《金融工程学》实验指导书.doc

1、153 金融工程学实验指导书金融工程学实验指导书 Guide on the experiments of financial engineering 154 实验一实验一验证货币供应量（验证货币供应量（Measures of Money Supply）M1、 M2、M3 的大小的大小 一一. 目的与要求：目的与要求： 1. 复习理解 Measures of Money Supply 的概念，Measures of Money Supply的变化对股票 与国债市场的影响； 2. 将 M1，M2，M3 数据利用 EXCEL 描绘在一张图上。通过实验进一步理解 M1， M2，M3 的概念。比较 M1

2、，M2，M3 的相对大小。 3. 学会利用 google 、百度、必应等搜索工具查找有关基本概念，起到辅助学习的功 能。 Financial Data Banka BeginningMeasures of Money SupplyCommercial ofPaper YearQuarterM1M2M3Outstanding 19801$389.0$1532.8$1785.3$116.718 2387.61548.01809.2120.865 3394.51609.21865.0122.259 4410.81653.61918.2122.383 19811416.11681.71978.2128

3、.656 2433.71738.12044.6134.229 3430.11760.12094.0151.013 4433.01798.82143.3164.026 19821448.61840.92204.0165.118 2452.31880.72258.1171.709 3451.31923.42320.2180.669 4468.41968.22382.1170.253 19831482.12008.12401.4165.705 2496.52075.12454.5170.659 3514.72127.42508.1172.199 4517.92162.02562.0175.924 1

4、9841523.02206.22720.5182.801 2535.32242.52709.8209.535 3545.62281.42856.2221.647 4545.52317.22917.3227.960 19851562.72398.33020.5245.322 2575.02428.03057.5255.236 3595.82490.23113.6262.769 4611.12533.43179.3280.930 19861627.12568.43222.1302.160 2646.12620.93228.3297.108 3676.12699.13375.1311.435 470

5、1.22765.23444.5329.516 19871737.62822.03515.7336.996 2750.42838.53540.8346.769 3747.62847.73583.5348.247 4756.62891.13657.7360.013 19881758.92925.03686.0380.475 2770.22992.73763.9406.484 3782.33025.93834.9423.599 4783.53037.53868.8424.160 19891786.33065.73924.1471.066 2783.23081.33958.1494.292 3777.

6、13117.44002.4506.095 4787.63176.44027.3507.902 19901794.73229.14044.7533.137 2807.43271.84065.1544.481 3809.03287.84076.9545.849 4820.13318.84091.7557.731 19911826.73332.94126.5569.378 2842.13385.24174.8542.603 3859.63390.54148.5544.048 4879.43398.84146.4531.886 19921910.33448.24174.4533.342 2942.93

7、468.24175.7537.020 3960.53462.24163.0547.242 41007.23496.54183.3557.915 155 199311033.23486.94140.6542.438 21043.23474.64142.0535.966 31085.33516.84165.1539.149 41116.43531.04177.7550.947 199411133.63571.04230.9559.443 21141.23587.54222.1553.355 31153.33603.34250.3572.925 41148.53591.74257.9592.518

8、199511148.83626.94327.7612.554 21149.73642.94377.9651.128 31145.03714.64489.8657.938 41131.83642.14557.5673.392 199611119.13686.04611.8685.797 21123.73736.14692.4710.749 31108.43742.94720.0734.731 41075.73773.44816.3757.718 199711076.14041.35383.7775.371 21065.13904.75067.5838.366 31063.23934.45100.

9、8864.758 41076.14041.35383.7908.640 199811081.94126.65537.5973.761 21075.94193.05625.41049.222 31071.84213.25653.01091.554 41078.54339.65843.21152.337 199911093.44402.05996.91163.303 21108.44490.06104.11204.627 31099.44543.96182.41221.020 41093.44583.46218.61274.3 200011121.14675.76513.71403.1 21115

10、.54759.46636.11449.1 31103.24779.06731.81516.2 41095.34871.46909.71557.7 11088.24945.17101.31625.3 200121113.15101.17311.31511.3 31123.55208.97581.21501.1 实验实验 2 验证主利率（验证主利率（PrimePrime RateRate）、贴现率（）、贴现率（DiscountDiscount RateRate）、联帮基）、联帮基 金利率（金利率（FederalFederal FundsFunds RateRate）等利率的大小关系）等利率的大小关

