40, Premium=$4 Call: X=$50, Premium=$6 You bought the stock at $45 Scenarios: S=20, S=45, S=90 Given above information, please calculate the net payouts for a covered call strategy for each different scenario. (Points : 4) $6, $6, $11 $6, $0, $51 -$19, $6, $11 -$19, $6, $51 -$6, -$6,$45 Question 19. 19. You have the following information: Put: X=$40, Premium=$4 Call: X=$50, Premium=$6 You bought the stock at $45 Scenarios: S=20, S=45, S=90 Given above information, please calculate the net payouts for a collar strategy for each different scenario. (Points : 4) -$3, $2, $7 -$9, $6, $11 $16, $2, $52 -$4, $0, $6 Question 20. 20. You have the following information: S=65, X=60, T=1, r=0, C=7, P=4 Evaluating the situation from a Put-Call Parity framework, what steps would you take to implement an arbitrage strategy? (Points : 4) Sell Call, Buy Put, Short Stock, Invest remainder Sell Call, Buy Put, Buy Stock, Borrow remainder Buy Call, Sell Put, Buy Stock, Borrow remainder Buy Call, Sell Put, Short Stock, Invest remainder Buy Call, Sell Put, Short Stock, Borrow remainder Question 21. 21. Given the information and the solution you found for Question #20, what is the arbitrage amount? (Points : 4) If S>X, then $6 and if SX, the arbitrage will be $4 If S>X, then $3 and if SX, then $2 and if SX, the arbitrage will be $2 Question 22. 22. You have the following information: S=26, X=20, T=2, r=3.4%, C=15, P=6 Evaluating the situation from a Put-Call Parity framework, what steps would you take to implement an arbitrage strategy? (Points : 4) Sell Call, Buy Put, Buy Stock, Borrow remainder Sell Call, Buy Put, Short Stock, Invest reaminder Buy Call, Sell Put, Buy Stock, Borrow remainder Buy Call, Sell Put, Buy Stock, Invest remainder Buy Call, Sell Put, Short Stock, Invest remainder Question 23. 23. Using the information and the solution from Question #22, what would be the final arbitrage amount? (approximately) (Points : 4) If S>X or SX then $9, if SX or SX then $3, if SX or S

orchidporcupine923

Please read the article and answer these questions. Thanks.

Article:

TESTING THE GLOBAL CENTRAL BANK SWAP NETWORK

In the last few weeks, the ECB has been drawing on its liquidity swap line with the Fed, first $308 million for a week, then $658 million for a week, and last week back down to $358 million. Whatâs that about?

Itâs not such a large amount. Bank of Japan borrowed more in the past, $810 million in March and $1528 million in January. But the question then repeats, what was that about?

Both of these drawings are part of the new set of central bank swap lines linking what I call the C6: the Fed, ECB, Bank of Japan, Bank of England, Swiss National Bank, and Bank of Canada. On October 31, 2013these lines were made permanent and unlimited; contract details may be found here. Ever since then I have had a slide in my powerpoints saying âForget the G7, Watch the C6.â

So now weâre watching. What are we seeing?

Central bank swaps are in some ways quite similar to a standard commercial FX swap, but the differences are important and significant.

A standard swap involves exchange of two currencies today at the spot exchange rate prevailing today, plus a promise to reverse the transaction at maturity using the forward exchange rate prevailing today. Suppose that forward rate is calculated using covered interest parity as

F = S(1+r)/(1+r*)

where r and r* are respectively the dollar and foreign interest rate for a given term T, s is the spot exchange rate and f is the forward exchange rate for date T.

In this case, the exposure of the standard swap contract is identical to a swap of IOUs between the contracting parties at the prevailing interest rates in their respective currencies. One party borrows dollars at rate r and the other party borrows euros at the rate r*.

Central bank swaps are different. First, the forward rate in the contract is usually exactly the same as the current spot exchange rate. This means that central banks are never in the position of realizing profits or losses from the swap (although of course there will be implicit profits and losses), that come from deviation between the agreed forward rate and the spot rate at expiry.

