Over the past three years, gold has found itself in an odd place: while it still remains the ultimate "safety" trade and store of value should everything go to hell following social and monetary collapse, when it comes to "coolness" it has been displaced by various cryptocurrencies, all of which have vastly outperformed the yellow metal in recent months. Meanwhile, central banks continue to pressure the price of gold to avoid a repeat of 2011 when gold nearly broke out above $2,000, putting the fate world's "reserve currency" increasingly under question. As a result, gold has traded in a rather somnolent fashion, range bound between $1,100 and $1,300 over the last few years, failing to break out on either side.

But is that a fair price for gold?

That is the question Deutsche Bank's Grant Sporre set out to answer in a special report released overnight, which among other things finds that gold is a "metal" full of paradoxes.

Here is what Deutsche Bank found: as Sporre contends, in order to determine whether gold is cheap or expensive, one must first define what gold actually is.

At its simplest form and yes we are stating the obvious, gold is a shiny yellow metal, relatively scarce and mined from the earth’s crust. Valuing the metal should then be just as easy? Gold is a simple commodity, governed by supply and demand, and valuing it should bear some relationship to the cost of digging it out of the earth? But it turns out; gold’s nature is far more mercurial. Gold can be many things to many different people – a store of value, a financial asset, a medium of exchange, a currency, an insurance policy against disruptive events or global uncertainty and even a “barbarous relic*” according to John Maynard Keynes. (*As with any famous quote, there are suggestions that the term was not originally coined by Keynes himself, nor that he was actually referring to gold, but rather to the constraints of the gold standard at the time). All of this means that finding an absolute valuation method which will be accepted by all is rather optimistic; and that the value of gold is more likely to be determined on a relative basis depending on the individual’s perception of gold. Whilst we contend that there is something of an art to valuing gold, we have used a more scientific framework to come up with that true fair value. There are flaws in any one of the individual approaches, and even averaging out the different approaches still seems like a bit of a cop out. However, in our table below the average of all the selected metrics would suggest that gold should trade around USD1,015/oz, with relative G7 per capita income valuing gold at USD735/oz, whilst the bloated size of the big four central bank balance sheets suggesting that gold should travel at USD1,648/oz.

Here is a summary of DB's findings:

And DB's take: the reason why gold is trading with a roughly 20% premium to "fair value" is because "there is a heightened perception of risk or uncertainty in the broader markets."

Although gold screens as expensive, there is a short term scenario (3 month) which would justify gold trading higher, in our view. In the near term, our US rates economist Dominic Konstam sees scope for the US 10-year bond yield to fall to 2% (before rising to 2.75% by year-end), as falling excess liquidity points to softer US growth momentum ahead. If we apply a US 10 year bond yield of 2%, a USD 2% weaker from current levels (not our FX strategist view) and the S&P500 down 5% from current levels, our fair value model points to a gold price of USD1,320/oz. Our own simple four factor model points to a value of USD1,185/oz. Our conclusion is that gold is still trading at a premium versus a wide variety of metrics; 20% versus the average or 6% versus our fair value model. This suggests to us that the certainly through the lens of gold, there is a heightened perception of risk or uncertainty in the broader markets.

And some additional thoughts from DB on how it scores gold's value across its various roles in society:

* * *

Gold as a commodity – scarce but always in surplus?

Many investors are uncomfortable with treating gold as a commodity in that gold is not “consumed” like other commodities – it is not eaten, or burned or forged as food, energy or industrial metals would be. At first glance the price of gold relative to the marginal producer on the cost curve would provide a perfect yardstick to determining the fair value of gold. There are however two fundamental problems with this method. The first is that the conventional supply demand analysis does not work very well for gold. Partly due to its value and enduring nature (and high incentive to recycle), very little gold is actually consumed or lost every year. Thus every year, we add to the stocks of gold, with the industrial surplus being “consumed” by financial investors. We would argue that even the jewellery market is not “pure” consumption and the motivation is linked to a store of wealth.

Gold’s price trajectory relative to the marginal producer on the cost curve should be reasonable determinant of value. However, the mined supply of gold is relatively stable and only responds to pricing signals with a four to five year lag. Gold has been falling since 2012, the bump in 2016 notwithstanding and we only forecast mined supply to finally decline in 2017. It turns out, the gold miners are very good at adjusting their cost bases to the prevailing gold price, not least by targeting the richer parts of their ore bodies. The practice of “high grading” is much frowned upon in the industry, as certain less economic parts of the ore body may be sterilized thereby reducing the NPV of the mine. However, when faced with significant cash burn, many miners have little choice.

