This one concept from CFA level I QM curriculum can make a big difference in your wealth

What is the most important concept from CFA level I -‘ Quantitative Methods’ that you have learned? The concept, which if applied in your investments, can make a lot of difference in your wealth. If you are thinking that it would be NPV/IRR, then you are wrong as to apply NPV and IRR, one needs to forecast the cash flows and there comes the estimation part which is quite tough for a common investor. If you are thinking that it would be from concepts of hypothesis testing or may be Type I and Type II errors, then you are again wrong. Now please do not say that it is probability as if you can master probability and the outcomes, then you’d rather go to Vegas to earn yourself a fortune.

The concept which I am talking about is the simplest of all and its application is also pretty simple. Even Geoffrey Boycott‘s mother can apply that concept. It’s that simple. Yes, it is none other than the concept of harmonic mean. We learn from the CFA level I curriculum that among all the means, the harmonic mean is the least. But then how can it help you in creating more wealth out of your investment. Ever heard of Benjamin Graham‘s dollar cost averaging? Benjamin Graham said that for a passive investor, it is better to invest in an index fund rather than mutual funds (as more than 80% of mutual funds fail to beat the return from the index fund for a long term horizon). The passive investors can further enhance their returns by using the dollar cost of averaging i.e. investing a certain amount of time at regular intervals of time.

The dollar-cost averaging utilizes the concept of harmonic mean. In that, you have to invest a certain constant amount at regular intervals. The number of units you will get from the investments will be different as the market would be at different levels as different intervals of time. The cost per unit will be the harmonic mean of the market levels which would be the least. This kind of strategy is famously known as SIP (systematic investment plan).

I did a research on this and extracted data from NSE and applied the SIP from Mar-98 to Aug-09 period (I did this research in Aug-09 and sharing the results today. The data was available from Mar-98 only in NSE. Even if we apply it for further dates, we will find the same results.)

Investment comparisons (SIP+Index, Index without SIP, FD at 8%):

