The previous post looked at the effect of gold in a portfolio for the 10-year period 1990-2009. Some may say that 10 years is not statistically long enough to be meaningful. So in this post I take a look at the 38 years from 1972 through 2009.

To start, I selected a widely-followed portfolio of stocks and bonds. The Fund Advice Vanguard Moderate portfolio has the following composition:

(Fund Advice recently split their recommended 12% of VDMIX into 6% VDMIX and 6% VFSVX, the All-World ex-US Small Cap index.)

The Fund Advice portfolio placed 32% in fixed-income and 68% in equities. For the period 1972 through 2009, the portfolio achieved a compound annual growth rate (CAGR) of 10.95% with a standard deviation (risk) of 11.6%. This works out to a Sharpe ratio of 0.51.

Let’s now see what would have happened if instead of 100%, we placed 75% of our investment in the Fund Advice portfolio and the remaining 25% in gold. We would have achieved a CAGR of 11.09%, a risk of 10.08%, and a Sharpe ratio of 0.58. So gold did add to the returns for the period while reducing the risk. How could that be since gold itself was very risky over the period? Gold by itself returned only 8.62% while being a whopping 26.88% risky.

How about instead of investing the 25% in risky gold, we had placed the 25% in safe but similarly rewarding Treasury Money Market fund? The Vanguard VMPXX by itself for 1972 through 2009 had a CAGR of 5.66% with a risk of only 3.03%. The resulting combination with the Fund Advice portfolio shows a CAGR of 9.75%, a risk of 8.77%, and a Sharpe ratio of 0.5.

The return vs. risk of the three portfolio mixes and the individual components gold and money market (MM) are shown in the following graph.

So against our intuition, investing in risky gold actually reduced risk in the overall portfolio while adding to the returns. It even beat a comparable portfolio that invested in money markets. This is the power of Modern Portfolio Theory in action showing that while some assets zig, others zag to combine in wonderful ways.

Sources: Vanguard.com, Simba’s spreadsheet (with 2009 data added), Bogelheads.org, FundAdvice.com.

Should a portfolio own gold? I am on the quest to obtain the definitive answer to that question. Here are the results of one exercise in which I take a model Vanguard portfolio and compare it with the same portfolio with a 25% allocation to gold for the time period 1999 through 2009.

Here is the model portfolio composition which is based on the IFA Index Portfolio 25 (source). We will call this the Vanguard 25 portfolio:

I am going to use the time period from 1999 through 2009 for the analysis. Crunching the numbers in Simba’s spreadsheet (Revised with 2009 data added. More info about the spreadsheet at the Bogleheads forum.) I come up with a compound annual growth rate (CAGR) of 5.6% with a average annualized standard deviation (risk) of 7.1%. This works out to a Sharpe ratio of 0.41 for the time span.

So, what if instead of having 100% of our total investment in the Vanguard 25 portfolio we placed just 75% of our investment in it and placed the remaining 25% in gold? Running the numbers in Simba’s spreadsheet (Simba uses this source for gold’s annual return.)  I come up with a CAGR of 7.5% with a risk of 6.9% resulting in a Sharpe ratio of 0.70. Call this one Vanguard 25 w/ Gold. The following chart plots these two results. As a reference I also show on the following charts the Harry Browne Permanent Portfolio which is comprised of 25% each of Total Stock Market (VTSMX), Long Term Gov’t Bond (VUSTX), Money Market (VMPXX), and Gold.

Also shown in the chart is the same exercise but instead of placing 25% in gold we substitute a Treasury bill money market fund (VMPXX) for the 25%. The portfolio with money market fund added resulted in a CAGR of 5.0%, risk of 5.3%, and a Sharpe ratio of 0.41. Call it the Vanguard 25 w/ T-Bills. Note that the Sharpe ratio is the same as the original portfolio because in a Sharpe ratio calculation we subtract out the risk-free rate of return of money markets. So adding money markets to a portfolio does not change the ratio of return vs. risk.

The next chart adds the individual return vs. risk of gold and money market for the same time period showing the higher risk with accompanying higher return of gold for the period.