11、系 一. 目的与要求： 1、将 Prime Rate，Discount Rate、Federal Funds Rate，Three-Month CommercialPaper Rate（Annualized），Three-Month Certificate of Deposit Rate（Annualized）描绘在一张图上。通过实验进一步理解 Prime Rate，Discount Rate、Federal Funds Rate，Three-MonthCommercialPaper Rate （Annualized），Three-Month Certificate of Deposit Ra

12、te（Annualized）的概 念，希望能对比分析它们利率差的原因。 2、将 Three-Month Eurodollar Rate（Annualized），Three-Month Treasury Bill Rate（Annualized），One-Year Treasury Bill Rate（Annualized），Five- Year TreasuryNote Yield，Ten-YearTreasuryBond Yield，Thirty-Year TreasuryBond Yield，Municipal Bond Yields (AAA)与Municipal Bond Yields

13、 (BAA) 描绘在一张图上。通过实验进一步理解 Three-Month Eurodollar Rate（Annualized），Three-Month Treasury Bill Rate（Annualized），One-Year Treasury Bill Rate（Annualized），Five-Year TreasuryNote Yield，Ten-Year TreasuryBond Yield，Thirty-YearTreasuryBond Yield，Municipal Bond 156 Yields (AAA)与Municipal Bond Yields (BAA)的概念，希望

14、能对比分析它们 利率差的原因。 3、将任意几个变量（如 Prime Rate，Discount Rate、Federal Funds Rate 等） 描绘在一张图上。通过实验进一步理解它们的概念，希望能对比分析它们利率差的原 因。 二. 数据 Data source: Federal Reserve Bulletin, numerous issues. Three-MonthThree-Month BeginningCommercialCertificate of ofPrimeDiscount RateFederalPaper RateDeposit Rate YearQuarterRate

15、(FRB of NY)Funds Rate(Annualized)(Annualized) 1980115.25%12.00%13.82%13.04%13.39% 219.77%13.00%17.61%15.78%16.14% 311.48%11.00%9.03%8.41%8.65% 413.79%11.00%12.81%12.52%12.94% 1981120.16%13.00%19.08%16.58%17.19% 217.15%13.00%15.72%14.56%15.08% 320.39%14.00%19.04%17.00%17.76% 418.45%14.00%15.08%14.85%

16、15.39% 1982115.75%12.00%13.22%13.09%13.51% 216.50%12.00%14.94%14.06%14.44% 316.26%12.00%12.59%12.94%13.44% 412.52%10.00%9.71%9.20%9.51% 1983111.16%8.50%8.68%8.17%8.36% 210.50%8.50%8.80%8.53%8.63% 310.50%8.50%9.37%9.25%9.50% 411.00%8.50%9.48%8.99%9.18% 1984111.00%8.50%9.56%9.20%9.42% 211.93%8.50%10.2

17、9%10.18%10.41% 313.00%9.00%11.23%11.19%11.56% 412.58%9.00%9.99%10.12%10.38% 1985110.61%8.00%8.35%8.03%8.14% 210.50%8.00%8.27%8.37%8.49% 39.50%7.50%7.88%7.56%7.64% 49.50%7.50%7.99%7.80%7.88% 198619.50%7.50%8.14%7.71%7.82% 28.83%7.00%6.99%6.60%6.60% 38.16%6.50%6.56%6.33%6.37% 47.50%5.50%5.85%5.68%5.69

18、% 198717.50%5.50%6.43%5.84%5.87% 27.75%5.50%6.37%6.45%6.52% 38.25%5.50%6.58%6.65%6.70% 49.07%6.00%7.29%7.89%8.02% 198818.75%6.00%6.83%6.87%6.92% 28.50%6.00%6.87%6.86%6.92% 39.29%6.00%7.75%7.82%7.94% 410.00%6.50%8.30%8.24%8.36% 1989110.50%6.50%9.12%9.04%9.20% 211.50%7.00%9.84%9.81%9.94% 310.98%7.00%9

