Diversification a la Markowitz #3: Gold

[McQ]

If you are a veteran reader of the forum, then you know that this is but the nnth of a large number of threads on gold as an investment (e.g., viewtopic.php?t=396210. Odds that I will say anything new must be considered low.

In an attempt to contribute something new, I will hew pretty strictly to the approach used in Parts 1 and 2: given some expected return, standard deviation, and correlation for gold, how much diversification benefit might one expect from adding gold to an all stock portfolio?

Gold—the ultimate diversifier?

Probably not.

If I had a dollar for every journalist who quoted some expert who said that “you should keep 5% of your portfolio in gold for diversification,” I’d have enough for a very good bottle of California Cabernet.

More legitimately, the Permanent Portfolio has been around for quite a long time, with a substantial allocation to gold. (see this post by nisiprius: viewtopic.php?p=7157009#p7157009)

A rational newcomer to investing might suppose, given the number of mentions in the press, that there must be something to the idea of holding gold as part of a portfolio. But wishing and hoping doesn’t make it so.

Let’s start with the obvious argument AGAINST the use of gold to diversify a stock portfolio.

1. Gold is a store of value
2. To store is to keep, maintain, and preserve unchanged
3. To store is NOT to grow and NOT to lose; it is to KEEP
4. Therefore, the expected value of gold, in real terms, is the same tomorrow as today; the same next decade as last decade; the same one hundred years from now as … oh wait: gold has only been a traded asset since 1971, after the collapse of the Bretton Woods agreement, the true end of the gold standard, which had held for centuries until that first thunderous crack in February 1934.

Anyway, you get the idea: over the very long term, the expected real return on gold is exactly zero (minus storage costs). If that statement is not true, then it cannot be true that gold is a store of (real) value.

I believe gold to be a store of value. Full stop.

I also believe that productive business enterprises CREATE value, rather than store it, and that when I buy a broad stock market index fund, I own a share of global value production, and can reasonably expect to see the value of that stock investment grow in real terms over time, as those productive enterprises of which I own a share continue to create value.

Therefore, addition of gold to a stock portfolio may have a diversification effect, in terms of reducing portfolio standard deviation; but will almost certainly NOT be able to enhance portfolio return. Gold might function as a stabilizer, analogous to short-term TIPS, delivering inflation as their only return. Which means that an allocation to gold—or to short-term TIPS-- must necessarily drag down the long term return on holding 100% of the portfolio in shares of productive enterprises which CREATE value.

In addition, the reduction in portfolio standard deviation from holding gold is likely to be less than that for holding short-term TIPS, because gold is more subject to speculative influences, hence swings about to an even greater degree than the inflation expectations that drive the price of short-term TIPS.

H1: Low return + high volatility = inferior diversifier, relative to, say, an intermediate bond fund.

UNLESS … there is some unsuspected magic in negative correlation, whereby addition of a small allocation to gold both reduces portfolio standard deviation AND increases portfolio geometric return, per the analyses in Part I of the thread.

That is the question to be investigated in this post.

The data

I’ve been using SBBI data from 1926 throughout these threads. That’s not going to work here in Part 3. The dollar price of gold was constant from December 1925 to February 1934, when it leaped by about 75% in a day (~$20 -- $35), after which it was constant again through the late 1960s, after which it exploded for a decade after Nixon took the dollar off gold.

Beastly series to analyze; accordingly, I begin the data series anchored to the end of 1972 (which is also when Total Bond returns become available). This allows about eighteen months for the initial pricing chaos, post delinking of the dollar to gold in August 1971, to settle down.

*You could alternatively begin the gold series in 1792 same as my stock and bond series, where the gold price would be constant and annualized return would be zero until 1934, excepting two small revaluations in in the 1830s and 1840s, and temporary deviations in 1814 and 1862-79. By temporary I mean the positive paper dollar returns initially received were exactly reversed once the movement in these periods was concluded, i.e., gold price at t-begin = price at t-end = ~$20 per ounce = ~1792 price.

*But adding back 140 years of 0% returns is probably not going to be acceptable to the investor seriously contemplating whether to add gold to their portfolio in 2023; that stretch of returns data will be dismissed as “ancient history.” No problem, I won’t go there.

For the fifty years through 2022, the inputs to the Markowitz analysis are as follows. In contrast to prior threads, for this exercise I will use exact historical amounts to the fourth decimal for return and SD. Gold price is from Simba, London pm fixing.

Stocks: arithmetic return = 11.85%, SD = 17.51 *
Gold: return = 9.59%, SD = 26.83%, correlation with stocks = negative 0.21.

*BTW, only periods that include the crash of 1929-1933 give a stock SD greater than or equal to 20%; the 130 years before and the 90 years after typically run an SD of 12% to 18% over twenty-year windows, see https://papers.ssrn.com/sol3/papers.cfm ... id=3805927.

In short, for these fifty years gold had a somewhat lower return, was rather more volatile, and did indeed have a negative correlation with stocks.

Here is the Markowitz chart*

*Because the kluge—geometric return = AR + ½ variance—is increasingly inaccurate for SD over 20%, for this chart the vertical axis is also computed using the approximation labeled QE in Markowitz. It’s still not exact, but it is closer. For comparison the kluge is also shown (solid blue line).



Whoa—that looks quite a bit different than the stock - bond charts we saw in Part 2 of this thread.

Good news: a small allocation to gold could have reduced standard deviation substantially, and—very slightly—increased geometric return. By about 7 basis points at the peak. The stock investor desirous of achieving risk reduction without any reduction in return could justify up to a 30% allocation to gold.

Next, I add the total bond-stock risk return line for this period, using the exact 50-year returns: AR for Total Bond = 6.76%, SD = 7.12%, correlation = .34. As before, a very positive return-risk ratio, with risk far less than stocks or gold, and correlation with stocks moderately positive, i.e., none of that negative correlation benefit with total bond.



The orange line is below the blue and gray lines down through a 50-50 allocation to stocks and gold. Gold is the superior diversifier in that range. However, a 50-50 allocation performs identically to an 80-20 stocks/total bond allocation. At all lower stock allocations, a mix with total bond provides the same return as a mix with gold, for lower risk.

There you have it: the diversification benefit of gold, such as it is, based on the exact series of returns for the cherry-picked 50-year period December 1972-2022.

Hmm, I think you know where this is going.

A rational skeptic of gold might opine: “If the paper dollar price of gold was artificially constrained for decades, I don’t think pegging the start of the price series to seventeen months after the collapse of Bretton-Woods is quite enough time for a new equilibrium to be established.”

Okay; what if we started the series 10 years later, at the end of 1982? Forty years still qualifies for the “long run,” does it not?

Whoa, says the gold advocate. “You are throwing out the baby with the bathwater. Sure, go ahead and arbitrarily exclude the once-in-a-century-or-two-or-three crucible that was the 1970s. Fine, wipe the (barely controlled) galloping inflation of that era from the record. I agree, the performance record for gold won’t look so good if you exclude exactly those circumstances under which gold might shine.”

Hmmm.

Without taking a stance on this dispute, it can’t do any harm to look at the 40-year record from 1982 to 2022—can it? That’s not as “much” history as the 50 years from 1972, but it is still a lot of history. In fact, my personal accumulation history tops out at about 40 years (first IRA contribution 1983, last (spousal) IRA contribution 2022). YMMV.

Might be good to know if gold is so fitful an asset that it might fail to shine throughout your entire accumulation horizon.

But:
“How nice for you,” snarks the gold advocate. “Oh, right, I remember now: the gold price last peaked in the early 1980s. How convenient. Come to think of it, my dear professor, aren’t you on record as stating that 1982 was a generational low in stock and bond prices? So you go, guy: you’ve decided to measure the performance of gold from its top and stocks from their bottom. What could be more fair?”

Got me there.

Still, no harm in looking at the post-1982 data? Right? With the caution that still other slices on the historical data might also be worth a look.

Pause for comments.

[ivgrivchuck]

Gold is a very interesting and - as you said - controversial asset class.

What I find interesting is to compare two portfolios:

A) 60/40 stocks/bonds (the classic portfolio)
B) 60/30/10 stocks/bonds/gold

https://www.portfoliovisualizer.com/bac ... tion3_2=30

I've run the comparison for the last 30 years (to avoid picking a very good or a very bad start date for any asset class). As we can see this 10% transition from bonds to gold has almost zero impact to expected return, portfolio volatility or the max drawdown. So in some sense these portfolios are approximately equally good.

A Gold bug might say: I can get a hyperinflation insurance almost for free with the second portfolio! I should absolutely go for it.
A die hard 3-funder might say: That's cheating. You are replacing low volatility assets with high volatility assets. Correlations may change quickly and you are taking unnecessary risk.

[seajay]

Let's go back to Victorian Britain, say 1899. Gold Sovereign coins, weighing a little under a quarter of a ounce were One Pound currency value, actual coins in circulation/use. Along side that there were One Pound Notes, paper currency, that could directly be swapped for a gold sovereign - by law, in banks ...etc.

Individuals with surplus money (Sovereigns or Pound Notes) might have been inclined to deposit that into banks or state bonds, in return for interest. Fundamentally they were the same, where savers with gold or bonds yielded the same investment total returns. Being finite gold based inflation broadly averaged 0% such that interest was a form of real rate of return, and where the total returns compared to stocks.

That all changed when money and gold were decoupled. Instead of a long term median 0% inflation rate (but at times with clusters of high inflation/deflation that tended to average back to 0%), the tendency became for inflation to dominate, and where after inflation and taxation bonds transitioned from comparing to stocks to being more broad 0% net real total returns.

Anything in demand will tend to broadly 0% real, but at times may see less demand, at other times see high demand, so not consistently yield 0% real but instead do so with volatility. That applies to gold, so fundamentally both bonds and gold transitioned over to 0% real assets after the ending of the gold standard (decoupling of money being gold).

Physical in-hand gold has no counter-party risk, yields its 0% real reward expectancy without paying interest/dividends and so avoids regular income taxation risk. But its favor waxes and wanes so has tended to exhibit high volatility. However that volatility has tended to be counter-direction to that of stocks, at least over multiple years (not a regular shorter term reliable inverse correlation). The 'bonds' with the most comparable default risk are ... T-Bills. Such that appropriate comparisons to stock/gold is stock/T-Bills.

Some like to take on more risk on the bond side, hold longer duration or even corporate bonds etc. Others suggest keeping the bond side risk low and instead scale up stock exposure to add more risk/reward.

