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ECMC71-11Mid1A

# ECMC71-11Mid1A - UNIVERSITY OF TORONTO AT SCARBOROUGH...

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UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Term Test-1 (Solutions) A. Mazaheri Instructions : This is a closed book examination. You are allowed one side of a one 4”x6" crib card and the use of a calculator. Show all your work otherwise you will not get full credit . Make sure you allocate time appropriately . You have 2 hour. Good Luck! NAME: _____________________________________________ ID#: _____________________________________________ Answer all the following 4 questions: Q-1 _______________ (25 points) Q-2 _______________ (15 points) Q-3 ________________ (20 points) Q-4 _______________ (20 points) Total _____________ (80 points)

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2 Question-1 (25 Points) Short questions . 1a: [5 Points] Is the futures price of the S&P 500 index greater than or less than the expected future value of the index? Briefly explain your answer? Solution: We have again F = E(ST)e(r-r k )(T-t).=> F = E(ST)e-(risk Premium of the underlying)(T-t). Since the S&P has a positive risk premium the futures on S&P always underestimates the expected future spot. 1b: [5 Points] You observe the following data today: Money market: Forward Oil prices: r = 5% F = \$90/ barrel Where r is the 1-year spot rate (continuously compounded), and F, is the 1-year forward prices – all observed today. Suppose you are currently long a forward oil contract with an exercise price of 70. What is the value of your contract? Solution: 025 . 19 ) 70 90 ( ) ( 05 . 0 = × - = × - = - - e e K F V rT
3 1c. [5 Points] The effect of a financial hedge is to replace uncertainty about the future spot price with basis risk. True/False, explain using formulas when required. True because: Without Hedge: Payoff = St With Hedge: Payoff = St-(Ft-Fo) = Fo+(St-Ft) = Fo+bt So the hedger is replacing the spot price with that of the basis. 1d. [5 points] The spot price of oil is \$94 per barrel. The futures price on a six months oil contract is \$85. Suppose the T-bill rate is 3% per year and the storage cost is 1% both C.C. What is the net convenience value of oil over the next year? Explain briefly what it implies. [ ] 2413 . 0 5 . 0 ) 85 ln( 5 . 0 01 . 0 5 . 0 03 . 0 ) 94 ln( ) ln( ) ln( 0 0 ) ( 0 0 - × + × + = - × + × + = = - + T F T u T r S y e S F T y u r The convenience yield measures the value of holding the good today (in other words the opportunity cost of the consumption goods, the convenience driven from holding the underlying…). High convenience yields are consistent with short supply (or high marginal benefit from having the good for consumption). The convenience value if the yield multiplied by the price and reflect how much you are giving up by holding the spot

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