Month Nifty Investment Units 8% 10% 11% 13% 15% 16.23%
Mar-98 1060.75 10000 9.427292 25092.9039 31581.929 35430.93 44593.37 56125.21 64653.04
Apr-98 1116.9 10000 8.953353 24926.17426 31319.84 35107.63 44112.88 55428.01 63784.49
May-98 1159.35 10000 8.625523 24760.55245 31059.926 34787.28 43637.57 54739.47 62927.61
Jun-98 1063.15 10000 9.40601 24596.03111 30802.168 34469.85 43167.38 54059.49 62082.25
Jul-98 941.65 10000 10.61966 24432.60294 30546.55 34155.32 42702.26 53387.95 61248.24
Aug-98 931.4 10000 10.73653 24270.26066 30293.053 33843.66 42242.15 52724.76 60425.43
Sep-98 852.8 10000 11.72608 24108.99706 30041.66 33534.85 41786.99 52069.8 59613.68
Oct-98 904.95 10000 11.05033 23948.80498 29792.353 33228.85 41336.74 51422.98 58812.83
Nov-98 824 10000 12.13592 23789.6773 29545.115 32925.64 40891.34 50784.19 58022.75
Dec-98 817.75 10000 12.22868 23631.60694 29299.929 32625.2 40450.75 50153.34 57243.27
Jan-99 884.25 10000 11.30902 23474.58687 29056.777 32327.51 40014.89 49530.32 56474.27
Feb-99 966.2 10000 10.34982 23318.61013 28815.644 32032.52 39583.74 48915.05 55715.6
Mar-99 981.3 10000 10.19056 23163.66977 28576.511 31740.23 39157.23 48307.42 54967.11
Apr-99 1078.05 10000 9.276008 23009.75891 28339.363 31450.61 38735.32 47707.33 54228.69
May-99 978.2 10000 10.22286 22856.87071 28104.183 31163.63 38317.95 47114.7 53500.18
Jun-99 1132.3 10000 8.831582 22704.99838 27870.955 30879.27 37905.08 46529.43 52781.47
Jul-99 1187.7 10000 8.419635 22554.13516 27639.662 30597.5 37496.66 45951.44 52072.4
Aug-99 1310.15 10000 7.632714 22404.27435 27410.288 30318.31 37092.63 45380.62 51372.86
Sep-99 1412 10000 7.082153 22255.40928 27182.818 30041.66 36692.97 44816.89 50682.72
Oct-99 1413.1 10000 7.07664 22107.53336 26957.236 29767.54 36297.6 44260.17 50001.85
Nov-99 1325.45 10000 7.544607 21960.63999 26733.526 29495.91 35906.5 43710.36 49330.13
Dec-99 1376.15 10000 7.26665 21814.72265 26511.672 29226.77 35519.62 43167.38 48667.43
Jan-00 1480.45 10000 6.754703 21669.77487 26291.66 28960.08 35136.9 42631.15 48013.64
Feb-00 1546.2 10000 6.467469 21525.79018 26073.473 28695.83 34758.3 42101.57 47368.63
Mar-00 1654.8 10000 6.043026 21382.7622 25857.097 28433.99 34383.79 41578.58 46732.28
Apr-00 1528.45 10000 6.542576 21240.68458 25642.516 28174.53 34013.3 41062.08 46104.48
May-00 1406.55 10000 7.109594 21099.55098 25429.716 27917.44 33646.82 40552 45485.11
Jun-00 1380.45 10000 7.244015 20959.35514 25218.683 27662.7 33284.28 40048.25 44874.07
Jul-00 1471.45 10000 6.796018 20820.09084 25009.4 27410.29 32925.64 39550.77 44271.23
Aug-00 1332.85 10000 7.50272 20681.75188 24801.854 27160.18 32570.87 39059.46 43676.5
Sep-00 1394.1 10000 7.173087 20544.33211 24596.031 26912.34 32219.93 38574.26 43089.75
Oct-00 1271.65 10000 7.863799 20407.82542 24391.916 26666.78 31872.76 38095.08 42510.88
Nov-00 1172.75 10000 8.526967 20272.22575 24189.494 26423.45 31529.34 37621.85 41939.79
Dec-00 1268.15 10000 7.885503 20137.52707 23988.753 26182.34 31189.61 37154.51 41376.38
Jan-01 1263.55 10000 7.91421 20003.7234 23789.677 25943.43 30853.55 36692.97 40820.53
Feb-01 1371.7 10000 7.290224 19870.80879 23592.254 25706.7 30521.11 36237.16 40272.15
Mar-01 1351.4 10000 7.399734 19738.77732 23396.469 25472.13 30192.24 35787.01 39731.13
Apr-01 1148.2 10000 8.709284 19607.62314 23202.308 25239.71 29866.93 35342.46 39197.39
May-01 1125.25 10000 8.886914 19477.34041 23009.759 25009.4 29545.12 34903.43 38670.81
