Bonds and Stocks

Motivated by comments on the Motley Fool

I read this comment:

For Fools with a long investing horizon, I'd recommend keeping much of your money in stocks, as opposed to bonds. According to research from business professor Jeremy Siegel, stocks outperformed bonds 74% of the time over all five-year periods between 1871 and 2001. Over all 10-year periods in the same span, that figure rises to 82%. Meanwhile, stocks outperformed bonds 95% of the time over all 20-year periods, and 99% of the time over all 30-year periods!
>They're recommending 100% stocks?
Actually, the comment was directed at the "young or patient" investor, so ...

>Yeah, so why would anybody invest in bonds.
Take a gander at Vanguard's Total Bond Index fund (VBMFX) and their 500 Index fund (VFINX):

A $1.00 investment in the bond fund would have grown to $3.40 (over the period 1990-2008).

>Aah, but the stock fund grew to over $7.00!!
Did you check out the lower charts? They indicate the maximum loss one might suffer, from a previous high to a ...

>You're talking drawdown, eh?
Yes, so ...

>So that's why people invest in bonds?
I guess so. There's comfort in Bonds ... hence the Comfort Index:
Comfort Index = SQRT(250)*MeanDailyReturn / DailyVolatility

>Square root of 250? What's that for?
To "annualize", we multiply the Mean Daily Return by 250 and the Daily Volatility by SQRT(250) so the ratio gets multiplied by SQRT(250) and ...

>Because there are 250 market days in a year?
Something like that.

>So where's the spreadsheet?
It's here. Just click on the picture to download:

Note that there's a chart on the growth of $1,000 rather than $1 ... as we had earlier.

Type in a couple of Yahoo symbols, click a Download button then gaze in awe at the pretty charts.

Here are a couple more:

>In your definition of Comfort Index you use the Mean or Average return. I always thought the compound return was more meaningful since ...
Since that's how your money grows? Yes, you're right, so I've modified the spreadsheet so you can choose either. There's now a pair of button like so:
You make your choice before you download the data.
If you click on Average? you get the above formula. If you click on Compound? it uses a compound return.
>Which is?
We showed here that, for small returns (and daily returns are small), the compound return is: Average - 0.5*Volatility2.
Then Average/Volatility would become (Average - 0.5*Volatility2)/Volatility.
Since we're "annualizing" everything in sight, we multiply the daily Average by 250 and the Volatility by SQRT(250) to switch to annual values.
That changes our magic formulas to:
Comfort Index (average) = SQRT(250)*(MeanDailyReturn) / DailyVolatility
Comfort Index (compound) = SQRT(250)*(MeanDailyReturn - 0.5*DailyVolatility2) / DailyVolatility

>I don't imagine there's much difference, eh?
Not much. The latter "compound" version is smaller. For example, the VBMFX and VFINX Comfort Indexes are like so:

>Did you give them different names?
I was thinking of calling the Comfort Index Average the CIA.