With stock/T-Bills you have nominal high volatility stocks blended with low volatility T-Bill diversification. With stock/Gold you have both being high volatility but potential greater multi-year negative correlations. How does that all pan-out in the broader time sense? Well broadly similar outcomes. The two are interchangeable according to whichever you might generally prefer. Gold is more a global currency that pays no interest etc., T-Bills in contrast are tied to a single geopolitical risk that pay interest and hence interest taxation ... etc.

At the longer dated or corporate bond end, bonds can be as volatile/rewarding as stocks, as can some stocks be more bond-like. What HB's PP does is in effect have volatile stocks and long dated treasury bonds, paired with T-Bills and Gold. Diversifies equally across the different choices, such that it tends to middle road. Others might opt for 50/50 stock/T-Bills, or 50/50 LTT/STT treasuries only (that combine to a central 10 year Treasury bullet), or 50/50 stock/gold ...etc. according to their preference and/or particular circumstances (such as costs/taxation rates) PV

Now you can pick particular choices of start and end dates to make each/any of those different choices look good, or bad. A better measure is to calculate the log linear regressions (trend line slope), and the r-squared (variation/volatility) of each progression around that trend line.

For T-Bills/LTT using full calendar years for the available data in the above PV link I measure a 6.2% slope, with 0.942 r-squared
For Stock/T-bills 7.3% slope, 0.958 r-squared
For Stock/Gold 7.7% slope, 0.985 r-squared.

As a form of Sharpe ratio we might simplify to slope / r-square measures, where the higher the number the better, and for that, at least over that 1978-2022 inclusive year range, stock/gold was the better risk/adjusted reward. But again that isn't consistent, applies over just that period, in other cases stock/T-Bills or even T-Bills/LTT might have yielded the better outcome. Whether you might predict which might be the better in forward times is ... timing, but there can be some big clues at times. In 1980 for instance gold had risen such that it required near just a single ounce of gold to buy a Dow stock index share. In contrast in 1999 it took around 40 ounces of gold to buy a Dow stock index share. In other cases long dated treasury yield have at times been very high, or very low. The PP somewhat trades those swings, using a simple automatic mechanical trading method of ... periodic rebalancing back to equal weightings.

Personally however, for my own circumstances stock/gold works best for me. A UK (Pounds) home, some US stocks (US dollars), some gold (commodity and global currency), is, for me, very tax efficient. Three assets, three currencies, low taxation. The ancient Talmud advocated equal thirds allocations (land (house), business/merchandise (stocks), in-hand (gold)). A home avoids having to find/pay rent to others, liability matches that aspect, where house price increases + imputed rent might broadly compare to stock price increases + dividends. So is somewhat 67/33 equity/bond like. If events that drive house and stock prices to halve see gold prices double, then 67 'equity' halving to 33, alongside 33 gold doubling to 67, and rebalancing has you back to 67/33 equity/gold, no overall portfolio loss, and where you've doubled up on the number of stock shares you hold. A Martingale betting sequence (where you double up your stake (stock) after each losing play (stock prices halving). Not that you actually play that way, a house for instance is illiquid, you can't add or remove some of the value, at least not easily. Best to just leave the home value as a consumable.

Does rebalancing actually value-add? Broadly no. If you buy 50/50 stock/gold initially and just draw your SWR from the most-up asset at the time of each withdrawal, then that is a form of partial rebalancing (or if saving, you add to the lowest valued at the time). Broadly not-rebalancing tends to compare to rebalanced, but where non-rebalanced will tend to end up with more weighting in the asset that performed the best. So tends to greater concentration risk, but where that higher risk is negated by prior higher rewards (in having held more in the asset(s) that performed the best).

Measuring all of those differences mathematically is fraught with variance. Tends to just incite perpetual disagreements. Better would be to accept that different people prefer different choices and that no one will consistently be the better choice. Fundamentally just boils down to luck.

I like the retirement option of at the time of retiring moving into a approximate thirds each house, stock, gold asset allocation and then just spending down (SWR or whatever) the higher valued out of stock or gold at the time, no other activity required (assuming a broad accumulation stock index fund is being held). 3% SWR drawn from the stock/gold liquid assets, around 2% of total wealth (including home), where owning a home adds 1.33% imputed rent benefit (4% historic rental yields), so a 3.33% combined effective SWR, the return of your inflation adjusted capital via 30 yearly instalments, and where at the end of that 30 years from long term (since 1793) you were inclined to still have the same, or more, of the inflation adjusted start date portfolio value available. A PWR (perpetual). With simplicity, once bough/loaded, just a matter of selling some stock shares, or gold each month (assuming you prefer to draw your SWR/whatever on a monthly-wage type basis).

[Logan Roy]

Without taking a stance on this dispute, it can’t do any harm to look at the 40-year record from 1982 to 2022—can it? That’s not as “much” history as the 50 years from 1972, but it is still a lot of history. In fact, my personal accumulation history tops out at about 40 years (first IRA contribution 1983, last (spousal) IRA contribution 2022). YMMV.

Might be good to know if gold is so fitful an asset that it might fail to shine throughout your entire accumulation horizon.

You may be aware of my position on this, but I'd say '82-'22 is like safety testing a new car without ever taking it out in cold weather. 40 years is a long time for an investor, but interest rates only really did one thing, and the chances of that 40 years simply repeating seem unlikely (without something that takes rates very high again).

So obviously the way All Weather investors look at it is there are only four states: Inflation rising or falling; with Growth rising or falling.. And without the 70s, you don't have a proper period of +Inflation and -Growth (Stagflation). So it's unequivocally incomplete – knowing that any decade can put us in any one of these environments.

With the backtesting problem, I really like PortfolioCharts' solution of using rolling 15 year periods. And as an engineering problem – re: getting useful data that includes gold – I might almost be tempted to graft 1972 onto 2022, with some reasonable adjustments. Maybe find a point where one can align the rates, then adjust the asset classes by their real values(?) – so we'd avoid gold simply getting more expensive. It's a tricky one. But I think All Weather investors have always felt that each decade we don't get stagflation only further justifies hedging for it.

[abc132]

I think there is a mismatch between people saying they expect 0% real from gold and then forming conclusions from backtesting data with 6% real returns. Other than that, I believe gold has been a good diversifier over the last 40 years. If I had 8 figures ($10 million) gold would almost certainly make up at least 10% of my portfolio. I'm not there yet so its a soft pass for now. I do enjoy the gold threads. I'm interested in what will be said here.

[GRP]

I believe gold to be a store of value. Full stop.

This part was good enough for me. Satisfying.

[White Coat Investor]

I think there is a mismatch between people saying they expect 0% real from gold and then forming conclusions from backtesting data with 6% real returns. Other than that, I believe gold has been a good diversifier over the last 40 years. If I had 8 figures ($10 million) gold would almost certainly make up at least 10% of my portfolio. I'm not there yet so its a soft pass for now. I do enjoy the gold threads. I'm interested in what will be said here.

What changes when you go from $8M to $12M? Not much that I know of. Something change in your personal life? Seems like it would do just as much good or bad at $8M as $12M. There's not some magic amount where it starts making a dramatic difference in a portfolio.

As people get wealthier, their need to take risk goes down and their ability to take risk goes up. Those two seem to offset each other pretty well such that I have had the same basic asset allocation over 4 or 5 orders of magnitude in wealth.

[HanSolo]

That is the question to be investigated in this post.

I'd say the answer was given in the first reply (concluding statement here):

A Gold bug might say: I can get a hyperinflation insurance almost for free with the second portfolio! I should absolutely go for it.
A die hard 3-funder might say: That's cheating. You are replacing low volatility assets with high volatility assets. Correlations may change quickly and you are taking unnecessary risk.

Depending on criteria chosen, one can "prove" that one should include gold, and one can "prove" that one should not.

My personal experience is that I've included some gold in my portfolio for many years. It hasn't caused a problem.

If someone sees a problem in gold (or some other thing), then they shouldn't own gold (or that other thing).

The main "problem" is that some people think their preferences are generalizable to everyone. That is a mistake.

[abc132]

I think there is a mismatch between people saying they expect 0% real from gold and then forming conclusions from backtesting data with 6% real returns. Other than that, I believe gold has been a good diversifier over the last 40 years. If I had 8 figures ($10 million) gold would almost certainly make up at least 10% of my portfolio. I'm not there yet so its a soft pass for now. I do enjoy the gold threads. I'm interested in what will be said here.

What changes when you go from $8M to $12M? Not much that I know of. Something change in your personal life? Seems like it would do just as much good or bad at $8M as $12M. There's not some magic amount where it starts making a dramatic difference in a portfolio.

As people get wealthier, their need to take risk goes down and their ability to take risk goes up. Those two seem to offset each other pretty well such that I have had the same basic asset allocation over 4 or 5 orders of magnitude in wealth.

It makes some sense to me to have some independence from the financial system when you can afford to do so. If you have $100 million and want to buy a fallout shelter with security guards I say go for it. For me that independence would be real assets such as art and gold. What changes from 7 figures to 8 is that you can succeed when the financial system fails. You can guess from that number that I need less than 0.5 million per year to meet my basic needs. You can compare 10 million to 100 million if you wish, at some point you could take measures to succeed in a country that fails. I certainly don't expect the US to fail but this has been some very cheap insurance since historically these types of assets have also improved a portfolio.

[petulant]

The results from the first post will not hold up if expected returns from gold are reduced to 0% real. Gold has to have positive returns that exceed intermediate treasuries, e.g. because actual inflation exceeds expected inflation by a material amount over an entire study period (like 30 years). It's reasonable to imagine scenarios where gold at a 10% allocation helps. It's hard to reasonably expect gold returns in the future will support a 30-40% allocation on the efficient frontier.

[secondopinion]

The results from the first post will not hold up if expected returns from gold are reduced to 0% real. Gold has to have positive returns that exceed intermediate treasuries, e.g. because actual inflation exceeds expected inflation by a material amount over an entire study period (like 30 years). It's reasonable to imagine scenarios where gold at a 10% allocation helps. It's hard to reasonably expect gold returns in the future will support a 30-40% allocation on the efficient frontier.

Well, the point is reduction of risk over having greater returns. If I want better returns, I need something besides a "store of value" and take the risk anyway.

Remember that gold cares nothing about a country-specific inflation or taxes. If gold is globally accurate as a basis of 0% global real returns and that long-term TIPS are fairly priced, then the expected real returns of gold would be greater than 0% for US investors. Why? Because TIPS only consider US taxes and inflation (with its US real returns); the US dollar could devalue globally and hence it is not a free lunch. When one thinks globally, it is possible to resolve the paradox of gold still having an expected positive US real returns without resorting to either a US dollar collapse or a speculative spike as the reason (which I doubt either will happen).

Of course, I much rather hold foreign stock as the hedge against a weaker dollar at this point of investing.