19、.24%8.68%8.76% 410.50%7.00%8.84%8.53%8.60% 1990110.11%7.00%8.23%8.10%8.16% 210.00%7.00%8.26%8.30%8.42% 310.00%7.00%8.15%7.99%8.10% 410.00%7.00%8.11%7.98%8.06% 199119.52%6.50%6.91%7.10%7.17% 29.00%5.50%5.91%6.07%6.06% 38.50%5.50%5.82%6.05%5.98% 48.00%5.00%5.21%5.35%5.33% 199216.50%3.50%4.03%4.07%4.05

20、% 26.50%3.50%3.73%4.04%4.00% 36.00%3.00%3.25%3.44%3.37% 46.00%3.00%3.10%3.30%3.26% 199316.00%3.00%3.02%3.25%3.19% 26.00%3.00%2.96%3.14%3.09% 36.00%3.00%3.06%3.20%3.16% 46.00%3.00%2.99%3.26%3.24% 199416.00%3.00%3.05%3.19%3.15% 26.45%3.00%3.56%4.05%4.01% 37.25%3.50%4.26%4.75%4.73% 47.75%4.00%4.76%5.51

21、%5.51% 199518.50%4.75%5.53%6.22%6.24% 29.00%5.25%6.05%6.12%6.11% 38.80%5.25%5.85%5.79%5.77% 48.75%5.25%5.76%5.82%5.79% 199618.50%5.25%5.56%5.40%5.39% 28.25%5.00%5.22%5.39%5.36% 157 38.25%5.00%5.40%5.53%5.53% 48.25%5.00%5.24%5.43%5.41% 199718.25%5.00%5.51%5.41%5.39% 28.30%5.00%5.56%5.71%5.71% 38.50%5

22、.00%5.52%5.65%5.66% 48.50%5.00%5.50%5.48%5.65% 199818.50%5.00%5.46%5.57%5.54% 28.50%5.00%5.45%5.48%5.56% 38.50%5.00%5.56%5.50%5.57% 48.12%4.50%4.68%5.00%5.14% 199917.75%4.50%4.63%4.77%4.89% 27.75%4.50%4.74%4.78%4.88% 38.00%4.50%4.99%5.00%5.34% 48.25%4.75%5.22%5.29%5.34% 200018.50%5.00%5.45%5.59%5.58

23、% 29.00%5.50%5.85%6.11%6.10% 39.50%6.00%6.54%6.49%6.56% 49.50%6.00%6.51%6.47%6.56% 200119.05%6.00%6.40%6.51%6.62% 27.80%4.50%5.3%5.02%5.89% 36.75%3.50%3.9%3.82%3.86% Three-MonthThree-Month BeginningEurodollarTreasury BillOne-YearFive-Year ofRateRateTreasury BillTreasury YearQuarter(Annualized)(Annua

24、lized)RateNote Yield 1980114.33%12.00%12.06%10.74% 217.81%13.20%13.30%11.84% 39.33%8.06%8.65%9.53% 413.55%11.62%12.49%11.86% 1981118.07%15.02%14.08%12.77% 215.95%13.69%14.32%13.99% 318.49%14.95%15.72%14.79% 416.34%13.54%15.38%15.41% 1982114.29%12.28%14.32%14.65% 215.18%12.70%13.98%14.00% 314.37%11.3

25、5%13.24%14.07% 410.43%7.71%9.32%10.80% 198318.97%7.86%8.62%10.03% 29.23%8.21%8.98%10.03% 310.00%9.08%10.20%11.21% 49.54%8.64%9.81%11.28% 198419.78%8.90%9.90%11.37% 210.83%9.69%10.90%12.37% 312.02%10.12%12.03%13.28% 410.77%9.74%10.90%12.06% 198518.37%7.76%9.02%10.93% 28.74%7.95%9.14%11.01% 37.89%7.08

26、%7.86%9.70% 48.08%7.16%8.01%9.69% 198618.02%7.07%7.73%8.68% 26.80%6.06%6.44%7.05% 36.54%5.83%6.27%7.06% 45.88%5.18%5.72%6.83% 198716.10%5.43%5.78%6.64% 26.73%5.64%6.50%7.57% 36.87%5.69%6.68%8.01% 48.29%6.13%7.59%9.08% 198817.11%5.81%6.99%8.18% 27.05%5.91%7.01%8.19% 38.09%6.73%7.75%8.66% 48.51%7.34%8

