Historical Results and Commentary
This section aims to analyze some of the salient characteristics of the Bandy 20 and its behavior as a portfolio using some simple mathematics.
The Bandy 20 has had an exceptional run over the last 7+ years. If an investor had chosen to put $10,000 of his or her money in the portfolio in February 2000, such an investor would have had questionable judgment. The portfolio was managed at the time by a 19 year-old geology student with only 8 years of investment experience and no formal training in finance. Nonetheless, such an investment would have yielded $35,887 by May 11, 2007 (minus trading and rebalancing costs). A similar investment in major indices would have resulted in much less money as the following table and subsequent figure demonstrate:
|
Index |
Value on May 11, 2007 |
|
Bandy 20 |
$35,886.70 |
|
S&P
500 |
$10,855.95 |
|
NASDAQ |
$5,829.26 |
|
DOW |
$12,817.27 |
In another form, the results look like this1:
|
|
Average
Quarterly Results (Feb 2000 - May 2007) |
Standard
Deviation |
|
Bandy 20 |
4.93% |
9.66% |
|
S&P
500 |
0.47% |
6.20% |
|
NASDAQ |
-1.20% |
11.36% |
|
DOW |
1.01% |
5.61% |
|
|
|
|
|
|
Average 6
Month Results (May 2000 - May 2007) |
Standard
Deviation |
|
Bandy 20 |
9.79% |
13.54% |
|
S&P
500 |
0.83% |
8.50% |
|
NASDAQ |
-1.09% |
15.14% |
|
DOW |
1.99% |
7.65% |
|
|
|
|
|
|
Average
Yearly Results (May 2000 - May 2007) |
Standard
Deviation |
|
Bandy 20 |
21.73% |
22.33% |
|
S&P
500 |
2.39% |
14.90% |
|
NASDAQ |
0.41% |
25.12% |
|
DOW |
3.86% |
11.72% |
What has caused these results?
First, we can rule out the Capital Asset Pricing Model (CAPM) as a descriptive model for the returns of the Bandy 20 (in this investor’s opinion, we can throw out the CAPM as a model for describing most things that are not theoretical). The CAPM states:
E(Ri) = Rf +βi[E(Rm)-Rf]
Where:
E(Ri) = Expected return on asset i
Rf = Risk free rate
E(Rm) = Expected Return on market portfolio (S&P 500 in this case)
βi =Beta of asset i
I calculated the normalized covariance of the following for indices on a quarterly basis (the 11th of Feb, May, Aug, and Nov) using the S&P 500 as a benchmark.
|
Index |
Beta (with S&P 500 as
reference) |
|
Bandy 20 |
1.34 |
|
S&P
500 |
0.97* |
|
Nasdaq |
1.49 |
|
Dow |
0.80 |
*I hate MS Excel
Notwithstanding the weakness of the CAPM in predicting the performance of either the Bandy 20 or the Nasdaq (or the performance of a whole range of other things one might want to predict in the financial world), one must question the usefulness of Betas as proxies for risk in analyzing the Bandy 20. This is because the Bandy 20 has had considerable positive deviations from its 30 quarter average return, and it has had few quarters of substantial negative deviation, as the following chart shows:
Note: Quarterly results have
been rounded to the nearest percentage.
Though risk in its formal definition can mean the probability that a number differs from its expected value (either upside or downside), for most investors it is downside risk that causes them to lose sleep. Ironically, by investing the portfolio in a risk free asset in its 4 best quarters, one could significantly lower the beta of the portfolio. Would this make the portfolio a more attractive investment? Of course not! In other words, the positive skew of the data is not reflected fairly by the beta that is calculated by using the S&P 500 as a reference point.