[Logan Roy]

The results from the first post will not hold up if expected returns from gold are reduced to 0% real. Gold has to have positive returns that exceed intermediate treasuries, e.g. because actual inflation exceeds expected inflation by a material amount over an entire study period (like 30 years). It's reasonable to imagine scenarios where gold at a 10% allocation helps. It's hard to reasonably expect gold returns in the future will support a 30-40% allocation on the efficient frontier.

Well, the point is reduction of risk over having greater returns. If I want better returns, I need something besides a "store of value" and take the risk anyway.

I think that is unless there are situations in which everything that generates a return (above inflation) loses value.. Such as the base rate rising.

Over the past 50 years, there have been two 20 year stretches (from the top of my memory) in which gold at up to 30% (with 70% stocks) has beaten stocks at 100%.. At some point, diversification has value. If a diversifier tempers an 80% loss into a 60% loss, it may put the diversified investor 20-30 years ahead, in terms of returns, at some point.

[McQ]

[Do read Logan Roy’s comments above]

Gold post-1982

Over these 40 years through 2022:

Stock return 12.63% / SD 16.67%
Gold 4.55% /14.74%, correlation -.12

In short, a strong period for stocks, but one that saw much weaker performance for gold, with also much less volatility, and a moderately smaller but still negative correlation. Here is the risk return line.



Over these 40 years there was no return enhancement from adding gold to a stock portfolio. Even a 10% allocation to gold would have reduced final wealth (geometric return compounded over 30 years)* from a 100% stock portfolio by over 3x the starting value. Ouch.

*I suppose the time frame should be 40 years here, but 30 years keeps the frame consistent with Part 1 and Part 2. Compounding over 40 years … would magnify the shortfalls described.

Over this period there WAS STILL a substantial reduction in volatility on offer, as expected from a negatively correlated asset.

If you had been willing to go 50-50 gold and stocks, you could have cut six points off the portfolio standard deviation relative to 100% stocks. But you would also have sacrificed about $140,000 off the wealth you could have gotten from investing $10,000 in a 100% stock portfolio for thirty years.

How do you like that trade-off?

Okay, got it: reducing standard deviation must be really, really important to you. It is no longer possible for you to sleep at night with a 100% stock portfolio and you are crying out for risk reduction. So that $140,000 wealth loss doesn’t faze you. It’s an acceptable opportunity cost to drive that standard deviation DOWN. You still turn the $10,000 starting value into over $100,000 with the 50-50 gold / stocks mix.

But if you are that desirous of reducing the standard deviation on your portfolio, may I recommend an allocation to Total Bond instead? Orange line shows the return risk line for combining stocks with total bond. Stats for the 40 years are:

Total bond return = 6.49%, SD = 6.35%, correlation = .30



Despite its much higher correlation, I would argue from this post-1982 chart that Total Bond was superior to gold as a diversifier for the 100% stock investor. At 90% and 80% allocations to stock, the return reduction and risk reduction from Total Bond were both on a par with adding gold. As the allocation to stocks drops further, the return reduction is on a par with adding gold, but the comparative risk reduction gets greater and greater as the stock allocation drops below 75%.

Conclusion: the stockholder who is willing to give up large amounts of return in order to reduce risk substantially should add some kind of intermediate bond fund to the portfolio. Not gold.

…If you take the 40 years from December 1982 through 2022 as a representative period for setting expectations for how these assets might perform relative to one another.

Which a gold advocate need not. Refer again to the Logan Roy comments above.

More time periods to come. Suggestions welcome as to where to make the next split.

Reflections: asset correlation as a weak force

The metaphor is from nuclear physics: some particles are strongly bound, others more weakly so.

The great hope placed on an investment in gold is that negative correlation will save the day and overcome any shortfall in return consequent to gold being only a store of value rather than a productive asset.

But that is not what happened post-1982.

1. As argued earlier in these threads, substantially negative correlations over the long term, among two risk assets with semi-equivalent positive returns, are scarce on the ground. The 50-year correlation for gold, including the 1970s, was only negative .21 (minimum possible = -1.0).

2. In the post 1982 data, Total Bond, with correlation of +.30, was a better risk-reducer than gold, with a correlation of negative .12. Total Bond had a higher return than gold, a smaller standard deviation, and a much more favorable return-risk ratio.

3. Which swamped the effect of a 40 point difference in correlation.

Within reason, any asset with a “low” correlation to a high risk, high return asset like stocks (low means less than or equal to .50) will produce the characteristic “bulge left” we’ve seen in stock-bond return-risk lines. Ceteris paribus, the lower the correlation, the farther the bulge to the left, i.e., reduction in standard deviation.

Gold achieves that bulge; but an intermediate bond fund will give a greater bulge: less risk for the same return.

But again, starting the dataset at the end of 1982 is arguably prejudicial to gold--more so than 40 years of subsequent data can overcome. Even if that 40 years was my entire accumulation period.

Next post looks at other data splits.

[watchnerd]

My GLDM was up 2.26% today.

I have no idea why.

I also own some physical gold coins that my wife bought for me one year for my birthday and buried in the woods at the back of our property as treasure hunt.

I only found 3 of the 5 she bought.

That's why I like gold -- it's mischievous and entertaining.

[ivgrivchuck]

Just stating the obvious, but in January 1982 the U.S. Treasury 10 year yield was 14.4%. Today it's 3.5%-4.0%.

So there has been a strong tailwind for bond returns for the last 40 years. And this tailwind can't repeat since the yields can't go significantly negative. So that also skews the stocks/gold vs. stocks/bonds comparison for that time period. But every time period has its own problems...

Luckily the correlation between bonds and gold is also near zero, so most real World portfolios containing gold, are also going to contain bonds, so one doesn't have to choose between them. Adding 5%-10% of gold in your portfolio is not going to take you far from the theoretical efficient frontier. And the reason for holding gold is mainly addressing the left-tail risk of portfolio. Fiat currency going through a significant devaluation is not uncommon at all if we study the history.

So 60/30/10 stocks/bonds/gold is not a bad retirement portfolio at all. It may not be for everybody, it may not be the theoretically best, but it's a perfectly reasonable choice in my books.

[seajay]

Just stating the obvious, but in January 1982 the U.S. Treasury 10 year yield was 14.4%. Today it's 3.5%-4.0%.

So there has been a strong tailwind for bond returns for the last 40 years. And this tailwind can't repeat since the yields can't go significantly negative. So that also skews the stocks/gold vs. stocks/bonds comparison for that time period. But every time period has its own problems...

Bond returns primarily come from interest payments, where regular interest payments are typically taxed. Discounting a 20% average tax rate and comparing to gold since the ending of money = gold



Broadly comparable, and hence interchangeable.

[HootingSloth]

I think there is a mismatch between people saying they expect 0% real from gold and then forming conclusions from backtesting data with 6% real returns. Other than that, I believe gold has been a good diversifier over the last 40 years. If I had 8 figures ($10 million) gold would almost certainly make up at least 10% of my portfolio. I'm not there yet so its a soft pass for now. I do enjoy the gold threads. I'm interested in what will be said here.

What changes when you go from $8M to $12M? Not much that I know of. Something change in your personal life? Seems like it would do just as much good or bad at $8M as $12M. There's not some magic amount where it starts making a dramatic difference in a portfolio.

As people get wealthier, their need to take risk goes down and their ability to take risk goes up. Those two seem to offset each other pretty well such that I have had the same basic asset allocation over 4 or 5 orders of magnitude in wealth.

At $2M net worth, I do not own any gold. Because I do not know when I am going to retire, I generally have used a portfolio-size based asset allocation glidepath, rather than an age-based asset allocation glide path. It makes more sense in my circumstances. Because I am still in my mid-30s and don't have current plans to retire particularly early or start spending a great deal more, it seems plausible that I will reach these kinds of amounts, so I have put some thought into what asset allocation I would have in that case, and I believe I would invest some amount in gold.

Why? It is basically a matter of the declining marginal utility of holding more stocks and bonds. At some amount between around $5M and $10M, I would have: (i) enough in a paid-off house, Social Security, I bonds, and TIPS to provide a federal-government guaranteed inflation-adjusted life-long liability matching portfolio covering all of my needs and some wants; plus (ii) a classic Boglehead three- or four-fund risk portfolio that is able to cover all other wants at relatively low withdrawal rates. Investing additional amounts in the risk portfolio won't give me nothing--it would give me the ability to give away larger sums to family or charity during my lifetime, which I value to some degree--but there is definitely a declining utility. At these kinds of levels having some "insurance" in the form of physical gold as a store of value starts to look relatively more appealing to me in a way that it doesn't at lower net worth.

Of course, individuals plans and preferences may vary, but I do not think what abc123 is saying is irrational or particularly unusual.

[seajay]

I think there is a mismatch between people saying they expect 0% real from gold and then forming conclusions from backtesting data with 6% real returns. Other than that, I believe gold has been a good diversifier over the last 40 years. If I had 8 figures ($10 million) gold would almost certainly make up at least 10% of my portfolio. I'm not there yet so its a soft pass for now. I do enjoy the gold threads. I'm interested in what will be said here.

What changes when you go from $8M to $12M? Not much that I know of. Something change in your personal life? Seems like it would do just as much good or bad at $8M as $12M. There's not some magic amount where it starts making a dramatic difference in a portfolio.

As people get wealthier, their need to take risk goes down and their ability to take risk goes up. Those two seem to offset each other pretty well such that I have had the same basic asset allocation over 4 or 5 orders of magnitude in wealth.

It makes some sense to me to have some independence from the financial system when you can afford to do so. If you have $100 million and want to buy a fallout shelter with security guards I say go for it. For me that independence would be real assets such as art and gold. What changes from 7 figures to 8 is that you can succeed when the financial system fails. You can guess from that number that I need less than 0.5 million per year to meet my basic needs. You can compare 10 million to 100 million if you wish, at some point you could take measures to succeed in a country that fails. I certainly don't expect the US to fail but this has been some very cheap insurance since historically these types of assets have also improved a portfolio.

Rewards wise and broadly the insurance cost via gold compares to the insurance cost via bonds. Bonds however can have the same geopolitical/taxation etc. risks as stocks, are within the same financial system. Gold in contrast is more diversified, where physical in-hand gold has no counter party risk, doesn't pay out regular interest/dividend taxable events, is global ...etc.

If stock/bond or stock/gold are broadly comparable reward wise, a coin-flip as to which may be better over your own particular investment horizon period, then generally the more broader diversification of risk factors will tend to have the lower overall risk. In a increasingly depository based world (bank deposits becomes the banks money, brokers buy shares in their name etc.) concentration risks have increased, not declined and concentration risk is a major risk factor. Inter-dependencies further amplify that risk, a single failure point can see entire domino stacks crashing. Bonds are too interconnected to stocks, if/when they do both suffer then gold is more inclined to counter-correlate, but where more generally the insurance cost is no different to had bonds been held instead.

