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Portfolio Diversification and Risk Revisited

 -- Published: Monday, 31 December 2018 | Print  | Disqus 

My Two Cents

By Andy Sutton / Graham Mehl


This article was originally written by Andy Sutton on 7/24/2009; roughly 4 months after the markets bottomed from the 2008 blowout. Anything ‘new’ will be bolded. The ‘Two Cents’ series at the time was going through something of a post mortem of the meltdown and trying to give people a ‘reset’ so to speak regarding what was true and what wasn’t. People found out in 2008 – many the hard way – that mutual funds and ETFs didn’t really diversify away risk as advertised. Granted, when the broadest market measures are cut in half, let’s face it – everything got hit eventually. This was, of course, the plan as 2008 was little more than another consolidation of wealth from weak hands to strong hands. Would a solid diversification strategy have saved people the heartache of 2008? Almost definitely not. What it would have done, however, was minimize losses until on the ball investors had enough information to realize it was time to get out. That time came long before the worst losses were realized.


Most people still think that you need exposure all over the board to get good diversification. We’re talking paper exposure, since the world still insists on playing the paper game. That assumption is still a fallacy, just like it was a decade ago. Given the near 15% chop most US Indexes have gotten in the past month and change, we felt it appropriate to put this before readers again. For those inclined to act, the mathematics below should be fairly easy to follow and/or online ‘calculators’ exist for most of it. You can be assured, especially if you are a small (less than $1 million) client at any brokerage house that your ‘rep’ or ‘broker’ is not stress-testing your holdings in the manner below. Those services are reserved for preferred clients – the kind who were privy to Morgan Stanley’s up to date info right before the Facebook IPO debacle. Remember that? They gave their preferred clients the up to date info and sent the little guy to the gallows. That still goes on. If you don’t choose to believe us, that is your loss. Literally. Without further hesitation we present you with ‘Portfolio Diversification and Risk’ from 2009. There will be brief inline comments, but the entirety of the original column is below. With that said, we wish all of you a healthy 2019.


The clichés are plentiful and well known. Putting all of one’s eggs in a single basket is probably the most popular example. One of the biggest manifestations is when an investor looks at their portfolio and realizes that it is grossly underperforming a particular market index or that the same portfolio has performed much worse than a given benchmark. Even if you’ve done everything right and selected the right themes, industries, and firms, if you get the portfolio mix wrong, you can still have problems. This is one of headaches that mutual funds are generally supposed to relieve investors of, but for a litany of reasons, it doesn’t seem to always work out that way. In truth, every individual portfolio is a mutual fund of sorts, and so the same rules apply.



Types of Risk


In general, there are two broad types of risk: systematic (non-diversifiable) and non-systematic (diversifiable). Keep in mind that what we are discussing here is slightly different from geopolitical risk, currency risk, interest rate risk, etc. although each of those specific types of risk do contribute to the overall riskiness of a particular stock and as such cannot just be ignored.


The data in the chart below is from a 1987 study on diversification just after the market crashed. Obviously, at that time, diversification was a hot topic as investors scrambled to adjust portfolios and recoup the losses. The data below lists the number of components, the standard deviation of annual returns for each portfolio, and a comparison of the standard deviation of the portfolio to that of a single component. We have reformulated this study with current data and have found the axiom holds to the model below:


Below is a graphic representation of the data in the chart above. It may clearly be observed that standard deviation of the portfolio is asymptotic (law of diminishing returns) as it relates to eliminating the systematic (diversifiable) risk. In fact, once the number of portfolio assets surpasses 30, the standard deviation does not drop appreciably, even when another 970 components are added! Obviously, this reality enforces that quality is better than quantity.


Think of the case of the individual investor who buys 100 stocks thinking he is diversifying away all his risk.  He has borne a significant opportunity cost in the form of commissions without purchasing much in the way of additional protection from non-systematic risk. The upper portion of the chart deals with non-systematic risk, which can be largely diversified away. Notice though that even when the portfolio contains 1000 components that the standard deviation is still 19.21%. That constitutes the systematic risk.


