Part 2: Modern Portfolio Theory in Five Minutes
By Patrick Rau, CFA ∙ May 2016
I have no desire to write a textbook about complicated portfolio theory, and I bet you have no real desire to read one right now, either. However, there are a few general financial concepts that are important for you to know, in order to put the asset allocation process in context. So how about we compromise. You give me five minutes, and I’ll lay out these ideas as quickly and simply as I can.
First, A Few Thoughts About Diversification
Diversification speaks to the old investment cliché of “not putting all your eggs in one basket.” I think there has to be some sort of unwritten rule among investment professionals and academics that they must explain the concept in exactly that way. But the metaphor is a good one. The main goal of diversification is to protect yourself in case some of your investments lose value. If you spread your risk among several different investments, the idea is some should rise when others fall, or at least others may not fall as much. That helps keep your losses in check. If some of your securities zig when others zag, you won’t suffer as great a loss as if all of them zig or zag together.
To set the table on how diversification impacts the risk of your portfolio, allow me to reintroduce an example I used in the first paper of this series. In Part 1, I showed that the expected return of a portfolio is simply the weighted average of the expected returns of its individual components. For example, if a portfolio is 50% invested in a security with an expected return of 12%, and the other 50% in a security with an expected return of 6%, the expected return for the entire portfolio is (.5)(.12) + (.5)(.06) = .09, or 9%. Now let’s assume these two securities also have individual standard deviations of .12 and .06. As long as the returns of those two assets do not move perfectly in tandem – as long as there is any difference in the return patterns of those two securities – then combining them will lower the overall standard deviation of the portfolio. Said differently, as long as the correlation coefficient between two assets is less than 1, then combining them will produce a portfolio standard deviation that is lower than the weighted average of those individual standard deviations.
I won’t bore you to tears with the exact formula for this (well, any more than I have already….), but if you would like to see it, you can find it here. If we assume the two assets in the example above have a correlation coefficient of 0.6, the standard deviation for this portfolio is 8.2%. If they have a correlation coefficient of -0.3, the portfolio standard deviation falls even more, to 5.8%. The calculation gets significantly more complicated with three or more securities, but you get the general idea. Note that the expected return between these two securities is still 9%. It’s just that the lower the correlation coefficient between the two, the lower the portfolio risk. Please see the table below for recent correlation coefficients among the various major asset classes.
About the Author
Patrick Rau, CFA, is a former Wall Street equity research analyst on both the sell and buy sides. He has covered a number of industries over the years, including specializing in the oil & gas and semiconductor sectors, and serving as a generalist. For examples of his previous stock picks, please see the Equity Research tab. Pat is married to Brenda Rau, Licensed Real Estate Salesperson with Compass Real Estate in NYC.
Other Articles in this Series
Part 1 - Historical Asset Class Returns
Part 3 - The Asset Allocation Process
Part 4 - Mutual Funds vs. ETFs
Part 5 - Managed vs. Index Funds
Part 6 - Should I Hire An Investment Professional?
Part 7 - Things That May Improve Your Portfolio's Performance
Part 8 - Thoughts on Retirement Spending
Part 9 - Diagnostic Portfolio Checklist
Whoa, whoa, hold it a minute. In the last article, you basically said it makes sense to just pick asset classes with the highest expected return over long-term investment horizons. You even suggested putting up to 100% of one’s long-term focused portfolio in stocks. So how is that diversification? It’s not. In fact, it’s the very opposite of diversification. But remember, diversification is about spreading risk over a number of different investments, in order to guard against severe negative movements in any one or more of those. In other words, in order to protect against severe negative differences from a particular asset’s expected return.
Past results are no guarantee of future performance, so it is certainly possible that stocks could underperform their historical returns going forward. However, even if future stock returns disappoint, they should still outperform bonds and cash over the long run. Take another look at the section in Part 1 about time diversification, and the Jeremy Siegel data in particular. Siegel shows that stocks outperform fixed income securities and cash ~100% of the time over 30-year investment horizons. Moreover, stocks are much more likely to keep pace with future inflation than are bonds and cash. Better to have a larger percentage of your long-term portfolio in stocks, everything else being equal.
However, diversification among asset classes (stocks vs. bonds vs. cash, etc.) becomes much more important for smaller investment horizons, say less than thirty years, and for all investors who are conservative in their willingness and ability to accept risk, regardless of their time horizons. Furthermore, unless you are super risk aggressive and have enough financial reserves to afford sustaining major losses, diversification within asset classes is always important, regardless of your time horizon. For example, say you have a nicely diversified portfolio that is 40% stocks, 40% bonds, 10% REITs, and 10% cash. Now further assume the entire stock portion of your portfolio is equally invested in just two stocks. What if one or both of those companies loses a substantial part of their value? Stocks in general should achieve positive returns over time, but any particular stock could suffer significant losses. Many employees at Enron held a large part of their retirement accounts in company stock, and unfortunately, lost a major part of their retirement savings when the company declared bankruptcy in 2001.
