Today we have a guest post on the topic of asset allocation from a physician contributor that goes by the pseudonym Gasem. For those following physician personal finance blogs and forums, he needs no introduction; his insightful, helpful, and witty comments are ubiquitous in the physician PF space.
However, many readers on this blog may not be acquainted with him yet. So here’s the scoop. Gasem is a 66 year old retired anesthesiologist from Florida who has worn many hats throughout his decidedly unconventional life. He has worked as an electrical engineer, college professor, commodities trader, and investor. And if that wasn’t enough, he has built three successful medical practices as an anesthesiologist and pain physician. He is also the proud father of two exceptional daughters.
Gasem has always lived life on his own terms and is financially independent, enjoying retirement, and “having a gas”!
Asset Allocation Quantitative Style
There are many simple passive portfolios floating around.
A simple portfolio is one that consists of a mixture of asset classes valuations that are tracked by mutual funds. The reason people choose mutual funds is they lower risk compared to single issue assets like a stock. The risk drops as stocks are added, but the risk eventually becomes asymptotic so more and more issues yields virtually no change in risk (1977 study Elton and Gruber).
The asymptotic number is about 20. In their study, 50 stocks gave an average SD of 20.1 while 1000 stocks gave a SD of 19.2. Therefore, owning 950 more issues gave only a tiny bit more diversity. But owning 950 more issues certainly gives considerably more expense, which is a risk in itself.
The point is: diversification is asymptotic and not without cost.
Therefore, piling more and more issues on the portfolio heap is not necessarily efficient. Once you reach market risk, you reach market risk and should turn your attention elsewhere when choosing a portfolio.
Asset Correlation
Nobel winner and University of Chicago professor Harry Markowitz sought to understand how individual assets in a portfolio join with each other in a quantitive way.
For example, you can create a binary portfolio of stocks and bonds or stock and bond mutual funds or a more complicated portfolio like stocks, bonds, REITS, commodities etc. Each of these individual issues has an associated reward and risk and each has a correlation between itself and the other assets in the portfolio.
A VTSMX, VBMFX portfolio would look like this:
| Asset | Reward | Risk | Correlation | |
| VTSMX | 10.82 | 14.44 |
1 |
|
| VBMFX | 5.17 | 3.55 |
0.01 |
|
| 70/30 | 9.14 | 10.27 | ||
| 50/50 | 7.93 | 7.38 | ||
| 30/70 | 6.85 | 5.04 | ||
| Tangent | 15/85 | 6.01 | 3.73 |
What we see is stocks are riskier and give a greater return compared to bonds. Also, stocks and bonds are uncorrelated, meaning as one changes the other is indifferent.
Combining Assets
It turns out through some higher-level math, you can combine these assets in a portfolio to form a “new asset” with its own risk and its own return. In the table above, we see several asset combinations with the relative risk and return for each combo.
Since variance is a S^2 function, it generates a curve and is not linear. It looks parabolic.
It further turns out you can compare this (reward, risk) to an asset called a risk-free asset (typically a 3-month T-Bill). From that you can understand your relative increase of return and your relative increase of risk.
Tangent Portfolio
There is a point on the curve called the tangent portfolio. This is the point of maximum return for minimum risk.
Here is a pictorial of what I have just described.
Efficient Frontier
This is an efficient frontier.
Every point on the line lays on the frontier and is a maximally optimized ratio of VTSMX and VBMFX. The most optimized is the tangent portfolio (best bang for the buck).
If your portfolio is not on the frontier, you pay too much risk for your return.
What does that statement mean?
Suppose you play a game. Choice A has a 50/50 chance of doubling your money. Choice B has a 1/10 chance of doubling your money. Which do you choose?
Choice A of course! Every single time. The return is the same (100%, or doubling your money), but the risk is much larger in choice B.
When you choose a portfolio not on the efficient frontier you are precisely choosing B, a choice that is riskier for the same return.
Portfolio Comparisons
So far, we have taken a look at a two fund portfolio containing VTSMX and VBMFX.
Let’s take a look at the Boglehead 3 fund portfolio, which adds VGTSX (total international stock index fund).
