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JiangHan · 2023年04月26日

一道题

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2022070602000014

问题如下：

The treasurer of a London-based insurance company expects that 3 years from today the company will receive GBP 800,000. The treasurer plans to invest the funds for 1 year after that and decides to lock in a rate of return on the funds at today’s forward rate for the period. The current 3-year and 4-year spot rates are 1.5% and 2% respectively, and the company can borrow and lend at these rates. Assuming continuous compounding, how much interest income will the company earn in the 1-year period beginning 3 years from today, and what transactions should the treasurer enter into today in order to lock in this return?

选项：

A.

Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,000.

B.

Lend at the 3-year spot rate and borrow at the 4-year spot rate to earn a return of GBP 28,000.

C.

Borrow at the 3-year spot rate and lend at the 4-year spot rate to earn a return of GBP 28,119.

D.

Lend at the 3-year spot rate and borrow at the 4-year spot rate to earn a return of GBP 28,119.

解释：

中文解析：

A正确。从第3年年末至第4年年末的远期利率：

F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}

=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%

或者，𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).

英镑3.5%的利率等价于在第1年有28000英镑。为了获得这些利息，公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年。

---------------------------------------------------------------------------------------------------------------------------------

A is correct. The forward rate for the period from the end of year 3 to the end of year 4 is:

F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}

=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%

Alternatively, 𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).

3.5% interest on the GBP 800,000 invested equals GBP 28,000 in 1 year. To earn this

interest, the company would need to borrow GBP 800,000 today at 1.5% for 3 years and

invest the proceeds at 2% for 4 years.

B is incorrect. The company needs to borrow at the 3-year spot rate and lend at the 4-

year spot rate.

C and D are incorrect. GBP 28,119 is the interest income if annual compounding is used

instead of continuous compounding

老师，这个题不明白，28000是怎么算出来的啊

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2 个答案
已采纳答案

品职答疑小助手雍 · 2023年04月28日

1.5%和2%是3年和4年的spot rate，是用来计算3-4年的forward rate的。

这题的操作思路是先借80万借3年，投出去4年。然后在第三年底的时候收到80万就把借款的本金还了，投资出去的钱不变。

问最后赚多少钱，其实最后赚的钱就等同于3-4年之间的forward rate赚到的钱。

品职答疑小助手雍 · 2023年04月27日

同学你好，前面通过3年和4年的spot rate，求出来3-4年的forward rate 等于3.5%。

那么3-4年期间这一年，800000投资就能赚800000*3.5%=28000

JiangHan · 2023年04月27日

但是题目的意思不是说三年之后公司有800000磅吗，为什么答案是现在借入800000磅呢，还有一个疑问，题目给的1.5％，2.5％的利率有什么用呢

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NO.PZ2022070602000014 问题如下 The treasurer of a Lonn-baseinsurancompany expects th3 years from toy the company will receive G800,000. The treasurer plans to invest the fun for 1 yeafter thancis to loin a rate of return on the fun toy’s forwarrate for the perio The current 3-yean4-yespot rates are 1.5% an2% respectively, anthe company cborrow anlenthese rates. Assuming continuous compounng, how muinterest income will the company earn in the 1-yeperiobeginning 3 years from toy, anwhtransactions shoulthe treasurer enter into toy in orr to loin this return? A.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,000. B.Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,000. C.Borrow the 3-yespot rate anlenthe 4-yespot rate to earn a return of G28,119. Lenthe 3-yespot rate anborrow the 4-yespot rate to earn a return of G28,119. 中文解析A正确。从第3年年末至第4年年末的远期利率 F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%或者，𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).英镑3.5%的利率等价于在第1年有28000英镑。为了获得这些利息，公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年。---------------------------------------------------------------------------------------------------------------------------------A is correct. The forwarrate for the periofrom the enof ye3 to the enof ye4 is:F=R2T2−R1T1T2−T1F=\frac{R_{2} T_{2}-R_{1} T_{1}}{T_{2}-T_{1}}F=T2​−T1​R2​T2​−R1​T1​​=0.02∗4−0.015∗34−3=0.035 or 3.5%=\frac{0.02 * 4-0.015 * 3}{4-3}=0.035 \text { or } 3.5 \%=4−30.02∗4−0.015∗3​=0.035 or 3.5%Alternatively, 𝐹 = 𝑙𝑛(𝑒𝑥𝑝(0.02 ∗ 4)/𝑒𝑥𝑝(0.015 ∗ 3)).3.5% interest on the G800,000 investeequals G28,000 in 1 year. To earn thisinterest, the company woulneeto borrow G800,000 toy 1.5% for 3 years annvest the procee 2% for 4 years.B is incorrect. The company nee to borrow the 3-yespot rate anlenthe 4-yespot rate.C anare incorrect. G28,119 is the interest income if annucompounng is usensteof continuous compounng 公司需要现在借入800000英镑，用1.5%的利率借3年期，并且把钱用2%的利率投资4年，这些操作就是为了锁定3.5%的远期利率吗？

2023-04-12 14:46 1 · 回答