[nedsaid]

In one of the Gold threads, I came across the J.P. Morgan quote that "Gold is money, everything else is credit." That is really at the center of this discussion. If Gold indeed is money, no wonder why it has had zero real return over millennia. I suppose money just is, it defines itself. But since, I don't know, 1933 or 1944 or 1971, Gold hasn't been money so we are left with credit.

So it just might be that most of the history of Gold is irrelevant to this discussion. Perhaps since 1933 or 1944 or 1971, Gold has different characteristics now than it did before. Gold is reduced to being a hedge against fiat currencies, and a volatile hedge at that, and in a currency crisis might not be the ultimate safe haven we hope it will be. Fiat currencies have value because sovereign governments declare they have value and there is public confidence in that declaration, ultimately it is the strength of the underlying economy that gives a currency its value. Perhaps the dual forces of government declaration and the productivity of the currency issuer's economy are a better backstop to a currency's value than shiny metallic stuff.

If Gold isn't money, then what is it? If money now is credit, what exactly does that mean? So it seems to me that the traditional role of Gold as money itself or at least the backstop to money has been severed since, pick the date, 1933 or 1944 or 1971; it seems like there is a difference dynamic operating here. The whole game has changed.

So does this change mean that Gold now is a genuine investment instead of merely a store of value, or does it mean that Gold is just another volatile commodity? Perhaps we could as easily pick another important commodity in place of Gold as an investment.

Just raising the questions. I don't have the answer myself. I am leaning towards the volatile commodity scenario. Is it worth having some in a portfolio? Maybe.

[watchnerd]

In one of the Gold threads, I came across the J.P. Morgan quote that "Gold is money, everything else is credit." That is really at the center of this discussion. If Gold indeed is money, no wonder why it has had zero real return over millennia. I suppose money just is, it defines itself. But since, I don't know, 1933 or 1944 or 1971, Gold hasn't been money so we are left with credit.

So it just might be that most of the history of Gold is irrelevant to this discussion. Perhaps since 1933 or 1944 or 1971, Gold has different characteristics now than it did before. Gold is reduced to being a hedge against fiat currencies, and a volatile hedge at that, and in a currency crisis might not be the ultimate safe haven we hope it will be. Fiat currencies have value because sovereign governments declare they have value and there is public confidence in that declaration, ultimately it is the strength of the underlying economy that gives a currency its value. Perhaps the dual forces of government declaration and the productivity of the currency issuer's economy are a better backstop to a currency's value than shiny metallic stuff.

If Gold isn't money, then what is it? If money now is credit, what exactly does that mean? So it seems to me that the traditional role of Gold as money itself or at least the backstop to money has been severed since, pick the date, 1933 or 1944 or 1971; it seems like there is a difference dynamic operating here. The whole game has changed.

So does this change mean that Gold now is a genuine investment instead of merely a store of value, or does it mean that Gold is just another volatile commodity? Perhaps we could as easily pick another important commodity in place of Gold as an investment.

Just raising the questions. I don't have the answer myself. I am leaning towards the volatile commodity scenario. Is it worth having some in a portfolio? Maybe.

See:

Niall Ferguson's The Ascent of Money

Money is a social construct.

Gold just happens to have been one among many physical objects or substances that have been used as money.

Copper, silver, cowry shells, grains, livestock, spices, beer....

While it does have some properties that may help it retain value (doesn't corrode, can be smelted into new forms to make it untraceable), it may also just be the beneficiary, after millennia of various specie, of simply having been the last man standing.

[seajay]

In one of the Gold threads, I came across the J.P. Morgan quote that "Gold is money, everything else is credit." That is really at the center of this discussion. If Gold indeed is money, no wonder why it has had zero real return over millennia. I suppose money just is, it defines itself. But since, I don't know, 1933 or 1944 or 1971, Gold hasn't been money so we are left with credit.

So it just might be that most of the history of Gold is irrelevant to this discussion. Perhaps since 1933 or 1944 or 1971, Gold has different characteristics now than it did before. Gold is reduced to being a hedge against fiat currencies, and a volatile hedge at that, and in a currency crisis might not be the ultimate safe haven we hope it will be. Fiat currencies have value because sovereign governments declare they have value and there is public confidence in that declaration, ultimately it is the strength of the underlying economy that gives a currency its value. Perhaps the dual forces of government declaration and the productivity of the currency issuer's economy are a better backstop to a currency's value than shiny metallic stuff.

If Gold isn't money, then what is it? If money now is credit, what exactly does that mean? So it seems to me that the traditional role of Gold as money itself or at least the backstop to money has been severed since, pick the date, 1933 or 1944 or 1971; it seems like there is a difference dynamic operating here. The whole game has changed.

So does this change mean that Gold now is a genuine investment instead of merely a store of value, or does it mean that Gold is just another volatile commodity? Perhaps we could as easily pick another important commodity in place of Gold as an investment.

Just raising the questions. I don't have the answer myself. I am leaning towards the volatile commodity scenario. Is it worth having some in a portfolio? Maybe.

The UK ended direct convertibility between Sovereigns (one Pound gold coins) and Pound notes, in 1931. The US followed that lead in 1933 but where instead of just ending convertibility the US compulsory purchased all investment gold held by Americans.

Gold is like a global currency form of T-Bills, indeed pre 1930's and holders of surplus money (gold Sovereigns) would have been more inclined to deposit those coins in return for interest.

Compare a investor in global stock/gold to that of a another investor holding US stock/T-Bills and the ratio of the two has historically waxed and waned. Broadly both served as 30 year inflation bonds, 3.33% 30 year SWR return of your money via instalments, more often leaving a decent residual amount remaining at the end of the 30 years, but in some cases leaving very little. You might have held either to similar overall effect.

Post world war two and the US did well in global terms, up until the 1970's, but then relatively lagged as Japan rose to take a significant chunk of global cap (rise of Yamaha, Sony ...etc. as global household names), but where that faltered in the 1990's and saw the US recoup much of its share of global market cap. And so on ... similar to the argument of whether to hold domestic only stocks, international stocks, or a blend of the two. Conceptually and blending the two is the more middle road/smoother choice.

For a more recent measure from 1985 seems to be a reasonable choice of start date, as the ending of gold being 'outlawed' prior to that in the US induced some exceptional movements. As US stocks also include relatively high exposure to foreign earnings, comparing 50/50 stock/T-Bills to 50/50 stock/gold or 50/25/25 stock/T-Bills/Gold since 1985 ... and generally they yielded similar overall rewards.

[McQ]

Other time periods

As noted, a time frame that starts about 1982 begins at a secular bottom for both bonds and stocks, and a secular top for gold. Really problematic, from the standpoint of giving gold its due.

Let’s try another split. Back in Harvard case world, where I spent decades, the go-to maneuver in the face of uncertain estimates was always “take the midpoint.” I propose to split the 50 years into two.

-The period from 1972 to 1997 will give gold the 1970s and stocks the 1980s and 1990s, stopping before the blowoff in 1998 and 1999. Over these decades bonds will first tank and then rally.
-The years from 1998 to 2022 will give gold the Great Financial Crisis, while hitting stocks with the dot.com bust plus the GFC, even as bonds rally up to the negligible yields of the 2010s and then take it on the chin in 2022.

Neither period is clearly prejudicial to gold in the way that a 1982 start was.

Stats for the first half are:
Stocks: arithmetic return = 14.41%, SD = 16.77%
Gold: return = 10.63%, SD = 35.25, correlation with stocks = negative .36
Total bond 9.43%%/7.87%, correlation = .53

In short: gold over this period 1972-1997 was even more volatile, with an even more negative correlation to stocks—larger than I thought possible, actually. Here is the chart, with stock-gold the gray line (QE approximation) and orange the total bond – stock blend.*

*reminder: bottom markers are 5% increments, 0,5,10,15,20 to stocks; markers starting from the top are spaced every 10%: 100%, 90%, 80% and so forth to stocks.



We see again the “flying fishhook” pattern for gold: for smaller allocations, a tiny drop in geometric return combined with some points of reduction in standard deviation, relative to all stocks. But as the allocation to gold increases past 25-30%, the huge standard deviation of gold starts to overcome the effect of the (to me surprisingly large) negative correlation, dragging geometric return on the portfolio lower and lower.

Looking now at the orange line for total bond mixes: once the allocation to gold surpasses 30-40%, a mix of stocks with total bond is superior: the same return for much greater reduction in risk. There is no bulge left for the orange line, in light of the substantial correlation of +.53; what carries the day is the much lower standard deviation that Total Bond brings to the table.

Next, here are returns from 1998 to 2022 inclusive.

Stocks: arithmetic return = 9.29%, SD = 17.86%
Gold: return = 8.55%, SD = 13.97%, correlation with stocks = +.03
Total bond 4.10%/5.03%, correlation = 0.0

A very different pattern than any seen thus far, with no negative correlation for gold and with gold now a little LESS volatile than stocks. Total bond pokes along, lower return than before, but with again that favorable return-risk profile.

Not a few BH were actively engaged with investing by the late 1990s. And BND, in mutual fund form, had been in existence for a dozen years by 1998. That makes this next chart closer to the lived experience of today’s investors than any of the prior ones. You really could have diversified out of stocks into gold three years into the irrational exuberance of the great boom, continuing to hold gold as stocks ran up another 50-60% in 1998-99 before topping out. How would you have fared?

Here is the chart:



The gold mixes now fit what might be called a “shark jaw” pattern. For the first time, adding gold to a stock portfolio not only reduces standard deviation by a handful of points, but actually ADDS to geometric return, by almost 50 bp at a 40% allocation to gold. The free lunch of diversification reappears! And this tasty result did not require a negative correlation. Rather, what was needed was one of the very worst 25-year performances for stocks in all of the 20th century: about 7.70% geometric, as opposed to the post-1926 average of 10.0%.

Turning to the orange line, showing total bond mixes: it is dominated by the gold mixes down through a 50/50 stock/total bond allocation. As the stock allocation is reduced further, the superior risk-reduction of adding an intermediate bond duration comes to the fore. The investor willing to sacrifice return can scrub much more risk out of their portfolio with an intermediate bond asset than with gold.

Preliminary conclusions

1. For the original position of 100% in stocks, a small allocation to gold—10% to 20%--probably won’t do too much harm, unless your timing is exactly wrong, i.e., you exchange stocks for gold when stocks are at a generational low and gold is at a generational high (1982 case). And if your timing is very good, you might even be able to boost portfolio return by a dozen or two basis points, while modestly reducing risk.