Below is a pictorial that relates the Bogelhead 3 (provided portfolio as shown in picture) to the efficient frontier. Notice 7.84% return for 12.31% risk.
Boglehead 3 Portfolio
Boglehead 3 compared to the efficient frontier of a 2 fund portfolio with the same expected return…
To illustrate this point further, the table below relates an efficient frontier portfolio of 60% VTSMX / 40% VBMFX, to the Bogelhead 3 Portfolio (50% VTSMX / 30% VGTSX / 20% VBMFX).
| Asset | Reward | Risk | Correlation | ||
| VTSMX | 10.82 | 14.44 | 1 | ||
| VBMFX | 5.17 | 3.55 |
0.01 |
||
| VGTSX | 6.65 | 17.16 |
0.86 |
||
| 50/30/20 | 7.84 |
12.31 |
|||
| 60/40 | 7.82 | 9.35 | |||
Notice for the same return of 7.8%, owning the 2-fund portfolio is 25% less risky.
Recall the game. The reason you chose A is because it is less risky.
What if we add more to the portfolio?
Let’s look at the Bogelhead 4 portfolio, which adds VIPSX.
The equivalent expected return in a efficient frontier 2 fund (6.92% return / 9.23% risk) compared to the Boglehead 4 ( 6.94% return / 12.18 risk) is 28% riskier.
As you can see, diversification is asymptotic and adding more issues to your portfolio is not necessarily more efficient.
What are the conclusions?
- Risk needs to be considered in every asset allocation. The returns are combined in a linear fashion BUT the risks are combined in a quadratic fashion so asset combinations are not straight forward
- By using the right tool you can choose the most bang for the buck (aka most return for least risk).
- You can choose your risk with some level of rationality beyond just guessing
- Once you reach market risk adding more and more is pointless. Market risk is asymptotic.
The pictorials and data for this article were provided by Portfolio Visualizer using the historical efficient frontier module.
Editor’s Note:
I want to thank Gasem for this article and for all of his contributions to the physician personal finance space.
Because of the work of my fellow physician bloggers and frequent commenters (like Gasem), I’ve come a long way from being just a frugal resident (approximately ten years ago) to where I am today.
If you would like to read more of Gasem’s articles on other great blogs, here are a few you should check out:
- Early Retirement is for Suckas! (guest post on Half Life Theory)
- Retirement Portfolio: Buckets of Time or Buckets of Risk? (guest post on XrayVsn)
- A Quantitative Method To Look At Retirement Portfolio Risk (guest post on XrayVsn)
- Efficient Frontier (guest post on Doctor of Finance MD)
- Home Schooling: Educational Independence (guest post on Crispy Doc)
- The Zen of Diversity: Asset Classes, Epochs, and the Efficient Frontier (guest post on Physician on Fire)
- Monte Carlo Analysis (guest post on Doctor of Finance MD)
- Make Efficient Roth Conversions and Optimize Taxes (guest post on Dads Dollars Debts)
If I missed a guest post, let me know. I’ll be sure to add it! 🙂
As always, Gasem provides very insightful posts. He definitely has one of the most analytical minds I have come across in the blogosphere.
Its a great sign that you feel smarter after reading a post and this certainly qualifies.
I agree with you 100%. He must get his analytical mind from his engineering days. And his ability to teach complex subjects in a simple way must go back to the days when he was a professor!
I always feel smarter (and entertained) after reading his posts and comments!!!
Your accolades are kind but the real credit goes to financial giants like Harry Markowitz. My goal in my articles is to add a little quantitative twist to the common understanding. plus it’s a gas.
I am alerting my American based Cdn colleagues about all this stuff. As a Canadian investor, I get to buy indexes with Canadian and All World without Canada ETF’s. We get hammered on the currency exchanges and taxation issues with foreign stocks. Plus when I enter my ETFs into portfolio visualizer, it will not work since my ETFs are so new. But I really enjoy learning from how Gasem thinks.
