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In: Finance

Hi there, I just got a homework spread sheet and have no idea how to solve...

Hi there, I just got a homework spread sheet and have no idea how to solve it. can you explain it to me? I would really appriciate your help.  Here are the questions With a tiny part from the spread sheet.

A) Construct a time series of the ratio of the price of the fifth contract each day to the price of the fourth contract followed through time till the fourth contract expires. Pick a starting year below 2007 and a start date as a trading day closest to your birthday in that year.

B) Compare the standard deviations for the continuously compounded returns on the ratios with the continuously compounded returns on the respective numerators and denominators of the ratio.

C) Comment on the results obtained. In particular explain the di§erences in the standard deviations observed.

Maturities Contract Prices
date 1 2 3 4 5
19990601 199907 199910 199912 200003 200005 57.83 57.13 57.68 58.66 59.13
19990602 199907 199910 199912 200003 200005 58.21 57.6 57.69 58.6 59.1
19990603 199907 199910 199912 200003 200005 57.91 57.68 57.36 58.28 58.8
19990604 199907 199910 199912 200003 200005 57.53 57.7 57.48 58.45 58.98
19990607 199907 199910 199912 200003 200005 57.97 58.28 58.1 59 59.5
19990608 199907 199910 199912 200003 200005 57.48 57.7 57.75 58.57 59.15
19990609 199907 199910 199912 200003 200005 57.42 57.48 57.28 58.15 58.5
19990610 199907 199910 199912 200003 200005 56.31 56.91 56.72 57.72 58.25
19990611 199907 199910 199912 200003 200005 55.58 56.18 56.06 57.07 57.6
19990614 199907 199910 199912 200003 200005 56.39 57.19 56.67 57.53 58.03
19990615 199907 199910 199912 200003 200005 56.66 57.2 56.77 57.63 58.2
19990616 199907 199910 199912 200003 200005 55.26 56.37 55.74 56.65 57.33
19990617 199907 199910 199912 200003 200005 54.31 55.18 55.19 56.35 57.09
19990618 199907 199910 199912 200003 200005 55.03 56.16 56.05 57.08 57.7
19990621 199907 199910 199912 200003 200005 55.4 55.9 55.38 56.33 57.03
19990622 199907 199910 199912 200003 200005 54.35 55.88 55.92 56.83 57.55
19990623 199907 199910 199912 200003 200005 51.43 54.74 55.29 56.37 57.05
19990624 199907 199910 199912 200003 200005 52.34 55.34 55.95 56.81 57.48
19990625 199907 199910 199912 200003 200005 51.51 54.74 55.57 56.49 57.1
19990628 199907 199910 199912 200003 200005 50.1 53.58 54.25 55.31 56.13
19990629 199907 199910 199912 200003 200005 50.15 53.35 54 55.01 55.7
19990630 199907 199910 199912 200003 200005 50.1 53.64 54.39 55.18 55.9
19990701 199907 199910 199912 200003 200005 49.5 52.75 53.16 54.2 55.03
19990702 199907 199910 199912 200003 200005 49.7 52.23 52.93 53.95 54.68
19990706 199907 199910 199912 200003 200005 48.9 52.83 53.16 54.11 54.95
19990707 199907 199910 199912 200003 200005 48.75 51.68 52.24 53.26 54.05
19990708 199907 199910 199912 200003 200005 48.37 51.17 51.69 52.75 53.55
19990709 199910 199912 200003 200005 200007 50.01 50.61 51.78 52.6 53.6
19990712 199910 199912 200003 200005 200007 48.45 49.45 50.45 51.35 52.25
19990713 199910 199912 200003 200005 200007 49.53 50.23 51.23 52.03 52.9
19990714 199910 199912 200003 200005 200007 48.55 49.51 50.51 51.25 52.06
19990715 199910 199912 200003 200005 200007 48.95 49.93 50.88 51.53 52.3
19990716 199910 199912 200003 200005 200007 49.52 50.48 51.3 51.9 52.6
19990719 199910 199912 200003 200005 200007 50.44 51.37 52.1 52.78 53.55
19990720 199910 199912 200003 200005 200007 49.89 50.67 51.43 52.2 53
19990721 199910 199912 200003 200005 200007 51.21 51.7 52.45 53.1 54.05
19990722 199910 199912 200003 200005 200007 51.09 51.87 52.85 53.58 54.45
19990723 199910 199912 200003 200005 200007 52.01 52.4 53.43 54.05 54.95
19990726 199910 199912 200003 200005 200007 50.85 51.72 52.7 53.5 54.3
19990727 199910 199912 200003 200005 200007 50.82 51.43 52.35 53.13 53.8
19990728 199910 199912 200003 200005 200007 50.05 50.88 51.86 52.63 53.4
19990729 199910 199912 200003 200005 200007 51.46 52.13 53.08 53.8 54.65
19990730 199910 199912 200003 200005 200007 52.38 53.11 53.93 54.55 55.38
19990802 199910 199912 200003 200005 200007 51.57 52.35 53.12 54 54.63
19990803 199910 199912 200003 200005 200007 51.31 52.16 53 53.75 54.5
19990804 199910 199912 200003 200005 200007 51.59 52.52 53.45 54.15 54.8
19990805 199910 199912 200003 200005 200007 51.48 52.46 53.45 54.15 54.9
19990806 199910 199912 200003 200005 200007 52.09 52.99 53.85 54.8 55.4
19990809 199910 199912 200003 200005 200007 52.89 53.76 54.7 55.45 56.1
19990810 199910 199912 200003 200005 200007 51.81 52.72 53.69 54.53 55.35
19990811 199910 199912 200003 200005 200007 51.75 52.52 53.55 54.45 55.28
19990812 199910 199912 200003 200005 200007 53.15 54.19 55 55.9 56.8