2. Under more ordinary circumstances, that small allocation to gold may not decrease your return much relative to 100% stocks, if at all, even as it cuts portfolio standard deviation by a handful of points. But it won’t add anything to return.

3. That’s the expected payoff for adding a volatile risk asset with a zero to moderately negative correlation with stocks.

4. However, as the allocation away from stocks to gold increases beyond a small fraction, the risk reduction effect of adding gold becomes more and more inferior to that of adding an intermediate duration bond fund instead. Simultaneously, the return-reduction effect of adding an asset with a lower geometric return (consequent to volatility) begins to bite harder and harder--unless your timing is superlative, i.e., allocating out of stock just before a great boom goes bust.

5. Negative correlations emerge as distinctly unnecessary in the context of diversifying a stock portfolio: gold’s best performance across the scenarios came when its correlation with stocks was merely zero.

6. If you want to de-risk a stock portfolio, add a low-risk asset.

Stepping back, the case for adding gold to a stock portfolio emerges as distinctly meh. If you were serious about de-risking your stock portfolio, you would add intermediate bonds, not gold. If you are totally committed to maximizing return, then you are indifferent between holding 100% stocks versus 80-90% stocks and 10-20% gold.

Why then the passion for gold, the intensity of the devotion it inspires, the enduring appeal?

Next post steps back from the Markowitzian analysis to address this question from a different angle. Clearly, gold offers investors something they crave and believe they can’t get anywhere else from any other asset. What is that something?

[seajay]

Clearly, gold offers investors something they crave and believe they can’t get anywhere else from any other asset. What is that something?

Counter-party/geopolitical risk diversification

Pre 1932 and gold = bonds, gold was money, such as British gold Sovereign one Pound coins, savers would deposit that gold for safekeeping, and interest. Inflation broadly averaged 0% so the interest was like a real rate of return. Bonds compared to stock total returns.

From early 1930's after money was free-floated, there's been predominately inflation. Both bonds and gold transitioned to being more broad 0% real assets, after inflation and taxation.

When you substitute gold for bonds then physical in-hand gold has no counter-party or default risk. Whilst being a globally accepted 'currency'.

A investor might hold 100% TSM or 50/50 2x stock/bonds (or stock/gold) ... to similar overall effect. 1930's to recent and the lowest 30 year SWR for 50/50 2x stock/gold was 4.4%, for 100% TSM it was 3.8%. This is for PV data since 2003 showing the differences PV. Someone holding 50% of their portfolio in-hand (physical gold) tends to feel more comfortable when the likes of bank runs/failing periodically occur, or when the domestic currency is relatively falling ...etc.

[Logan Roy]

Why then the passion for gold, the intensity of the devotion it inspires, the enduring appeal?

I would say a potentially much smoother ride from a worst case.. And my perspective on risk – and the whole backtesting issue – is that it's the worst case we should really be designing portfolios around. Knowing that we can be at the start of a worst-case for any asset class, on any day.. It's the 20 year loss in real value that'll derail an investing plan; not a little volatility. (imo)

I'd say you can see what adding 30% treasuries does here, and while it might cushion volatility, it has so little useful effect on the real value of a portfolio over meaningful periods. The twists and turns that might derail an investor are not really insured against, and you wind up a lot poorer for the policy.

[ScubaHogg]

oh wait: gold has only been a traded asset since 1971, after the collapse of the Bretton Woods agreement, the true end of the gold standard, which had held for centuries until that first thunderous crack in February 1934.

I think gold has been traded for a little bit longer than that…

“rich as Croesus” comes to mind

[NiceUnparticularMan]

Interesting series so far.

I'll just once again flag this Vanguard white paper on various assets and unexpected inflation, which did well out of sample recently, and I think helps clarify which assets (including free-floating gold) should be expected to do what in terms of dealing with unexpected inflation:

https://static.vgcontent.info/crp/intl/ ... t-tips.pdf

I note this because this is typically an alternate argument for "real" assets, that they hedge unexpected inflation/currency-devaluation independent from whatever effect they may or may not have on volatility generally.

There certainly is something to that idea, but Vanguard's research confirms what theory would suggest--rolling collateralized commodities futures are likely to do this more efficiently than simply holding commodities for spot price changes, and gold in the free-floating era has not been an exception.

So, to the extent precious metals futures, including gold futures, might be part of a diversified CCF strategy, that might in turn be part of an unexpected inflation hedging strategy.

The case for instead only holding gold, and not in CCF form, for that purpose is poor both theoretically and empirically.

[seajay]

oh wait: gold has only been a traded asset since 1971, after the collapse of the Bretton Woods agreement, the true end of the gold standard, which had held for centuries until that first thunderous crack in February 1934.

I think gold has been traded for a little bit longer than that…

“rich as Croesus” comes to mind

Coinage also included silver as well as gold, such as silver dollars. If in 1934 you were no longer permitted to hold gold coins/currency, had those compulsory purchased from you, then the obvious alternative option was to hold silver instead.

Using the leveraged ETF (LETF) version of Simba's spreadsheet, loaded with silver from 1934 to 1975, gold thereafter (and calling that Precious Metals (PM)), with that 50/50 yearly rebalanced blended with 2x leveraged stock, and comparing to 100% TSM

2x stock/PM real CAGR 7.886 stdev 20.544
TSM real CAGR 7.337 stdev 18.257

2x/PM 50/50 was more volatile (higher standard deviation in yearly changes), but also a bit more rewarding (higher compound average growth rate). Also in 30 year 4% SWR terms was safer



The LETF spreadsheet only has 2x stock data for 1954 onward, for years earlier than that I assumed a cost of borrowing of T-Bills + 2% i.e. as the cost that might have been incurred to borrow in order to double-up on the amount of stock held.

Silver price changes from ... https://www.gyroscopicinvesting.com/for ... 14#p121214 appear to align closely to that of data from Kitco for yearly spot silver price changes but that are based on yearly average silver price rather than year end.

As a notable sideline, if instead of 2x stock you held straight Small Cap Value, 50/50 with PM, then the minimum SWR increased to 4.8% PV data for that since 1972. This is the MC for a 4% SWR

[seajay]

Adding to that 50/50 SCV/Gold (silver pre 1976), for a 5% SWR there was a high probability of success since 1934



In a couple of the failure cases the Dow/Gold ratio was at relatively low levels at the start, suggestive of a relatively high price of gold (1930's, 1980's).

https://www.macrotrends.net/1378/dow-to ... ical-chart

So ballpark indicator of around a 95% or so confidence, perhaps better odds than a 65 year old retiree living another 30 years to age 95. But maybe with half of their portfolio value in-hand (physical gold), the prospect of longevity might be higher compared to another that had the periodic fear of bank-runs or other such counter-party/geopolitical factors. That "risk" however might be negated in having more spending available for wine/raving

[watchnerd]

My market cap weight allocation to GLDM has done quite nicely, with gold being up to $2000.

Sadly, though.....it's just market cap weight.

[GRP]

My market cap weight allocation to GLDM has done quite nicely, with gold being up to $2000..

Yeah, it’s almost as if it’s a diversifier for economic calamities!

[watchnerd]

Nouriel Roubini was making the case on YouTube that there will be increased demand for gold by regimes that are hostile to the US that also hold a lot of US Treasuries.

In this thesis, they fear confiscation in the event of a conflict, so will start to move from Treasuries to gold.

[GRP]

Nouriel Roubini was making the case on YouTube that there will be increased demand for gold by regimes that are hostile to the US that also hold a lot of US Treasuries.

In this thesis, they fear confiscation in the event of a conflict, so will start to move from Treasuries to gold.

Jokes aside, I think that seems like a reasonable scenario. I actually think it's already happening. Countries like China have been loading up on gold for a while now.

https://www.kitco.com/news/2023-02-10/C ... e-you.html

[McQ]

Interesting series so far.

I'll just once again flag this Vanguard white paper on various assets and unexpected inflation, which did well out of sample recently, and I think helps clarify which assets (including free-floating gold) should be expected to do what in terms of dealing with unexpected inflation:

https://static.vgcontent.info/crp/intl/ ... t-tips.pdf

I note this because this is typically an alternate argument for "real" assets, that they hedge unexpected inflation/currency-devaluation independent from whatever effect they may or may not have on volatility generally.

There certainly is something to that idea, but Vanguard's research confirms what theory would suggest--rolling collateralized commodities futures are likely to do this more efficiently than simply holding commodities for spot price changes, and gold in the free-floating era has not been an exception.

So, to the extent precious metals futures, including gold futures, might be part of a diversified CCF strategy, that might in turn be part of an unexpected inflation hedging strategy.

The case for instead only holding gold, and not in CCF form, for that purpose is poor both theoretically and empirically.

Thanks for adding this reference, NiceUnparticularMan. I do think the conversation around gold has to change now that we have well-established TIPS markets, short and long. You don't need gold to be your primary inflation hedge; you have an alternative.

Rather, you need gold if you don't trust the full faith and credit of the United States Treasury anymore (on which TIPS depend). And if that's true, then per seajay, you don't want any counter-party risk, and must hold physical gold in hand.

If you don't trust the US Treasury, you can hardly trust the clearing house for commodity futures. If you do trust the Treasury, it's hard to see how any inflation protection could be less risky and more certain of outcome than TIPS.

And if, alas, you no longer have confidence in the US Treasury--or any other fiat-currency issuer--then we need to play out the implications of that distrust, as I hope to do in subsequent posts.

[spencydub]

Interesting series so far.

I'll just once again flag this Vanguard white paper on various assets and unexpected inflation, which did well out of sample recently, and I think helps clarify which assets (including free-floating gold) should be expected to do what in terms of dealing with unexpected inflation:

https://static.vgcontent.info/crp/intl/ ... t-tips.pdf

I note this because this is typically an alternate argument for "real" assets, that they hedge unexpected inflation/currency-devaluation independent from whatever effect they may or may not have on volatility generally.

There certainly is something to that idea, but Vanguard's research confirms what theory would suggest--rolling collateralized commodities futures are likely to do this more efficiently than simply holding commodities for spot price changes, and gold in the free-floating era has not been an exception.

So, to the extent precious metals futures, including gold futures, might be part of a diversified CCF strategy, that might in turn be part of an unexpected inflation hedging strategy.

The case for instead only holding gold, and not in CCF form, for that purpose is poor both theoretically and empirically.

Thanks for adding this reference, NiceUnparticularMan. I do think the conversation around gold has to change now that we have well-established TIPS markets, short and long. You don't need gold to be your primary inflation hedge; you have an alternative.

Rather, you need gold if you don't trust the full faith and credit of the United States Treasury anymore (on which TIPS depend). And if that's true, then per seajay, you don't want any counter-party risk, and must hold physical gold in hand.

