Growth versus Value and Golden Ratios
a continuation of Part I 
We're searching for an optimal allocation to each of
Large Cap Growth stocks and
Large Cap Value and Small Cap Growth and Small Cap Value
... the Golden Ratios
... by playing with a spreadsheet which contains
FamaFrench data. The
FamaFrench definitions of Growth and Value are like those of Barra; they're based upon
booktoprice ratios (or booktomarket or btm).
The spreadsheet looks like so:
>Can I play?
Sure. To download the spreadsheet, Rightclick the picture of the spreadsheet, above,
and save the file (not the picture!).
In the meantime, I've played with various allocations, using annual returns for the period
from 1950 to 2000, and get the following:
>So what are your Golden Ratios?
Let me think on it for a while ...
>What's to think? I'd pick lots of Small Cap Value.
The spreadsheet uses a particular set of parameters and ignores any correlation between
asset classes and ...
>You'd better think on it.
In Figure 1 we selected the annual returns at random from the entire spectrum of annual
returns, from 1950 to 2000, ignoring any correlations. The chart
orders them in order of increasing percentages. Now, if we pick just a year at random
(from 1950 to 2000) and choose the four annual returns from that same year, then we
get the chart in Figure 2:
>Quite a difference, but I still like Small Cap Value.
Actually, the proportions which held up seem to be 25% + 25% + 0% + 50%, wouldn't you say?
>Yeah, and I like 25% + 0% + 0% + 75% too.

Fig. 1
Fig. 2

Okay, here's a picture of the annualized gains over a twenty year period, starting in 1928,
including the Total Stock Market (TSM):
Fig. 3
>See? I told you! 25%+0%+0+75%!
And what about the next umpteen years?
>Looks like ... uh, Standard Deviation goes down as ... uh ...
Let's look at Standard Deviation per unit of 20year Annualized Gain so we ...
>So you plot "SD divided by Gain", right?
Right, and here it is:
>That's 20 years starting at the year shown, eh?
Right again, and ...
>So I guess I'd like the minimum 'cause that'd give me the smallest
volatility associated with the largest gain, right?
That depends upon your risk tolerance, I guess. Actually, the interesting thing  to me, at least 
is that all those graphs wind up at nearly the same place, over the past twenty years.
 Fig. 3a

>So the Standard Deviation has been decreasing since ...
Uh ... well, that's a bit misleading. It depends upon how many years we consider.
In Figures 3 and 3a, we determined the Standard Deviation of twenty
annual returns (for twenty years), starting in the year indicated.
Here's another view where, at each month of each year, we calculate the Standard Deviation over
the previous umpteen months then multiply by the square root of 12 in order to annualize.
Fig. 4
