Optimizing the Dow
Earlier this week I distributed some internal notes to GGT subscribers which outlined concepts on picking stocks out of major indexes with the intent of beating the index but not taking on a huge amount of risk in the process. The following describes this process a bit more.
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Here are some terms that you will need to understand, at least in basic concept:
Risk-Free Asset: think Government bonds, typically 3 months in duration. The principal in guaranteed, as is the rate of return. For all intensive purposes the variability of returns is 0. As of this writing I'm using 0.25% as the annualized rate of return for risk-free assets.
Volatility: many people equate risk and volatility as the same thing. They are not, but one does approximate the other over various time frames. Typically, they are directly proportional -- as volatility goes up, risk goes up. As you will see, this does not mean that gains go up in direct proportion; it's possible to have incredibly high risk but overall poor return in a security, which obviously is a bad place to have your money.
Return or Excess Return: "Return", by itself, is how much gain you have on a security in some particular time frame. "Excess Return" is the same thing, but you subtract the return of the Risk-Free Asset described above. In most of my plots I will plot "Return", as we are most familiar with it.
Correlation: this is a mathematical value between -1 and +1 that describes how well two securities, or a security and an index, move with respect to each other. If something has a correlation of +1, they move exactly the same, e.g., if the broad index S&P500 goes up 1%, the ETF SPY will also go up 1% by design, and the correlation is +1. Conversely, if two securities are negatively correlated with a value of -1, then if the S&P500 goes up +1%, the ETF SH will drop by -1%, again by design, because they have a correlation of -1. Stocks and bonds tend to be negatively correlated between 0 and -1, stocks (in general) are positively correlated with other stocks and their correlation is generally between 0 and +1. When two securities have a correlation of 0 they do not move at all with respect to each other.
Capital Allocation Line: if all your money is in a risk-free asset, then your return is the risk free asset return and the volatility is 0. If all your money is 100% in one security, then your return is that security's return, and the volatility (risk) is the volatility of that security. Hence, the line connecting a security's return/risk value to that of a risk free asset represents all the combinations possible for owning the security (100%), owning a portion of the security (e.g. 40% security, 60% risk-free asset), or owning 100% of the risk-free asset. Typically, the line connects the risk-free-asset return (volatility = 0) to the return/risk of an index that you are comparing to.
Efficient Frontier: In the Capital-Allocation-Line (CAL) description above, where we have the choice of 100% in a risk-free asset, some percentage X in the risk free asset and the balance (1-X) in a security, or 100% in the security, the CAL describes a curve called the Efficient Frontier. In this two-security case (one risk-free with 0 variance), the Efficient Frontier is a straight line. In the case where no risk-free asset exists, two securities combine to have variable rates of return as well as variable levels of risk. This rates of return and the risks are related by the term correlation as described above, AND ARE NOT LINEAR (a straight line). The more securities that are introduced that have positive and negative correlations, the more "bullet shaped" or "hyperbolic"-looking the Efficient Frontier becomes.
Portfolio: a combination of securities, and as I use it in my work, all have variance (risk) > 0. This means that while I'll compare to a risk-free-asset, I'll not actually invest in a risk-free asset in my portfolio until I understand how my portfolio behaves (more on this later). The basket of 30 stocks comprising the Dow Jones Industrials is considered a portfolio.
Tangency Portfolio: You'll see this below in a figure, but it represents where the Efficient Frontier of all securities being considered intersects the Capital Allocation Line. The point of intersection represents the best possible combination of return and risk, given the alternative of simply investing in an index AND a risk-free asset. At the point of intersection, which is where the line is tangent to the curve, you are 100% invested in stocks in some ratio that represents an optimum reward/risk level. More on this below.
The diagram above was taken from the Wiki link on Modern Portfolio Theory. Here, they use "Standard Deviation" on the x-axis, where I normally use "Volatility". The two are related -- all things equal, standard deviation is the square root of volatility. Many people use either term interchangeably, which is mathematically incorrect, but the concepts are equivalent.