Second, the interest rate on the contract is negotiated rather than calculated from market prices. But, given the choice of forward rate, the analogous commercial contract would call for payment of the interest differential, so anything different from that is significant. Significantly, the documentation of the current C6 swap line leaves open the question of who pays interest to who, and how much.

Usual practice has been for the party who draws on the line to pay interest on the line at some penalty rate. Thus the May 9, 2010 swap agreement between the Fed and ECB called for the ECB to pay the USD Overnight Index Swap Rate plus 100 basis points on its dollar borrowing, and the Fed to pay nothing on its euro borrowing. In effect, the ECB was simply borrowing dollars at the discount window, like any other bank, but with its own monetary liability serving as collateral instead of some financial asset.

This kind of arrangement is still in effect a swap of IOUs but at a price that is away from the market. Central bank swap lines thus in effect operate as a kind of outside spread providing bounds within which normal commercial dealing takes place. So long as prices stay at or near CIP, private agents prefer to do business directly with each other. But when CIP comes under pressure, because of one-sided liquidity flows, the central bank moves from backstop to market-maker and the outside price becomes the market price.

The ECB is borrowing dollars from the Fed and lending them on to banks in Europe who have dollar liquidity needs. Here is the tender documentation. Presumably it is doing this for banks who are unable, for whatever reason, to access dollar funding in the open market, or only at a premium that is higher than the ECB charges.

During the financial crisis, dollar funding needs like this got met by central bank liquidity swaps that rose almost to $600 billion, raising questions in Congress. Now, in normal times, smaller sums are becoming a routine way of handling the normal stresses and strains of world funding flows.

For lack of a world central bank, we have a network of central bank liquidity swaps.

(Council on Foreign Relations has a fun interactive app that shows the rest of the emerging swap network as well.)

Questions:

2. Forward rates in standard swaps are set relative to spot rates to eliminate arbitrage opportunities. Using a numerical example, demonstrate that an arbitrage opportunity would exist if a forward exchange rate quote differed from the formula given in Mehrlingâs article.

3. How do swap lines between central banks differ from standard foreign exchange swap contracts? How are forward rates set? How are interest rates determined?

Amongst corporations, sole proprietorships and partnerships, approximately what percentage of revenues are generated by corporations?

50%

42%

33%

82%

Question 2

What should be the financial goal of any firm?

attracting and acquiring capital and investing it

maximization of the ownersâ wealth

offering quality products at fair prices

quality customer service

Question 3
4 pts
Which of the following statement(s) is \ are true regarding the corporate management team?

In a corporation, ownership and direct control are typically separate.

Board of Directors is elected by shareholders and has ultimate decision-making authority

The Chief Executive Officer (CEO) â the Board typically delegates day-to-day decision making to the CEO.

All of the above

Question 4
4 pts
When calculating the present value of either a future single sum or a future annuity, it involves a process called discounting. The applicable interest rate to perform the discounting function is usually called the

yield to maturity

compound interest rate

discount rate

none of the above

Question 5
4 pts
_________________ are used to present additional information about items included in the financial statements and to present additional financial information.

stock certificates

Notes to financial statements

Preferred stocks

Convertible securities
Question 6
4 pts
What should be the financial goal of any firm?

maximization of the ownersâ wealth

attracting and acquiring capital and investing it

offering quality products at fair prices

quality customer service

Question 7
4 pts
A competitive market is one in which a _____ numbers of producers compete with each other to satisfy the wants and needs of a _____ number of consumers.

Large, small

Small, small

Large, large

Small, large

Question 8
4 pts
The Valuation Principle is an analysis between the value of the ______ of a financial alternative and the value of its ______.

revenues, income

benefits, costs

expenses, costs

Question 9
4 pts
The Net Present Value rule implies that we should compare a projectâs net present value (NPV) to___________. (zero \ future value \ the past).