If you don't trust the US Treasury, you can hardly trust the clearing house for commodity futures. If you do trust the Treasury, it's hard to see how any inflation protection could be less risky and more certain of outcome than TIPS.

And if, alas, you no longer have confidence in the US Treasury--or any other fiat-currency issuer--then we need to play out the implications of that distrust, as I hope to do in subsequent posts.

When other people lose faith in the government it seems like you can gain. Flight to safety and all that.

[seajay]

Rather, you need gold if you don't trust the full faith and credit of the United States Treasury anymore (on which TIPS depend). And if that's true, then per seajay, you don't want any counter-party risk, and must hold physical gold in hand.

Governments can "partially default" in many ways. UK iBonds were in effect withdrawn from new holders post the 2008/9 financial crisis. inflation and taxation can erode the real returns on existing conventional bonds ..etc.

Pre 1933 and bonds (gold) were generally good enough. Money was gold, so inflation broadly was 0% and depositing gold coins in return for interest was a real rate of return. Total returns compared to stocks. Savers might have opted for a 1 and 20 year treasury barbell, or maybe a 10 year bullet. From 1934 the introduction of positive inflation bias became another form of taxation, where prior real returns on bonds (and gold) declined to broadly 0% real. In view of that savers might have opted to roll into a 50/50 stock/gold barbell, or stock/bond, to somewhat similar overall effect



Pre 1930's and real returns on bonds (gold) were a relatively straight upward sloping line, similar to stocks. Since then and the line flattened, but in a zig-zag motion. Gold in effect tracked the same pre 1930's pattern, and also broadly flat-lined since, but where its zig-zag motions have differed to that of bonds since the 1930's.

Generally, interchangeable, but where gold in paying no interest and being in-hand has different benefit/risk characteristics to that of bonds. Those opting for gold aren't doing so due to absence of any trust in the state, but rather in anticipation that at times the faith/confidence will wax and wane and see gold as a alternative (or supplement) to bonds.

With the same reward expectancy from stock (price only), bonds, and gold of 0% real, as per any asset/item that is in demand, stocks additionally yield dividends on top. Some are comfortable with just stocks alone for that dividend (real) benefit. Others might hold all three and trade the volatility - such a via a simple mechanical trading method of periodically rebalancing back to target weightings. Such trading gains can compare to dividends. As concentration risk is a major risk factor a reasonable choice is to diversify, such as perhaps holding some of each of stocks, bonds and gold.

[seajay]

When other people lose faith in the government it seems like you can gain. Flight to safety and all that.

When inflation is viewed as just another form of taxation then pre 20th century under a finite gold backed based money system that taxation averaged 0%. Kings/states had to pay real rates of returns in order to borrow other peoples money/gold. Decoupling money from gold facilitated being able to print/spend money, create inflation such that after inflation and taxation kings/states could in effect borrow money for nothing (no cost). I guess the price of gold is a form of confidence measure, in some concerning times investors might be content to flight to bonds, in other cases investors may have concerns about such bonds and instead opt to flight to gold. At the other extreme, high confidence, and investors might prefer stocks. A barbell of the two, stocks and gold, combine to a central bullet similar to how a 1 and 20 year Treasury barbell combines to a central 10 year bullet.

[Actin]

Good is not an investment, it's a hobby. Change the mindset on gold and you won't have to become an Olympian athlete in mental gymnastics to rationalize. Life is much easier to understand when you stop trying to put the square peg through the circular hole. I don't consider gold as part of my portfolio in the same way that Pokemon cards and crypto are not considered part of my portfolio

[Fremdon Ferndock]

Looking at gold returns since the currency decoupling in 1972, I have found that - unlike stocks - the longer you hold gold the less benefit it provides. It is a great short-term holding if you happen to know which short-term to hold it. Timing is everything.

[GRP]

As someone who has time and again reaped the benefits of contrarianism in investing (seeking value plays, rebalancing into cratering assets, and selling my house when inflation showed up but before the rate hikes started), I’ve grown to appreciate the dissenting tones of the people who disagree with me and who support “The System”.

It lets me know I’m on the right track.

[Logan Roy]

Good is not an investment, it's a hobby.

Holding a Gold ETF is not a hobby. Playing the piano and oil painting are hobbies.

We can come up with a thousand snappy aphorisms for why investing in financial assets (bonds, stocks, etc.) is like building a house on wet sand, or whatever. But there's a lot of good information and research and market history in this thread that should warrant a slightly more nuanced view by now.

[jatwell]

Stepping back, the case for adding gold to a stock portfolio emerges as distinctly meh. If you were serious about de-risking your stock portfolio, you would add intermediate bonds, not gold. If you are totally committed to maximizing return, then you are indifferent between holding 100% stocks versus 80-90% stocks and 10-20% gold.

Why then the passion for gold, the intensity of the devotion it inspires, the enduring appeal?

Next post steps back from the Markowitzian analysis to address this question from a different angle. Clearly, gold offers investors something they crave and believe they can’t get anywhere else from any other asset. What is that something?

What about if you were drawing down your portfolio during these times instead of accumulating?

Seems gold tends to increase the Safe & Perpetual Withdrawal rate due to decreasing the standard deviation. This would allow you to draw down at a higher rate and save less. I looked at getting close to 100% stock returns while greatly increasing Perpetual Withdrawal rates when landing on an asset allocation for draw down. Gold in 10-20% range always seemed to have a huge impact on increasing PWR.

Disclaimer, I'm crazy and have strong SCV tilt as well. 25% SP500, 25% US-SCV, 10% ExUS-SCV, 7% EMV, 10% LTT, 5% I-Bond, 18% GLD

[Logan Roy]

Looking at gold returns since the currency decoupling in 1972, I have found that - unlike stocks - the longer you hold gold the less benefit it provides. It is a great short-term holding if you happen to know which short-term to hold it. Timing is everything.

Usually more the case with bonds. The optimal holding period for gold has tended to be about 20 years. Bonds often benefit from flights to safety and the expectation of easing, but longer-term, stock and bond valuations have some tendency to converge. Which is why there's very rarely any real 'rebalancing bonus' with bonds, and a rare, strong bonus with gold.. Market history clearly makes a very strong case for gold in a portfolio. Arguments against would be speculation on gold's current fair value, and whether another asset might become a preferred safe haven.

[seajay]

Market history clearly makes a very strong case for gold in a portfolio. Arguments against would be speculation on gold's current fair value, and whether another asset might become a preferred safe haven.

https://www.forbes.com/sites/nathanlewi ... d14a0e23fa

On February 3, 2014, Janet Yellen's first day in office at the Federal Reserve, the dollar's value compared to gold was 1261:1, or "$1,261 per oz." On February 3, 2018, her last day, it was 1331:1, a difference of 5.6%.

Did Yellen use gold as a target, as her predecessor Alan Greenspan says he did?

Paul Volcker, head of the Fed in August 1979-August 1987

When I was Chair of the Federal Reserve I used to testify before U.S. Congressman Ron Paul, who was a very strong advocate of gold. We had some interesting discussions. I told him that US monetary policy tried to follow signals that a gold standard would have created. That is sound monetary policy even with a fiat currency. In that regard, I told him that even if we had gone back to the gold standard, policy would not have changed all that much. --Alan Greenspan, 2017

when monetary policy more closely resembles a gold standard system (that is, the value of the dollar is more stable vs. gold), good things happen; and when it does not, bad things happen.

Currencies strive to somewhat peg to gold, but periodically falter and see the price step up to a new plateau level ... in reflection of inflationary type increases. Persistently held and at times gold steps-up, often at times when stock struggle, inter-spaced with periods of when stocks do OK, gold lags inflation. Different, and where being different can be a useful diversifier.

[McQ]

Gold outside of a Markowitz framework

I debated whether to start a fresh thread at this point. However, because one of the best ways to understand a conceptual framework is to find its limit or boundary, the point where it ceases to be informative or applicable, I have placed these next few posts in this existing thread.

But from here on out, no mean-variance analysis will be attempted. The goal is to probe why (some) investors seek (something) from gold other than portfolio diversification in the Markowitzian sense. (Refer to the preceding posts in this thread for a Markowitzian analysis of gold as a diversifier.)

If not M-diversification, then what?

Elsewhere on the forum one routinely hears that such and such can’t really be compared to stocks because X is an insurance product, not an investment. The classic case is fire insurance. Payment for fire insurance on your home, considered as an investment, makes no sense. The odds you will recover your investment, i.e., breakeven, no matter how many decades you pay in, are very low. The odds that your return on those payments will be minus 100% are very high (= your house never does burn down). And yet, I gladly pay my fire insurance premium every year. Disaster, although so unlikely that my insurance company only charges me a thousand-plus dollars per year for protection, would be … disastrous.

Note that if those odds were not structured that way—if it were not highly likely that the fire insurance purchaser will “lose” every penny spent, then no insurance company would offer fire insurance. That’s why, by contrast, flood insurance is not available without a government subsidy; for the most part, the only buyers are those that live next to the creek, who see substantial odds that their flood insurance payments will be, um, a store of value. For insurance to be written at a price buyers would be willing to pay, the odds of a claim must be very low.

Fire insurance can alternatively be conceived as the recurring purchase of a put option on your home that is far, far out of the money. In the event of a fire, you have the right to put the house remnants back to the insurance company for the amount insured. But almost every time, that put will expire worthless and you will have to re-up the payment next year.

The analogy is inexact, however. Although it is not uncommon to speak of hedging a portfolio with options as a kind of insurance, the payoff functions can look quite different. The remainder of this post will pursue the gold-as-fire-insurance analogy. A later post will consider gold as out-of-the-money-put.

Returning to the US investor and the fire insurance analogy, the expected shortfall in the return on gold, relative to the return on stocks—the accumulating loss for holding a store of value rather a share in a productive enterprise—might be of no more concern than the “lost” dollars spent on fire insurance premiums. Personally, I’m down about $70,000 in constant 2023 dollars at this point on my lifetime fire insurance premiums, and I intend to shovel in more money every year on this losing investment until my homeownership days come to an end.

Rational decision-making

I believe it is rational for me to continue to purchase fire insurance on my home—even though, as retirees nearing our peak wealth accumulation, we could potentially withstand the loss, without a meaningful decrease in lifestyle, by deducting it as a casualty expense against an excess withdrawal from retirement accounts. However, we’d still be worse off, even after taxes; enough so to make the annual bite of a thousand or more dollars appear worthwhile, i.e., as an expenditure that maximizes utility.

The question now: whether it is also rational to purchase “fire insurance” on a stock portfolio, by means of an allocation away from stocks into gold. To answer the question we need to quantify the cost of this insurance, and then compare it to the payoff that might be received if the insurance is triggered.