Starting on the left of the figure above, where Standard Deviation = 0, we have the Risk Free Rate (RFR) as described above. As we introduce a security to the equation -- just 1 -- we have a choice of some proportion of our money in the RFR and some remaining proportion in the security. This is described by the "Best Possible Capital Allocation Line". It is assumed that the single security being considered has a rate of return greater than the RFR -- why would we invest in the security if we could get a higher rate of return at no risk by investing 100% in the RFR? This guarantees that the line moves from the lower left of the figure towards the upper right.
The golden dots of Individual Assets shows their performance, over some period in the past, of Standard Deviation and Expected Return. Let's make this more concrete in the figure below.
Here, I'm using the RFR (risk free return) = 0.25%, and you see two stocks: AA and IBM.
- The unmarked yellow diamond in the middle represents some arbitrary portfolio ratio between some percentage in AA and the remaining percentage in IBM. In this case it was 50/50. Note that the yellow diamond is ON THE BLUE CURVE.
- The blue curve is constructed by running through all the combinations of owning IBM and AA. This is why you see that a 50/50 ratio between the two stocks falls on the blue curve. It is a coincidence that AA lies on the Efficient Frontier of these two portfolios; that is not normally the case.
- The red line is the CAL that connects the RFR and the unknown portfolio. At the point of intersection (purple diamond) the percentage in IBM and AA is unknown, but common sense would tell you that if the yellow diamond is 50/50, and AA is to the right of the yellow diamond and IBM to the left, that the intersection of the two lines is where we have "more" in IBM and "less" in AA.
- Again, I'm using the risk-free-return value as 0.25% per year, based on 3-month Treasury notes.
- The unmarked yellow diamond represents the portfolio performance with 100 shares held in each stock (arbitrary).
- The close proximity of the yellow diamond and the purple diamond is pure co-incidence; if I weighted the stocks by equal dollar value the yellow diamond would have moved to a different location on the blue curve.
- Quadrant I. These stocks have above average gain than our optimum point, which is what we want, but above average volatility, which is what we do NOT want. Despite this, we expect that higher volatility (risk) means that we should have higher gain, and these stocks meet that criteria.
- Quadrant II: There are no stocks here, by definition, because the origin (crossing of the two axis lines) lies directly on the Efficient Frontier boundary, and there is no combination of stocks that gives us higher gain than the optimum point but lower volatility than the optimum point. Of course, there are stocks that fall into Quadrant II -- but they are NOT part of the Dow Jones 30. These would be GREAT stocks to find, relative to the stocks in the DJ30, because they would boost gain but lower risk. Note that for future reference, we want stocks that have historically returned more than 20.9% over the last year and have volatility below 13.1%; this is where the "optimum" point lies.
- Quadrant III: These stocks have lower volatility, but poor gain. There is no way that adding these stocks to a portfolio can increase gain -- all they can do is reduce portfolio volatility AND reduce gain at the same time. They may be candidates for balancing reward/risk, but in general, they are to be avoided.
- Quadrant IV: These stocks have above average volatility and below average gain than our ideal point. Again, adding these to a portfolio cannot result in any form of increase in gain, all they can do is lower it. Furthermore, adding these to a portfolio cannot reduce volatility, all they can do is increase it. Hence, stocks in Quadrant IV MUST be avoided.
- The concept that there exists an optimum reward/risk ratio given a set basket of stocks. We can find this optimum reward/risk ratio using standard tools.
- The concept that we can eliminate under-performing stocks in a given basket, based upon historical return and volatility, and improve the basket performance (in hind sight, of course)
- The concept that we can selectively pick stocks from a subset of stocks that comprise an index and improve our chances of outperforming the index without taking significant additional risk.
- That we can take these new candidates, apply GGT timing methods, and the result will improve overall performance because we will not be participating in the stock when it is underperforming.