This next chart adds the individual return vs. risk of all of the other components of the Vanguard 25 portfolio for the same time period.

And for the fun of it, I computed the optimal portfolio for the time span based upon the highest Sharpe ratio and as computed by Excel Solver. This tool allows you to specify an attribute you wish to maximize while varying the percentage amounts of the various funds. In this case, we chose to maximize the Sharpe ratio and allow Excel Solver to pick which combination of which funds achieved it. The following table shows the result.

The OPTIMAL portfolio resulted in a CAGR of 5.8%, a risk of 2.6%, and the resulting Sharpe ratio of 1.12. Its addition to the first chart is shown below.

How about continuing to optimize with a high Sharpe ratio yet obtaining greater return? To do that I subtracted some short-term bonds and added some gold leaving the other two components the same. That is, gold at 35% and bonds at 57%. This resulted in a CAGR of 7.6%, risk of 7.7% and Sharpe ratio of 0.99 and can be seen in the following chart.

Therefore, to answer the original question, “Should a portfolio own gold?” it appears that for the period 1999 through 2009 the answer would have been a resounding “yes.” We find that adding gold to the portfolio resulted in higher returns with less risk.

I caution that this process is called data mining and should only serve as input into future portfolio analysis and not serve as the only decision regarding future investments. In subsequent analysis I will not limit the possibilities to just the Vanguard 25 fund set but will open it up to Vanguard funds available since 1972 and/or 1985.

Sources: Vanguard.com, Bogleheads.org, IFA.com, and http://www.finfacts.ie/Private/curency/goldmarketprice.htm

Let’s go back and gather up the gains for 2005 and 2006 to add to our analysis with this chart.

As you can see, the Harry Browne Permanent Portfolio still has the best “top-leftedness” of these select Lazy Portfolios. It had an annualized return of 8% with an annualized standard deviation of 8.8%. That results in a nicely high Sharpe ratio of 0.75, assuming a risk-free rate of return of 1.37% for all 5 years (not likely).

The HBPP’s out-performance is due to the stellar performance of gold through all of these years. I am still not convinced this is the one for all seasons. So I will be performing some analysis of this portfolio for the years that were most favorable to equities and not gold and see how the HBPP would have held up.

Here is a chart that sort of goes with the previous posting’s table. I have taken just a few of the portfolios of interest and computed their standard deviation for the time period of three years. Then plotted their ANNUALIZED return on the Y axis vs. their annualized standard deviation along the X axis.

Remember that you’d want your portfolio to be at the top left of the chart because their you get the higher return with the lower risk.

So for the three year period from 2007 through 2009 the Harry Browne Permanent Portfolio showed the best return and the least risk of any of the featured lazy portfolios. More analysis to come…

Here’s an early look at how the professional Lazy Portfolios have performed for the past 3, 2, and 1 years ending 31 December 2009. These are cumulative returns, with dividends reinvested. Data comes from Yahoo! Finance into my spreadsheet. There may be errors in the data. Some funds may not yet have reported dividends for 2009, for example. I have sorted the results by the 3-year performance.

Here are some takeaways from the table:

1. These portfolios have different objectives, different asset class mixtures, and different risk profiles. Simply comparing them on historic returns is not a way to pick one for an investment.
2. Therefore, a better way to view these would be to look at them on a return vs. risk graph where risk is defined as the standard deviation of the portfolio. Then we could see at a glance which portfolio has the more desired “top-leftedness” (meaning it had higher return for its level of risk).
3. Only two of the portfolios invested in gold, the two top performers. Future results may vary.
4. I believe most funds have no load.
5. I changed the Harry Browne Permanent Portfolio cash holding from VFISX to SHY which results in a slightly lower return (about 1% less). I would prefer to hold it in a money market fund, but Yahoo! Finance does not give me historical returns for them.
6. Remember, this table probably has errors!

Yeah, Cramer v. Stewart . I’ll be watching (once my DVR has finished recording it). Thanks Barry for doing the compilation. I especially like #3.

