Quiz continued on Forward and Futures Pricing - 2

Proudly I can say that i do not have a habit of copying and pasting the questions from anywhere. I have framed the questions, based on the formulae used in core readings (Hull chapter -5) and (McDonald chapter) on forwards and futures pricing.

Before attempting these questions, please consider that the risk-free rate of interest is quoted in continuous terms and it is quoted per annum.

Understand the difference between each formula and how it changes and why it changes with change of scenarios and circumstances.

A trader who is already holding an asset, entered into a short position in futures contract with an agreed period of 3 months. The opportunity cost to the trader is equal to the risk-free rate of interest of 5.5% (annual terms). The cost of acquisition to the holder is $40. What should be the fair price quoted in the futures market? Solution: S0 x ert 40 x ert 40 x e0.055 x 0.25 40 x 1.013845 $40.55

A trader who is already holding an asset, entered into a short position in futures contract with an agreed period of 6 months. The risk-free rate of interest is 5.5% per annum. The asset was acquired for a price of $80. The trader who is holding the asset is expecting $2 as income on the asset on the first day of agreement. Calculate the fair value of the futures price quoted in the market? Solution: (S0 –I) e(rt) ($80-$2)xe(rt) $78 x e0.055x0.5 $80.175 Here the income of $2 is received on the first day of initiation of the contract. So there is no need to convert it again into present value. This is where a student has to be cautious.

A trader who is already holding an asset, entered into a short position in futures contract with an agreed period of 6 months. The risk-free rate of interest is 5.5% per annum. The asset was acquired for a price of $80. The trader who is holding the asset is expecting $4 as income on the asset on the last day of agreement. Calculate the fair value of the futures price quoted in the market? Solution: The income is expected at the end of the maturity. So we need to calculate its present value at the initiation of the contract. Please understand that the value of the asset is $80 on the first day of the contract. So find the value of $4 (income value also on the first day). For which, we need to calculate its present value using risk-free rate. The present value of $4 is: $4 x e-rt; $4 x e-0.055x0.5; Its value is $3.89. Now, use the formula: (S0 –I) e(rt) ($80-3.89) e(rt) $76.11 x e(0.055x0.5) $78.23

A trader who is already holding an asset, entered into a short position in futures contract with an agreed period of 6 months. The risk-free rate of interest is 5.5% per annum. The asset was acquired for a price of $80. The trader who is holding the asset is expecting $4 as income in next 3 months. Calculate the fair value of the futures price quoted in the market? Solution: The income is expected at the end of the maturity. So we need to calculate its present value at the initiation of the contract. Please understand that the value of the asset is $80 on the first day of the contract. So find the value of $4 (income value also on the first day). For which, we need to calculate its present value using risk-free rate. The present value of $4 is: $4 x e-rt; $4 x e-0.055x0.25; Its value is $3.95 Now, use the formula: (S0 –I) e(rt) ($80-3.95) e(rt) $76.05 x e(0.055x0.5) $78.17

A trader who is already holding an asset, entered into a short position in futures contract with an agreed period of 6 months. The risk-free rate of interest is 5.5% per annum. The asset was acquired for a price of $80. The trader who is holding the asset is expecting 3% as income yield on the asset during the period of holding. Calculate the fair price of the contract? Solution: Here the income is given in the form of yield. The income can either be expressed in dollar terms or also in % terms. When the income is expressed in dollar terms, we use: (S0 –I) e(rt) (Please S0 is at Time-T0 and therefore even income (I) should also be calculated at T0. When the income is expressed in yield or % terms, we use: S0 x e(r-q)T; Here the income while holding the asset is expressed in % terms. We use: S0 x e(r-q)T . This gives us: $80 x e(0.055-0.03)0.5 = $81.00;

Please do not go to the solution directly. First understand yourself, where you are struggling. Do not mug up the formulae. Understand the logic behind that formula.

Please attempt the remaining questions in the next two days. With that we will be able to complete forward and futures pricing.