
J. Lin, J. Sung
panies that compose the Dow Jones ind e x [4]. The rule that we followed was tha t if the sto ck reached a RGV
over our predetermined criterion, it wo u ld be bought and if the RGV we n t belo w it, it wo u l d be sold. Several
assumptions were u se d in findi ng the input va lues for the Graham formulas:
1) The time period used in the comparison went from 1997 until 2013.
2) Diluted EPS of the 30 blue c hi p stocks was used.
3) Growth rate used was the annualized growth in EPS over the pr evious five years; to prevent negative stock
prices, we li mited t he growth factor to −4.25% which would make 8.5 + 2 g = 0.
4) For corpor a te bond rates, we used an nualized yield based on monthly bond yields.
5) Stock prices and Dow Jones data were taken from the adj usted close on J une 30th each year or the nearest
previous tr ad in g day; further more stocks were ad justed fo r stoc k splits.
6) We checked to see if we needed to buy or sell stocks only on June 30th.
7) As the Do w Jo ne s has changed c omposition, we followe d suit; we o nly invested in sto cks that were in the
composite as of June 30thand divested of stocks that left the composite.
Furthermore , our anal ysis wa s split in two separate trials wit h RGV le vels of 1.25 and 1.50 respectively. We
bought the stock wh en its RG V was above the level and so ld it when the RGV went bel o w one. The por tfolio
was composed of equal market value s of every stock invested in at the beginning of each year. Fina l ly, for the
purpose of this portfolio we liq uida ted o ur positions in 2013 regardless of the RGV.
We attempted to remove all sources of survivor ship b ias by usi ng t he curre nt Dow Jo nes component compa-
nies for each year. We were able to find most of the companies still exist in one form or another b ut two stocks’
data were har d to come by, AT & T before the merger with SB C and Union Carbide. In both of these cases, the
company became a wholly owned subsid iary of another company and t here is no currently traded stock that re-
flects thei r historical prices.
4. Results
Our findings related to Graham’s formula’s predictive power are quite remarkable. As stated b efore, we wanted
to know whether or not Gra ham’s formula coul d be used to achieve excess returns above the market as an in-
vesto r. Benjamin Graham wa s a proponent of taking co nsiderable margin of sa fet y in investment decisions to
allow for error in analysis and to provide for a str onger a rgument in favor of the same inve s tment decisio n
(Graham, 2006) [1]. Fo r this reason, we assumed a position in the companies with RGV’s greater tha n o ne at
two different margins of safety levels. An RGV above one s ugges ts tha t the company is currently underpriced in
the mark et and shoul d be bo ught, whereas an RGV below 1 suggests t hat the company is overvalued. W ith this
in mind and to t e st t he strength of Graham’s formula, we assu med a portfolio that purchased i nt o companies
whe never their RGV wa s above one by a margin of safety of 25% and 50% (two separa te trials) and sold the
company’s securities whe never their RGV fe ll belo w one. We felt that pur cha si ng and se lli ng at these respective
levels was the best way to test the predictive power of Graham’s for m ula because that is what it implied-an
RGV above one means t he company’s stock is undervalued and an RGV below one means the company is
overval ued. A gain, what we f ound was p re tt y impressive.
If, startin g before 1997, you selected companies to invest in based solely on Graham’s formula and held the
criteria that t he companies mus t be trading at an RGV below one wi th a margin of safety of at 25%, you would
have o utperformed the Do w Jones Indust rial Average in every year from 1997 to 2013 except for thre e years
(1998, 2003, and 2011). The following Table 1 shows our resul ts wi th t he firs t column be i ng how much excess
return Graham’s formul a was able to generate above the Dow Jones Industr i al Average each year. The second
column is measuring year over year, how much did the Graham’s over perform the market on a cumulative ba si s.
In the years that Graham’s formula underperformed the market, it only underperformed marginall y. Whe n Gr a-
ham’s formula over performed the market, however, it did so substantially as we can see by 2013, the cumula-
tive over p erformance by Graham’s formu la was 119.44% over the seve nteen years.
For the portfolio where we took considerably more margin of safety at 50%, the results were even better.
Graham’s formul a performed better t han the DJIA in every single year. The second ha l f of the Ta bl e 1 summa-
rizes our r e s ul ts for holding this portfolio. This phe nome nal track record leads to the cu mulative r eturn over t he
DJIA in our second p or tfolio to be substantial l y higher, almo st double that of our first portfolio.
If we look at the ret urns as a year over year compounded effect on total returns, we can see the difference in a
measurable dollar amount. From 1997 to 2013, the Dow Jones Ind ustr i al Ave rage went from 7672 to 14,975. If