The Austrian economists anticipated the present crisis. Should we listen to them when it comes to their predictions about what comes next? In one voice they are saying we will experience inflation unlike we’ve seen in the USA in over 100 years. Inflation is defined as the increase in the supply of money and credit. We are certainly experiencing an increase in the supply of money at present. But the draw-down of credit is counter-acting the monetary inflation and we are hovering in inflationary stasis at present.

Fed Chairman Ben Bernanke said the same thing on February 18th:

Some observers have expressed the concern that, by expanding its balance sheet, the Federal Reserve will ultimately stoke inflation. The Fed’s lending activities have indeed resulted in a large increase in the reserves held by banks and thus in the narrowest definition of the money supply, the monetary base. However, banks are choosing to leave the great bulk of their excess reserves idle, in most cases on deposit with the Fed. Consequently, the rates of growth of broader monetary aggregates, such as M1 and M2, have been much lower than that of the monetary base. At this point, with global economic activity weak and commodity prices at low levels, we see little risk of unacceptably high inflation in the near term; indeed, we expect inflation to be quite low for some time.

He acknowledged that they are inflating. But he threw a red herring into the mix by talking about weak economic activity and low commodity prices (Heh, except gold, right Ben?) trying to infer that they are somehow the cause of inflation. No, they are the result of inflation. Next, he went into how they will correct their inflation:

However, at some point, when credit markets and the economy have begun to recover, the Federal Reserve will have to moderate growth in the money supply and begin to raise the federal funds rate. To reduce policy accommodation, the Fed will have to unwind some of its credit-easing programs and allow its balance sheet to shrink. … However, the principal factor determining the timing and pace of that process will be the Federal Reserve’s assessment of the condition of credit markets and the prospects for the economy.

Bernanke recognized that the plane is in a nosedive and at the last minute he plans to push on the stick and go airborne again. I hope it is not a cloudy day when he has to judge how far the plane is from the ground. He wrapped up his thoughts on inflation and how to avoid it:

As we consider new programs or the expansion of old ones, the Federal Reserve will carefully weigh the implications for the exit strategy. And we will take all necessary actions to ensure that the unwinding of our programs is accomplished smoothly and in a timely way, consistent with meeting our obligation to foster maximum employment and price stability.

What do *you* think the chances are that the Fed will get all of the necessary actions right? Have they gotten the necessary actions right up to this point? Let us examine a scenario where they are not able to get it right and we do indeed experience undesirable inflation, which I will define to be anything above 5% annually.

How might the various asset classes be affected in times of inflation? To answer this question, I utilized Simba ’s spreadsheet for back-testing portfolios (which I imported into Google Spreadsheets) to do a correlation between CPI (Consumer Price Index, the government’s official inflation number) and various stock fund, bond fund, and gold returns. The data in the spreadsheet uses annual returns of Vanguard index funds along with the yearly closing price of gold from the years 1971 – 2008.  The spreadsheet already calculated the cross-correlation between each of the mutual funds and it lists the annual CPI index. So it was very easy to drop the CPI into one of the mutual fund slots and instantly see the correlation between every asset class and inflation. Here are the results, sorted by correlation:

The table shows those asset classes that were most closely correlated with the CPI at the top. Note in the third column that a value of 1 would mean the asset is perfectly correlated, -1 would mean perfectly correlated inversely (it went down exactly as CPI went up), and 0 means there was no correlation: it was random.

So we see that those assets that were most highly correlated with CPI were T-bills, gold, long-term government bonds (inversely), short-term Treasuries, and commodities.  Everything else was below 0.25 correlation. Interestingly, micro cap stocks were totally uncorrelated with inflation.

So how did a portfolio of those assets perform during the years 1973-1981 in which CPI was 8.7, 12.3, 6.9, 4.9, 6.7, 9, 13.3, 12.5, and 8.9%?

