LadyGeek wrote:longinvest wrote:LadyGeek wrote:Update: I did a quick test. Enter the value of "42" in Account1 cell E18 (8/31/2013 balance). This may not be a realistic situation, I'm just testing the limits. Consider auto-scaling the graph. Also, the returns after that point stay negative and trend in a negative direction. Is this correct?

Good test! You're really testing the limits of Bernstein's approximation formula, though. 42 causes the approximation to estimate a loss greater than 100%, which the spreadsheet is not able to handle correctly. (Look at cell Calculations!I7). The problem is that the approximation assumes that the investor added half of $1,300 at month end, but the final portfolio value $42 was less than $650, which means that the portfolio had to get negative before the $650 contribution.

This is a good example on the consequences of extrapolating performance to predict future results. That's why it's important to state the conditions the numbers were calculated - the date is very important.

You really got me looking deeper at what was happening there. I've been thinking about it ever since you posted this.

I am now convinced that my first assessment (e.g. my answer to you, above) was incorrect; the observed growth behavior is not due to Bernstein's approximation. It is also false to say that the spreadsheet cannot cope with a loss bigger than 100%.

The problem was in my own understanding of the chart.

Here's a simple example to illustrate my new understanding.

I invest $100 in some investment A in January 2000. In June 2000, A goes bankrupt (leaving me with a portfolio of 0$). In January 2001, I make a new $100 investment in company B. In January 2002, my portfolio is valued $400 (B has quadrupled).

If I was to chart a growth of $10,000 chart of my portfolio, what would it look like?

To answer this, I must first understand what this graph is meant to illustrate. It is meant to illustrate the growth of a

**single lump sum** investment in the personal portfolio managed by longinvest from January 2000 to January 2002.

What we know is that, had somebody invested $10,000 in January 2000 in longinvest's portfolio, the $10,000 would have dropped to $0 in June 2000. As no new money is added, this $0 doesn't growth back higher than $0 when longinvest's management (or luck?) improves in 2001, growing the portfolio by 300% in a single year. Why? Simply because $0 + 300% = $0.

So, the chart must necessarily look as a line dropping from $10,000 to $0 within the first 6 months of 2000, and then staying there.

What about losses bigger than 100%?

A growth of $10,000 always assumes that the "remaining" investment grows at the same rate as the portfolio. What does it mean to grow -$100 by 5%? If I grow a $100 debt by 5%, it will transform into a $105 debt. So, -$100 "grows" to -$105.

In other words, when the balance gets negative, a growth of $10,000 assumes that the investor is now shorting the market!

Interesting, isn't it?

Bogleheads investment philosophy |
Lifelong Portfolio: 25% each of (domestic/international)stocks/(nominal/inflation-indexed)bonds |
VCN/VXC/VLB/ZRR