Chartered Financial Analyst Level 1

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Explanation:

The correct answer is A ($126.78). The futures price for a commodity with known storage costs is calculated as:

$f_0(T) = [S_0 + PV_0(C)] \times (1 + r)^T$

Where:

$PV_0(C)$ is the present value of the storage cost, discounted from the settlement date to today.
$S_0$ is the spot price of the commodity.
$r$ is the risk-free rate.
$T$ is the time to settlement.

For this question:

Calculate the present value of the storage cost: $PV_0(C) = \`$5` \times (1 + 3\%)^{-182/365}$
Plug into the futures price formula: $f_0(T) = [\`$120` + PV_0(C)] \times (1 + 3\%)^{182/365}$ $f_0(T) = \`$126.78`$

Option B ($126.86) is incorrect because it does not discount the storage cost to its present value. Option C ($126.93) is incorrect because it compounds the storage cost instead of discounting it.

Explanation:

The correct answer is A ($126.78). The futures price for a commodity with known storage costs is calculated as:

$f_0(T) = [S_0 + PV_0(C)] \times (1 + r)^T$

Where:

$PV_0(C)$ is the present value of the storage cost, discounted from the settlement date to today.
$S_0$ is the spot price of the commodity.
$r$ is the risk-free rate.
$T$ is the time to settlement.

For this question:

Calculate the present value of the storage cost: $PV_0(C) = \`$5` \times (1 + 3\%)^{-182/365}$
Plug into the futures price formula: $f_0(T) = [\`$120` + PV_0(C)] \times (1 + 3\%)^{182/365}$ $f_0(T) = \`$126.78`$

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An analyst gathers the following information:

The current spot price of crude oil is `$120` per barrel.

The risk-free rate is 3% with annual compounding.

A futures contract has 182 days until settlement.

The storage cost is `$5` per barrel, payable at the end of the futures contract.

Based on 365 days per year, the futures price per barrel of crude oil is closest to:

Exam-Like

$126.78

100.0%

$126.86

0.0%

$126.93