If indeed gold is a commodity, gold’s perceived value relative to copper and oil should revert to a long run equilibrium level, based on the relative abundance of various commodities in the earth’s crust. There is no doubt that gold is scarce relative to copper for instance (10,000x less abundant). However the perception of utility will vary according to global growth. In a high global growth environment, copper should be seen as more valuable relative to gold.

* * *

Gold as Money – a medium of exchange with little intrinsic value?

Gold is often seen as a medium of exchange and one that is officially recognized (if not publically used as such) in our view. Simply, gold is widely held by most of the world’s larger central banks as a component of reserves. The ideal medium of exchange must balance the paradox of representing value while having little intrinsic value itself. Fiat currencies physically have no use other than that which is ascribed to them by government and accepted by the public. Arguably, gold is a purer form of money because it actually costs something to produce, compared to fiat currencies which cost very little. However, the concept of relative scarcity or abundance comes into play. If the rate at which fiat currencies have been printed exceeds that rate at which gold has been mined, then ceteris paribus, gold should become scarcer and rerate versus fiat currencies. Since 2005, central bank balance sheets have expanded nearly fourfold. In contrast the global above ground stocks of gold have expanded a mere 20%. The gold price has rerated accordingly, but not enough to keep the value of gold at parity with the global (big four central banks to be precise) money stock. The average ratio since 2005 between global money stocks and the value of global gold stocks is c.1.8x. In order for gold to get back to this level, the price should appreciate to USD1,648/oz, nearly USD300/oz above the current spot price.

If we assume that gold reverts to the long run ratio of these two commodities, then at an oil price of USD50/bbl, gold should be trading at USD840/oz, and at a copper price of USD5,600/t, gold should be trading at USD960/oz. Gold remains expensive versus other commodities

* * *

Gold as a store of value – capital appreciation but no yield

We all need ways to store the fruits of our physical or intellectual labour for use at a later stage. We all have our preferences, be it bricks and mortar, the equity markets or gold. It depends on your confidence in how well you believe your asset of choice will preserve and in many instances grow your wealth or capital. We have examined the level of the gold price in real terms i.e. versus US CPI, relative to the per capita income and versus an alternative financial asset, the US equity market.

In terms of the relationship between gold and the S&P500, we have adjusted both for inflation and applied a further equity time value adjustment. Both should rise with inflation, but the S&P 500 should rise more and its retained and reinvested earnings should generate real EPS growth. We find that the adjusted gold to S&P500 ratio at 0.65x is still above its historical average of 0.54x. To bring this ratio back to its long run average would require the gold price to fall to USD990/oz. The average G7 per capita income since 1971 could buy just over 62 ounces of gold. Currently the average per capita income can purchase 47 ounces which implies that gold should trade at USD740/oz.

The real gold price average since 1971 when the gold standard was relinquished in the US is USD735/oz in PPI adjusted terms and USD810/oz in CPI adjusted terms.

Gold as a measure of market uncertainty

In order to adjust for the current gap between the actual gold price and our model forecast, we have adjusted our model (yes all models have dummy variables to account for the periods when they don’t quite work) for global risk perceptions. The adjustment we apply is simply a risk perceptions adjustment factor derived by plotting the model residual against the VIX index. We note that any significant period above 20 on the VIX index causes gold to trade above its “fair value”. The scale we apply ranges from -20 to 20, with each point accounting for USD10/oz. This is the minimum and maximum range of the deviation. The current gap of USD80/oz or 8 on our scale would suggest an above average sense of risk or uncertainty in the market. If we apply the DB house view forecasts at year end for the US 10 year bond yield of 2.75%, a US 10 year break even of 2.15%, an S&P year-end target of 2600, IMF gold purchases of 5 tonnes and a USD up 7.6% versus the broad trade weighted basket, then gold should trade all the way down to USD1,031/oz. Even if we increase our risk perception index from 8 to 12, this brings us back to USD1,150/oz by year end. In the near term however, our US rates economist Dominic Konstam sees scope for the US 10-year bond yield to fall to 2% (before rising to 2.75% by year-end), as falling excess liquidity points to softer US growth momentum ahead. If we apply a US 10 year bond yield of 2%, a USD down 2% from current levels and the S&P500 down 5% from current levels, our fair value model points to a gold price of USD1,320/oz.