There are too many folks in the PF blogs who have only seen bull markets. They simply don’t know what they don’t know. There is zero correlation of “believing” that you will not sell during a prolonged down market. It’s like marriage- I am certain everyone thinks divorce will not happen to them till it does!
Gasem has invested and likely profited during many dips in the investment cycle. I would listen to this man. And I am tired of hearing physicians state that they held during the great financial crisis of 2008/2009. Based on their age- they probably have extremely little money during that time so it would have been very easy to hold on. Try doing that when you have multimillions in stocks and watch it halved or more.
Market failure is the main reason to optimize. In a downturn risk dominates. Much of my stuff has as an underlying theme, risk mitigation. I read your recent post on the one fund solution and tried to do a quant analysis but the funds are too new to be able to generate the statistical distributions. I did an analysis on (VOO, VBMFX) v VASGX which is the American version of life growth strategy and (VOO, VBMFX) was lower risk at similar return compared to the single fund VASGX. My lack of detail on the why’s and wherefores of currency exchange and Canadian taxes kept me from posting.
Yea, I’ve been through many downturns and lost a lot of money and have the tax loss harvest to prove it but the investing vehicles we have these days are very efficient and accessible, That in itself reduces the risk. Using Personal Capital is a boon to modern day investing. The aggregation of assets is necessary to understand risk specific to your personal portfolio, and the analytic tools like the efficient frontier asset allocator and Monte Carlo module is 21st century class when it comes to portfolio management. I would just use that as a guide compared to some one fund solution.
Thanks Gasem! You and I are inherent risk mitigators. The difference is you are waaay more sophisticated than I am while I truly am LAZY!! I have come to accept that about myself and starting to revel in it.
I have watched plenty of my colleagues go back to work after the markets went bust in the past. That’s why I’m probably more careful than most. You will never see me going 80% in equities. This stuff is for those who never saved enough money and I am using it for my “never need money”.
I too enjoy Gasem’s posts and point of view. No one seems to care about risk any more. I consider myself a survivor. I know what it is like to lose several million dollars in a few months (twice). It is very bad but I survived without panicking so it can be done. Gasem helps quantify our thoughts and provides cool graphs.
Thanks Hatton1. The trick is to not think of your “property” in terms of dollars. If you own 1000 shares of BRK.B and the market value drops in half, you still own 1000 shares and need to rev up your engines to buy some more. Eventually the market value will recover and your cheap purchase will shine. Buy low, the Buffet mantra!
Gasem, in your 2 vs 3 fund Bogleheads example, can you instead compare 70/30 (TSM/TBM) vs 50/20/30 (TSM/TISM/TBM)? It seems a bit disingenuous to compare a 60/40 portfolio with a 50+20/30 portfolio and applaud the portfolio with 40% bonds for having lower risk—this would be expected. The surprising point there is that the higher stock allocation (when adding Int’l) doesn’t increase return. A major limitation of Portfolio Visualizer is inception dates of funds—the Int’l fund is much younger, if I recall, which would also effect the results, no?
I held return constant. I chose 60/40 because that gave me the same return as 50/30/20. I didn’t choose 60/40 it just worked out that way statically. It’s exactly the same as in my game example. The return was the same but the risk different. The reason 50/30/20 fares worse is International is inherently a crappy choice over time. It has a much higher risk and a much lower return on the risk reward plane as evidenced in the graph and table. It also is more expensive to own and has issue with currency exchange rates and tax treatment. It also is highly correlated to US stocks so provides little in improved diversity. When the bear comes International heads into the ground with virtually the same velocity as US so what’s the point of owning crappy return, crappy risk, and crappy diversity? This is precisely the value of the efficient frontier. You buy your return without paying too much in terms of risk, and you can understand your relative risk in a quantitative way. Your understanding is based on mathematics not politics or blogoland echo chamber.