Jun-01 1167.9 10000 8.562377 19347.92334 22818.808 24781.19 29226.77 34469.85 38151.31
Jul-01 1107.9 10000 9.026085 19219.36619 22629.441 24555.07 28911.86 34041.66 37638.79
Aug-01 1072.85 10000 9.320968 19091.66323 22441.646 24331.01 28600.33 33618.79 37133.15
Sep-01 1053.75 10000 9.489917 18964.80879 22255.409 24109 28292.17 33201.17 36634.3
Oct-01 913.85 10000 10.94271 18838.79724 22070.718 23889.01 27987.33 32788.74 36142.16
Nov-01 971.9 10000 10.28912 18713.62297 21887.56 23671.03 27685.77 32381.43 35656.63
Dec-01 1067.15 10000 9.370754 18589.28042 21705.921 23455.03 27387.46 31979.18 35177.62
Jan-02 1059.05 10000 9.442425 18465.76406 21525.79 23241.01 27092.36 31581.93 34705.05
Feb-02 1075.4 10000 9.298866 18343.06841 21347.154 23028.94 26800.44 31189.61 34238.82
Mar-02 1142.05 10000 8.756184 18221.188 21170 22818.81 26511.67 30802.17 33778.86
Apr-02 1129.55 10000 8.853083 18100.11743 20994.317 22610.59 26226.01 30419.54 33325.07
May-02 1084.5 10000 9.220839 17979.85132 20820.091 22404.27 25943.43 30041.66 32877.39
Jun-02 1028.8 10000 9.720062 17860.38431 20647.311 22199.84 25663.89 29668.48 32435.71
Jul-02 1057.8 10000 9.453583 17741.7111 20475.965 21997.27 25387.37 29299.93 31999.97
Aug-02 958.9 10000 10.42862 17623.82641 20306.041 21796.55 25113.82 28935.96 31570.09
Sep-02 1010.6 10000 9.895112 17506.725 20137.527 21597.66 24843.23 28576.51 31145.98
Oct-02 963.15 10000 10.3826 17390.40168 19970.412 21400.59 24575.54 28221.53 30727.56
Nov-02 951.4 10000 10.51083 17274.85126 19804.683 21205.31 24310.74 27870.95 30314.77
Dec-02 1050.15 10000 9.522449 17160.06862 19640.33 21011.82 24048.8 27524.74 29907.52
Jan-03 1093.5 10000 9.144947 17046.04865 19477.34 20820.09 23789.68 27182.82 29505.75
Feb-03 1041.85 10000 9.598311 16932.78629 19315.704 20630.11 23533.35 26845.15 29109.37
Mar-03 1063.4 10000 9.403799 16820.2765 19155.408 20441.87 23279.78 26511.67 28718.32
Apr-03 978.2 10000 10.22286 16708.51428 18996.443 20255.34 23028.94 26182.34 28332.52
May-03 934.05 10000 10.70606 16597.49466 18838.797 20070.51 22780.81 25857.1 27951.9
Jun-03 1006.8 10000 9.932459 16487.21271 18682.46 19887.37 22535.35 25535.89 27576.39
Jul-03 1134.15 10000 8.817176 16377.66353 18527.419 19705.91 22292.53 25218.68 27205.93
Aug-03 1185.85 10000 8.43277 16268.84224 18373.666 19526.09 22052.33 24905.41 26840.45
Sep-03 1356.55 10000 7.371641 16160.74402 18221.188 19347.92 21814.72 24596.03 26479.88
Oct-03 1417.1 10000 7.056665 16053.36406 18069.976 19171.38 21579.67 24290.49 26124.15
Nov-03 1555.9 10000 6.427148 15946.69758 17920.018 18996.44 21347.15 23988.75 25773.2
Dec-03 1615.25 10000 6.190992 15840.73985 17771.305 18823.1 21117.14 23690.76 25426.96
Jan-04 1879.75 10000 5.319856 15735.48615 17623.826 18651.35 20889.61 23396.47 25085.38
Feb-04 1809.75 10000 5.525625 15630.93181 17477.571 18481.16 20664.52 23105.83 24748.38
Mar-04 1800.3 10000 5.55463 15527.07219 17332.53 18312.52 20441.87 22818.81 24415.91
Apr-04 1771.9 10000 5.643659 15423.90265 17188.693 18145.42 20221.61 22535.35 24087.91
May-04 1796.1 10000 5.567619 15321.41863 17046.049 17979.85 20003.72 22255.41 23764.32
Jun-04 1483.6 10000 6.740361 15219.61556 16904.588 17815.79 19788.19 21978.95 23445.07
Jul-04 1505.6 10000 6.64187 15118.48892 16764.302 17653.22 19574.97 21705.92 23130.11
Aug-04 1632.3 10000 6.126325 15018.03421 16625.18 17492.14 19364.05 21436.29 22819.38
Sep-04 1631.75 10000 6.12839 14918.24698 16487.213 17332.53 19155.41 21170 22512.82