27、.11%8.51% 198919.28%8.27%9.05%9.15% 210.04%8.65%9.36%9.30% 38.85%7.88%7.89%7.83% 48.67%7.64%7.99%7.97% 199018.22%7.64%7.92%8.12% 28.44%7.77%8.40%8.77% 38.09%7.62%7.94%8.33% 48.06%7.17%7.55%8.51% 199117.23%6.22%6.64%7.70% 26.11%5.65%5.85%7.70% 36.01%5.58%6.31%7.91% 45.34%4.99%5.33%6.87% 199214.06%3.8

28、0%4.15%6.24% 24.05%3.75%4.30%6.78% 33.40%3.21%3.60%5.84% 43.30%2.86%3.30%5.60% 199313.22%3.00%3.50%5.83% 23.10%2.87%3.24%5.13% 33.17%3.04%3.47%5.09% 43.26%3.02%3.39%4.71% 199413.15%2.98%3.54%5.09% 24.00%3.68%4.57%6.52% 34.74%4.33%5.17%6.91% 45.52%4.95%5.75%7.40% 199516.23%5.71%6.59%7.76% 158 26.13%5

29、.65%5.88%6.86% 35.79%5.42%5.28%6.01% 45.81%5.28%5.28%5.86% 199615.40%5.00%4.82%5.36% 25.36%4.95%5.23%6.30% 35.49%5.15%5.52%6.64% 45.41%4.99%5.25%6.27% 199715.38%5.01%5.22%6.18% 25.70%5.16%5.64%6.76% 35.66%5.05%5.38%6.38% 45.63%4.97%5.17%5.93% 199815.61%5.06%5.32%6.22% 25.56%4.95%5.10%5.61% 35.57%4.9

30、8%5.13%5.52% 45.17%3.96%3.95%4.18% 199915.13%4.39%4.31%4.45% 24.87%4.29%4.50%5.08% 35.09%4.57%4.89%5.81% 45.48%4.68%5.00%5.80% 200015.94%5.32%5.75%6.50% 26.13%5.69%5.84%6.50% 36.67%5.96%6.08%6.18% 46.59%6.00%6.13%5.93% 16.43%5.77%5.60%5.28% 24.89%4.42%4.31%4.62% 33.73%3.49%3.57%4.81% BeginningTen-Ye

31、arThirty-YearMunicipal Bond Yields ofTreasuryTreasury YearQuarterBond YieldBond Yield(AAA)(BAA) 1980110.80%10.60%6.58%7.60% 211.47%11.40%7.95%9.19% 310.25%10.24%7.35%8.46% 411.75%11.59%8.38%9.41% 1981112.57%12.14%8.98%9.90% 213.68%13.20%9.78%10.85% 314.28%13.59%10.21%11.55% 415.15%14.68%12.05%13.34%

32、 1982114.59%14.22%12.30%13.95% 213.87%13.37%11.66%13.29% 313.95%13.55%11.47%13.17% 410.91%11.17%9.15%10.66% 1983110.46%10.63%9.00%10.98% 210.40%10.48%8.28%9.75% 311.38%11.40%8.70%10.06% 411.54%11.58%8.93%10.04% 1984111.68%11.75%9.00%10.10% 212.63%12.65%9.54%10.30% 313.36%13.21%10.10%10.61% 412.16%11

33、.98%9.72%10.51% 1985111.38%11.45%9.08%10.16% 211.43%11.47%8.92%9.95% 310.31%10.50%8.34%9.18% 410.24%10.50%8.58%9.54% 198619.19%9.40%7.74%8.79% 27.30%7.39%6.81%7.45% 37.30%7.27%7.24%7.95% 47.43%7.70%6.44%7.23% 198717.08%7.39%6.12%6.93% 28.02%8.25%7.20%8.29% 38.45%8.64%7.18%8.37% 49.52%9.61%7.90%8.85%

