# The Efficient Frontier of the Current Dow 30

Many of us pick our stocks based on previous performance – assuming that the future will, at least somewhat, track the past. Modern Portfolio Theory follows a similar line of thought, with the assumption that a stock (or portfolio’s) annual rate of return can be modeled as a random variable – with a future mean and variance that correlates with that of the past.

Of course the nice thing about random variables with a fixed distribution is that you can use the mean and variance to predict the general range of future samples. For example, if a variable has a Gaussian or normal distribution, there is a high probability that future values will fall within 1 or 2 standard deviations of that mean. You can see how useful that can be in estimating next year’s most likely best and worst case rates of return.

Modern Portfolio Theory uses mean, standard deviation, and covariance to put together a portfolio that – again assuming the future will track the past – should yield the highest return possible given the portfolio owner’s risk comfort zone.

But let’s keep things simple for now and just stick to the mean and standard deviation of individual stocks – particularly the current Dow 30. Below is a plot of the average yearly return versus standard deviation over 1988 to 2006 for all 30 stocks plus one S&P 500 index fund – the Vanguard 500 (ticker VFINX).

Figure 1. Mean vs. Std. Dev. ROR for all 30+1 Stocks

Observations?

1. About 20 of the 30 current Dow stocks have, on average, beaten the S&P 500 over the past 19 years.

2. But as mentioned in a previous article, 1 of these 20 “market beaters” is a true gem as it not only trumped the S&P 500, it did so with less risk (lower standard deviation)! It’s Exxon Mobil (XOM).

3. Modern Portfolio Theory would say that if your portfolio is only going to consist of 1 of these 30+1 stocks, a “rational investor” would only pick from the 7 stocks in the table below.

Table 1. ROR Statistics of “Rational” Choices
Ticker Mean Std Dev
XOM 15.5% 12.3%
PG 16.5% 17.8%
JNJ 17.0% 18.4%
UTX 17.9% 19.5%
C 22.1% 32.6%
HD 25.2% 49.8%
MSFT* 28.6% 51.1%

* MSFT statistics computed over previous 18 years instead of 19 as MSFT did not have an IPO before January 1, 1988 unlike the other stocks

Why only these 7? Because they lie along the efficient frontier – meaning that there is no other stock in our set of 30+1 that achieved a higher average return with less risk. A “rational investor” would not choose a stock outside of these 7 because it would mean taking on more risk for the same or worse expected return.

Figure 2. Mean vs. Std. Dev. ROR for the 7 “Rational” Stocks

The next thing to figure out is where your comfort zone intersects with the efficient frontier. Obviously the higher the potential ROR the better – but the higher ROR choice also has a larger yearly fluctuation – and if you happen to catch the stock in a bad year, it can severely set you back. Again, remember that a 50% loss has to be followed by a 100% return just to break even.

Finally, some further insight can be obtained by examining the individual yearly returns to make sure that you don’t end up selecting a stock that had stellar returns a decade ago, but has been overtaken by the competition in the last 5 or 10 years.

It can also be insightful to examine the stock’s performance in rolling 5 year intervals over the 19 years to see if it generally always stays on the efficient frontier. ðŸ˜‰