Zero

Future Value

The Past

An Estimate

Question 10
4 pts
The internal rate of return (IRR) rule will _______ agree with the Net Present Value rule on a given investment project.

always

never

sometimes

none of the above

Question 11
5 pts
The law of one price exists due to arbitrage opportunities. If the price of a security, commodity or asset is different in two different markets, then an arbitrageur will ______ the asset in the more expensive market and ________ it where prices are lower.

sell, purchase

purchase, sell

purchase, purchase

sell, sell

Question 12
5 pts
Approaching every problem using a timeline is a(n) ________ idea because timelines identify events in a transaction or investment which might otherwise be easily overlooked.

good

bad

indifferent

unrealistic

Question 13
5 pts
The present value (PV) of a stream of cash flows is the _______ the present values of each individual cash flow

difference between

product of

sum of

same as

Question 14
5 pts
As the number of periods increases, present value (increases\decreases\stays the same).

increases

decreases

stays the same

is unrelated

Question 15
5 pts
When a constant cash flow will occur at regular intervals for a finite number of periods of time, it is called a(n) __________.

annuity

perpetuity

interest payment

principle payment

Question 16
5 pts
When a constant cash flow will occur at regular intervals forever, it is called a(n) ___________.

annuity

perpetuity

interest payment

principle payment

Question 17
5 pts
The NPV measures the ______ change in shareholder wealth that arises from undertaking a project.

consistent

dollar

annual

semi-annual

Question 18
5 pts
When calculating the present value of either a future single sum or a future annuity, the applicable interest rate is usually called the _______ rate

compounding

inverted

market

discount

Question 19
5 pts
To endow a perpetuity is the same as calculating the present value (PV) of a perpetuity. Say you want to endow an annual graduation party at your alma mater. You want the event to be a memorable one, so you budget $30,000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one yearâs time, how much will you need to donate to endow the party?
The formula for PV of a perpetuity = C\r; = $30,000 \ 0.08; =

$3,750

$37,500

$375,000

$3,750,000

Question 20
5 pts
With an Ordinary Annuity, payments are required at the ________ of each period. An example of this is bonds which usually pay coupon payments at the end of every six months until the bond's maturity date.

beginning

middle

end

payments are not required

Question 21
5 pts
Sales of securities that the seller does not own is called a:

stop-loss order

short sale

limit order

maintenance margin

Question 22
5 pts
What is the name of the market where money market securities, bonds, and mortgages are originated and traded?

debt securities market

foreign exchange market

derivative securities market

equity securities market

Question 23
5 pts
If an investor feels the price of a stock will decline in the future, which trade should the investor undertake?

market order

buy on margin

limit order

short sale

Question 24
5 pts
For risk averse investors, how much return is expected for taking on more risk?

lower

equal

zero

higher

Question 25
5 pts
A ___________________ is a highly regulated document which details the issuers operations and finances and must be provided to each buyer of a newly issued security.

Prospectus

An underwriting agreement

A best efforts agreement

none of the above

Question 26
5 pts
Which of the following statements about liquidity ratios is true?

The lower the quick ratio relative to the current ratio, the safer a firm is in terms of liquidity.

The higher the current ratio, the more likely a firm is able to pay its short-term obligations.

The quick ratio is always between 0 and 1.

All the above statements are true.

Question 27
5 pts
The ability of a firm to meet its short-term debt obligations as they come due is indicated by which of the following ratios:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 28
5 pts
Which one of the following financial statements reports a firmâs assets and the claims on assets?

balance sheet

income statement

statement of changes in financial position

cash flow statement

Question 29
5 pts
The extent to which assets are used to support sales is indicated by which of the following ratios:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 30
5 pts
The extent to which assets are financed by borrowed funds and other liabilities is indicated by:

liquidity ratios

asset utilization ratios

financial leverage ratios

profitability ratios

Question 31
5 pts
The basic price that equates the demand for and supply of loanable funds in the financial markets is the __________:

interest rate

yield curve

term structure

cash price

none of the above

Question 32
5 pts
Federal obligations usually issued for maturities of two to ten years are called:

Treasury bonds

Treasury notes

Treasury bills

Agency issues

Question 33
5 pts
An increase in the demand for loan-able funds, holding supply constant, will cause interest rates to:

increase

decrease

stay the same

none of the above

Question 34
5 pts
As interest rates rise, the prices of existing bonds will:

rise

stay the same

fall

either a or b

Question 35
5 pts
In an inflationary period, interest rates have a tendency to:

rise

fall

stay the same

act erratically

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Financial Modelling 2557A/B Lecture Notes - Lecture 3: Arbitrage, Risk Management

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