This specific company risk is called idiosyncratic, or non-systematic risk. The stock market will always carry a certain amount of systematic risk that impacts all stocks, but this unsystematic, company specific risk can be diversified away by holding a large enough number of equities, preferably spread among companies that operate in a number of different industries. Many experts recommend holding anywhere between 15-30 individual securities in order to achieve an optimal level of diversification. Anything above this range will still provide some additional benefits, but by a lower and lower incremental amount. It can also greatly increase transaction costs.
Purchasing so many individual securities would be far too cost prohibitive for most investors, but fortunately, there are mutual funds and exchange trade funds (ETFs) that will take care of this for you, and you do not need to hold many of them to properly diversify. I explain the differences between mutual funds and ETFs in Part 4 of this series.
Modern Portfolio Theory
As Fidelity.com so aptly describes, “the goal of diversification is not to boost performance—it won’t ensure gains or guarantee against losses. But once you choose to target a level of risk based on your goals, time horizon, and tolerance for volatility, diversification may provide the potential to improve returns for that level of risk.” In some cases, diversification may even actually do both: increase return and reduce risk. To illustrate, I’d like to borrow an example created by Morningstar.com.
In this scenario (and remember, this is just an example. Actual figures in the market today may be very different from these), assume an investor holds Portfolio A, comprised 100% of large stocks. His or her annual expected return is 12.3%, with a standard deviation of 16.2%. By changing this to the 60% small and mid-cap 40% large-cap mix in Portfolio C, our investor has the same 16.2% portfolio standard deviation, but a higher 14.4% expected annual return. Greater expected return for the same risk. The expected return of the 70% large-cap 30% smaller cap mix in Portfolio D is less than that for Portfolio C, but still more than that for Portfolio A, and its standard deviation is lower than that for Portfolios A and C. Portfolios C & D both have better risk-return profiles than that for Portfolio A. Not bad, eh? Similarly, several prominent studies conducted the same test on U.S. vs. EAFE (Europe, Australia, Far East) stocks, and found the optimal portfolio mix for U.S. investors to be 60% domestic, 40% EAFE.
Now imagine continuing this process among many different asset classes, with different expected returns, standard deviations, and correlation coefficients. If you did, you could determine the portfolio mix that would produce the highest expected return for the given amount of risk. This concept is called (Harry) Markowitz mean-variance optimization, and is represented by the efficiency frontier, which shows the best possible expected outcomes an investor can expect to earn for a given amount of risk. The graph below shows a two asset class mix, which I have done for simplicity. This concept assumes that most people are risk averse, meaning in order to take on increased risk, they require a higher expected return. The shape of the curve reflects this. If you add in investor utility curves, then the intersection of a utility curve to the efficiency frontier gives the theoretical optimum portfolio allocation for a particular investor. Investor A is willing or able to take less risk than Investor B, so the optimum portfolio for investor A features a lower expected return than that for Investor B.
Note, however, that this efficiency frontier only has risky assets. If we include risk free assets (such as treasury bills), and assume we have a portfolio with enough securities so that we have diversified away non-systematic (company specific) risk, then the efficiency frontier becomes a straight line called the capital market line, the risk measure becomes beta (how your portfolio differs from a market portfolio of all risky assets), and your portfolio composition depends on how much of your portfolio you want in risk-free assets. For you finance heads, this is the basis of the Capital Asset Pricing Model (CAPM).
For you non-financial folks, these models attempt to show exactly what your proper asset allocation should be, given your ability and willingness to accept risk. That is a good thing. But applying these models is much easier said than done, since they are based on a labyrinth of mathematical calculations that ideally should be handled by specialized software. Many investment professionals have access such software, and would love to charge you for the expertise they are able to derive from it. However, I believe you can create a reasonable proxy for what those models would tell you by considering the principles I cover in the next article.
Next Time
In Part 3, I dive into the asset allocation process, and provide a few hypothetical target allocations for investors with different investment goals, risk profiles, and time horizons.
Patrick Rau, CFA, is a former equity research analyst, both on the sell-side specializing in energy and the buy-side as a generalist for a financial advisory firm. He holds a B.A. in Economics from the College of William & Mary, and an MBA in Finance from Georgetown University. He is married to Brenda Rau, Licensed Real Estate Salesperson with Compass Real Estate in New York City.
Disclaimer: All information and calculations are based on information deemed to be reliable. Patrick Rau, CFA is not an investment advisor, and this paper is for educational purposes only. Nothing herein should be considered financial or investment advice. Moreover, Patrick Rau, CFA shall not be liable for any losses or damages that may result from any decisions you make based on any of this content.