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薛真 · 2020年10月12日

问一道题：NO.PZ2020012005000038

  1. FRM I
  2. Financial Markets And Products

问题如下：

Suppose that the storage costs for crude oil are USD 2 per barrel per year payable at the beginning of the year. The current spot price is USD 75, and the two-year futures price is USD 72. The risk-free interest rate is 8% per annum (compounded annually). Estimate the convenience yield of crude oil per year.

选项：

解释：

The present value of the storage costs per barrel over two years is

2 + 2/ 1.08 = 3.85

The convenience yield Y is given by solving:

72=(75+3.85)∗(1.081+Y)272 = (75 + 3.85) * (\frac{1.08}{1+Y})^2

The solution is

Y=(78.8572)1/2∗1.08−1=0.130Y = (\frac{78.85}{72})^{1/2}*1.08-1=0.130

that is, the convenience yield is about 13% per year.

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1 个答案

品职答疑小助手雍 · 2020年10月12日

嗨，从没放弃的小努力你好：


本来storage cost可以直接当成Y的减项来算的，不过这题比较特殊，是直接给了两年每年期初2的数值，所以解析就把storage cost求现值直接加进期初S0里面来算了。

总的来说就是storage cost算不算进S0计算（是不是要一起剔除convenience yield的影响）的问题，我觉得都可以，这个误差考试不影响选择。


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NO.PZ2020012005000038 问题如下 Suppose ththe storage costs for cru oil are US2 per barrel per yepayable the beginning of the year. The current spot priis US75, anthe two-yefutures priis US72. The risk-free interest rate is 8% per annum (compounannually). Estimate the convenienyielof cru oil per year. The present value of the storage costs per barrel over two years is2 + 2/ 1.08 = 3.85The convenienyielY is given solving: 72=(75+3.85)∗(1.081+Y)272 = (75 + 3.85) * (\frac{1.08}{1+Y})^272=(75+3.85)∗(1+Y1.08​)2The solution is Y=(78.8572)1/2∗1.08−1=0.130Y = (\frac{78.85}{72})^{1/2}*1.08-1=0.130Y=(7278.85​)1/2∗1.08−1=0.130 this, the convenienyielis about 13% per year. No.PZ2020012005000038 (问答题)来源: 原版书Suppose ththe storage costs for cru oil are US2 per barrel per yepayable the beginning of the year. The current spot priis US75, anthe two-yefutures priis US72. The risk-free interest rate is 8% per annum (compounannually). Estimate the convenienyielof cru oil per year.问题按照课程上和前面习题的答案，convenienyiel是我持有这个资产，能立刻投入生产给我带来的收益这题我可以理解为是short position，我手上有spot，我要承担仓储费，我也可以获得convenienyiel以为什么是除以（1+Y）^2，我可以获得这个convenienyiel难道不是乘以（1+Y）^2吗？（75+3.85）*（1+Y）^2，得不到的是减去或除以，得到的是加上或乘以

2023-12-08 10:00 1 · 回答

NO.PZ2020012005000038 问题如下 Suppose ththe storage costs for cru oil are US2 per barrel per yepayable the beginning of the year. The current spot priis US75, anthe two-yefutures priis US72. The risk-free interest rate is 8% per annum (compounannually). Estimate the convenienyielof cru oil per year. The present value of the storage costs per barrel over two years is2 + 2/ 1.08 = 3.85The convenienyielY is given solving: 72=(75+3.85)∗(1.081+Y)272 = (75 + 3.85) * (\frac{1.08}{1+Y})^272=(75+3.85)∗(1+Y1.08​)2The solution is Y=(78.8572)1/2∗1.08−1=0.130Y = (\frac{78.85}{72})^{1/2}*1.08-1=0.130Y=(7278.85​)1/2∗1.08−1=0.130 this, the convenienyielis about 13% per year. 助教你好，我看见题目第一句说说到cost是年初发生的，那convenienyiel每年何时发生？

2023-06-08 22:33 1 · 回答

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2023-02-23 15:10 1 · 回答

请问一下这道题带公式的话为什么U要加上 2 / 1.08 ? 2 + 2/ 1.08 = 3.85

2020-02-10 23:23 1 · 回答