Assignment Risk Essay

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Exercise 2.27: A company enters into a short futures contract to sell 5000 bushels of wheat for 450 cents per bushel. The initial margin is $3000 and the maintenance margin is $2000. a. What price change would lead to a margin call? Loss: $3000 - $2000 = $1000 * F = $ 1000 5000 = $0.2 = 20 cents/bushel * F2= $450 + $ 20 = $470 b. Under what circumstance could $1500 be with-drawn from the margin account? F = 15005000 = $ 0.3 = 30 cents F2 < F1 => F2 = F1 – 30 cents = 450 cents – 30 cents = 420 cents Exercise 4.28: The 6-month, 12-month, 18-month, 24-month zero rates are 4%, 4.5%, 4.75% and 5% with semiannual compounding. a. What are the rates with continuous compounding? 6-month: Rc = m x ln [ Rmm+1] = 2 x ln [0.04/2 +1] = 3.96% 12-month: Rc = m x ln [ Rmm+1] = 2 x ln [0.045/2 +1] = 4.45% 18-month: Rc = m x ln [ Rmm+1] = 2 x ln [0.0475/2 +1] = 4.69% 24-month: Rc = m x ln [ Rmm+1] = 2 x ln [0.0475/2 +1] = 4.69% b. What is the forward rate for the 6-month period beginning in 18-month? Maturity (months) | Rate (% per annum) | Forward Rate | 6 | 3.96 | | 12 | 4.45 | 4.94 | 18 | 4.69 | 5.17 | 24 | 4.94 | 5.69 | c. What is the value of FRA that promises to pay you 6% (compounded semi-annually) on a principal of $1 million for 6-month period starting in 18 months? K = 6% (compounded semi-annually) F = 5.69% (continuous compounding) => Rm = m x ( eRc/m – 1) =2 x ( e0.00569/2 – 1) = 5.77% So, the value of FRA = $1 million x (6% - 5.77%) x 0.5 x e-0.0494 * 2 = $ 1,041.812456 Exercise

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