The “fund newness” is nor relevant. This is a common misunderstanding. What the length of time does to the calculation is enhance the signal to noise on both return and variance. 10 years gives a better average return and variance prediction compared to one year. In my game example you don’t understand your relative risk until you get past 10. So if you played only 5 times, your return picture is constant at 100% but your risk picture would still be noisy. Each additional play adds clarity to the probability until you get past 10 where it becomes asymptotic and you can make your best choice. In my experience Portfolio Visualizer is pretty good after about 4 years of history in terms of signal to noise. If you put in other non correlated assets like gold or TIPs you may get a different mix of portfolio assets not just stocks and bonds depending on correlation and risk. The efficient frontier isn’t perfect. We could get an EMP and the data wouldn’t save you. At that point you better own bullets. It is a way to understand risk and reward that’s better than a Bogelhead’s guess IMHO.
I forgot one point. Good questions. I ran TSM and TBM along with the Bogelhead 3 and the program chose 70% VBMFX and 30% TSM to give a return of 7,84% and a risk of 11.28% slightly better than the Bogelhead 3 in terms of risk. TSM (Tiwan Semiconductor) is a single stock with a return of 15% and a SD of 36%. This would not be as good a choice as the 60/40 choice but better than the Bogelhead 3. This example points out the difference between single stock risk and market risk. Since most of your money is in bonds TSM adds return and risk to an extent slightly better than the BH3. If TSM fell in half it would only affect about 15% of the portfolio’s return as the bulk is VBMFX.
I added AMZN AAPL FB and BRK.B to the mix and the suggestion for a 7.8% return was:
BRK.B 12%
TSM 1%
AMZN 5%
FB 4%
VTSMX 6%
VBMFX 72%
With an expected return of 7.77% and a risk of 3.88% Not bad! FWIW I own individual shares like AMZN BRK.B FB exactly for this reason. A little dab lowers risk while maintaining return. My portfolio is risked at about 2/3 of SPY (10%) for an 8% expected return, and sits on the efficient frontier.
Here’s a new post over on XRAYVSN’s site
https://xrayvsn.com/2018/08/16/guest-post-gasem-buckets-of-time-or-buckets-of-risk-retirement-portfolio/
I appreciate your aggregating my posts!
Awesome! I just added it 🙂
Essentially, this is an argument against holding international funds, or at least a total international fund. If the return is indeed lower and the risk is higher, it’s not a good bet.
Yet, Vanguard’s target date funds allocate 40% of their stock allocations to international funds. P/E ratios for international funds are much lower than for US Stocks.
Based on the above analysis, I can understand someone wanting to avoid international stocks, but I don’t know how wise it is to have all your eggs in America’s basket. And I know some very smart people, including Jack Bogle, have said you don’t necessarily need international funds. But the Japanese who didn’t own international funds haven’t fared well over the last few decades. Diversity can be your friend.
Cheers!
-PoF
Hey PoF! One thing to consider is Vanguard is a seller of funds. That’s how they make their money, and even though they are the most efficient fund seller around based on corporate structure they still are fund salesmen. If all you hear is “BUY Bogelhead 3” honking everywhere and you were a fund company why would you not also sell a “Bogelhead 3” knockoff as a product? If I were the marketing dude at Vanguard I sure would.
The numbers speak for themselves. Personally I’m not willing to bet against the US by choosing an inferior product funded with a significant amount of assets on a “what if” basis. What if America doesn’t become Japan? You spent 20 years in an inferior portfolio. That is what the lower return and higher SD tells you. 30% of a portfolio is a lot to devote to poor performance. In addition much of the “American” portfolio has significant international exposure already unless you are all small cap. My foreign equity is 13% split, 10% international and 3% emerging markets. If America catches the flu everybody catches the flu, period. This was not the case with Japan. As long as America remains the reserve currency holder, the chance of America becoming Japan is pretty small in my opinion. Diversity is your friend, but only non correlated diversity. Once you reach market risk with a fund then your choice is entirely based on diversity return and risk.
Seem above
VSTMX is 10.82% 14.84% and a correlation of 1 with iself
VGSTX is 6.65% 17.16% with a correlation of ,86 relative to VSTMX
This means your VGSTX product looses at least 86 cents for every dollar your VTSMX product looses. on a correlation basis, BUT BUT it has a much higher SD which means it falls faster and deeper. In 2008 SPY lost 50%. The diversified interationals lost as much as 70%. One word: BUMMER. On the other hand if the correlation was close to 0 the money you had in the non correlated asset was indifferent to SPY’s antics. The correlation between VTSMX and VBMFX is 0.01. This is the saving grace of owning bonds, it’s almost perfectly uncorrelated and indifferent to stocks.