Rational decision-makers seek to maximize expected utility.

Cost to insure stocks with gold

A little math to start.

-If Jeremy Siegel is to be believed, US stocks return a real 6.6% +/- per year. That means they are expected to double in value about every eleven years.

-Gold, as a store of value, has an expected real return of 0%. Therefore, one dollar invested in stocks for eleven years produces two real dollars; one dollar invested in gold stores that one dollar. On the expectations.

-the cost of insurance is the difference, as developed next.

Sticking with round numbers, and assuming a 10% gold /90% stock portfolio, you begin with $10 in gold and $90 in stock. After eleven years you have $10 real in gold (store of value) and $180 real in stocks (productive enterprises doubling in value), or $190 in all. Without the insurance, all in stock, you would have $200 real.

From one perspective, you’ve sacrificed 5% of your future portfolio as the cost of insurance: $10/$200.

From another perspective, the $10 you allocated to gold at the outset has all been consumed; it reduced your future real wealth by $10. Put another way, if your house doesn’t burn down, the money you spent on eleven years of fire insurance is gone.

To complete the equation, we need to compute what happens if fire does break out, i.e., the wealth we’d have with and without gold, if something bad were to happen to stocks. It will be convenient to assume that the fire occurs at the end of the eleventh year.

Insurance payout possibilities

This is where the potential for irrational behavior creeps onto the stage. The nature of the fire that burns into the stock portfolio must be carefully specified. Else, a bait-and-switch may occur, falsely flattering the outcome to be expected from the gold insurance.

-It must be a blaze that is equally destructive to Treasuries. Else, diversification into Treasuries, with their modest expected real return (more than a store of value), would outperform gold when stocks head south.

At this point the battle cry will be heard: fiat currency has no intrinsic value!

Clearly, if something bad happens to the US dollar, both your US stocks and your US Treasuries will lose value.

But that’s not enough.

If you are worried about loss of value for the US dollar, then you would be better off splitting your stock portfolio into US and World ex-US stocks (and if Treasuries are part, splitting that part into Treasuries and World ex-US bonds). A loss of value peculiar to the US dollar is best hedged with international stocks, which, in the absence of disaster, and given a globalized economy, have the same long-term expected return as any other set of productive enterprises.

For there to be an otherwise uninsurable loss on your US stock portfolio, the fire must burn worldwide: all or most fiat currencies must lose value at roughly the same time. Meteor strike? Whatever, they are all fiat currencies now, so something bad could indeed happen to them all, and it is not necessary to be specific about the triggering event.

Assume a meteor strike. The value of financial assets, their ability to support spending in the world, to fund the costs of living, falls by half. This occurs after exactly eleven years. What is the payout from our fire (gold) insurance now that the house has suffered a serious fire?

With no gold insurance: our $100 starting investment had doubled to $200 real; now, at a stroke, it only has $100 of real spending power.

With gold insurance: our $90 starting stock investment had appreciated to $180, then falls to $90. Our gold insurance is worth … still $10 real. We have $100 of spending power in total on this branch as well.

Wait—shouldn’t the gold be worth $20 real? No. When fiat currencies suddenly lose half in real spending power, gold will suddenly be worth twice as much … in fiat currency. Which now has half its spending power. Hence, $10 real.

Therefore, if the paper dollar falls by half at the end of the eleventh year, that merely recovers the previous eleven years of premiums you paid on your gold insurance. No gain occurs. Riding the metaphor, it’s as if a windstorm caused a large tree branch to crush one corner of your carport. The insurance payment for its repair might well equal the last eleven years of insurance premiums (switching from California to Florida metaphors But the insurance payment, put into reconstructing the carport, does not add real wealth beyond what you had before the carport corner was crushed. It dials back your loss on the ongoing insurance premiums; but that dial will begin moving again.

Insurance payout, second try

If you are really into gold, perhaps you read the preceding with a grim chuckle, or maybe a guffaw. “Only 50% loss of value? On fiat currencies with no intrinsic worth? Haw haw. In your fever dreams. I’m buying gold to insure against something much worse.”

I take your point. Any disaster that would depress fiat currency spending power worldwide could see a drop quite a bit worse than 50%.

I’ll go with a 90% drop, but on one condition: that we lengthen the period of time. (The bigger the disaster, the less frequent the occurrence base rate, I would think.) Putting my finger up to the wind, I’ll say that disaster happens 36 years into the payment of annual fire/gold insurance premiums.

Let’s do the math again. Stocks, at 6.6% real, held for 36 years, will double in value three times and a bit more, call it 10X. Our $90 has turned into $900. Our $10 in gold is still storing that $10 in value.

When the 90% fall comes, if we had been all $100 in stock, we would have seen the $100 go to $1000, and then fall to $100. With only $90 in stock, the stock value goes to $900 and then falls to $90. Adding the $10 in gold gives us … $100.

That’s how fire insurance works:
1. If the house never burns down, your total wealth is the house value minus the years of insurance premium;
2. If the house does burn down, total wealth is the fire insurance proceeds, minus the years of insurance premium.

Insurance is not an investment. It doesn’t create value in the way an investment can.

At a cost of 6.6% real per year, gold is very, very expensive insurance on your stock portfolio.

Mea Culpa

I can almost hear the snorting and harrumphing: “It’s not going to happen 36 years from now—that worldwide currency collapse is coming, and it is coming SOON!”

Okay; if you have the ability to time market events, you can do much better with gold than in my calculations. Market timers always win. I cede the field to your superior prowess.

And actually, I would listen to your case here in 2023, on one condition: that you did not make this prediction last year, or the year before, or …. To have greatest credibility in my eyes, you must never before have made this prediction of collapse. If so, I would encourage you to post your arguments for a 2023-24 date-of-disaster here in this thread. If the meteor strike is imminent, I would like to know.

If you have been making this prediction for a while … then you sound like a late night infomercial. My Daddy taught me not to buy anything from that source.

Insurance payout, third try

[best preceded by an evil chuckle]: “You think 90% equals disaster? Did you never hear of the Weimar Republic?”

I take the point: maybe 90% isn’t disaster, just a no good, terrible, horrible bad year. Perhaps gold is bought to insure against some much worse devlopment.

But if so, then I think the fire insurance framework begins to fall apart. For these more apocalyptic scenarios, a better metaphor would be the deep out of the money put.

I’ll pursue that analysis next.

[Phyneas]

If you are a veteran reader of the forum, then you know that this is but the nnth of a large number of threads on gold as an investment (e.g., viewtopic.php?t=396210. Odds that I will say anything new must be considered low.

In an attempt to contribute something new, I will hew pretty strictly to the approach used in Parts 1 and 2: given some expected return, standard deviation, and correlation for gold, how much diversification benefit might one expect from adding gold to an all stock portfolio?

Gold—the ultimate diversifier?

Probably not.

If I had a dollar for every journalist who quoted some expert who said that “you should keep 5% of your portfolio in gold for diversification,” I’d have enough for a very good bottle of California Cabernet.

More legitimately, the Permanent Portfolio has been around for quite a long time, with a substantial allocation to gold. (see this post by nisiprius: viewtopic.php?p=7157009#p7157009)

A rational newcomer to investing might suppose, given the number of mentions in the press, that there must be something to the idea of holding gold as part of a portfolio. But wishing and hoping doesn’t make it so.

Let’s start with the obvious argument AGAINST the use of gold to diversify a stock portfolio.

1. Gold is a store of value
2. To store is to keep, maintain, and preserve unchanged
3. To store is NOT to grow and NOT to lose; it is to KEEP
4. Therefore, the expected value of gold, in real terms, is the same tomorrow as today; the same next decade as last decade; the same one hundred years from now as … oh wait: gold has only been a traded asset since 1971, after the collapse of the Bretton Woods agreement, the true end of the gold standard, which had held for centuries until that first thunderous crack in February 1934.

Anyway, you get the idea: over the very long term, the expected real return on gold is exactly zero (minus storage costs). If that statement is not true, then it cannot be true that gold is a store of (real) value.

I believe gold to be a store of value. Full stop.

I also believe that productive business enterprises CREATE value, rather than store it, and that when I buy a broad stock market index fund, I own a share of global value production, and can reasonably expect to see the value of that stock investment grow in real terms over time, as those productive enterprises of which I own a share continue to create value.

Therefore, addition of gold to a stock portfolio may have a diversification effect, in terms of reducing portfolio standard deviation; but will almost certainly NOT be able to enhance portfolio return. Gold might function as a stabilizer, analogous to short-term TIPS, delivering inflation as their only return. Which means that an allocation to gold—or to short-term TIPS-- must necessarily drag down the long term return on holding 100% of the portfolio in shares of productive enterprises which CREATE value.

In addition, the reduction in portfolio standard deviation from holding gold is likely to be less than that for holding short-term TIPS, because gold is more subject to speculative influences, hence swings about to an even greater degree than the inflation expectations that drive the price of short-term TIPS.

H1: Low return + high volatility = inferior diversifier, relative to, say, an intermediate bond fund.

UNLESS … there is some unsuspected magic in negative correlation, whereby addition of a small allocation to gold both reduces portfolio standard deviation AND increases portfolio geometric return, per the analyses in Part I of the thread.

That is the question to be investigated in this post.

The data

I’ve been using SBBI data from 1926 throughout these threads. That’s not going to work here in Part 3. The dollar price of gold was constant from December 1925 to February 1934, when it leaped by about 75% in a day (~$20 -- $35), after which it was constant again through the late 1960s, after which it exploded for a decade after Nixon took the dollar off gold.

Beastly series to analyze; accordingly, I begin the data series anchored to the end of 1972 (which is also when Total Bond returns become available). This allows about eighteen months for the initial pricing chaos, post delinking of the dollar to gold in August 1971, to settle down.

*You could alternatively begin the gold series in 1792 same as my stock and bond series, where the gold price would be constant and annualized return would be zero until 1934, excepting two small revaluations in in the 1830s and 1840s, and temporary deviations in 1814 and 1862-79. By temporary I mean the positive paper dollar returns initially received were exactly reversed once the movement in these periods was concluded, i.e., gold price at t-begin = price at t-end = ~$20 per ounce = ~1792 price.

*But adding back 140 years of 0% returns is probably not going to be acceptable to the investor seriously contemplating whether to add gold to their portfolio in 2023; that stretch of returns data will be dismissed as “ancient history.” No problem, I won’t go there.

For the fifty years through 2022, the inputs to the Markowitz analysis are as follows. In contrast to prior threads, for this exercise I will use exact historical amounts to the fourth decimal for return and SD. Gold price is from Simba, London pm fixing.