If betas are not valid for analyzing risk (specifically downside risk) in the Bandy 20, then perhaps a more appropriate measure of risk would be to compare the margin of profit (or loss) that one would gain by investing in the Bandy 20 instead of investing in the market portfolio (in this case the S&P 500). This seems to make sense for a real life investor who has decided to put a share of his or her fortunes in the stock market. If such a commitment has already been made, then understanding the expected opportunity cost of not investing in the Bandy 20 and instead investing in the S&P 500 would be a reasonable line of inquiry for an investor evaluating the Bandy 20. The following chart shows in a qualitative manner that the Bandy 20 seems to outperform the three other indices in a good number of quarters (the big blue squares are generally above the other shapes in most years).
The following chart demonstrates this fact in slightly clearer terms. The graph shows the return of the Bandy 20 minus the return on the S&P 500, so the percentage shown is in absolute terms (like per mil or basis point notation) rather than as a relative percentage above or below the return on the S&P 500.
Over the time period analyzed, the average quarterly excess return of the Bandy 20 was 446 basis points, with 24 quarters of excess returns and 5 quarters of excess losses. I don’t know much about Wall Street pay scales, but it is my hunch that had I been a senior portfolio manager at a buy side firm over the past 7 years, my bonuses would have gotten me several yachts and possibly a private island by now (if you happen to be a portfolio manager at a buy side firm and have copied me for the last 7 years, don’t you think it would be a kind gesture to give me just one yacht, perhaps even your smallest one. Or, if you are stingy, a car would do I suppose).
The following scatter plot shows this same data with slightly richer texture2.
It is also worthwhile to note that in quarters where the S&P 500 decreased, the Bandy 20 was only worse than the S&P 500 in three quarters (As of May 11th, 2007, the S&P 500 had 14 positive quarters and 15 negative quarters since the Bandy 20 was founded in February 2000). In other words, in a down market, the Bandy 20 historically has been a good buffer against declines in the S&P 500, and in an up market the Bandy 20 has almost always outperformed the S&P 5003.
While I do feel some tingles of pride when I consider the performance of the portfolio over the past few years, I cannot rule out the possibility that I have been extremely lucky. Basically, the whole performance of the portfolio over the last 7 years can be explained by 4 rather basic decisions that in hindsight were not all that well thought out:
- I understood the market was irrationally poised for an exuberant decline when I started the index back in 2000.
- I called the market bottom in August 2002, reasonably close to the actual trough.
- I made
well-timed bets on the Balkans and
- I periodically (and randomly) neglected the index during times of intense media bru-ha-ha-ing (studying abroad, traveling, and working a job will have that effect). Had I bitten my nails too much during these periods, I very well may have mucked up my results by not sticking with my rough intuition and investing principles.
1There is the unfortunate risk that average results calculated using percentage gains and losses will corrupt the integrity of data. This is indeed what has happened to some extent here. This is because losing X percent and then gaining it back will still net a loss, though the average of such results will show no net change. For example, consider a $100 investment that loses 30 percent in its first year and then gains 30 percent in its second year. The chap who made such an investment will end up with only $91, not $100. This phenomenon explains why some of the data (especially the figures for the Nasdaq index) are somewhat perverse.
2I don’t think a linear regression is necessarily the best way of comparing the two data sets, but nonetheless the R-squared of .79 shows a reasonable correlation using a linear regression. (Essentially, if one believes that the beta is not a valid way of measuring the performance of the Bandy 20, then a linear regression should also be ruled out, as the two are essentially the same thing [multiplying the results of the S&P 500 by a linear coefficient to predict the results of another asset]). My hunch is that the best-fit curve would have a different slope in the negative portion of the graph (bottom left-hand corner), and then curve out and bend towards the right in the upper right portion. I haven’t bothered to calculate this regression as I don’t think there are enough data points in the negative areas to create a statistically significant model (what a nice problem to have ;) ).
3The three quarters where the S&P 500 was both negative and better than the Bandy 20 were the three quarters ending 5-02, 8-02, and 8-06. In quarters where the S&P 500 was positive, it was better than the Bandy 20 in only 2 quarters, those ending in 8/00 and 5/07.
Historical Results and Commentary