Oct-04 1745.5 10000 5.729017 14819.12278 16350.39 17174.37 18949.01 20907.02 22210.39
Nov-04 1786.9 10000 5.596284 14720.65721 16214.703 17017.66 18744.84 20647.31 21912.01
Dec-04 1958.8 10000 5.105166 14622.84589 16080.142 16862.38 18542.87 20390.83 21617.65
Jan-05 2080.5 10000 4.806537 14525.68449 15946.698 16708.51 18343.07 20137.53 21327.24
Feb-05 2057.6 10000 4.860031 14429.16867 15814.361 16556.05 18145.42 19887.37 21040.73
Mar-05 2103.25 10000 4.754547 14333.29415 15683.122 16404.98 17949.91 19640.33 20758.07
Apr-05 2035.65 10000 4.912436 14238.05666 15552.972 16255.29 17756.5 19396.35 20479.21
May-05 1902.5 10000 5.256242 14143.45198 15423.903 16106.96 17565.18 19155.41 20204.09
Jun-05 2087.55 10000 4.790304 14049.47591 15295.904 15959.99 17375.92 18917.46 19932.67
Jul-05 2220.6 10000 4.503287 13956.12425 15168.968 15814.36 17188.69 18682.46 19664.9
Aug-05 2312.3 10000 4.324698 13863.39287 15043.085 15670.06 17003.49 18450.38 19400.72
Sep-05 2384.65 10000 4.193488 13771.27764 14918.247 15527.07 16820.28 18221.19 19140.09
Oct-05 2601.4 10000 3.844084 13679.77448 14794.445 15385.39 16639.04 17994.84 18882.96
Nov-05 2370.95 10000 4.217719 13588.8793 14671.67 15245 16459.76 17771.31 18629.29
Dec-05 2652.25 10000 3.770384 13498.58808 14549.914 15105.9 16282.41 17550.55 18379.03
Jan-06 2836.55 10000 3.525409 13408.89679 14429.169 14968.06 16106.96 17332.53 18132.12
Feb-06 3001.1 10000 3.332112 13319.80146 14309.425 14831.48 15933.41 17117.22 17888.54
Mar-06 3074.7 10000 3.25235 13231.29812 14190.675 14696.14 15761.73 16904.59 17648.22
Apr-06 3402.55 10000 2.938972 13143.38285 14072.911 14562.04 15591.9 16694.6 17411.14
May-06 3557.6 10000 2.810884 13056.05172 13956.124 14429.17 15423.9 16487.21 17177.24
Jun-06 3071.05 10000 3.256215 12969.30087 13840.306 14297.51 15257.71 16282.41 16946.48
Jul-06 3128.2 10000 3.196727 12883.12643 13725.45 14167.04 15093.31 16080.14 16718.82
Aug-06 3143.2 10000 3.181471 12797.52458 13611.546 14037.77 14930.68 15880.39 16494.22
Sep-06 3413.9 10000 2.929201 12712.4915 13498.588 13909.68 14769.81 15683.12 16272.64
Oct-06 3588.4 10000 2.786757 12628.02343 13386.567 13782.76 14610.67 15488.3 16054.03
Nov-06 3744.1 10000 2.670869 12544.11661 13275.476 13656.99 14453.24 15295.9 15838.36
Dec-06 3954.5 10000 2.528765 12460.76731 13165.307 13532.38 14297.51 15105.9 15625.59
Jan-07 3966.4 10000 2.521178 12377.97182 13056.052 13408.9 14143.45 14918.25 15415.68
Feb-07 4082.7 10000 2.449359 12295.72646 12947.703 13286.54 13991.06 14732.93 15208.59
Mar-07 3745.3 10000 2.670013 12214.02758 12840.254 13165.31 13840.31 14549.91 15004.27
Apr-07 3821.55 10000 2.616739 12132.87155 12733.697 13045.18 13691.18 14369.17 14802.71
May-07 4087.9 10000 2.446244 12052.25476 12628.023 12926.14 13543.66 14190.68 14603.85
Jun-07 4295.8 10000 2.327855 11972.17363 12523.227 12808.19 13397.73 14014.4 14407.66
Jul-07 4318.3 10000 2.315726 11892.6246 12419.301 12691.32 13253.37 13840.31 14214.11
Aug-07 4528.85 10000 2.208066 11813.60413 12316.236 12575.52 13110.57 13668.38 14023.16
Sep-07 4464 10000 2.240143 11735.10871 12214.028 12460.77 12969.3 13498.59 13834.77
Oct-07 5021.35 10000 1.991496 11657.13485 12112.667 12347.07 12829.56 13330.91 13648.92
Nov-07 5900.65 10000 1.694729 11579.67909 12012.147 12234.4 12691.32 13165.31 13465.56
Dec-07 5762.75 10000 1.735283 11502.73799 11912.462 12122.77 12554.57 13001.76 13284.66