I constructed a portfolio along the lines of the Harry Browne Permanent Portfolio (HBPP invests 25% each into total US stock market, long-term bonds, money market, and gold) but I added some small cap value, micro cap, and eliminated the long-term bond fund. I then back-tested that portfolio during those inflation years. Here is the portfolio what I came up with:

The Inflation Portfolio:

VISVX (Small Cap Value) 15%
BRSIX (Micro Cap) 15%
PCRIX (Commodities) 10%
VMPXX (Money Market) 45%
Gold 15%

The "Inflation Portfolio" had a CAGR (Compound Annual Growth Rate) of 15.5% and a risk (as measured by standard deviation) of 10.5%. Plotting that on a chart, here’s what it looks like compared with some other portfolios and the assets themselves:

The chart shows plots for various portfolios during those inflation years. The plot point directly above HBPP simply substituted BRSIX for VTSMX in the HBPP. The major components of the Inflation Portfolio are also plotted separately showing how volatile gold and BRSIX were themselves. When tempered together with VMPXX, the risk came down considerably while retaining significant returns. You can see all of the rest of the details in the Google spreadsheet that I created for this scenario and you can test out other hypotheses yourself.

The Inflation Portfolio worked from 1973 through 1981. If we see inflation return, would it work again? Some folks are discussing these findings at the Bogleheads forum if you want to chime in.

Please note this is not a recommendation to invest your net worth in the Inflation Portfolio!

In a previous posting , I calculated the 12 month rolling returns for all IFA portfolios.

That posting is in error (that I do not believe was my fault). I have corrected it. It turns out that Feb 1, 2008 thru Jan 31, 2009 was not the worst 12-month rolling period, but it did come close.

I’ll be watching to see what happens at the end of this month.

Here is the corrected chart.

[Update: Corrected the image. Note that the Bogle portfolio is corrected in the Google Spreadsheet - to some extent.]

I have copied Simba’s Backtest Portfolio spreadsheet from the Bogleheads forum into a Google Spreadsheet that you can use to back test a portfolio of Vanguard mutual funds and compare their performance from 1972 – 2008 to the IFA Index Portfolios. Combine the funds any way you like and compare them against IFA’s twenty portfolios. I included the "returns" for gold there for your convenience.

This graph from that spreadsheet shows the plots of a few others including the Coffeehouse portfolio, Harry Browne’s Permanent Portfolio, Scott Burns’ Four Square portfolio, and a couple of others along with IFA’s portfolios (they follow a nice line). Unfortunately, Google spreadsheets doesn’t do labeling very well on the data points. I would have liked each point to be colored and have a legend identifying those colors. Anyway, remember you want to be at a point at the top left on this graph. The line that is formed is called "The Efficient Frontier" beyond which it is difficult if not impossible to achieve. The strong correlation between returns and risk is evident.  However, it is easy to be bottom right!

If you want to play with the spreadsheet yourself, feel free to bring it up. You’ll need a Google account. Leave the years to be 1972 – 2008 in order for the comparisons to be valid. Here’s the link:

https://spreadsheets.google.com/ccc?key=pOjc3ot10vgs0eml-DJZKcw&newcopy

But wait, there’s more!

IFA is now allowing you to submit your past financial statements to them so that they can compare you’re portfolio’s performance against their index portfolios. Go their web site at ifa.com to learn more. Here are some comparisons they have already performed.

I just remembered a web site that was a Tool many many shows ago. This tool will help you benchmark your portfolio or to test out a new portfolio. It will allow you to compare it against another benchmark and it will calculate returns, standard deviations, and also Sharpe ratios.

The web site is http://www.icarra.com

Get over there and create an account and try it out. They have really made some nice improvements since I last used it.

At the end of October 2008 we experienced the worst 12-month rolling period for stocks in 50 years. Then at the end of November we outdid that.  Now at the end of January 2009 we have a new low for a 12-month rolling period in many indexes and portfolios. We came close to the worst rolling 12 months again, but did not pass it.

The following table is taken from ifa.com, combining the returns for 11 months from 1 Feb 08 through 31 Dec 08 and the 1 month return for Jan 09.

Here is the corrected table.

Previous table, wrong:

Source: http://www.ifa.com/portfolios/PortReturnCalc/index.aspx and http://www.ifa.com/portfolios/