An interesting side light:
BRK.B is 12.63% 19% and only 42% correlated with VTSMX
A suggested VTSMX VBMFX BRK.B portfolio is
VTSMX 21%
VBMFX 53%
BRK.B 26%
With 7.84% return and only 7.14% risk So tell me do you want to own some BRK.B (Buffet) or a Turkey? Oh wait Buffet is going to die someday, but what about Turkey?
Good discussion it show cases the power of quant analysis. Thanks PoF
Gotta love how you never let the sleeping dogmas lie, Gasem.
Have you ever tried a head on debate via the Bogleheads forum or inquiring about the risk discrepancy of Taylor Larimore himself? It would be less about the conflict than seeing great minds work out a few thorny issues of interest to those of us in awe of the fire power you bring to the battle.
Fondly,
CD
I’m retired!
Imagine a Catholic and a Calvinist going at it. It would devolve into a battle of religion seasoned with testosterone. The only sane way to approach this is to offer the argument and the bread crumbs to the data (like the asymptotic nature of diversity) and let the people actually do a little research and thinking and bake in the conclusion. Some people approach their future with 6th grade reward looking fractions, some with PhD level forward looking predictive statistics, neither is determinant. Some approach with dreams of being RICH, some with dreams of not dying poor. One thing I love is creative disruption. Creative disruption given time virtually, always yields a more resilient result.
There was a time when we used leeches.
Gassem, always comes through with very insightful thoughts! Love this! Seeing the numbers right in front of you makes it even that more compelling. Sometimes the added “diversification” we think we are getting only further increases risk.
Might not sound logical at first glance, but actually makes perfect sense. Cheers!
Half Life look up over-diversification. It is a thing in the finance community.
One other thing diversity is related to correlation. Think of a wheel with an elastic perimeter, then think of spokes in the wheel. Imagine the spokes are vectors with direction and magnitude. Imagine the value of your portfolio is related to the area of the wheel. Lets say you start with a round wheel, then one day the vertical spoke (stocks) falls in half. Your wheel lost a lot of area. Imagine you have a spoke going in the other direction (VIX or GLD) that grows as STOCKS shrink. The area stays more constant. Imagine you have spokes that go right and left (BONDS) These don’t change with respect to stocks but are extremely important to keeping area constant. This is how diversity actually works. Combination is by vector not just magnitude. Having 2 spokes that go in virtually the same direction (highly correlated) just means when one crashes the other tends to crash also. SD is a further culprit as the higher the SD the farther the crash it’s a kind of multiplier. Is that diversity? EM made a lot of money last year, better than US. This year they are underwater. EM correlation is 0,77 and SD is 22% compared to 15% on the US. Return on the US is 11.29% v 9.17 on the EM. So EM is moderately correlated BUT hugely risky (46% more risk) and has 20% less return than US. Sound like a good deal to you? I own a tiny but of EM about 3%. The wheel spoke analogy isn’t perfect (and certainly not quantitative), but it gives a different flavor to understanding how true diversity gives a portfolio protection.
There are times something like EM can hit it out of the park. Those times are when creative destruction comes to market. Imagine the world pre MSFT and post MSFT. Imagine the world pre AAPL and post AAPL. Imagine the world pre FB and post FB. Imagine pre AMZN and post. Each of these brought creative destruction to the market. Sometimes the creative destruction causes a vertical increase in value such that the initial purchase becomes trivial. I bought BTC at $275 and am up about 2400%. My trading tactic after I bought was to just sit on it. One day it was up 1000% and I sold my initial stake. That means what is left is free money. There is no absolute downside as my money is already out. Yes at one time I was up almost 7000% I put the seed money into BRK.B so if BTC goes 100% bust I still own BRK.B. But it won’t go 100% bust. It’s volatility has settled. It’s still volatile but not crazy.