Solutions

Expert Solution

Date Contract 4 Contract 5 Contract (5) / Contract (4) Return (Contract 5/ Contract 4) Return (Contract 5) Return (Contract 4)
19990601 58.66 59.13 1.0080
19990602 58.6 59.1 1.0085 0.0005 -0.0005 -0.0010
19990603 58.28 58.8 1.0089 0.0004 -0.0051 -0.0055
19990604 58.45 58.98 1.0091 0.0001 0.0031 0.0029
19990607 59 59.5 1.0085 -0.0006 0.0088 0.0094
19990608 58.57 59.15 1.0099 0.0014 -0.0059 -0.0073
19990609 58.15 58.5 1.0060 -0.0038 -0.0110 -0.0072
19990610 57.72 58.25 1.0092 0.0031 -0.0043 -0.0074
19990611 57.07 57.6 1.0093 0.0001 -0.0112 -0.0113
19990614 57.53 58.03 1.0087 -0.0006 0.0075 0.0081
19990615 57.63 58.2 1.0099 0.0012 0.0029 0.0017
19990616 56.65 57.33 1.0120 0.0021 -0.0149 -0.0170
19990617 56.35 57.09 1.0131 0.0011 -0.0042 -0.0053
19990618 57.08 57.7 1.0109 -0.0022 0.0107 0.0130
19990621 56.33 57.03 1.0124 0.0015 -0.0116 -0.0131
19990622 56.83 57.55 1.0127 0.0002 0.0091 0.0089
19990623 56.37 57.05 1.0121 -0.0006 -0.0087 -0.0081
19990624 56.81 57.48 1.0118 -0.0003 0.0075 0.0078
19990625 56.49 57.1 1.0108 -0.0010 -0.0066 -0.0056
19990628 55.31 56.13 1.0148 0.0040 -0.0170 -0.0209
19990629 55.01 55.7 1.0125 -0.0022 -0.0077 -0.0054
19990630 55.18 55.9 1.0130 0.0005 0.0036 0.0031
19990701 54.2 55.03 1.0153 0.0022 -0.0156 -0.0178
19990702 53.95 54.68 1.0135 -0.0018 -0.0064 -0.0046
19990706 54.11 54.95 1.0155 0.0020 0.0049 0.0030
19990707 53.26 54.05 1.0148 -0.0007 -0.0164 -0.0157
19990708 52.75 53.55 1.0152 0.0003 -0.0093 -0.0096
19990709 52.6 53.6 1.0190 0.0038 0.0009 -0.0028
19990712 51.35 52.25 1.0175 -0.0015 -0.0252 -0.0238
19990713 52.03 52.9 1.0167 -0.0008 0.0124 0.0132
19990714 51.25 52.06 1.0158 -0.0009 -0.0159 -0.0150
19990715 51.53 52.3 1.0149 -0.0008 0.0046 0.0055
19990716 51.9 52.6 1.0135 -0.0014 0.0057 0.0072
19990719 52.78 53.55 1.0146 0.0011 0.0181 0.0170
19990720 52.2 53 1.0153 0.0007 -0.0103 -0.0110
19990721 53.1 54.05 1.0179 0.0025 0.0198 0.0172
19990722 53.58 54.45 1.0162 -0.0016 0.0074 0.0090
19990723 54.05 54.95 1.0167 0.0004 0.0092 0.0088
19990726 53.5 54.3 1.0150 -0.0017 -0.0118 -0.0102
19990727 53.13 53.8 1.0126 -0.0023 -0.0092 -0.0069
19990728 52.63 53.4 1.0146 0.0020 -0.0074 -0.0094
19990729 53.8 54.65 1.0158 0.0012 0.0234 0.0222
19990730 54.55 55.38 1.0152 -0.0006 0.0134 0.0139
19990802 54 54.63 1.0117 -0.0035 -0.0135 -0.0101
19990803 53.75 54.5 1.0140 0.0023 -0.0024 -0.0046
19990804 54.15 54.8 1.0120 -0.0019 0.0055 0.0074
19990805 54.15 54.9 1.0139 0.0018 0.0018 0.0000
19990806 54.8 55.4 1.0109 -0.0029 0.0091 0.0120
19990809 55.45 56.1 1.0117 0.0008 0.0126 0.0119
19990810 54.53 55.35 1.0150 0.0033 -0.0134 -0.0166
19990811 54.45 55.28 1.0152 0.0002 -0.0013 -0.0015
19990812 55.9 56.8 1.0161 0.0008 0.0275 0.0266

Return = (Present Price / Previous Price) - 1

Contract Standard Deviation
Ratio (Contract 5 / Contract 4) 0.001823
Contract 5 0.011564
Contract 4

0.011656

It is evident that the standard deviation value of Contract (5) and Contract (4) is almost same. While the standard deviation value of Ratio 5 / Ratio 4 is very less. Two contracts which have similar standard deviations around their expected value, when put in the form of one divided by the other, produce a set of values that has much lesser standard deviation when compared with that of the original contracts.


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