A good example of systematic risk is pure market risk. Obviously if the capital markets crash again as they did in 2008, it will be exceedingly difficult to put together a basket of stocks that will withstand such a downward draft. There are other types of risk such as geopolitical, currency, inflation, interest rate, industry, and geographic. By using a crosscut approach to diversification, one is able to not only mitigate much of the non-systematic risk, but a good portion of the systematic risk as well. This is accomplished by looking at your themes selected several weeks ago, then addressing each type of systematic risk in your selection of assets. This approach is one of the main reasons that our Centsible Investor Model Portfolio has done so well while the broad markets have languished. The CI newsletter is no longer available, but was a model portfolio built using the methodology used in this article. Most people would consider it to be too conservative, but that’s what it was designed for. This is an important point. You can design a portfolio for almost any purpose – the iterations are only limited by our imaginations. You can use the methodology in this article to build a high growth model portfolio just as easily. Even in that situation, you’d still want to eliminate as much risk as possible, correct?


Beta (ß)


Quantitatively, Beta is the generally accepted measure of systematic risk for a stock and is defined as the amount of systematic risk present in a particular risky asset relative to that in an average risky asset (or an Index). Essentially what Beta does is compares a particular stock in this case with an average stock, or more accurately, a benchmark basket of stocks:


where ra measures the return of the asset, rp measures the return of a portfolio of risky assets (often the stocks in an index), and Cov(ra,rp) is the covariance of the returns.

Interpreting Beta is rather simple. 1.0 is the Rubicon so to speak. Betas lower than 1.0 indicate that the stock in question has a lower level of systematic risk than the ‘market’ while a Beta of greater than 1.0 indicates a stock that has a greater level of systematic risk than the ‘market’.


Knowing this, it becomes a rather simple matter to calculate the Beta of your portfolio simply by ascertaining the weight of each component and then multiplying it by that component’s Beta. Let’s use a hypothetical example where we have a 3-stock portfolio; Stock A is 25% of the portfolio, Stock B is 40% of the portfolio, and Stock C is 35% of the portfolio. The Beta of Stock A is .75, Stock B is .50, and Stock C is 1.25:


Betaportfolio= .75(.25) + .50(.40) + 1.25(.35)
Betaportfolio = .83


This calculation indicates that this 3-stock portfolio has systematic risk that is lower than that of the market, however, its non-systematic risk would be considerably higher than one would desire since there are only 3 components. All else being equal, the ideal would be to find a portfolio of perhaps 25-30 stocks that has a Betaportfolio of .83, as this would mitigate much of the non-systematic risk as well. Again, please keep in mind that just because you have diversified away non-systematic risk, this is no guarantee that your portfolio will never fall in value. While this exercise is valuable, in that it assists you in eliminating some of your risk, it is impossible to eliminate ALL risk. Even the ‘riskless asset’ used in most pricing models has currency, interest rate, and geopolitical risks embedded in it at a minimum. ALL allocation possibilities have at least some risk – even cash, which carries inflation, currency, and geopolitical risk. These risks will ebb and flow depending on the time period in question, but there is always risk.


Remember, the goal of all investment strategies should be to make sure that the return is commensurate with the risk taken. Using a 2018 example, we wouldn’t want to select an asset that has a beta of 2.0 that has a theoretical (or actual) return of 2.5%. We could get close to that from a bank CD. With a combined 60 years of economic and investment experience between the two of us, we have both observed that the biggest problem facing investors today is balancing risk and return. There are few in the investment community that take the time to properly explain this concept to their clients and fewer still who actually go through the trouble required to build a properly balanced portfolio. We have seen countless examples where investors were taking on way too much risk given the returns they were experiencing.