Stocks: arithmetic return = 11.85%, SD = 17.51 *
Gold: return = 9.59%, SD = 26.83%, correlation with stocks = negative 0.21.

*BTW, only periods that include the crash of 1929-1933 give a stock SD greater than or equal to 20%; the 130 years before and the 90 years after typically run an SD of 12% to 18% over twenty-year windows, see https://papers.ssrn.com/sol3/papers.cfm ... id=3805927.

In short, for these fifty years gold had a somewhat lower return, was rather more volatile, and did indeed have a negative correlation with stocks.

Here is the Markowitz chart*

*Because the kluge—geometric return = AR + ½ variance—is increasingly inaccurate for SD over 20%, for this chart the vertical axis is also computed using the approximation labeled QE in Markowitz. It’s still not exact, but it is closer. For comparison the kluge is also shown (solid blue line).



Whoa—that looks quite a bit different than the stock - bond charts we saw in Part 2 of this thread.

Good news: a small allocation to gold could have reduced standard deviation substantially, and—very slightly—increased geometric return. By about 7 basis points at the peak. The stock investor desirous of achieving risk reduction without any reduction in return could justify up to a 30% allocation to gold.

Next, I add the total bond-stock risk return line for this period, using the exact 50-year returns: AR for Total Bond = 6.76%, SD = 7.12%, correlation = .34. As before, a very positive return-risk ratio, with risk far less than stocks or gold, and correlation with stocks moderately positive, i.e., none of that negative correlation benefit with total bond.



The orange line is below the blue and gray lines down through a 50-50 allocation to stocks and gold. Gold is the superior diversifier in that range. However, a 50-50 allocation performs identically to an 80-20 stocks/total bond allocation. At all lower stock allocations, a mix with total bond provides the same return as a mix with gold, for lower risk.

There you have it: the diversification benefit of gold, such as it is, based on the exact series of returns for the cherry-picked 50-year period December 1972-2022.

Hmm, I think you know where this is going.

A rational skeptic of gold might opine: “If the paper dollar price of gold was artificially constrained for decades, I don’t think pegging the start of the price series to seventeen months after the collapse of Bretton-Woods is quite enough time for a new equilibrium to be established.”

Okay; what if we started the series 10 years later, at the end of 1982? Forty years still qualifies for the “long run,” does it not?

Whoa, says the gold advocate. “You are throwing out the baby with the bathwater. Sure, go ahead and arbitrarily exclude the once-in-a-century-or-two-or-three crucible that was the 1970s. Fine, wipe the (barely controlled) galloping inflation of that era from the record. I agree, the performance record for gold won’t look so good if you exclude exactly those circumstances under which gold might shine.”

Hmmm.

Without taking a stance on this dispute, it can’t do any harm to look at the 40-year record from 1982 to 2022—can it? That’s not as “much” history as the 50 years from 1972, but it is still a lot of history. In fact, my personal accumulation history tops out at about 40 years (first IRA contribution 1983, last (spousal) IRA contribution 2022). YMMV.

Might be good to know if gold is so fitful an asset that it might fail to shine throughout your entire accumulation horizon.

But:
“How nice for you,” snarks the gold advocate. “Oh, right, I remember now: the gold price last peaked in the early 1980s. How convenient. Come to think of it, my dear professor, aren’t you on record as stating that 1982 was a generational low in stock and bond prices? So you go, guy: you’ve decided to measure the performance of gold from its top and stocks from their bottom. What could be more fair?”

Got me there.

Still, no harm in looking at the post-1982 data? Right? With the caution that still other slices on the historical data might also be worth a look.

Pause for comments.

This thread reminds me of a paper I read recently re: Swiss Francs vs gold as a portfolio diversifier. I was reading it after finding out from nisiprius that the original Harry Browne Permanent Portfolio held Swiss Francs, not gold. I realize it's not directly the subject under discussion, but I thought it may add some interesting reading to the matter.

[NoRegret]

Anyway, you get the idea: over the very long term, the expected real return on gold is exactly zero (minus storage costs). If that statement is not true, then it cannot be true that gold is a store of (real) value.

Some time ago in another thread I wrote:

Gold is an enigma. In the last decade it has had high negative correlation to real rates. During other times, such as the 2000's it had inverse correlation to USD. Real rates peaked in 2018 and continued dropping from an ultra easy Fed despite fairly strong growth, culminating in the repo crisis in the fall of 2019. The dollar index is a relative measure against other fiat currencies so does not capture any competitive devaluation dynamics.

Ultimately gold is a monetary reserve asset and has to compete against other major currencies and sovereign bonds. Due to its low weighting in global asset allocation, a small shift in allocation can cause a big change in price since its annual production is low vs. total stock and not very elastic.

Gold standard went out of favor precisely because the monetary base cannot expand easily to support a growing economy, so it acted as a deflationary force. Under a fiat regime, assuming the monetary base expands to support economy growth (and more), a priori my base case is for gold to have a positive real return assuming stable preference to different kinds of money. Unlike under a gold standard where by definition its real return is 0.

My point was that gold can have a positive real return in a fiat regime where 1) fiat monetary base grows faster than gold which has an annual production of ~1.5%; 2) global economic growth justifies monetary base growth of > 1.5%; 3) there is a stable long term preference for gold to remain a constant percentage of the global monetary base. Note I don't know what's the right amount of base money growth, although I'm pretty sure it's greater than 1.5%.

But all this is academic, gold's price can respond violently to point #3 above. In the same thread I also wrote:

BHs are conditioned to look at everything through the lens of long term buy-and-hold, which historically worked well only for stocks (even that may have to be qualified for certain countries), and perhaps certain real estate. For everything else, buy-and-hold is at best a so-so strategy. This has to do with the persistence of trend and the magnitude of cycles in relation to the the trend mean.

Your own back tests showed significant date dependence. These days I'm far more interested in the practice (rather than theory) of portfolio construction, I won't distract from this thread here.

[seajay]

Gold, as a store of value, has an expected real return of 0%.
.
.
At this point the battle cry will be heard: fiat currency has no intrinsic value!

Pre 1933 and gold was money/currency, a troy ounce of gold being worth around 20.8 US dollars. At the end of 2022 and a ounce of gold converted to around 1826 US dollars, nearly 88 times more. Over those years a item that cost one dollar in the early 1930's increased to costing 23 dollars at the end of 2022. So a US dollar lost considerable purchase power. But what if that dollar was invested in T-Bills, perhaps incurring a 20% yearly taxation on the 'interest/gains', well in that case it lost only a little over half of its purchase power, required 2.11 dollars to buy the same item at the end of 2022 as it cost one dollar to buy back in the early 1930's.

But that's measuring individual start to end single points in time, a more reasonable comparison is to measure the log linear regressions as that smooths down otherwise potential start and end date variance, and on that measure T-Bills lost -0.33% annualized compared to gold gaining +1.22%, a 1.5% difference/spread.

But what about if total bonds had been held instead of T-Bills, well the log linear regression for bonds compared to T-Bills yielded a +1.3% higher/better slope, so narrowed down the gap compared to gold.

Factor in additional costs, such as the cost of storing gold, or the brokers fees, market makers spread etc. of repeatedly buying bonds and ??? In past times a single trade cost a $100 broker fee, the low fees/spreads of nowadays were just a dream, and that's a un-inflated figure, inflation since 1960 for instance has seen a ten-fold increase, so imagine each present day trade costing a $1000 broker fee, and some investors traded via post, where market makers could make a killing, such as widening spreads out to the likes of 10% or more.

Your basis of comparing gold with stock could equally be applied to hard US dollar currency, or T-Bills, or Bonds. But let's stick with bonds and ... comparing 67/33 stock/bond to that of 67/33 stock/gold since 1933 and both supported a 4% SWR worst case 30 year type outcome. Stock/gold annualized (real) 6.22% with a 13% standard deviation, whilst for stock/bond the figures were 5.9% and 12.8%. Fundamentally and gold broadly was better as a partner to stocks than both hard US dollars, and T-Bills, whilst somewhat aligning with treasury bonds.

Yes in the US investment gold trading was prohibited from 1933, but that only applied in the US as the state wanted to compulsory purchase all such gold held within America in order to lock it up as reserves in Fort Knox. Silver might have been used as a alternative to similar effect (former gold coins as a currency also included silver coins), or a phone call to a London/Swiss broker could have supported still holding/trading gold (I don't know the legal implications for anyone doing that, the US compulsory purchase of gold was specifically ... Executive Order 6102 signed on April 5, 1933, by US President Roosevelt "forbade the hoarding of gold coin, gold bullion, and gold certificates within the continental United States.", i.e. didn't expressly prohibit Americans from hoarding gold outside of continental US).

[seajay]

This thread reminds me of a paper I read recently re: Swiss Francs vs gold as a portfolio diversifier. I was reading it after finding out from nisiprius that the original Harry Browne Permanent Portfolio held Swiss Francs, not gold.

The Swiss Franc was pretty much the last currency to officially end it being backed by gold in May 2000. Prior to that and holding/depositing/investing Swiss Francs was much like pre 1933 when gold was money. British gold Sovereigns for instance, one Pound currency value, that ran alongside and was directly convertible between paper one Pound notes. Under such circumstances savers wouldn't hold 'cash' such as gold Sovereign coins at home, but instead deposited/invested them, in return for interest/rewards (more gold). As in pre 1930 years, when a domestic currency is pegged to gold so inflation broadly tends to = 0%, as was Swiss inflation very low/zero. Which highlights how inflation is a form of taxation. Fiat currency has to be invested in a manner that negates both inflation and taxation in order to maintain its purchase power. Gold in contrast can negate inflation without having to pay regular (taxable) interest/dividends.

[Gaston]

Depending on criteria chosen, one can "prove" that one should include gold, and one can "prove" that one should not.

Just curious: Do proponents of gold tend to favor gold stocks/ETFs, owning the physical metal in a bank safety deposit box or other 3rd party location, or owning the physical metal at home?

I know there will different preferences but, as a general rule, what does “including gold” tend to mean?

[HanSolo]

Depending on criteria chosen, one can "prove" that one should include gold, and one can "prove" that one should not.

Just curious: Do proponents of gold tend to favor gold stocks/ETFs, owning the physical metal in a bank safety deposit box or other 3rd party location, or owning the physical metal at home?

I know there will different preferences but, as a general rule, what does “including gold” tend to mean?

Just as you said, different preferences, so it tends to mean any of the above, or so I've heard.

My preference is the Sprott gold/silver closed-end fund (ticker CEF, formerly known as Central Fund of Canada).

I'm not a "proponent" of gold. My opinion is, people who want it should own it, and people who don't, shouldn't.