Efficient Frontier

It’s no secret I’m a big fan of efficient investing.  Efficient investing means you pay for your return with no more risk than necessary.  If your in a cup game where a ball is hidden under a cup, you want the least number of cups in the game.  3 cups 1/3 odds.  8 cups 1/8 odds.  The bet (return) is the same so what is varying is risk.  Less cups means risk optimization and a greater chance of success.  I play a lotto game every week.  I don’t play power ball or mega million, I play lucky money.  Power ball has a 300M:1 chance, lucky money is 3M:1 so my 1 dollar ticket is equal to 100 bux worth of tickets on the other game.  Lucky Money caps at a 2M payout.  If the cap is reached the excess trickles down to lesser prizes so the $10 dollar payout with much better odds may grow to $15.  I don’t win a lot but I do win sometimes.  I win enough to buy myself a more expensive ticket on another game when that game hits 1.6 billion and the cost of playing for the 1.6 billion ticket is free because it’s from the free money out of winnings from the less risky bet.  Over the years I’ve hit $800-$1000 a couple times so at one buck a week the whole shootin’ match is free.  Playing for free is good risk management.   I could cash out and buy hamburgers, but I already have a source of hamburgers so I’ll risk a little free money.  You never know, plus it’s a hoot optimizing my risk.   Risk management is the driver for my play, not return.  

This is no different with portfolios.  IMHO that is all about risk management as well.  The beloved Harry Markowitz published a paper, the year I was born, on optimal portfolio selection which included risk, asset correlation, return, variance and co-variance.  The zero point or origin is called a risk free asset.  It is an asset where you can park your wealth and be virtually assured of your return.  The risk free asset is typically short term govenment paper called T-Bills.  Your risk and return on any other asset is therefore judged against the Risk free asset. 

Here is a pic of a Bogglehead 50/50 2 fund efficient frontier.  You see the curve sits on a plane.  Every point on the plane represents a risk (SD) on the horizontal axis and a reward (% return) on the vertical.  0.0, 0.0 is the risk free asset (T-Bill).  Every this else is related to this.  You see VBMFX which has a 4.79% return and a 3.4% risk compared to a T-Bill.  You see VTSMX which has a 9.9% return and a 15.19% risk.  Remember when you own stocks and bonds you own property.  What those numbers tell you is when the value of the bond property drops say 50% the value of the stock property drops 4.6 times more, mucho risk. (there is a correlation factor in there yet to be addressed I just want to let the risk nature of two assets to sink in.  To own bonds you can expect to get 4.79% back on your money.  To own stocks 9.9%.  Owning stocks gives you only 2 x the return that owning bonds yields, but at 4.6 times the risk.  You are paying for your return with a hell of a lot of risk.  Note these values are averaged values for each asset from 1997 to 2018.  The calculations are quadratic which means they are not linear but curved, and id you have a curve you can define a maximum point.  The maximum point on this curve is called the tangent portfolio.  It is the ratio of these assets that pays the most return for the least risk.  Those values are 16% VTSMX and 84% VBMFX and you can expect 5.55% return for only 3.58% risk.  Best bang for the buck.  The risk goes up a measly .18% (3.58-3.4) and the return goes up 0.76%.  How many boggleheads kvetch over saving 3 bp on the cost of a fund?  This is a whole 76 bp increased return!  

Notice the provided 50/50 portfolio.  It still lives on the efficient frontier.  You still pay an optimum amount of risk for your reward, it’s just that you choose to own a more risky portfolio in hopes of greater return.  The R/R of a 50/50 is 7.69 risk 7.32 return.  You pay 46% more risk for 31% more return.  The curve is curved because Bonds and Stocks have almost zero correlation so when the value of one is oscillating the value of the other is pretty much static.  The efficient frontier calculator likes non correlated assets because of this because it further reduces risk.  In fact some assets tend to grow in the face of a stock down turn.  Gold is such an asset.

Here is a picture of gold v S&P 500 during the 2008 down turn.  If you owned some gold and S&P, and you needed some money in 2009 what would you sell?  Buy low sell high of course, sell the gold!  This is why I own some gold.  It’s not investing it’s insurance,  it also points out the value of non-correlation.  