Jan-08 6138.6 10000 1.629036 11426.30812 11813.604 12012.15 12419.3 12840.25 13106.2
Feb-08 5137.45 10000 1.946491 11350.38609 11715.566 11902.54 12285.48 12680.75 12930.13
Mar-08 5223.5 10000 1.914425 11274.96852 11618.342 11793.93 12153.11 12523.23 12756.43
Apr-08 4734.5 10000 2.112155 11200.05206 11521.925 11686.31 12022.16 12367.66 12585.06
May-08 5165.9 10000 1.935771 11125.63338 11426.308 11579.68 11892.62 12214.03 12415.99
Jun-08 4870.1 10000 2.053346 11051.70918 11331.485 11474.02 11764.48 12062.3 12249.19
Jul-08 4040.55 10000 2.474911 10978.27617 11237.448 11369.32 11637.72 11912.46 12084.64
Aug-08 4332.95 10000 2.307896 10905.33108 11144.192 11265.58 11512.33 11764.48 11922.29
Sep-08 4360 10000 2.293578 10832.87068 11051.709 11162.78 11388.28 11618.34 11762.13
Oct-08 3921.2 10000 2.55024 10760.89174 10959.994 11060.92 11265.58 11474.02 11604.12
Nov-08 2885.6 10000 3.465484 10689.39106 10869.04 10959.99 11144.19 11331.48 11448.23
Dec-08 2755.1 10000 3.629632 10618.36547 10778.842 10859.99 11024.11 11190.72 11294.43
Jan-09 2959.15 10000 3.379349 10547.8118 10689.391 10760.89 10905.33 11051.71 11142.71
Feb-09 2874.8 10000 3.478503 10477.72693 10600.683 10662.7 10787.83 10914.42 10993.02
Mar-09 2763.65 10000 3.618403 10408.10774 10512.711 10565.41 10671.59 10778.84 10845.34
Apr-09 3600 10000 2.777778 10338.95114 10425.469 10469 10556.61 10644.94 10699.64
May-09 4300 10000 2.325581 10270.25404 10338.951 10373.47 10442.86 10512.71 10555.9
Jun-09 4450 10000 2.247191 10202.0134 10253.151 10278.82 10330.34 10382.12 10414.09
Jul-09 4636 10000 2.157032 10134.22619 10168.063 10185.02 10219.03 10253.15 10274.19
Aug-09 4732 10000 2.113271 10066.88938 10083.682 10092.09 10108.92 10125.78 10136.17
Sum 1380000 859.9621 2271490.422 2600637.4 2787018 3210562 3713127 4068278
Nifty 4732 Value 4069341
Without SIP 0.130032 Difference 857716.51
Investing in Index Funds(10000 per month)
Dividends ignored which can further add up 1-2% in interest yield
That dividend yield is ignored by taking .5% of fund fee and .5% as under-performance

We can clearly see the results. I am not advocating here that one should not invest in fixed income securities and should invest in equity only. The allocation of the portfolio will depend on the requirement and risk-return characteristics of an individual investor. But if one person is investing in equity and investing in index funds then that person is better off investing that money via the route of SIP rather than simple lump sum investment. The difference in the yield between two investments in the above case is around 3.23% which is quite high. If 3.23% is compounded for 11 years, it has a large impact on the net portfolio. In the above example, the difference is around 857,716 which is around 25% more than the portfolio value obtained when SIP technique is not used.

That’s the impact that a simple concept of the harmonic mean can make on your portfolio value. The excel file which contains all the calculations can be downloaded from here – SIP+Index Fund

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A blog of the NYU Colloquium on Market Institutions and the Leipzig Colloquium on the Market OrderEconomic Processes & the Leipzig Colloquium on the Foundations of the Market Order

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Thoughts of a teacher & practitioner of value investing and behavioral economics

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