34、 198818.67%8.83%7.29%8.12% 28.72%8.95%7.33%7.82% 39.06%9.14%7.50%7.86% 48.80%8.89%7.25%7.72% 198919.09%8.93%7.23%7.67% 29.18%9.03%7.37%7.82% 38.02%8.08%6.69%7.17% 48.01%8.00%6.93%7.33% 199018.21%8.26%6.81%7.35% 28.79%8.76%7.04%7.43% 38.47%8.50%6.96%7.13% 48.72%9.03%7.23%7.43% 199118.09%8.27%6.57%7.1

35、7% 28.04%8.21%6.89%7.30% 38.27%8.45%6.82%7.18% 47.53%7.93%6.28%6.70% 199217.03%7.58%6.13%6.47% 27.48%7.96%6.36%6.85% 36.84%7.60%5.72%6.10% 46.59%7.53%6.10%6.51% 199316.60%7.34%5.91%6.28% 25.97%6.85%5.47%5.88% 35.81%6.63%5.27%5.74% 45.33%5.94%5.13%5.63% 199415.75%6.29%5.14%5.60% 26.97%7.27%5.44%5.87%

36、 37.30%7.58%5.88%6.26% 47.74%7.94%6.05%6.37% 159 199517.78%7.85%6.55%7.05% 27.06%7.36%5.74%5.98% 36.28%6.72%5.68%5.91% 46.04%6.37%5.74%5.95% 199615.65%6.05%5.27%5.59% 26.51%6.79%5.62%5.94% 36.87%7.03%5.83%5.96% 46.53%6.81%5.52%5.73% 199716.44%6.71%5.52%5.79% 26.89%7.09%5.66%5.85% 36.49%6.77%5.33%5.5

37、3% 46.03%6.33%5.19%5.32% 199815.64%6.61%5.32%5.50% 25.50%5.92%5.00%5.21% 35.52%5.70%5.00%5.08% 44.53%5.01%4.76%5.10% 199914.65%5.12%4.93%5.14% 25.18%5.55%4.89%5.27% 35.90%6.04%5.22%5.59% 45.92%6.07%5.56%6.06% 200016.70%6.63%5.91%6.38% 25.99%5.85%5.60%6.18% 35.80%5.83%5.40%6.12% 45.24%5.49%5.11%5.85%

38、 200115.16%5.54%4.99%5.76%2 4.89%5.34%5.00%5.80% 35.28%5.67%5.03%5.82% 实验三实验三 验证验证 Corporate Bond Yields（公司证券收益率）等利率的大小（公司证券收益率）等利率的大小 一. 目的与要求： 1.将 Corporate Bond Yields (AAA), Corporate Bond Yields (AA), Corporate Bond Yields (A), Corporate Bond Yields (BAA), Dividend Ratio on Common Stock 描绘在一张图

39、上。通过实验进一步理解 Corporate Bond Yields (AAA), Corporate Bond Yields (AA), Corporate Bond Yields (A), Corporate Bond Yields (BAA), Dividend Ratio on Common Stock的概念，希望能对比分析它们利率差的原因。 2. 将 Stock Indexes(NYSE, Industrials, Transportation, Utility, Financial, S 或 Stock Indexes(NYSE, Industrials, Transportatio

40、n, Utility, Financial, S X40.0622; X60.0565; X80.1614; 1 i X 表 6 中得出的数据是最低的安全边界，也就是说，在实际外汇储备的管理中，为了 保证外汇储备可以发挥其作用和职能，各个货币的持有量不能低于最低安全边界。但这 并不意味着安全边界就是外汇储备的“实际”持有量。在实际的外汇储备中，各个币种 的持有量在绝大多数都高于这个安全边界，尤其是美元。因为中国不仅在进口美国的商 品与服务时需要用美元结算，进口世界上很多其他国家的商品与服务时也需要用美元结 算。以石油为例，国际贸易中石油是以美元结算的，所以中国在进口中东国家的石油 时，也需要用