The bogglehead 3!:

Boggle heads love their 3 fund.  The rap is all about “diversity”  If you own more piled higher and deeper you are more diverse (right?) so let’s own US International, AND Bonds by golly.  Lets look at that on the frontier:

Remember every point on the plane represents a risk and a reward and the above is the R/R of 50% VTSMX, 30% VGSTX and 20% VBMFX, the vaunted 3 fund.  The return is 7.84% and the risk a whopping 12.27%!  Recall the 50/50 2 fund was 7.32 return and 7.69 risk.  All I can say is DUH owning a 3 fund is stupid stupid stupid.  You pay 63 cents more risk for 7 cents more return.  BUT BUT BUT how can that be Mr Natural?  

The R/R for VGTSX is 6.5% and 17.10, super risky, shitty return.  The correlation between VGSTX and VTSMX is 0.85 an high correlation means the 2 assets act nearly identically as far as response to a crash.  So you own a shitty asset compared to VTSMX (6.5% return v 9.9% return) but your risk is greater (17.1% v 15.19%)  Note these are averages.   Any one year a given class can out perform but on the average… (complete this sentence).  

So there you have it, lesson 1 in efficient frontier.  I may write a follow up about market diversity.

You can play with the calculator yourself 

6 Replies to “Efficient Frontier”

  1. If I was an American, I’d use the two fund portfolio!! I believe in keeping things simple. And if you also get a good risk profile as well, then that’s a no brainer.

    I am Canadian and have to use whatever portfolio is offered to me. I wanted to invest in Vanguard mutual funds when I was 25 yrs old and recently graduated. We got Canadian Vanguard mutual funds this year. I am almost 50!

    But hey, I’m grateful to have Vanguard in Canada and low cost index options FINALLY.

  2. Always learn something from you Gasem. I read Bogleheads early on and did the 3 fund myself because they seemed knowledgeable but you really have a convincing argument. For minimum more potential return you do take on a lot more risk. Does seem not worth it.

    Why do you suppose the 3 fund got pushed so hard in the first place by what I think is a pretty savvy group of people in their own right?

    Thanks again. Future money will be directed in 2 fund from now on and will try and start moving the other stuff in international as well

  3. Great lessons. Ever since your guest post, I have been steering away from international markets. So much risk for shitty returns is right. The international stocks are not doing good at all right now. Who needs “international exposure” when the big American companies are global anyway…

    1. There is some controversy. Back in the early 90’s international was the bomb. It was heavily speculated in not just invested in. In those days it was hard to invest, nothing like today. You wanted a mutual fund they charged you 3% to 5.5% upfront plus a commission if you’re broker got involved. There was no internet and to get data you had to subscribe to something like Investors Business Daily or the Journal. Also brokers pushed international, and some still do today like Ken Fisher the legendary twerp. He’s always got a turkey to sell you. Back then my broker charged $200 a trade and if you didn’t watch him he’d churn your account to pay for his boat (actually to satisfy his slave driver boss), my BIL worked for Merrill and this is how he fed my sister. After the .com bust things changed. The creative destruction was the invention of Netscape. I knew Marc Anrdreesson when he and I were at U of I. Berners-Lee had created WWW and the markup language that allowed several protocols to be accessed. Prior to that to transfer a file required a specific client, and another friend of mine Phil Karn created TCP/IP so servers and clients could be cataloged by an address and packets of information could be dissembled and reassembled with fidelity. With those tools critical mass was hit and that was the day the universe changed. You could buy and sell online.

      When I adopted my daughters I was day trading and I brought a laptop to China and traded over a dial-up. It blew my mind. I would buy or short 3-5 issues (I called it my mini mutual fund) at night China time (day time here) get 6 hours sleep and get up and see what I needed to do. I made $50K in 3 weeks doing that in 1999 while picking up daughter #2. The internet caused the destruction of the brokerage industry. I had an account at Brown and Co because I could trade commodities and stocks and it was only 5 bux. Brown folded into E-Trade, also a traders platform. With the demise of brokers came the demise of salesmen hawking bon bon stocks from Singapore. Soon enough dot com bust happened and international led the way into the dirt because it has a lot higher volatility so people got good and burned. It never really recovered after that. We’ve had nearly 20 years of crappy international returns and the Japanese stock economy committed Seppuku in the 90’s, but people and averages still remember the halcyon of the 90’s when men were men and the sheep ran market scared. Some financial types claim there is opportunity in international because of it’s added “diversity” I think that’s a mirage because of the added risk. What good is diversity if the international issue drops 70% when the S&P drops 50%. They are very correlated (like 85%) so when one goes down the other does as well. Might just as well own the least risk, IMHO

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