Beta and the Risk Premium


While using the term ‘risk-free’ in today’s financial and economic climate might result in a shower of protest, the concept of the risk-free asset has an important place in the discussion of risk vs. reward, particularly when selecting portfolio assets.


Let’s use an example of a stock with an expected return of 20% and a Beta of 1.6. Let us also assume (entirely for illustrative purposes) that the risk-free asset has a return of 8%, with a Beta of zero since it has neither systematic nor non-systematic risk. In the case of expected return, we are relying on an educated guess, but in the case of stocks that pay dividends, one could easily plug the dividend yield into the expected return as well. When we plot out our stock and the risk-free rate and generate a Security Market Line (SML), we get the following:


The chart above is relatively easy to interpret; we consider the ‘risk-free’ asset Rf with its corresponding Beta of zero and return of 8% and our stock with its Beta of 1.6 and its expected return E(RA) of 20%. When we connect the dots and measure the slope of the line (rise/run), we get a slope of 7.5%. From this graph, we can ascertain that our stock has a reward to risk ratio of 7.5% meaning that our stock has a risk premium of 7.5% for each ‘unit’ of systematic risk. Obviously, the higher the reward to risk ratio, the better, meaning we’d want to see higher E(RA) and/or lower Beta; either of which would increase the slope.


In a final example, let us now compare our stock in the previous example (called Stock A) with a second stock (Stock B). Stock B has a Beta of 1.2 and an expected return E(RB) of 16%. When we construct our Security Market Line, we end up with a slightly different picture than we had with Stock A.


The reward to risk ratio (or slope of the line) for Stock B is 6.67%. What this tells us (all other things equal) is that in essence, Stock A is a ‘better’ choice than Stock B simply because it generates more reward for each unit of systematic risk undertaken.


This analysis is especially useful when one is selecting portfolio components and wants exposure to a particular industry or sector, has multiple candidates, but doesn’t want to include them all for fear of being overweight that particular area. In this manner, the candidates may be lined up and compared to see both visually and quantitatively where the best bang for the buck lies.


Of all the areas discussed in our sample exercise over the past few weeks, diversification and risk are the two areas where investors are most likely to stumble. Many fail to properly diversify because they don’t understand the value of it or because they don’t have enough capital to diversify by purchasing individual stocks and should look (very carefully) to ETFs, open-end or closed-end funds as an alternative, while keeping the above in mind. While the analysis above was primarily for stocks, those investors seeking to hedge their portfolios with precious metals can certainly plug their favorite shiny coins into this analysis. For those so inclined, Betas may be hand/Excel-calculated for commodities using the major indexes, or commodity indexes, such as the CRB as the ‘market’ portion of the calculation.


In summation, probably the most important takeaway from this article should be that a portfolio doesn’t need 100 components to be adequately diversified in terms of non-systematic risk. 30-40 will do just fine as the math above demonstrates. A second important point is that by using your economic themes and how they relate to systematic risks in your selection of an appropriate number of assets, you can mitigate a good deal of the systematic risk to your portfolio as well.


None of the above should be construed as investment advice. It is for educational and informational purposes only, using generally accepted financial analysis techniques to examine a basket of hypothetical assets. This is just one ‘tool’ in a comprehensive investment approach. Speak with a qualified investment professional before making any decisions.



Graham Mehl is a pseudonym. He is not an ‘insider’. He is required to use a pseudonym by the policies of his firm when releasing written work for public consumption. Although not an insider, he is astonishingly bright, having received an MBA with highest honors from the Wharton Business School at the University of Pennsylvania. He has also worked as an analyst for hedge funds and one G7 level central bank.



Andy Sutton is a research and freelance Economist. He received international honors for his work in economics at the graduate level and currently teaches high school business. Among his current research work is identifying the line in the sand where economies crumble due to extraneous debt through the use of economic modelling. His focus is also educating young people about the science of Economics using an evidence-based approach.



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