41、美元结算。所以说，外汇储备中常规的各个币种的持有量应该大于安全边 界。 180 (2)(2)限定币种最低持有比例的外汇储备币种结构的资产组合限定币种最低持有比例的外汇储备币种结构的资产组合 通过运算可以求出限定币种最低持有比例的外汇储备币种结构的最优资产组合，运 算结果见表 7 与图 2，图 2 代表限定币种最低持有比例的外汇储备币种结构的最优资产 组合图，在图 2 的有效边界的任意一点上，最优资产组合中同样都不含有 10 年期英 国、日本、美国债券。因为汇率波动幅度大，风险高，而汇率变动带来的收益又没有明 显优势，使得 10 年期英国、日本、美国债券在最优资产组合中没有一席之地。 从表 7

42、与图 2 可以看出，那么在组合风险为 0.0008 的目标下，最大收益为-0.87% （外币贬值是一个重要原因），最优资产的比例为：英国 3 月期国库券为 10.73%，欧 元 10 年期债券为 1.52%，欧元 3 月期债券为 6.2%，日本 3 月期国债为 5.65%，美国 3 月期国库券为 75.91%，8 种外币资产中的其余外币资产为 0。本文认为这是一个比较理 想的风险与投资收益组合。收益超出-0.87%后，风险水平加速增加，不利于外汇储备资 产组合的安全。如果风险承受能力很强，可以考虑风险水平处于 0.0048，则组合的收 益为 2.6%，组合收益为 2.6%是考虑外币贬值后的收益

43、，所以相当高，投资组合中英国 3 月期国债为 21.68%，欧元 10 年期国债为 50.05%，欧元 3 月期国债为 6.2%，日本 3 月 期国债为 5.65%，美国 3 月期国库券为 16.41%。 表表 7 7限定币种最低持有比例的外汇储备币种结构的最优资产组合 风险水平最优收益 英国 10 年期国 债 英国 3 月期国 债 欧元 10 年 期国债 欧元 3 月期债 券 日本 10 年期国 债 日本 3 月期国 债 美国 10 年期国 债 美国 3 月 期国库券 0.0005-0.078500.009300.06200.764600.1641 0.0005-0.066900.00930

44、0.06200.642500.2862 0.0005-0.055300.009300.06200.520400.4083 0.0005-0.043600.009300.06200.398400.5303 0.0006-0.03200.009300.06200.276300.6524 0.0006-0.020400.009300.06200.154300.7744 0.0008-0.008700.10730.01520.06200.056500.7591 0.00190.002900.54210.10230.06200.056500.2371 0.00330.014600.42440.29300

45、.06200.056500.1641 0.00480.026200.21680.50050.06200.056500.1641 0.00640.037800.00930.70810.06200.056500.1641 图图 2 限定币种最低持有比例的外汇储备币种结构的资产组合限定币种最低持有比例的外汇储备币种结构的资产组合 181 四、四、 结论结论 为满足偿还短期外债与最近 3 月进口用汇的需要，最好采用限制币种最低持有比例 的情形。通过考虑汇率变化导致持有外币资产收益变化的建模与计算分析发现：(1) 在 风险发生突变时，迅速增加的点为外币资产组合的最佳点，即有效前沿的转折点处； （2）就中

46、国目前的外债与进出口状态而言，选择组合风险为 0.0008 的目标下，对应组 合最大收益为-0.87%（外币贬值是一个重要原因），最优资产的比例为：英国 3 月期国 库券为 10.73%，欧元 10 年期债券为 1.52%，欧元 3 月期债券为 6.2%，日本 3 月期国债 为 5.65%，美国 3 月期国库券为 75.91%，8 种外币资产中的其余外币资产为 0。收益超 出-0.87%后，风险水平加速增加，不利于外汇储备资产组合的安全。（3）如果风险承 受能力很强，可以考虑风险水平处于 0.0048，则组合的收益为 2.6%，组合收益为 2.6% 是考虑外币贬值后的收益，所以相当高，投资组合

47、中英国 3 月期国债为 21.68%，欧元 10 年期国债为 50.05%，欧元 3 月期国债为 6.2%，日本 3 月期国债为 5.65%，美国 3 月 期国库券为 16.41%。 参考文献 1 Harry Markowitz, 1952, Portfolio Pelection J, The Journal of Finance, 7(1):77-91. 2Tobin J., 1956, the interest elasticity of transactions demand for cash J, Review of Economics and Statistics, (38):24

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