AFM474 - Derivatives Notes.docx

9 Pages
110 Views

Department
Accounting & Financial Management
Course Code
AFM 474
Professor
Hilary B Bergsieker

This preview shows pages 1,2 and half of page 3. Sign up to view the full 9 pages of the document.
Description
Derivatives Why?  Allow easier methods to short sell a stock without a broker lending it.  Facilitates hedging easily  Allows the ability to take long/short position on less available commodities (Rice, Cotton, etc.) Three types of traders Hedger – Attempts to reduce exposure to operating risk within firm Speculator – Profiting from a bet that markets will move in a certain direction Arbitrageurs – Profiting without any risk Forward contracts Forward – A binding agreement (obligation) to buy/sell an asset or a commodity in the future, at a price set today Contract specifies: Features and quantity of the asset to be delivered Delivery logistics (time/date/place) Underlying – Asset exchanged at maturity Long = S T K Short = K - ST T Forward Price with No storage cost: F =0S (0 + r ) F0= Spot price + Opportunity cost Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk E.g. Spot price is $450, risk free rate = 4%, F = $477. Is there arbitrage opportunity? (4% * 1) 0 Theoretical forward price = 450 e = 468.34 => There is an arbitrate opportunity. How? Time 0 1 Year Sell 1 forward contract 0 477 - ST Borrow $450 450 (468.36) Buy gold spot and sell it at time T (450) S T 0 8.64 If 0 = $460 Time 0 1 Year Buy 1 forward contract 0 ST– 460 Short 1oz. gold 450 -S T Borrow/repay the bank (450) 468.36 0 8.36 E.g. Bond is 1,074 and Forward price is 1,060. There are two $50 coupon payments semi-annually. Rates are 8% (6mo.) and 9% (1yr) with continuous compounding. Theoretical forward price: 1074 * e Arbitrage follows: Time 0 6 month 1 Year Buy Forward 0 0 -1060 + S T Sell bond 1,074 -50 - 50 -TS Borrow/repay the bank - 48.04 50 0 Borrow/repay the bank -1,025.96 0 1,122.58 0 0 12.58 Spot $600, rate is 5% (1 year continuous compounding). Storage cost is 2% continuously compounding proportionate to spot price. What is 1 year forward price? F0= 600e (5% + 2%)= 643.50 If 0 = 650, how is arbitrage realized? F theoretical < F0 so we take a short position Today 1 year Sell 1 forward contract 0 650 – ST 5% Borrow $612.12 612.12 -612.12e = -643.50 Buy underlying including storage fees 600*(e -1) -612.12 ST 0 6.50 Convenience yield – Ownership of physical commodity provides benefits that are not obtained by the holders of contracts for future delivery. (c–y )T F0= S 0 S0 < F0: Contango occurs when c > y S0 > F0: Backwardation occurs when y >c Currency Forwards F0= S 0 (r-rf)T r : T-year domestic risk-free interest rate rf : T-year foreign risk-free interest rate S0: Spot exchange rate e.g. S0 = 2.30 r = 0.04fr = 0.05, T = 1 (0.04 – 0.05) F0= 2.30e = 2.277 C$/£ Synthetic Long Currency Forward Today One Year 1 2 e.g. The 8 month rate in the U.S. is 5% with semi-annual compounding. The 8 month interest rate in France is 6% compounded continuously. The spot exchange rate is 1.89 US$/€. The 8 month forward exchange rate is 1.95 is there an arbitrage opportunity? S0= $1.89/€ F0= $1.95/€ RC= mln(1+Rm/m) = 2 ln(1+0.05/2) = 0.0494 (convert to domestic continuous rate) F hypothetical = S e (r-rf)= 1.89e (0.0494 – 0.06)= 1.8767 $/€ 0 Today 8 Months Sell Forward 0 1.95 - ST Borrow 0.9608€ * 1.89 = 1.8159USD @ 4.94% continuous 1.8159 -1.8767 Convert borrowed USD and invest in € for 8 months -1.8159 +ST 0 0.0733 Valuing a Forward Contract Value of a long forward contract f = (0 –K)e-rT -rT Value of a short forward contract f = (K –F0)e e.g. 1 year long forward contract on non-dividend paying stock was entered when stock is at $40 and the risk free rate is 10% p.a., continuously compounded. What is forward price and initial value of forward contract? f = 0 0 F0= 40e (10%) = 44.20 Six months later stock price is $45, what is forward price and value of forward contract? F6m = 45e (10%)(0= 47.31 –rf -(10%)(.5) f6m = F6m– F 0 = 47.31 – 44.20 e = 2.96 Margin Requirements Margin requirements are established based on the risk level of daily transactions. Underlyings which are highly volatile and prone to large daily fluctuations in spot price will have larger margin requirements relative to a more stable underlying. e.g. A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstance could they withdraw $1500 from the margin account? Initial value: 250 cents / 100 * 5000 = 12,500 3000/12500 = MI% Trigger a margin call 1000/12500 = 8% 250 * 8% = 20 cent drop $1500 margin withdrawn 1500 /12,500 = 12% 250 * 12% = 30 cent gain e.g. Suppose there are no storage costs for crude oil and the interest rate for borrowing or lending is 5% per annum. How could you have made money on January 8, 2007 by trading June 2007 and December 2007 contracts on crude oil? Prices below Open High Low Settle Change Jun 60.20 61.33 59.08 60.01 0.10 Dec 62.78 64.08 62.10 62.94 0.28 th 1/2 1/2 June 30 S =060.01 Fhypofor June = June(1+5%) = 60.01(1.05) = 61.49 January June December Long 1 June future 0 SJune– 60.01 0 Short 1 Dec future 0 0 62.94 - S Dec Borrow 60.01 @ 5% buy oil in June 0 60.01 -61.49 Dec delivery 0 -60.01 SDec 0 0 1.45 Why do we need derivatives? CDS Trading Initiation (event)  Creditworthiness – exchange rate drops, foreign reserves, credit rating  Risk – regional CDS index, global CDS index  Ex Debt – GDP Hypothesis Effect driven by opacity & riskiness Benefits of CDS Initiation  Facilitates risk sharing expansion of the risk return space  Allows hedging of adverse selection risk – Adverse selection, systematic risk Costs  Many more to infer asset value  Not that options push down the stock price but true value MSCI Emerging Markets Exposure – ETF vs EM forwards 1. Forward – Stack & Roll a. Liquidity b. Transaction costs 2. Full capitals w/ ETF vs. Margin a. Cost of Capital needs to be put up front for ETFs 3. Tracking Error a. Trading timing b. Premium/discount on ETF trading c. Dividend forecast error 4. Short position access is easier for fo
More Less
Unlock Document

Only pages 1,2 and half of page 3 are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit